Oluwaseun Adeyeye and Zurni Omar

Various algorithms have been proposed for developing block methods where the most adopted approach is the numerical integration and collocation approaches. However, there is another conventional approach known as the Taylor series approach, although it was utilised at inception for the development of linear multistep methods for first order differential equations. Thus, this article explores the adoption of this approach through the modification of the aforementioned conventional Taylor series approach. A new methodology is then presented for developing block methods, which is a more accurate method for solving second order ordinary differential equations, coined as the Modified Taylor Series (MTS) Approach. A further step is taken by presenting a generalised form of the MTS Approach that produces any k-step block method for solving second order ordinary differential equations. The computational complexity of this approach after being generalised to develop k-step block method for second order ordinary differential equations is calculated and the result shows that the generalised algorithm involves less computational burden, and hence is suitable for adoption when developing block methods for solving second order ordinary differential equations. Specifically, an alternate and easy-to-adopt approach to developing k-step block methods for solving second order ODEs with fewer computations has been introduced in this article with the developed block methods being suitable for solving second order differential equations directly.

]]>Jasmine Lee Jia Min and Syafrina Abdul Halim

Increased flood risk is recognized as one of the most significant threats in most parts of the world, resulting in severe flooding events which have caused significant property and human life losses. As there is an increase in the number of extreme flash flood events observed in Klang Valley, Malaysia recently, this paper focuses on modelling extreme daily rainfall within 30 years from year 1975 toyear 2005 in Klang Valley using generalized extreme value (GEV) distribution. Cyclic covariate is introduced in the distribution because of the seasonal rainfall variation in the series. One stationary (GEV) and three nonstationary models (NSGEV1, NSGEV2, and NSGEV3) are constructed to assess the impact of cyclic covariates on the extreme daily rainfall events. The better GEV model is selected using Akaike's information criterion (AIC), bayesian information criterion (BIC) and likelihood ratio test (LRT). The return level is then computed using the selected fitted GEV model. Results indicate that the NSGEV3 model with cyclic covariate trend presented in location and scale parameters provides better fits the extreme rainfall data. The results showed the capability of the nonstationary GEV with cyclic covariates in capturing the extreme rainfall events. The findings would be useful for engineering design and flood risk management purposes.

]]>Nurhaida Subanar Abdurakhman and Agus Maman Abadi

This article deals with problems of detecting abrupt changes in time series ba Change Point Model (CPM) framework. We propose a fuzzification in a Fuzzy Time Series (FTS) model to eliminate a trend in a contaminated dependent series. The independent residuals are then inputed on the CPM method. In simulating an abrupt change, an ARIMA(1,1,1) and variance of the model are considered. The abrupt change is modelled as an AO (Additive Outlier) type of outliers. The minimum weight or breaksize of the abrupt change is defined based on the ARIMA variance formulated in this article. The percentage of uncorrelated residuals obtained by the FTS model and the percentage of correct detection of the proposed procedure are shown by simulation. The proposed detecting algorithm is implemented to detect abrupt changes in monthly tourism series in literature, i.e., in Taiwan and in Bali. The first series shows a slowly increasing trend with one abrupt change while the second series exhibits not only a slowly increasing trend but also a strong seasonal pattern with two abrupt changes. For comparison, we detect the changes in the empirical examples on an existing automatic detection procedure using tso package in R. For the first example, the results show that both detecting procedures give exactly a similar location of one change point where the package recognises it as an AO type of outliers. The abrupt change is related to the period of SARS outbreak in Taiwan. On the second example, the proposed procedure locates 4 change points which form two locations of changes, i.e., the first two change points are within 2 time points so do the last two change points. The locations are closed to times of Bali Bombing events. Meanwhile, the automatic procedure recognizes only one AO outlier on the series.

]]>Kusno

Formulation of developable patches is beneficial for modeling of the plate-metal sheet in the based-metal-industries objects. Meanwhile, installing the developable patches on a frame of the items and making a hole on these objects surface still need some practical techniques for developing. For these reasons, this research aims to introduce some methods for fitting a curve segment, cutting the developable patches, and adjusting their formulas. Using these methods can design various profile shapes of rubber filer installed on a frame of the objects and create a fissure or hole on the patches' surface. The steps are as follows. First, we define the planes containing the patches' generatrixes and orthogonal to the boundary curves. Then, it fits the Hermite and Bézier curve, via arranging some control points data on these planes, to model the rubber filler shapes. Second, we numerically evaluate a method for cutting the patches with a plane and adjusting the patches' form by modifying their formula from a linear interpolation form into a combination of curve and vectors forms. As a result, it can present some equations and procedures for plotting required curves, cutting surfaces, and modifying the extensible or narrowable shape of Hermite patches. These methods offer some advantages and contribute to designing the based-metal-sheets' object surfaces, especially modeling various forms of rubber filer profiles installed on a frame of the objects and making hole shapes on the plate-metal sheets.

]]>Viliam Ďuriš

Various problems in the real world can be viewed as the Constraint Satisfaction Problem (CSP) based on several mathematical principles. This paper is a guideline for complete automation of the Timetable Problem (TTP) formulated as CSP, which we are able to solve algorithmically, and so the advantage is the possibility to solve the problem on a computer. The theory presents fundamental concepts and characteristics of CSP along with an overview of basic algorithms used in terms of its solution and forms the TTP as CSP and delineates the basic properties and requirements to be met in the timetable. The theory in our paper is mostly based on the Jeavons, Cohen, Gyssens, Cooper, and Koubarakis work, on the basis of which we've constructed a computer programme, which verifies the validity and functionality of the Constraint satisfaction method for solving the Timetable Problem. The solution of the TTP, which is characterized by its basic characteristics and requirements, was implemented by a tree-based search algorithm to a program and our main contribution is an algorithmic verification of constraints abilities and reliability when solving a TTP by means of constraints. The created program was also used to verify the time complexity of the algorithmic solution.

]]>Suparman Abdellah Salhi and Mohd Saifullah Rusiman

Moving average (MA) is a time series model often used for pattern forecasting and recognition. It contains a noise that is often assumed to have a Gaussian distribution. However, in various applications, noise often does not have this distribution. This paper suggests using Laplacian noise in the MA model, instead. The comparison of Gaussian and Laplacian noises was also investigated to ascertain the right noise for the model. Moreover, the Bayesian method was used to estimate the parameters, such as the order and coefficient of the model, as well as noise variance. The posterior distribution has a complex form because the parameters are concerened with the combination of spaces of different dimensions. Therefore, to overcome this problem, the Markov Chain Monte Carlo (MCMC) reversible jump algorithm is adopted. A simulation study was conducted to evaluate its performance. After it has worked properly, it was applied to model human heart rate data. The results showed that the MCMC algorithm can estimate the parameters of the MA model. This was developed using Laplace distributed noise. Moreover, when compared with the Gaussian, the Laplacian noise resulted in a higher order model and produced a smaller variance.

]]>Wilhemina Adoma Pels Atinuke Olusola Adebanji and Sampson Twumasi-Ankrah

The study focused on the Generalized Pareto Distribution (GPD) under the Peak Over Threshold approach (POT). Twenty-one estimation methods were considered for extreme value modeling and their performances were compared. Our goal is to identify the best method in various conditions by the use of a systematic simulation study. Some other estimators which were initially not created under the POT framework (NON-POT) were also compared concurrently with the ones under the POT framework. The simulation results under varying shape parameters showed the Zhang Estimator as "best" in performance for NON-POT in estimating both the shape and scale parameter for heavy-tailed cases. In the POT framework, the Zhang Estimator again performed "best" in estimating very heavy tails for the shape and very short tails for the scale regardless of the value of the scale parameter. When varying sample size, under the NON-POT framework, the Zhang estimator performed as "best" heavy-tailed whiles for the POT framework, the Pickands Estimator was "best" in performance at estimating the shape parameter for large sample sizes and the Zhang, small sample sizes.

]]>Yakhshiboev M. U.

The case of one-dimensional and multidimensional non-convolutional integral operators in Lebesgue spaces is considered in this paper. The convergence in the norm and almost everywhere of non-convolution integral operators in Lebesgue spaces was insufficiently studied. The kernels of non-convolutional integral operators do not need to have a monotone majorant, so the well-known results on the convergence almost everywhere of convolutional averages are not applicable here. The kernels of nonconvolutional integral operators take into account different behaviors at and depending on (which is important in applications) and cover the situation in the particular case of convolutional and non-convolutional integral operators. We are interested in the behavior of function as . Theorems on convergence almost everywhere in the case of one-dimensional and multidimensional nonconvolution integral operators in Lebesgue spaces are proved. The theorems proved are more general ones (including for convolutional integral operators) and cover a wide class of kernels.

]]>Vladimir A. Skorokhodov

The problem of reachability on graphs with restriction is studied. Such restrictions mean that only those paths that satisfy certain conditions are valid paths on the graph. Because of this, for classical optimization problems one has to consider only a subset of feasible paths on the graph, which significantly complicates their solution. Reachability constraints arise naturally in various applied problems, for example, in the problem of navigation in telecommunication networks with areas of strong signal attenuation or when modeling technological processes in which there is a condition for the order of actions or the compatibility of operations. General concepts of a graph with non-standard reachability and a valid path on it are introduced. It is shown that the classical graphs, as well as graphs with restrictions on passing through the selected arcs subsets are special cases of graphs with non-standard reachability. General approach to solving the shortest path problem on a graph with non-standard achievability is developed. This approach consists in constructing an auxiliary graph and reducing the shortest path problem on a graph with non-standard reachability to a similar problem on an auxiliary graph. The theorem on the correspondence of the paths of the original and auxiliary graphs is proved.

]]>E. N. Sinyukova and O. L. Chepok

It is well known that concepts of a geodesic line and a geodesic mapping are among the most fundamental concepts of classical theory of Riemannian spaces. In geometry, concept of Riemannian space has been formed as a generalization of the concept of a smooth surface in a three-dimensional Euclidean space. It has turned out to be possible to extend to Riemannian space the concept of a geodesic point of a curve and to represent a geodesic line of Riemannian space as a curve that consists exclusively of geodesic points. The fact has allowed understanding not only the local but also the global character of basic equations of geodesic mappings' theory of Riemannian spaces that have been originally received as a result of local investigations. An example of the global solution of the so-called new form of basic equations in the theory of geodesic mappings of Riemannian spaces is built in the article. Sphere that is considered as a subset of Euclidean space , forms its topological background. Investigations are based on the concept of equidistant Riemannian space. They are carried out according to the atlas that consists of two charts, obtained with the help of a stereographic projection.

]]>Adejumo T. Joel. Omonijo D. Ojo Owolabi A. Timothy Okegbade A. Ibukun Odukoya A. Jonathan and Ayedun C. Ayedun

Over the years, non-parametric test statistics have been the only solution to solve data that do not follow a normal distribution. However, giving statistical interpretation used to be a great challenge to some researchers. Hence, to overcome these hurdles, another test statistics was proposed called Rank transformation test statistics so as to close the gap between parametric and non-parametric test statistics. The purpose of this study is to compare the conclusion statement of Rank transformation test statistics with its equivalent non parametric test statistics in both one and two samples problems using real-life data. In this study, (2018/2019) Post Unified Tertiary Matriculation Examinations (UTME) results of prospective students of Ladoke Akintola University of Technology (LAUTECH) Ogbomoso across all faculties of the institution were used for the analysis. The data were subjected to nonparametric test statistics which include; Asymptotic Wilcoxon sign test and Wilcoxon sum Rank (both Asymptotic and Distribution) using Statistical Packages for Social Sciences (SPSS). In the same vein, R-statistical programming codes were written for Rank Transformation test statistics. Their P-values were extracted and compared with each other with respect to the pre-selected alpha level (α) = 0.05. Results in both cases revealed that there is a significant difference in the median of the scores across all faculties since their type I error rate are less than the preselected alpha level 0.05. Therefore, Rank transformation test statistics is recommended as alternative test statistics to non-parametric test in both one sample and two-sample problems.

]]>Retno Ayu Cahyoningtyas Solimun and Adji Achmad Rinaldo Fernandes

The purpose of this research is to develop structural modeling with metric and nonmetric measurement scales. Also, this study compares the level of efficiency between the first order and second-order models. The application of structural modeling in agriculture is the satisfaction of farmers in East Java. The data used in this study are about perceptions by distributing questionnaires to farmers in East Java Province in 2020. The respondents in this study were 155 districts in East Java Province. Therefore, the sampling technique chosen is probability sampling, which is a proportional area random sampling. The results are obtained that the first-order model is better than the second-order model because it has the lowest MSE value and the highest R2. The results of the path analysis for the first order and second-order models produce the same results that there is a significant positive effect between the gratitude variables on the farmer satisfaction variable. That is, the more gratitude felt by farmers, the satisfaction will be increased by East Java Farmers. On the other hand, the test results showed that demographic variables did not significantly influence gratitude variables.

]]>Priya Arora and V. P Tomar

Background: Measuring the information and removal of uncertainty are the essential nature of human thinking and many world objectives. Information is well used and beneficial if it is free from uncertainty and fuzziness. Shannon was the primitive who coined the term entropy for measure of uncertainty. He also gave an expression of entropy based on probability distribution. Zadeh used the idea of Shannon to develop the concept of fuzzy sets. Later on, Atanassov generalized the concept of fuzzy set and developed intuitionistic fuzzy sets. Purpose: Sometimes we do not have complete information about fuzzy set or intuitionistic fuzzy sets. Some partial information is known about them i.e either only few values of membership function or non membership function are known or a relationship between them is known or some inequalities governing these parameters are known. Kapur has measured the partial information given by a fuzzy set. In this paper, we have attempted to quantify partial information given by intuitionistic fuzzy sets by considering all the cases. Methodologies: We analyze some well-known definitions and axioms used in the field of fuzzy theory. Principal Results: We have devised methods to measure the incomplete information given about intuitionistic fuzzy sets. Major Conclusions: By devising the methods of measuring partial information about IFS, we can use this information to get an idea about the given set and use this information wisely to make a good decision.

]]>Jonathan Kwaku Afriyie Sampson Twumasi-Ankrah Kwasi Baah Gyamfi Doris Arthur and Wilhemina Adoma Pels

Unit root tests for stationarity have relevancy in almost every practical time series analysis. Deciding on which unit root test to use is a topic of active interest. In this study, we compare the performance of the three commonly used unit root tests (i.e., Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), and Kwiatkowski Phillips Schmidt and Shin (KPSS)) in time series. Based on literature, these unit root tests sometimes disagree in selecting the appropriate order of integration for a given series. Therefore, the decision to use a unit root test relies essentially on the judgment of the researcher. Suppose we wish to annul the subjective decision. In that case, we have to locate an objective basis that unmistakably characterizes which test is the most appropriate for a particular time series type. Thus, this study seeks to unravel this problem by providing a guide on which unit root tests to utilize when there is a disagreement between them. A simulation study of eight (8) univariate time series models with eight (8) different sample sizes, three (3) differencing orders, and nine different parameter values were performed. It was observed from the results that the performance of the three tests improved as the sample size increased. Based on comparing the overall performance, the KPSS was the "best" unit root test to use when there is disagreement.

]]>Jirapud Limthanakul and Nopparat Pochai

Chloride is a well-known chemical compound that is very useful in industry and agricultural, chloride can be transformed to hypochlorite, chlorite, chlorate and perchlorate, chloride and their substances are not dangerous if we used in the optimal level. Groundwater that contaminated chloride and their substances impacts human health, for an example, if we drink water that contaminated chloride exceed 250 mg/L it can cause heart problems and contribute to high blood pressure. to avoid this problem, we used mathematical models to explain groundwater contamination with chloride and their substances. Transient groundwater flow model provides the hydraulic head of groundwater, in this model we will get the level of groundwater, next, we need to find its velocity and direction by using the result in first model put into second model. Groundwater velocity model provides x- and z-direction vector in groundwater, after computation we will plugin the result into the last model to approximated the chloride concentration in groundwater. Groundwater contamination dispersion model provides chloride, hypochlorite, chlorite, chlorate and perchlorate concentration. The proposed explicit finite difference techniques are used to approximate the model solution. Explicit method was used to solved hydraulic head model. Forward space described groundwater velocity model. Forward time and central space used to predict transient groundwater contaminated models. The simulations can be used to indicate when each simulated zone becomes a hazardous zone or a protection zone.

]]>Aleksandr Bochkov Dmitrii Pervukhin Aleksandr Grafov and Veronika Nikitina

The quality of construction of Lorenz curves depends on the features of the information used. As a rule, information is represented by a sample of values of the studied indicator, which is checked for unevenness. Economic indicators of income and cost, and features of their samples are considered. The feature of the cost economic indicator associated with the presence in the sample of its values of the clot is highlighted (the concentration of values on a small segment of the entire range of sample). It is shown that the established order of constructing empirical laws based on such samples does not give the desired effect when constructing Lorenz curves due to the loss of information content of the sample in the places of the clot. The purpose of this article is to improve the quality of the Lorenz curve by increasing the information content of the sample with a clot by applying the clustering procedure when constructing an empirical law. A step-by-step clustering procedure is proposed for dividing the entire range of sample into intervals to construct an empirical distribution law, which is an element of the novelty of this study. A specific example shows how to improve the quality of building a Lorenz curve using this procedure. In addition, it is shown that Lorenz curves for economic indicators can be constructed directly on the basis of the empirical distribution law and at the same time take into account its features.

]]>Shams A. Ahmed and Mohamed Elbadri

Newell Whitehead Segal (NWS) equation has been used in describing many natural phenomena arising in fluid mechanics and hence acquired more attention. Studies in the past gave importance to obtaining numerical or analytical solutions of this kind of equations by employing methods like Modified Homotopy Analysis Transform method (MHATM), Adomian Decomposition method (ADM), Homotopy Analysis Sumudu Transform method (HASTM), Fractional Complex Transform (FCT) coupled with He's polynomials method (FCT-HPM) and Fractional Residual Power Series method (FRPSM). This research aims to demonstrate an efficient analytical method called the Sumudu Decomposition Method (SDM) for the study of analytical and numerical solutions of the NWS of fractional order. The coupling of Adomian Decomposition method with Sumudu transform method simplifies the calculation. From the numerical results obtained, it is evident that SDM is easy to execute and offers accurate results for the NWS equation than with other methods such as FCT-HPM and FRPSM. Therefore, it is easy to apply the coupling of Adomian Decomposition technique with Sumudu transform method, and when applied to nonlinear differential equations of fractional order, it yields accurate results.

]]>Temitope Olu Ogunlade Oluwatayo Michael Ogunmiloro Segun Nathaniel Ogunyebi Grace Ebunoluwa Fatoyinbo Joshua Otonritse Okoro Opeyemi Roselyn Akindutire Omobolaji Yusuf Halid and Adenike Oluwafunmilola Olubiyi

This work concerns a deterministic and stochastic model describing the transmission of typhoid fever infection in human host community, where the vaccination of susceptible births and immigrants as well as screening and treatment of carriers and infected individuals are considered in the model build - up. The well-posedness and computation of the basic reproduction number R_{typ} of the deterministic model are obtained and analysed. The deterministic model is further transformed into a stochastic model, where the drift and diffusion parts of the model are obtained, and the existence and uniqueness of the stochastic model are discussed. Numerical simulations involving the model parameters of R_{typ} showed that vaccination of susceptible births and influx of immigrants as well as screening and treatment of carriers and infected humans are effective in bringing the threshold R_{typ}(R_{typ})≈0.7944) below 1, and the results of other simulations suggest more health policies are to be implemented, as low R_{typ} may not be guaranteed because vaccination wanes over time. In addition, the numerical simulations of the stochastic model equations describing the sub - population of human individuals in the total human host community are carried out using the computational software MATLAB.

Chatarina Enny Murwaningtyas Sri Haryatmi Kartiko Gunardi and Herry Pribawanto Suryawan

This paper deals with an Indonesian option pricing using mixed fractional Brownian motion to model the underlying stock price. There have been researched on the Indonesian option pricing by using Brownian motion. Another research states that logarithmic returns of the Jakarta composite index have long-range dependence. Motivated by the fact that there is long-range dependence on logarithmic returns of Indonesian stock prices, we use mixed fractional Brownian motion to model on logarithmic returns of stock prices. The Indonesian option is different from other options in terms of its exercise time. The option can be exercised at maturity or at any time before maturity with profit less than ten percent of the strike price. Also, the option will be exercised automatically if the stock price hits a barrier price. Therefore, the mathematical model is unique, and we apply the method of the partial differential equation to study it. An implicit finite difference scheme has been developed to solve the partial differential equation that is used to obtain Indonesian option prices. We study the stability and convergence of the implicit finite difference scheme. We also present several examples of numerical solutions. Based on theoretical analysis and the numerical solutions, the scheme proposed in this paper is efficient and reliable.

]]>Piyali Mallick and Lakshmi Narayan De

In this work, we propose a stochastic inventory model under the situations that delay in imbursement is acceptable. Most of the inventory model on this topic supposed that the supplier would offer the retailer a fixed delay period and the retailer could sell the goods and accumulate revenue and earn interest with in the credit period. They also assumed that the trade credit period is independent of the order quantity. Limited investigators developed EOQ model under permissible delay in payments, where trade credit is connected with the order quantity. When the order quantity is a lesser amount of the quantity at which the delay in payment is not permitted, the payments for the items must be made immediately. Otherwise, the fixed credit period is permitted. However, all these models were completely deterministic in nature. In reality, this trade credit period cannot be fixed. If it is fixed, then retailer will not be interested to buy higher quantity than the fixed quantity at which delay in payment is permitted. To reflect this situation, we assumed that trade credit period is not static but fluctuates with the ordering quantity. The demand throughout any arrangement period follows a probability distribution. We have calculated the total variable cost for every unit of time. The optimum ordering policy of the scheme can be found with the aid of three theorems (proofs are provided). An algorithm to determine the best ordering rule with the assistance of the propositions is established and numerical instances are provided for clarification. Sensitivity investigation of all the parameters of the model is presented and deliberated. Some previously published results are special cases of the consequences gotten in this paper.

]]>R. Sivaraman

Computation of day of a week from given date belonging to any century has been a great quest among astronomers and mathematicians for long time. In recent centuries, thanks to efforts of some great mathematicians we now know methods of accomplishing this task. In doing so, people have developed various methods, some of which are very concise and compact but not much accessible explanation is provided. The chief purpose of this paper is to address this issue. Also, almost all known calculations involve either usage of tables or some pre-determined codes usually assigned for months, years or centuries. In this paper, I had established the mathematical proof of determining the day of any given date which is applicable for any number of years even to the time of BCE. I had provided the detailed mathematical derivation of month codes which were key factors in determining the day of any given date. Though the procedures for determining the day of given date are quite well known, the way in which they arrived is not so well known. This paper will throw great detail in that aspect. To be precise, I had explained the formula obtained by German Mathematician Zeller in detail and tried to simplify it further which will reduce its complexity and at the same time, would be as effective as the original formula. The explanations for Leap Years and other astronomical facts were clearly presented in this paper to aid the derivation of the compact form of Zeller's Formula. Some special cases and illustrations are provided wherever necessary to clarify the computations for better understanding of the concepts.

]]>Hani Syahida Zulkafli George Streftaris and Gavin J. Gibson

Hypoglycaemia is a condition when blood sugar levels in body are too low. This condition is usually a side effect of insulin treatment in diabetic patients. Symptoms of hypoglycaemia vary not only between individuals but also within individuals making it difficult for the patients to recognize their hypoglycaemia episodes. Given this condition, and because the symptoms are not exclusive to only hypoglycaemia, it is very important for patients to be able to identify that they are having a hypoglycaemia episode. Consistency models are statistical models that quantify the consistency of individual symptoms reported during hypoglycaemia. Because there are variations of consistency model, it is important to identify which model best fits the data. The aim of this paper is to asses and verify the models. We developed an assessment method based on stochastic latent residuals and performed posterior predictive checking as the model verification. It was found that a grouped symptom consistency model with multiplicative form of symptom propensity and episode intensity threshold ﬁts the data better and has more reliable predictive ability as compared to other models. This model can be used in assisting patients and medical practitioners to quantify patients' reporting symptoms capability, hence promote awareness of their hypoglycaemia episodes so that corrective actions can be quickly taken.

]]>Edy Nurfalah Irvana Arofah Ika Yuniwati Andi Haslinah and Dwi Retno Lestari

This work is a research development of two-tier multiples choice diagnostic test instruments on calculus material. The purpose of this study is; 1) Obtaining the construction of a two-tier multiples choice diagnostic test based on the validity of the contents and Constable, 2) obtaining the quality of two-tier multiples choice diagnostic tests based on the reliability value. The method used is focused on the construction of diagnostic tests. The development research was adapted from the Retnawati development model. The research generated: 1) Construction of a two-tier multiples choice diagnostic test based on the validity of the contents and the construction obtained that the two-tier multiples choice diagnostic test is proven valid. 2) The quality of two-tier multiples choice diagnostic tests based on the reliability value gained that the compiled two-tier diagnostic test instruments. The validity of the content is evidenced by the average validity index (V), for the two-tier multiples choice diagnostic test instrument obtained an average validity index (V) of 0.9333 and for an interview guideline instrument acquired the validity index (V) 0.7556 in which both the validity index (V) approaches the value 1. Whereas for the validity of the construction acquired three dominant factors based on the scree-plot and corresponds to many factors on the calculus material examined in this study. The quality of two-tier multiples choice diagnostic tests is compiled of two-tier diagnostic test instruments based on the reliability value gained.

]]>N. A. Abdul Rahman

Fuzzy delay differential equation has always been a tremendous way to model real-life problems. It has been developed throughout the last decade. Many types of fuzzy derivatives have been considered, including the recently introduced concept of strongly generalized differentiability. However, considering this interpretation, very few methods have been introduced, obstructing the potential of fuzzy delay differential equations to be developed further. This paper aims to provide solution for fuzzy nonlinear delay differential equations and the derivatives considered in this paper is interpreted using the concept of strongly generalized differentiability. Under this method, the calculations will lead to two cases i.e. two solutions, and one of the solutions is decreasing in the diameter. To fulfil this, a method resulting from the elegant combination of fuzzy Sumudu transform and Adomian decomposition method is used, it is termed as fuzzy Sumudu decomposition method. A detailed procedure for solving fuzzy nonlinear delay differential equations with the mentioned type of derivatives is constructed in detail. A numerical example is provided afterwards to demonstrate the applicability of the method. It is shown that the solution is not unique, and this is in accord with the concept of strongly generalized differentiability. The two solutions can later be chosen by researcher with regards to the characteristic of the problems. Finally, conclusion is drawn.

]]>Andy Liew Pik Hern Aini Janteng and Rashidah Omar

Let S to be the class of functions which are analytic, normalized and univalent in the unit disk . The main subclasses of S are starlike functions, convex functions, close-to-convex functions, quasiconvex functions, starlike functions with respect to (w.r.t.) symmetric points and convex functions w.r.t. symmetric points which are denoted by , and K_{S} respectively. In recent past, a lot of mathematicians studied about Hankel determinant for numerous classes of functions contained in S. The qth Hankel determinant for and is defined by . is greatly familiar so called Fekete-Szeg¨o functional. It has been discussed since 1930's. Mathematicians still have lots of interest to this, especially in an altered version of . Indeed, there are many papers explore the determinants H_{2}(2) and H_{3}(1). From the explicit form of the functional H_{3}(1), it holds H_{2}(k) provided k from 1-3. Exceptionally, one of the determinant that is has not been discussed in many times yet. In this article, we deal with this Hankel determinant . From this determinant, it consists of coefficients of function f which belongs to the classes and K_{S} so we may find the bounds of for these classes. Likewise, we got the sharp results for and K_{s} for which a_{2} = 0 are obtained.

Siti Hajar Khairuddin Mohd Hilmi Hasan and Manzoor Ahmed Hashmani

Fuzzy C-Means (FCM) is one of the mostly used techniques for fuzzy clustering and proven to be robust and more efficient based on various applications. Image segmentation, stock market and web analytics are examples of popular applications which use FCM. One limitation of FCM is that it only produces Gaussian membership function (MF). The literature shows that different types of membership functions may perform better than other types based on the data used. This means that, by only having Gaussian membership function as an option, it limits the capability of fuzzy systems to produce accurate outcomes. Hence, this paper presents a method to generate another popular shape of MF, the trapezoidal shape (trapMF) from FCM to allow more flexibility to FCM in producing outputs. The construction of trapMF is using mathematical theory of Gaussian distributions, confidence interval and inflection points. The cluster centers or mean (μ) and standard deviation (σ) from the Gaussian output are fully used to determine four trapezoidal parameters; lower limit a, upper limit d, lower support limit b, and upper support limit c with the assistance of function trapmf() in Matlab fuzzy toolbox. The result shows that the mathematical theory of Gaussian distributions can be applied to generate trapMF from FCM.

]]>Ali F Jameel Sardar G Amen Azizan Saaban Noraziah H Man and Fathilah M Alipiah

Delay differential equations (known as DDEs) are a broad use of many scientific researches and engineering applications. They come because the pace of the shift in their mathematical models relies all the basis not just on their present condition, but also on a certain past cases. In this work, we propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using the Homotopy Perturbation Method with double parametric form fuzzy numbers. The detailed algorithm of the approach to fuzzification and defuzzificationis analysis is provided. In the initial conditions of the proposed problem there are uncertainties with regard to the triangular fuzzy number. A double parametric form of fuzzy numbers is defined and applied for the first time in this topic for the present analysis. This method's simplicity and ability to overcome delay differential equations without complicating Adomian polynomials or incorrect nonlinear assumptions. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show the features of this proposed method, a numerical example is illustrated, involving first order fuzzy delay differential equation. These findings indicate that the suggested approach is very successful and simple to implement.

]]>O. S. Deepa

The reliability of the product has developed a dynamic issue in a worldwide business market. Generally acceptance sampling guarantees the superiority of the product. In acceptance sampling plan, increasing the sample size may lead to minimization of customers' risk of accepting bad lots and producers' risk of rejecting good lots to a certain level but will increase the cost of inspection. Hence truncation of life test time may be introduced to reduce the cost of inspection. Modified Average Sample Number (MASN) for Improved Double Sampling Plan (IDSP) based on truncated life test for popular exponentiated family such as exponentiated gamma, exponentiated lomax and exonentiated Weibull distribution are considered. The modified ASN creates a band width for average sample number which is much useful for the consumer and producer. The interval for average sample number makes the choice of consumer with a maximum and minimum sample size which is of much benefit without any loss for the producer. The probability of acceptance and average sample number based on modified double sampling plan for lower and upper limit is computed for the exponentiated family. Optimal parameters of IDSP under various exponentiated families with different shape parameters were computed. The proposed plan is compared over traditional double sampling and modified double sampling using Gamma distribution, Weibull distribution and Birnbaum-Saunders distribution and shows that the proposed plan with respect to exponentiated family performs better than all other plans. The tables were provided for all distributions. Comparative study of tables based on proposed exponentiated family and earlier existing plan are also done.

]]>Nor Syahmina Kamarudin and Syahida Che Dzul-Kifli

The dynamics of a multidimensional dynamical system may sometimes be inherited from the dynamics of its classical dynamical system. In a multidimensional case, we introduce a new map called a -action on space X induced by a continuous map as such that, where, and is a map of the form . We then look at how topological transitivity of f effects the behaviour of k-type transitivity of the -action, . To verify this, we look specifically at spaces called 1-step shifts of finite type over two symbols which are equipped with a map called the shift map, . We apply some topological theories to prove the -action on 1-step shifts of finite type over two symbols induced by the shift map, is k-type transitive for all whenever is topologically transitive. We found a counterexample which shows that not all maps are k-type transitive for all . However, we have also found some sufficient conditions for k-type transitivity for all. In conclusions, the map on 1-step shifts of finite type over two symbols induced by the shift map is k-type transitive for all whenever either the shift map is topologically transitive or satisfies the sufficient conditions. This study helps to develop the study of k-chaotic behaviours of -action on the multidimensional dynamical system, contributions, and its application towards symbolic dynamics.

]]>Ali F Jameel Akram H. Shather N.R. Anakira A. K. Alomari and Azizan Saaban

This research focuses on the approximate solutions of second-order fuzzy differential equations with fuzzy initial condition with two different methods depending on the properties of the fuzzy set theory. The methods in this research based on the Optimum homotopy asymptotic method (OHAM) and homotopy analysis method (HAM) are used implemented and analyzed to obtain the approximate solution of second-order nonlinear fuzzy differential equation. The concept of topology homotopy is used in both methods to produce a convergent series solution for the propped problem. Nevertheless, in contrast to other destructive approaches, these methods do not rely upon tiny or large parameters. This way we can easily monitor the convergence of approximation series. Furthermore, these techniques do not require any discretization and linearization relative with numerical methods and thus decrease calculations more that can solve high order problems without reducing it into a first-order system of equations. The obtained results of the proposed problem are presented, followed by a comparative study of the two implemented methods. The use of the methods investigated and the validity and applicability of the methods in the fuzzy domain are illustrated by a numerical example. Finally, the convergence and accuracy of the proposed methods of the provided example are presented through the error estimates between the exact solutions displayed in the form of tables and figures.

]]>Sirasak Sasiwannapong Saowanit Sukparungsee Piyapatr Busababodhin and Yupaporn Areepong

The control chart is an important tool in multivariate statistical process control (MSPC), which for monitoring, control, and improvement of the process control. In this paper, we propose six types of copula combinations for use on a Multivariate Exponentially Weighted Moving Average (MEWMA) control chart. Observations from an exponential distribution with dependence measured with Kendall's tau for moderate and strong positive and negative dependence (where ) among the observations were generated by using Monte Carlo simulations to measure the Average Run Length (ARL) as the performance metric and should be sufficiently large when the process is in-control on a MEWMA control chart. In this study, we develop an approach performance on the MEWMA control chart based on copula combinations by using the Monte Carlo simulations.The results show that the out-of-control (ARL_{1}) values for were less than for in almost all cases. The performances of the Farlie-Gumbel-Morgenstern×Ali-Mikhail-Haq copula combination was superior to the others for all shifts with strong positive dependence among the observations and . Moreover, when the magnitudes of the shift were very large, the performance metric values for observations with moderate and strong positive and negative dependence followed the same pattern.

Diah Ayu Widyastuti Adji Achmad Rinaldo Fernandes Henny Pramoedyo Nurjannah and Solimun

Regression analysis has three approaches in estimating the regression curve, namely: parametric, nonparametric, and semiparametric approaches. Several studies have discussed modeling with the three approaches in cross-section data, where observations are assumed to be independent of each other. In this study, we propose a new method for estimating parametric, nonparametric, and semiparametric regression curves in spatial data. Spatial data states that at each point of observation has coordinates that indicate the position of the observation, so between observations are assumed to have different variations. The model developed in this research is to accommodate the influence of predictor variables on the response variable globally for all observations, as well as adding coordinates at each observation point locally. Based on the value of Mean Square Error (MSE) as the best model selection criteria, the results are obtained that modeling with a nonparametric approach produces the smallest MSE value. So this application data is more precise if it is modeled by the nonparametric truncated spline approach. There are eight possible models formed in this research, and the nonparametric model is better than the parametric model, because the MSE value in the nonparametric model is smaller. As for the semiparametric regression model that is formed, it is obtained that the variable X_{2} is a parametric component while X_{1} and X_{3} are the nonparametric components (Model 2). The regression curve estimation model with a nonparametric approach tends to be more efficient than Model 2 because the linearity assumption test results show that the relationship of all the predictor variables to the response variable shows a non-linear relationship. So in this study, spatial data that has a non-linear relationship between predictor variables and responses tends to be better modeled with a nonparametric approach.

Habshah Midi and Jama Mohamed

The support vector regression (SVR) model is currently a very popular non-parametric method used for estimating linear and non-linear relationships between response and predictor variables. However, there is a possibility of selecting vertical outliers as support vectors that can unduly affect the estimates of regression. Outliers from abnormal data points may result in bad predictions. In addition, when both vertical outliers and high leverage points are present in the data, the problem is further complicated. In this paper, we introduced a modified robust SVR technique in the simultaneous presence of these two problems. Three types of SVR models, i.e. eps-regression (ε-SVR), nu-regression (v-SVR) and bound constraint eps-regression (ε-BSVR), with eight different kernel functions are integrated into the new proposed algorithm. Based on 10-fold cross-validation and some model performance measures, the best model with a suitable kernel function is selected. To make the selected model robust, we developed a new double SVR (DSVR) technique based on fixed parameters. This can be used to detect and reduce the weight of influential observations or anomalous points in the data set. The effectiveness of the proposed technique is verified by using a simulation study and some well-known contaminated data sets.

]]>Luthfatul Amaliana Solimun Adji Achmad Rinaldo Fernandes and Nurjannah

WarpPLS analysis has three algorithms, namely the outer model parameter estimation algorithm, the inner model, and the hypothesis testing algorithm which consists of several choices of resampling methods namely Stable1, Stable2, Stable3, Bootstrap, Jackknife, and Blindfolding. The purpose of this study is to apply the WarpPLS analysis by comparing the six resampling methods based on the relative efficiency of the parameter estimates in the six methods. This study uses secondary data from the questionnaire with 1 variable being formative and 2 variables being reflective. Secondary data for the Infrastructure Service Satisfaction Index (IKLI) were obtained from the Study Report on the Regional Development Planning for Economic Growth and the Malang City Gini Index in 2018, while secondary data for the Social Capital Index (IMS) and Community Development Index (IPMas) were obtained from the Research Report on Performance Indicators Regional Human Development Index and Poverty Rate of Malang City in 2018. The results of this study indicate that based on two criteria used, namely the calculation of relative efficiency and measure of fit as a model good, it can be concluded that the Jackknife resampling method is the most efficient, followed with the Stable1, Bootstrap, Stable3, Stable2, and Blindfolding methods.

]]>Azumah Karim Ananda Omutokoh Kube and Bashiru Imoro Ibn Saeed

Global temperature change is an important indicator of climate change. Climate time series data are characterized by trend, seasonal/cyclical as well as irregular components. Adequately modeling these components cannot be overemphasized. In this paper, we have proposed an approach of modeling temperature data using semiparametric additive generalized linear model. We have derived a penalized maximum likelihood estimation of the additive component of the semiparametric generalized linear models, that is, of regression coefficients and smooth functions. A statistical modeling with real time series data set was conducted on temperature data. The study has provided indications on the gain of using semiparametric modeling in situations where a signal component can be additively decomposed in to trend, cyclical and irregular components. Thus, we recommend semiparametric additive penalized models as an option to fit time series data sets in modelling the different component with different functions to adequately explain the relation inherent in data.

]]>S. Al-Ahmad I. M. Sulaiman M. Mamat and L. G. Puspa

The method of differential transform (DTM) is among the famous mathematical approaches for obtaining the differential equations solutions. This is due to its simplicity and efficient numerical performance. However, the major drawback of the DTM is obtaining a truncated series solution which is often a good approximation to the true solution of the equation in a specified region. In this study, a modification of DMT scheme known as MDTM is proposed for obtaining an accurate approximation of ordinary differential equations of second order. The scheme whose procedure is designed via DTM, the Laplace transforms and finally Padé approximation, gives a good approximate for the true solution of the equations in a large region. The proposed approach would be able to overcome the difficulty encountered using the classical DTM, and thus, can serve as an alternative approach for obtaining the solutions of these problems. Preliminary results are presented based on some examples which illustrate the strength and application of the defined scheme. Also, all the obtained results corresponded to exact solutions.

]]>Noraishikin Zulkarnain Noorhelyna Razali Nuryazmin Ahmat Zainuri Haliza Othman and Alias Jedi

Mathematics is one of the major subjects that every engineering student needs to learn. However, every student may have different views and interests on Mathematics subjects because of their different levels of thinking. To foster the appreciation of engineering students on the applications of Mathematics in engineering courses and help them apply and enhance their mathematical knowledge, the Fundamental Engineering Unit at the Faculty of Engineering and Built Environments, Universiti Kebangsaan Malaysia (UKM), organised the first ‘Mathematics Day' on Thursday, May 4, 2017. For their final year project, 12 students participated in a competition where they used mathematical or statistical applications to create a poster. The competition was judged by the academic assessors, industry and UKM alumni. This study examines the mathematical elements and applications in students' posters. The relevance of the elements and topics in the Engineering Mathematics course in the posters is reviewed. Reports from students who were present during the competition are also analysed to determine the effectiveness of the activity. The expected outcome of the student reports is interpreted using a statistical descriptive method, and results indicate that the students had a positive reaction to the activity.

]]>Amit Kumar Rana

Fuzzy sets theory is a very useful technique to increase effectiveness and efficiency of forecasting. The conventional time series is not applicable when the variable of time series are words variables i.e. variables with linguistic terms. As India and most of the Asian countries are of agriculture-based economy with very smaller farmer land holding area in comparison to America, Australia and Europe counterparts, it becomes more important for these countries to have an approximate idea regarding future crop production. It not only will help in planning policies for future but also will be a great help for farmers and agro based companies for their future managements. For small area production, soft computing technique is an important and effective tool for predicting production, as agriculture production involve a high degree of uncertainties in many parameters. In the present study, 21 years agricultural crop yield data is used and a comparative analysis of forecast is done with three fuzzy models. The robustness of the model is tested on real time agricultural farm production data of wheat crop of G.B. Pant University of Agriculture and Technology Pantnagar, India. As soft computing techniques involve uncertainty of the system under study, it becomes more and more important for forecasting models to be accurate with the prediction. The efficiency of the three models is examined on the basis of statistical errors. The models under study are judged on the basis of Mean Square Error and average percentage error. The results of the study are in case of small area production prediction and will encourage for predicting large scale production.

]]>Mahesh Puri Goswami and Naveen Jha

In this article, we investigate bicomplex triple Laplace transform in the framework of bicomplexified frequency domain with Region of Convergence (ROC), which is generalization of complex triple Laplace transform. Bicomplex numbers are pairs of complex numbers with commutative ring with unity and zero-divisors, which describe physical interpretation in four dimensional spaces and provide large class of frequency domain. Also, we derive some basic properties and inversion theorem of triple Laplace transform in bicomplex space. In this technique, we use idempotent representation methodology of bicomplex numbers, which play vital role in proving our results. Consequently, the obtained results can be highly applicable in the fields of Quantum Mechanics, Signal Processing, Electric Circuit Theory, Control Engineering, and solving differential equations. Application of bicomplex triple Laplace transform has been discussed in finding the solution of third-order partial differential equation of bicomplex-valued function.

]]>Solimun Adji Achmad Rinaldo Fernandes and Retno Ayu Cahyoningtyas

Nonlinear principal component analysis is used for data that has a mixed scale. This study uses a formative measurement model by combining metric and nonmetric data scales. The variable used in this study is the demographic variable. This study aims to obtain the principal component of the latent demographic variable and to identify the strongest indicators of demographic formers with mixed scales using samples of students of Brawijaya University based on predetermined indicators. The data used in this study are primary data with research instruments in the form of questionnaires distributed to research respondents, which are active students of Brawijaya University Malang. The used method is nonlinear principal component analysis. There are nine indicators specified in this study, namely gender, regional origin, father's occupation, mother's occupation, type of place of residence, father's last education, mother's last education, parents' income per month, and students' allowance per month. The result of this study shows that the latent demographic variable with samples of a student at Brawijaya University can be obtained by calculating its component scores. The nine indicators formed in PC1 or X_{1} were able to store diversity or information by 19.49%, while the other 80.51% of diversity or other information was not saved in this PC. From these indicators, the strongest indicator in forming latent demographic variables with samples of a student of Brawijaya University is the origin of the region (I_{2}) and type of residence (I_{5}).

Abdeslam Serroukh and Khudhayr A. Rashedi

The aim of this paper is to address the problem of variance break detection in time series in wavelet domain. The maximal overlapped discrete wavelet transform (MODWT) decomposes the series variance across scales into components known as the wavelet variances. We introduce all scale wavelet coefficients based test statistic that allows detecting a break in the homogeneity of the variance of a series through changes in the mean of wavelet variances. The statistic makes use of the traditional CUSUM (cumulative sum) based test designed to test for a break in the mean and constructed using cumulative sums of the square of wavelet coefficients. Under moments and mixing conditions, the test statistic satisfies the functional central limit theorem (FCLT) for a broad class of time series models. The overall performance of our test statistic is compared to the traditional Inclan [8] test statistic. The effectiveness of our statistic is supported by good performances reported in simulations and is as reliable as the traditional statistic. Our method provides a nonparametric test procedure that can be applied to a large class of linear and non linear models. We illustrate the practical use of our test procedure with the quarterly percentage changes in the Americans personal savings data set over the period 1970-2016. Both statistics detect a break in the variance in the second quarter of 2001.

]]>Iryna Halushchak Zoriana Novosad Yurii Tsizhma and Andriy Zagorodnyuk

In this paper, we extend complex polynomial dynamics to a set of multisets endowed with some ring operations (the metric ring of multisets associated with supersymmetric polynomials of infinitely many variables). Some new properties of the ring of multisets are established and a homomorphism to a function ring is constructed. Using complex homomorphisms on the ring of multisets, we proposed a method of investigations of polynomial dynamics over this ring by reducing them to a finite number of scalarvalued polynomial dynamics. An estimation of the number of such scalar-valued polynomial dynamics is established. As an important example, we considered an analogue of the logistic map, defined on a subring of multisets consisting of positive numbers in the interval [0; 1]: Some possible application to study the natural market development process in a competitive environment is proposed. In particular, it is shown that using the multiset approach, we can have a model that takes into account credit debt and reinvestments. Some numerical examples of logistic maps for different growth rate multiset [r] are considered. Note that the growth rate [r] may contain both "positive" and "negative" components and the examples demonstrate the influences of these components on the dynamics.

]]>Girija K. P. Devadas Nayak C Sabitha D’Souza and Pradeep G. Bhat

Graph labeling is an assignment of integers to the vertices or the edges, or both, subject to certain conditions. In literature we find several labelings such as graceful, harmonious, binary, friendly, cordial, ternary and many more. A friendly labeling is a binary mapping such that where and represents number of vertices labeled by 1 and 0 respectively. For each edge assign the label , then the function f is cordial labeling of G if and , where and are the number of edges labeled 1 and 0 respectively. A friendly index set of a graph is { runs over all f riendly labeling f of G} and it is denoted by FI(G). A mapping is called ternary vertex labeling and represents the vertex label for . In this article, we extend the concept of ternary vertex labeling to 3-vertex friendly labeling and define 3-vertex friendly index set of graphs. The set runs over all 3 ? vertex f riendly labeling f f or all is referred as 3-vertex friendly index set. In order to achieve , number of vertices are partitioned into such that for all with and la- bel the edge by where . In this paper, we study the 3-vertex friendly index sets of some standard graphs such as complete graph K_{n}, path P_{n}, wheel graph W_{n}, complete bipartite graph K_{m,n} and cycle with parallel chords PC_{n}.

Mahmoud M. El-Borai and Khairia El-Said El-Nadi

Some singular integral evolution equations with wide class of closed operators are studied in Banach space. The considered integral equations are investigated without the existence of the resolvent of the closed operators. Also, some non-linear singular evolution equations are studied. An abstract parabolic transform is constructed to study the solutions of the considered ill-posed problems. Applications to fractional evolution equations and Hilfer fractional evolution equations are given. All the results can be applied to general singular integro-differential equations. The Fourier Transform plays an important role in constructing solutions of the Cauchy problems for parabolic and hyperbolic partial differential equations. This means that the Fourier transform is suitable but under conditions on the characteristic forms of the partial differential operators. Also, the Laplace transform plays an important role in studying the Cauchy problem for abstract differential equations in Banach space. But in this case, we need the existence of the resolvent of the considered abstract operators. This note is devoted to exploring the Cauchy problem for general singular integro-partial differential equations without conditions on the characteristic forms and also to study general singular integral evolution equations. Our approach is based on applying the new parabolic transform. This transform generalizes the methods developed within the regularization theory of ill-posed problems.

]]>Z. R. Rakhmonov A. Khaydarov and J. E. Urunbaev

Mathematical models of nonlinear cross diffusion are described by a system of nonlinear partial parabolic equations associated with nonlinear boundary conditions. Explicit analytical solutions of such nonlinearly coupled systems of partial differential equations are rarely existed and thus, several numerical methods have been applied to obtain approximate solutions. In this paper, based on a self-similar analysis and the method of standard equations, the qualitative properties of a nonlinear cross-diffusion system with nonlocal boundary conditions are studied. We are constructed various self-similar solutions to the cross diffusion problem for the case of slow diffusion. It is proved that for certain values of the numerical parameters of the nonlinear cross-diffusion system of parabolic equations coupled via nonlinear boundary conditions, they may not have global solutions in time. Based on a self-similar analysis and the comparison principle, the critical exponent of the Fujita type and the critical exponent of global solvability are established. Using the comparison theorem, upper bounds for global solutions and lower bounds for blow-up solutions are obtained.

]]>Viliam Ďuriš and Timotej Šumný

The accuracy of geometric construction is one of the important characteristics of mathematics and mathematical skills. However, in geometrical constructions, there is often a problem of accuracy. On the other hand, so-called 'Optical accuracy' appears, which means that the construction is accurate with respect to the drawing pad used. These "optically accurate" constructions are called approximative constructions because they do not achieve exact accuracy, but the best possible approximation occurs. Geometric problems correspond to algebraic equations in two ways. The first method is based on the construction of algebraic expressions, which are transformed into an equation. The second method is based on analytical geometry methods, where geometric objects and points are expressed directly using equations that describe their properties in a coordinate system. In any case, we obtain an equation whose solution in the algebraic sense corresponds to the geometric solution. The paper provides the methodology for solving some specific tasks in geometry by means of algebraic geometry, which is related to cubic and biquadratic equations. It is thus focusing on the approximate geometrical structures, which has a significant historical impact on the development of mathematics precisely because these tasks are not solvable using a compass and ruler. This type of geometric problems has a strong position and practical justification in the area of technology. The contribution of our work is so in approaching solutions of geometrical problems leading to higher degrees of algebraic equations, whose importance is undeniable for the development of mathematics. Since approximate constructions and methods of solution resulting from approximate constructions are not common, the content of the paper is significant.

]]>R. Sivaraman

Huge amount of literature has been written and published about Golden Ratio, but not many had heard about its generalized version called Metallic Ratios, which are introduced in this paper. The methods of deriving them were also discussed in detail. This will help to explore further in the search of universe of real numbers. In mathematics, sequences play a vital role in understanding of the complexities of any given problem which consist of some patterns. For example, the population growth, radioactive decay of a substance, lifetime of an object all follow a sequence called "Geometric Progression". In fact, the rate at which the recent novel corona virus (COVID – 19) is said to follow a Geometric Progression with common ratio approximately between 2 and 3. Almost all branches of science use sequences, for instance, genetic engineers use DNA sequence, Electrical Engineers use Morse-Thue Sequence and this list goes on and on. Among the vast number of sequences used for scientific investigations, one of the most famous and familiar is the Fibonacci Sequence named after the Italian mathematician Leonard Fibonacci through his book "Liber Abaci" published in 1202. In this paper, I shall try to introduce sequences resembling the Fibonacci sequence and try to generalize it to identify general class of numbers called "Metallic Ratios".

]]>Savita Rathee and Priyanka Gupta

In late sixties, Furi and Vignoli proved fixed point results for α-condensing mappings on bounded complete metric spaces. Bugajewski generalized the results to "weakly F-contractive mappings" on topological spaces(TS). Bugajeski and Kasprzak proved several fixed point results for "weakly F-contractive mapping" using the approach of lower(upper) semi-continuous functions. After that, by modifying the concept of "weakly F-contractive mappings", the coupled fixed point results were proved by Cho, Shah and Hussain on topological space. On different spaces, common coupled fixed point results were discussed by Liu, Zhou and damjanovic, Nashine and Shatanawi and many other authors. In this work, we prove the common coupled fixed point theorems by adopting the modified definition of weakly F-contractive mapping r : T→T; where T is a topological space. After that, we extend the result of Cho, Shah and Hussain for Banach spaces to common coupled quasi solutions enriched with a relevant transitive binary relation. Also, we give an example in the support of proved result. Our results extend and generalize several existing results in the literature.

]]>Waego Hadi Nugroho Ni Wayan Surya Wardhani Adji Achmad Rinaldo Fernandes and Solimun

Robust regression analysis is an analysis that is used if there is an outlier in a regression model. Outliers cause data to be abnormal. The most commonly used parameter estimation method is Ordinary Least Squares (OLS). However, outliers in models cause the estimator of the least-squares in the model to be biased, so handling of outliers is required. One of the regressions used for outliers is robust regression. Robust regression method that can be used is M-Estimation. By using Tukey's Bisquare weighted function, a robust M-estimation method can estimate parameters in a model, for example in malnutrition data in East Java Province 2017 to 2012. This study aims to compare the robust method of M-estimation and OLS method on data with several different levels of significance, which is 1%, 5%, and 10%. The predictor variables used in this study were the percentage of poor society, population density, and some health facilities. R^{2} is used to compare the OLS method and the robust method of M-estimation. The results obtained that robust regression is the best method to handle the model if there are outliers in the data. It was supported by almost all results of the value of R^2 on each data that M-estimation has a higher value than the OLS method.

Gwang Hui Kim

The present work continues the study for the superstability and solution of the Pexider type functional equation , which is the mixed functional equation represented by sum of the sine, cosine, tangent, hyperbolic trigonometric, and exponential functions. The stability of the cosine (d'Alembert) functional equation and the Wilson equation was researched by many authors: Baker [7], Badora [5], Kannappan [14], Kim ([16, 19]), and Fassi, etc [11]. The stability of the sine type equations was researched by Cholewa [10], Kim ([18], [20]). The stability of the difference type equation for the above equation was studied by Kim ([21], [22]). In this paper, we investigate the superstability of the sine functional equation and the Wilson equation from the Pexider type difference functional equation , which is the mixed equation represented by the sine, cosine, tangent, hyperbolic trigonometric functions, and exponential functions. Also, we obtain additionally that the Wilson equation and the cosine functional eqaution in the obtained results can be represented by the composition of a homomorphism. In here, the domain (G; +) of functions is a noncommutative semigroup (or 2-divisible Abelian group), and A is an unital commutative normed algebra with unit 1A. The obtained results can be applied and expanded to the stability for the difference type's functional equation which consists of the (hyperbolic) secant, cosecant, logarithmic functions.

]]>Yousef Al-Qudah Faisal Yousafzai Mohammed M. Khalaf and Mohammad Almousa

The main motivation behind this paper is to study some structural properties of a non-associative structure as it hasn't attracted much attention compared to associative structures. In this paper, we introduce the concept of an ordered A^{*}G^{**}-groupoid and provide that this class is more generalized than an ordered AG-groupoid with left identity. We also define the generated left (right) ideals in an ordered A^{*}G^{**}-groupoid and characterize a (2; 2)-regular ordered A^{*}G^{**}-groupoid in terms of these ideals. We then study the structural properties of an ordered A^{*}G^{**}-groupoid in terms of its semilattices, (2; 2)-regular class and generated commutative monoids. Subsequently, compare -fuzzy left/right ideals of an ordered AG-groupoid and respective examples are provided. Relations between an -fuzzy idempotent subsets of an ordered A^{*}G^{**}-groupoid and its -fuzzybi-ideals are discussed. As an application of our results, we get characterizations of (2; 2)-regular ordered A^{*}G^{**}-groupoid in terms of semilattices and -fuzzy left (right) ideals. These concepts will help in verifying the existing characterizations and will help in achieving new and generalized results in future works.

Abdishukurova Guzal Narmanov Abdigappar and Sharipov Xurshid

The concept of differential invariant, along with the concept of invariant differentiation, is the key in modern geometry [1]-[10]. In the Erlangen program [3] Felix Klein proposed a unified approach to the description of various geometries. According to this program, one of the main problems of geometry is to construct invariants of geometric objects with respect to the action of the group defining this geometry. This approach is largely based on the ideas of Sophus Lee, who introduced continuous geometry groups of transformations, now known as Lie groups, into geometry. In particular, when considering classification problems and equivalence problems in differential geometry, differential invariants with respect to the action of Lie groups should be considered. In this case, the equivalence problem of geometric objects is reduced to finding a complete system of scalar differential invariants. The interpretation of the k- order differential invariant as a function on the space of k- jets of sections of the corresponding bundle made it possible to operate with them efficiently, and using invariant differentiation, new differential invariants can be obtained. Differential invariants with respect to a certain Lie group generate differential equations for which this group is a symmetry group. This allows one to apply the well-known integration methods to such equations, and, in particular, the Li- Bianchi theorem [4]. Depending on the type of geometry, the orders of the first nontrivial differential invariants can be different. For example, in the space R^{3} equipped with the Euclidean metric, the complete system of differential invariants of a curve is its curvature and torsion, which are second and third order invariants, respectively. Note that scalar differential invariants are the only type of invariants whose components do not change when changing coordinates. For this reason, scalar differential invariants are effectively used in solving equivalence problems. In this paper differential invariants of Lie group of one parametric transformations of the space of two independent and three dependent variables are studied. It is shown method of construction of invariant differential operator. Obtained results applied for finding differential invariants of surfaces.

V. I. Struchenkov and D. A. Karpov

The article discusses the solution of applied problems, for which the dynamic programming method developed by R. Bellman in the middle of the last century was previously proposed. Currently, dynamic programming algorithms are successfully used to solve applied problems, but with an increase in the dimension of the task, the reduction of the counting time remains relevant. This is especially important when designing systems in which dynamic programming is embedded in a computational cycle that is repeated many times. Therefore, the article analyzes various possibilities of increasing the speed of the dynamic programming algorithm. For some problems, using the Bellman optimality principle, recurrence formulas were obtained for calculating the optimal trajectory without any analysis of the set of options for its construction step by step. It is shown that many applied problems when using dynamic programming, in addition to rejecting unpromising paths lead to a specific state, also allow rejecting hopeless states. The article proposes a new algorithm for implementing the R. Bellman principle for solving such problems and establishes the conditions for its applicability. The results of solving two-parameter problems of various dimensions presented in the article showed that the exclusion of hopeless states can reduce the counting time by 10 or more times.

]]>Nik Muhammad Farhan Hakim Nik Badrul Alam Ajab Bai Akbarally and Silvestru Sever Dragomir

Hermite-Hadamard type inequalities related to convex functions are widely being studied in functional analysis. Researchers have refined the convex functions as quasi-convex, h-convex, log-convex, m-convex, (a,m)-convex and many more. Subsequently, the Hermite-Hadamard type inequalities have been obtained for these refined convex functions. In this paper, we firstly review the Hermite-Hadamard type inequality for both convex functions and log-convex functions. Then, the definition of composite convex function and the Hermite-Hadamard type inequalities for composite convex functions are also reviewed. Motivated by these works, we then make some refinement to obtain the definition of composite log-convex functions, namely composite-^{-1} log-convex function. Some examples related to this definition such as GG-convexity and HG-convexity are given. We also define k-composite log-convexity and k-composite-^{-1} log-convexity. We then prove a lemma and obtain some Hermite-Hadamard type inequalities for composite log-convex functions. Two corollaries are also proved using the theorem obtained; the first one by applying the exponential function and the second one by applying the properties of k-composite log-convexity. Also, an application for GG-convex functions is given. In this application, we compare the inequalities obtained from this paper with the inequalities obtained in the previous studies. The inequalities can be applied in calculating geometric means in statistics and other fields.

Leonid N. Yasnitsky and Sergey L. Gladkiy

One of the main problems in modern mathematical modeling is to obtain high-precision solutions of boundary value problems. This study proposes a new approach that combines the methods of artificial intelligence and a classical analytical method. The use of the analytical method of fictitious canonic regions is proposed as the basis for obtaining reliable solutions of boundary value problems. The novelty of the approach is in the application of artificial intelligence methods, namely, genetic algorithms, to select the optimal location of fictitious canonic regions, ensuring maximum accuracy. A general genetic algorithm has been developed to solve the problem of determining the global minimum for the choice and location of fictitious canonic regions. For this genetic algorithm, several variants of the function of crossing individuals and mutations are proposed. The approach is applied to solve two test boundary value problems: the stationary heat conduction problem and the elasticity theory problem. The results of solving problems showed the effectiveness of the proposed approach. It took no more than a hundred generations to achieve high precision solutions in the work of the genetic algorithm. Moreover, the error in solving the stationary heat conduction problem was so insignificant that this solution can be considered as precise. Thus, the study showed that the proposed approach, combining the analytical method of fictitious canonic regions and the use of genetic optimization algorithms, allows solving complex boundary-value problems with high accuracy. This approach can be used in mathematical modeling of structures for responsible purposes, where the accuracy and reliability of the results is the main criterion for evaluating the solution. Further development of this approach will make it possible to solve with high accuracy of more complicated 3D problems, as well as problems of other types, for example, thermal elasticity, which are of great importance in the design of engineering structures.

]]>Ni Wayan Surya Wardhani Waego Hadi Nugroho Adji Achmad Rinaldo Fernandes and Solimun

WANT-E is a tool created to purify methane gas from organic waste intended as a substitute for renewable gas fuel. The WANT-E product is new because it is necessary to do research related to the public interest in WANT-E products. This study uses primary data obtained from questionnaires with variables based on Theory of Planned Behavior (TPB), namely behavior attitudes, subjective norms, perceived behavior control, and behavior interests that are spread to the community of Cibeber Village, Cikalong Subdistrict, Tasikmalaya Regency that uses LPG gas cylinders or stove using sampling techniques in the form of the judgment sampling method. The analysis used is SEM with the WarpPLS approach, which is to determine the effect of relationships between variables. The results of the analysis obtained the effect of a positive relationship between behavior attitudes variables on subjective norms, behavior attitudes toward perceived behavior control, subjective norms of behavior interests, and perceived behavior control of behavior interests. Then the influence of indirect relations on subjective norms and perceived behavior control was obtained as mediation between behavior attitudes toward behavior interests.

]]>Artykbaev Abdullaaziz and Nurbayev Abdurashid Ravshanovich

This article discusses geometric quantities associated with the concept of surfaces and the indicatrix of a surface in four-dimensional Galileo space. In this case, the second orderly line in the plane is presented as a surface indicatrix. It is shown that with the help of the Galileo space movement, the second orderly line can be brought to the canonical form. The movement in the Galileo space is radically different from the movement in the Euclidean space. Galileo movements include parallel movement, axis rotation, and sliding. Sliding gives deformation in the Euclidean space. The surface indicatrix is deformed by the Galileo movement. When the indicatrix is deformed, the surface will be deformed. In the classification of three-dimensional surface points in the four-dimensional Galileo phase, the classification of the indicatrix of the surface at this point was used. This shows the cyclic state of surface points other than Euclidean geometry. The geometric characteristics of surface curves were determined using the indicatrix test. It is determined what kind of geometrical meaning the identified properties have in the Euclidean phase. It is shown that the Galilean movement gives surface deformation in the Euclidean sense. Deformation of the surface is indicated by the fact that the Gaussian curvature remains unchanged.

]]>M. Khalifa Saad R. A. Abdel-Baky F. Alharbi and A. Aloufi

In a theory of space curves, especially, a helix is the most elementary and interesting topic. A helix, moreover, pays attention to natural scientists as well as mathematicians because of its various applications, for example, DNA, carbon nanotube, screws, springs and so on. Also there are many applications of helix curve or helical structures in Science such as fractal geometry, in the fields of computer aided design and computer graphics. Helices can be used for the tool path description, the simulation of kinematic motion or the design of highways, etc. The problem of the determination of parametric representation of the position vector of an arbitrary space curve according to the intrinsic equations is still open in the Euclidean space E^{3} and in the Minkowski space . In this paper, we introduce some characterizations of a non-null slant helix which has a spacelike or timelike axis in . We use vector differential equations established by means of Frenet equations in Minkowski space . Also, we investigate some differential geometric properties of these curves according to these vector differential equations. Besides, we illustrate some examples to confirm our findings.

Narmanov Abdigappar and Parmonov Hamid

The problem of integrating equations of mechanics is the most important task of mathematics and mechanics. Before Poincare's book "Curves Defined by Differential Equations", integration tasks were considered as analytical problems of finding formulas for solutions of the equation of motion. After the appearance of this book, it became clear that the integration problems are related to the behavior of the trajectories as a whole. This, of course, stimulated methods of qualitative theory of differential equations. Present time, the main method in this problem has become the symmetry method. Newton used the ideas of symmetry for the problem of central motion. Further, Lagrange revealed that the classical integrals of the problem of gravitation bodies are associated with invariant equations of motion with respect to the Galileo group. Emmy Noether showed that each integral of the equation of motion corresponds to a group of transformations preserving the action. The phase flow of the Hamilton system of equations, in which the first integral serves as the Hamiltonian, translates the solutions of the original equations into solutions. The Liouville theorem on the integrability of Hamilton equations was created on this idea. The Liouville theorem states that phase flows of involutive integrals generate an Abelian group of symmetries Hamiltonian methods have become increasingly important in the study of the equations of continuum mechanics, including fluids, plasmas and elastic media. In this paper it is considered the problem on the Hamiltonian system which describes of motion of a particle which is attracted to a fixed point with a force varying as the inverse cube of the distance from the point. We are concerned with just one aspect of this problem, namely the questions on the symmetry groups and Hamiltonian symmetries. It is found Hamiltonian symmetries of this Hamiltonian system and it is proven that Hamiltonian symmetry group of the considered problem contains two dimensional Abelian Lie group. Also it is constructed the singular foliation which is generated by infinitesimal symmetries which invariant under phase flow of the system. In the present paper, smoothness is understood as smoothness of the class C^{∞}.

Jae Won Lee Dae Ho Jin and Chul Woo Lee

Jin [1] defined an ()-type connection on semi-Riemannian manifolds. Semi-symmetric nonmetric connection and non-metric ∅-symmetric connection are two important examples of this connection such that () = (1; 0) and () = (0; 1), respectively. In semi-Riemannian geometry, there are few literatures for the lightlike geometry, so we expose new theories for non-degenerate submanifolds in semi-Riemannian geometry. The goal of this paper is to study a characterization of a (Lie) recurrent lightlike hypersurface M of an indefinite Kaehler manifold with an ()-type connection when the charateristic vector field is tangnet to M. In the special case that an indefinite Kaehler manifold of constant holomorphic sectional curvature is an indefinite complex space form, we investigate a lightlike hypersurface of an indefinite complex space form with an ()-type connection when the charateristic vector field is tangnet to M. Moreover, we show that the total space, the complex space form, is characterized by the screen conformal lightlike hypersurface with an ()-type connection. With a semi-symmetric non-metric connection, we show that an indefinite complex space form is flat.

]]>Mohammad Almousa

Many different problems in mathematics, physics, engineering can be expressed in the form of integral equations. Among these are diffraction problems, population growth, heat transfer, particle transport problems, electrical engineering, elasticity, control, elastic waves, diffusion problems, quantum mechanics, heat radiation, electrostatics and contact problems. Therefore, the solutions which are obtained by the mathematical methods play an important role in these fields. The most two basic types of integral equations are called Fredholm (FIEs) and Volterra (VIEs). In many instances, the ordinary and partial differential equations can be converted into Fredhom and Volterra integral equations that are solved more effectively. We aim through this research to present an improved Adomian decomposition method based on modified Bernstein polynomials (ADM-MBP) to solve nonlinear integral equations of the second kind. We introduced efficient method, constructed on modified Bernstein polynomials. The formulation is developed to solve nonlinear Fredholm and Volterra integral equations of second kind. This method is tested for some examples from nonlinear integral equations. Maple software was used to obtain the solutions of these examples. The results demonstrate reliability of the proposed method. Generally, the proposed method is very convenient to apply to find the solutions of Fredholm and Volterra integral equations of second kind.

]]>Moustafa Omar Ahmed Abu-Shawiesh Muhammad Riaz and Qurat-Ul-Ain Khaliq

In this study, a robust control chart as an alternative to the Tukey's control chart (TCC) based on the modified trimmed standard deviation (MTSD), namely MTSD-TCC, is proposed. The performance of the proposed and the competing Tukey's control chart (TCC) is measured using different length properties such as average run length (ARL), standard deviation of run length (SDRL), and median run length (MDRL). Also, the study covered normal and contaminated cases. We have observed that the proposed robust control chart (MTSD-TCC) is quite efficient at detecting process shifts. Also, it is evident from the simulation results that the proposed robust control chart (MTSD-TCC) offers superior detection ability for different trimming levels as compared to the Tukey's control chart (TCC) under the contaminated process setups. As a result, it is recommended to use the proposed robust control chart (MTSD-TCC) for process monitoring. An application numerical example using real-life data is provided to illustrate the implementation of the proposed robust control chart (MTSD-TCC) which also supported the results of the simulation study to some extent.

]]>Anuradha and SeemaMehra

In 2016, Muralisankar and Jeyabal introduced the concept of ε-Compatible maps and studied the set of common fixed points. They generalized the Banach contraction, Kannan contraction, Reich contraction and Bianchini type contraction to obtain some common fixed point theorems for ε-Compatible mappings which don't involve the suitable containment of the ranges for the given mappings in the setting of metric spaces. Motivated by this new concept of mappings, we establish a new approach for some common fixed point theorems via ϵ -compatible maps in context of complete partial metric space including a directed graph G=(V,E). By the remarkable work of Jachymski in 2008, we extend the results obtained by Muralisankar and Jeyabal in 2016. In 2008, Jachymski obtained some important fixed point results introduced by Ran and Reurings (2004) using the languages of graph theory instead of partial order and gave an interesting approach in this direction. After that, his work is considered as a reference in this domain. Sometimes, there are some mappings which do not satisfy the contractive nature on whole set M(say) but these can be made contractive on some subset of M and this can be done by including graph as shown in our Example 2.6 which is provided to substantiate the validity of our results.

]]>Zahari Md Rodzi and Abd Ghafur Ahmad

In this paper, by combining hesitant fuzzy soft sets (HFSSs) and fuzzy parameterized, we introduce the idea of a new hybrid model, fuzzy parameterized hesitant fuzzy soft sets (FPHFSSs). The benefit of this theory is that the degree of importance of parameters is being provided to HFSSs directly from decision makers. In addition, all the information is represented in a single set in the decision making process. Then, we likewise ponder its basic operations such as AND, OR, complement, union and intersection. The basic properties such as associative, distributive and de Morgan's law of FPHFSSs are proven. Next, in order to resolve the multi-criteria decision making problem (MCDM), we present arithmetic mean score and geometry mean score incorporated with hesitant degree of FPHFSSs in TOPSIS. This algorithm can cater some existing approach that suggested to add such elements to a shorter hesitant fuzzy element, rendering it equivalent to another hesitant fuzzy element, or to duplicate its elements to obtain two sequence of the same length. Such approaches would break the original data structure and modify the data. Finally, to demonstrate the efficacy and viability of our process, we equate our algorithm with existing methods.

]]>Solimun and Adji Achmad Rinaldo Fernandes

The use of regression analysis has not been able to deal with the problems of complex relationships with several response variables and the presence of intervening endogenous variables in a relationship. Analysis that is able to handle these problems is path analysis. In path analysis there are several assumptions, one of which is the assumption of residual normality. If the normality residual assumptions are not met, then estimating the parameters can produce a biased estimator, a large and not consistent range of estimators. Unmet residual normality problems can be overcome by using resampling. Therefore in this study, a simulation study was conducted to apply resampling with the blindfold method to the condition that the normality assumption is not met with various levels of resampling in the path analysis. Based on the simulation results, different levels of closeness occur consistently at different resampling quantities. At a low level of closeness, it is consistent with the resampling magnitude of 1000. At a moderate level, a consistent level of resampling of 500 occurs. At a high level of closeness, it is consistent with the amount of resampling 1400.

]]>Yona Eka Pratiwi Kusbudiono Abduh Riski and Alfian Futuhul Hadi

The development of an increasingly rapid industrial development resulted in increasingly intense competition between industries. Companies are required to maximize performance in various fields, especially by meeting customer demand with agreed timeliness. Scheduling is the allocation of resources to the time to produce a collection of jobs. PT. Bella Agung Citra Mandiri is a manufacturing company engaged in making spring beds. The work stations in the company consist of 5 stages consisting of ram per with three machines, clamps per 1 machine, firing mattresses with two machines, sewing mattresses three machines and packing with one machine. The model problem that was solved in this study was Hybrid Flowshop Scheduling. The optimization method for solving problems is to use the metaheuristic method Migrating Birds Optimization. To avoid problems faced by the company, scheduling is needed to minimize makespan by paying attention to the number of parallel machines. The results of this study are scheduling for 16 jobs and 46 jobs. Decreasing makespan value for 16 jobs minimizes the time for 26 minutes 39 seconds, while for 46 jobs can minimize the time for 3 hours 31 minutes 39 seconds.

]]>Muhammad Asim Khan and Norhashidah Hj. Mohd Ali

The fractional diffusion equation is an important mathematical model for describing phenomena of anomalous diffusion in transport processes. A high-order compact iterative scheme is formulated in solving the two-dimensional time fractional sub-diffusion equation. The spatial derivative is evaluated using Crank-Nicolson scheme with a fourth-order compact approximation and the Caputo derivative is used for the time fractional derivative to obtain a discrete implicit scheme. The order of convergence for the proposed method will be shown to be of . Numerical examples are provided to verify the high-order accuracy solutions of the proposed scheme.

]]>RaziraAniza Roslan Chin Su Na and Darmesah Gabda

The standard method of the maximum likelihood has poor performance in GEV parameter estimates for small sample data. This study aims to explore the Generalized Extreme Value (GEV) parameter estimation using several methods focusing on small sample size of an extreme event. We conducted simulation study to illustrate the performance of different methods such as the Maximum Likelihood (MLE), probability weighted moment (PWM) and the penalized likelihood method (PMLE) in estimating the GEV parameters. Based on the simulation results, we then applied the superior method in modelling the annual maximum stream flow in Sabah. The result of the simulation study shows that the PMLE gives better estimate compared to MLE and PMW as it has small bias and root mean square errors, RMSE. For an application, we can then compute the estimate of return level of river flow in Sabah.

]]>Khadizah Ghazali Jumat Sulaiman Yosza Dasril and Darmesah Gabda

In this paper, we proposed an alternative way to find the Newton direction in solving large-scale unconstrained optimization problems where the Hessian of the Newton direction is an arrowhead matrix. The alternative approach is a two-point Explicit Group Gauss-Seidel (2EGGS) block iterative method. To check the validity of our proposed Newton’s direction, we combined the Newton method with 2EGGS iteration for solving unconstrained optimization problems and compared it with a combination of the Newton method with Gauss-Seidel (GS) point iteration and the Newton method with Jacobi point iteration. The numerical experiments are carried out using three different artificial test problems with its Hessian in the form of an arrowhead matrix. In conclusion, the numerical results showed that our proposed method is more superior than the reference method in term of the number of inner iterations and the execution time.

]]>Mohd Saifullah Rusiman Siti Nasuha Md Nor Suparman and Siti Noor Asyikin Mohd Razali

This paper is focusing on the application of robust method in multiple linear regression (MLR) model towards diabetes data. The objectives of this study are to identify the significant variables that affect diabetes by using MLR model and using MLR model with robust method, and to measure the performance of MLR model with/without robust method. Robust method is used in order to overcome the outlier problem of the data. There are three robust methods used in this study which are least quartile difference (LQD), median absolute deviation (MAD) and least-trimmed squares (LTS) estimator. The result shows that multiple linear regression with application of LTS estimator is the best model since it has the lowest value of mean square error (MSE) and mean absolute error (MAE). In conclusion, plasma glucose concentration in an oral glucose tolerance test is positively affected by body mass index, diastolic blood pressure, triceps skin fold thickness, diabetes pedigree function, age and yes/no for diabetes according to WHO criteria while negatively affected by the number of pregnancies. This finding can be used as a guideline for medical doctors as an early prevention of stage 2 of diabetes.

]]>Nur Hanim Mohd Salleh Husna Hasan and Fariza Yunus

Extreme temperature has been carried out around the world to provide awareness and proper opportunity for the societies to prepare necessary arrangements. In this present paper, the first order Markov chain model was applied to estimate the probability of extreme temperature based on the heat wave scales provided by the Malaysian Meteorological Department. In this study, the 24-year period (1994-2017) daily maximum temperature data for 17 meteorological stations in Malaysia was assigned to the four heat wave scales which are monitoring, alert level, heat wave and emergency. The analysis result indicated that most of the stations had three categories of heat wave scales. Only Chuping station had four categories while Bayan Lepas, Kuala Terengganu, Kota Bharu and Kota Kinabalu stations had two categories. The limiting probabilities obtained at each station showed a similar trend which the highest proportion of daily maximum temperature occurred in the scale of monitoring and followed by the alert level. This trend is apparent when the daily maximum temperature data revealed that Malaysia is experiencing two consecutive days of temperature below 35℃.

]]>Puguh Wahyu Prasetyo Indah Emilia Wijayanti Halina France-Jackson and Joe Repka

In the development of Theory Radical of Rings, there are two kinds of radical constructions. The first radical construction is the lower radical construction and the second one is the upper radical construction. In fact, the class π of all prime rings forms a special class and the upper radical class of forms a radical class which is called the prime radical. An upper radical class which is generated by a special class of rings is called a special radical class. On the other hand, we also have the class of all semiprime rings which is weakly special class of rings. Moreover, we can construct a special class of modules by using a given special class of rings. This condition motivates the existence of the question how to construct weakly special class modules by using a given weakly special class of rings. This research is a qualitative research. The results of this research are derived from fundamental axioms and properties of radical class of rings especially on special and weakly special radical classes. In this paper, we introduce the notion of a weakly special class of modules, a generalization of the notion on a special class of modules based on the definition of semiprime modules. Furthermore, some properties and examples of weakly special classes of modules are given. The main results of this work are the definition of a weakly special class of modules and their properties.

]]>Suparman

A piecewise constant model is often applied to model data in many fields. Several noises can be added in the piecewise constant model. This paper proposes the piecewise constant model with a gamma multiplicative noise and a method to estimate a parameter of the model. The estimation is done in a Bayesian framework. A prior distribution for the model parameter is chosen. The prior distribution for the parameter model is multiplied with a likelihood function for the data to build a posterior distribution for the parameter. Because a number of models are also parameters, a form of the posterior distribution for the parameter is too complex. A Bayes estimator cannot be calculated easily. A reversible jump Monte Carlo Markov Chain (MCMC) is used to find the Bayes estimator of the model parameter. A result of this paper is the development of the piecewise constant model and the method to estimate the model parameter. An advantage of this method can simultaneously estimate the constant piecewise model parameter.

]]>Che Haziqah Che Hussin Ahmad Izani Md Ismail Adem Kilicman and Amirah Azmi

This paper aims to propose and investigate the application of Multistep Modified Reduced Differential Transform Method (MMRDTM) for solving the nonlinear Korteweg-de Vries (KdV) equation. The proposed technique has the advantage of producing an analytical approximation in a fast converging sequence with a reduced number of calculated terms. MMRDTM is presented with some modification of the reduced differential transformation method (RDTM) which is the nonlinear term is replaced by related Adomian polynomials and then adopting a multistep approach. Consequently, the obtained approximation results do not only involve smaller number of calculated terms for the nonlinear KdV equation, but also converge rapidly in a broad time frame. We provided three examples to illustrates the advantages of the proposed method in obtaining the approximation solutions of the KdV equation. To depict the solution and show the validity and precision of the MMRDTM, graphical inputs are included.

]]>Bahtiar Jamili Zaini and Shamshuritawati Sharif

Bivariate data consist of 2 random variables that are obtained from the same population. The relationship between 2 bivariate data can be measured by correlation coefficient. A correlation coefficient computed from the sample data is used to measure the strength and direction of a linear relationship between 2 variables. However, the classical correlation coefficient results are inadequate in the presence of outliers. Therefore, this study focuses on the performance of different correlation coefficient under contaminated bivariate data to determine the strength of their relationships. We compared the performance of 5 types of correlation, which are classical correlations such as Pearson correlation, Spearman correlation and Kendall’s Tau correlation with other robust correlations, such as median correlation and median absolute deviation correlation. Results show that when there is no contamination in data, all 5 correlation methods show a strong relationship between 2 random variables. However, under the condition of data contamination, median absolute deviation correlation denotes a strong relationship compared to other methods.

]]>Gautam Choudhury Akhil Goswami Anjana Begum and Hemanta Kumar Sarmah

The single server queue with two types of heterogeneous services with generalized vacation for unreliable server have been extended to include several types of generalizations to which attentions has been paid by several researchers. One of the most important results which deals with such types of models is the “Stochastic Decomposition Result”, which allows the system behaviour to be analyzed by considering separately distribution of system (queue) size with no vacation and additional system (queue) size due to vacation. Our intention is to look into some sort of united approach to establish stochastic decomposition result for two types of general heterogeneous service queues with generalized vacations for unreliable server with delayed repair to include several types of generalizations. Our results are based on embedded Markov Chain technique which is considerably a most powerful and popular method wisely used in applied probability, specially in queueing theory. The fundamental idea behind this method is to simplify the description of state from two dimensional states to one dimensinal state space. Finally, the results that are derived is shown to include several types of generalizations of some existing well- known results for vacation models, that may lead to remarkable simpliﬁcation while solving similar types of complex models.

]]>Inessa I. Pavlyuk and Sergey V. Sudoplatov

Approximations of syntactic and semantic objects play an important role in various ﬁelds of mathematics. They can create theories and structures in one given class by means of others, usually simpler. For instance, in certain situations, inﬁnite objects can be approximated by ﬁnite or strongly minimal ones. Thus, complicated objects can be collected using simpliﬁed ones. Among these objects, Abelian groups, their ﬁrst order theories, connections and dynamics are of interests. Theories of Abelian groups are characterized by Szmielew invariants leading to the study and descriptions of approximations in terms of these invariants. In the paper we apply a general approach for approximating theories to the class of theories of Abelian groups which characterizes the approximability of a theory of Abelian groups by a given family of theories of Abelian groups in terms of Szmielew invariants and their limits. We describe some forms of approximations for theories of Abelian groups. In particular, approximations of theories of Abelian groups by theories of ﬁnite ones are characterized. In addition, we describe approximations by quasi-cyclic and torsion-free Abelian groups and their combinations with respect to given families of prime numbers. Approximations and closures of families of theories with respect to standard Abelian groups for various sets of prime numbers are also described.

]]>Supawan Yena and Nopparat Pochai

Nitrogen is emitted extensively by industrial companies, increasing nitrogen compounds such as ammonia, nitrate, and nitrite in soil and water as a result of nitrogen cycle reactions. Groundwater contamination with nitrates and nitrites impacts human health. Mathematical models can explain groundwater contamination with nitrates and nitrites. Hydraulic head model provides the hydraulic head of groundwater. Groundwater velocity model provided x- and y- direction vector in groundwater. Groundwater contamination distribution model provides nitrogen, nitrate and nitrite concentration. Finite difference techniques are approximate the models solution. Alternating direction explicit method was used to clarify hydraulic head model. Centered space explained groundwater velocity model. Forward time central space was used to predict groundwater transportation of contamination models. We simulate different circumstances to explain the pollution in leachate water underground, paying attention to the toxic nitrogen, ammonia, nitrate, nitrite blended in the water.

]]>Mohammed M. B. Adam M. B. Zulkafli H. S. and Ali N.

This paper proposes three different statistics to be used to represent the magnitude observations in each class when estimating the statistical measures from the frequency table for continuous data. The existing frequency tables use the midpoint as the magnitude of observations in each class, which results in an error called grouping error. Using the midpoint is due to the assumption that the observations in each class are uniformly distributed and concentrated around their midpoint, which is not always valid. In this research, construction of the frequency tables using the three proposed statistics, the arithmetic mean, median, and midrange and midpoint are respectively named, Method 1, Method 2, Method 3, and the Existing method. The four methods are compared using root-mean-squared error (RMSE) by performing simulation studies using three distributions, normal, uniform, exponential distributions. The simulation results are validated using real data, Glasgow weather data. The ﬁndings indicated that using the arithmetic mean to represent the magnitude of observations in each class of the frequency table leads to minimal error relative to other statistics. It is followed by using the median, for data simulated from normal and exponential distributions, and using midrange for data simulated from uniform distribution. Meanwhile, in choosing the appropriate number of classes used in constructing the frequency tables, among seven different rules used, the freedman and Diaconis rule is the recommended rule.

]]>Ludwik Byszewski Denis Blackmore Alexander A. Balinsky Anatolij K. Prykarpatski and Mirosław Lu´styk

As a ﬁrst step, we provide a precise mathematical framework for the class of control problems with delays (which we refer to as the control problem) under investigation in a Banach space setting, followed by careful deﬁnitions of the key properties to be analyzed such as solvability and complete controllability. Then, we recast the control problem in a reduced form that is especially amenable to the innovative analytical approach that we employ. We then study in depth the solvability and completeness of the (reduced) nonlinearly perturbed linear control problem with delay parameters. The main tool in our approach is the use of a Borsuk–Ulam type ﬁxed point theorem to analyze the topological structure of a suitably reduced control problem solution, with a focus on estimating the dimension of the corresponding solution set, and proving its completeness. Next, we investigate its analytical solvability under some special, mildly restrictive, conditions imposed on the linear control and nonlinear functional perturbation. Then, we describe a novel computational projection-based discretization scheme of our own devising for obtaining accurate approximate solutions of the control problem along with useful error estimates. The scheme effectively reduces the inﬁnite-dimensional problem to a sequence of solvable ﬁnite-dimensional matrix valued tasks. Finally, we include an application of the scheme to a special degenerate case of the problem wherein the Banach–Steinhaus theorem is brought to bear in the estimation process.

]]>Fausto Galetto

Pooling p-values arises both in practical (in any science and engineering applications) and theoretical (statistical) issues. The p-value (sometimes p value) is a probability used as a statistical decision quantity: in practical applications, it is used to decide if an experimenter has to believe that his/her collected data confirm or disconfirm his/her hypothesis about the “reality” of a phenomenon. It is a real number, determination of a Random Variable, uniformly distributed, related to the data provided by the measurement of a phenomenon. Almost all statistical software provides p-values when statistical hypotheses are considered, e.g. in Analysis of Variance and regression methods. Combining the p-values from various samples is crucial, because the number of degrees of freedom (df) of the samples we want to combine is influencing our decision: forgetting this can have dangerous consequences. One way of pooling p-values is provided by a formula of Fisher; unfortunately, this method does not consider the number of degrees of freedom. We will show other ways of doing that and we will prove that theory is more important than any formula which does not consider the phenomenon on which we have to decide: the distribution of the Random Variables is fundamental in order to pool data from various samples. Manager, professors and scholars should remember Deming’s profound knowledge and Juran’s ideas; profound knowledge means “understanding variation (type of variation)” in any process, production or managerial; not understanding variation causes cost of poor quality (more than 80% of sales value) and do not permits a real improvement.

]]>Anton Epifanov

Paper contains the results of the analysis of the laws of functioning of discrete dynamical systems, as mathematical models of which, using the apparatus of geometric images of automatons, are used numerical sequences which interpreted as sequences of second coordinates of points of geometric images of automatons. The geometric images of the laws of the functioning of the automaton are reduced to numerical sequences and numerical graphs. The problem of constructing an estimate of the complexity of the structures of such sequences is considered. To analyze the structure of sequences, recurrence forms are used that give characteristics of the relative positions of elements in the sequence. The parameters of recurrent forms are considered, which characterize the lengths of the initial segments of sequences determined by recurrence forms of fixed orders, the number of changes of recurrent forms required to determine the entire sequence, the place of change of recurrence forms, etc. All these parameters are systematized into the special spectrum of dynamic parameters used for the recurrent determination of sequences, which is used as a means of constructing estimates of the complexity of sequences. In this paper, it also analyzes return sequences (for example, Fibonacci numbers), for the analysis of the properties of which characteristic sequences are used. The properties of sequences defining approximations of fundamental mathematical constants (number e, pi number, golden ratio, Euler constant, Catalan constant, values of Riemann zeta function, etc.) are studied. Complexity estimates are constructed for characteristic sequences that distinguish numbers with specific properties in a natural series, as well as for characteristic sequences that reflect combinations of the properties of numbers.

]]>Leontiev V. L.

The problem of approximating of a surface given by the values of a function of two arguments in a finite number of points of a certain region in the classical formulation is reduced to solving a system of algebraic equations with tightly filled matrixes or with band matrixes. In the case of complex surfaces, such a problem requires a significant number of arithmetic operations and significant computer time spent on such calculations. The curvilinear boundary of the domain of general type does not allow using classical orthogonal polynomials or trigonometric functions to solve this problem. This paper is devoted to an application of orthogonal splines for creation of approximations of functions in form of finite Fourier series. The orthogonal functions with compact supports give possibilities for creation of such approximations of functions in regions with arbitrary geometry of a boundary in multidimensional cases. A comparison of the fields of application of classical orthogonal polynomials, trigonometric functions and orthogonal splines in approximation problems is carried out. The advantages of orthogonal splines in multidimensional problems are shown. The formulation of function approximation problem in variational form is given, a system of equations for coefficients of linear approximation with a diagonal matrix is formed, expressions for Fourier coefficients and approximations in the form of a finite Fourier series are written. Examples of approximations are considered. The efficiency of orthogonal splines is shown. The development of this direction associated with the use of other orthogonal splines is discussed.

]]>Supawan Yena and Nopparat Pochai

Leachate contamination in a landfill causes pollution that flowing down to the groundwater. There are many methods to measure the groundwater quality. Mathematical models are often used to describe the groundwater flow. In this research, the affection of landfill construction to groundwater-quality around rural area is focused. Three mathematical models are combined. The first model is a two-dimensional groundwater flow model. It provides the hydraulic head of the groundwater. The second model is the velocity potential model. It provides the groundwater flow velocity. The third model is a two-dimensional vertically averaged groundwater pollution dispersion model. The groundwater pollutant concentration is provided. The forward time centered technique with the centered in space, the forward in space and the backward in space with all boundaries are used to obtain approximate hydraulic head, the flow velocity in x- and y- directions, respectively. The approximated groundwater flow velocity is used to input into a two-dimensional vertically averaged groundwater pollution dispersion model. The forward time centered space technique with the centered in space, the forward in space and the backward in space with all boundaries are used to obtain approximate the groundwater pollutant concentration. The proposed explicit forward time centered spaced finite difference techniques to the groundwater flow model the velocity potential model and the groundwater pollution dispersion model give good agreement approximated solutions.

]]>Jindrich Klufa

The entrance examinations tests were shorted from 50 questions to 40 questions at the Faculty of International Relations at University of Economics in Prague due to time reasons. These tests are the multiple choice question tests. The multiple choice question tests are suitable for entrance examinations at University of Economics in Prague - the tests are objective and results can be evaluated quite easily and quickly for large number of students. On the other hand, a student can obtain certain number of points in the test purely by guessing the right answers. This shortening of the tests from 50 questions to 40 questions has negative influence on the probability distributions of number of points in the tests (under assumption of the random choice of answers). Therefore, this paper is suggested a solution of this problem. The comparison of these three ways of acceptance of applicants to study the Faculty of International Relations at University of Economics from probability point of view is performed in present paper. The results of this paper show that there has been a significant improvement of the probability distributions of number of points in the tests. The obtained conclusions can be used for admission process at the Faculty of International Relations in coming years.

]]>GeorgiaIrina Oros and Alina Alb Lupas

In this paper, we define the operator I^{m} : differential-integral operator, where S^{m} is S˘al˘agean differential operator and Lm is Libera integral operator. By using the operator I^{m} the class of univalent functions denoted by is defined and several differential subordinations are studied. Even if the use of linear operators and introduction of new classes of functions where subordinations are studied is a well-known process, the results are new and could be of interest for young researchers because of the new approach derived from mixing a differential operator and an integral one. By using this differential–integral operator, we have obtained new sufficient conditions for the functions from some classes to be univalent. For the newly introduced class of functions, we show that is it a class of convex functions and we prove some inclusion relations depending on the parameters of the class. Also, we show that this class has as subclass the class of functions with bounded rotation, a class studied earlier by many authors cited in the paper. Using the method of the subordination chains, some differential subordinations in their special Briot-Bouquet form are obtained regarding the differential–integral operator introduced in the paper. The best dominant of the Briot-Bouquet differential subordination is also given. As a consequence, sufficient conditions for univalence are stated in two criteria. An example is also illustrated, showing how the operator is used in obtaining Briot–Bouquet differential subordinations and the best dominant.

Mostafa Ftouhi Mohammed Barmaki and Driss Gretete

The class of amenable groups plays an important role in many areas of mathematics such as ergodic theory, harmonic analysis, representation theory, dynamical systems, geometric group theory, probability theory and statistics. The class of amenable groups contains in particular all finite groups, all abelian groups and, more generally, all solvable groups. It is closed under the operations of taking subgroups, taking quotients, taking extensions, and taking inductive limits. In 1959, Harry Kesten proved that there is a relation between the amenability and the estimates of symmetric random walk on finitely generated groups. In this article we study the classification of locally compact compactly generated groups according to return probability to the origin. Our aim is to compare several geometric classes of groups. The central tool in this comparison is the return probability on locally compact groups. we introduce several classes of groups in order to characterize the geometry of locally compact groups compactly generated. Our aim is to compare these classes in order to better understand the geometry of such groups by referring to the behavior of random walks on these groups. As results, we have found inclusion relationships between these defined classes and we have given counterexamples for reciprocal inclusions.

]]>Zainidin Eshkuvatov Massamdi Kommuji Rakhmatullo Aloev Nik Mohd Asri Nik Long and Mirzoali Khudoyberganov

A hypersingular integral equations (HSIEs) of the first kind on the interval [ 1 ; 1 ] with the assumption that kernel of the hypersingular integral is constant on the diagonal of the domain is considered. Truncated series of Chebyshev polynomials of the third and fourth kinds are used to find semi bounded (unbounded on the left and bounded on the right and vice versa) solutions of HSIEs of first kind. Exact calculations of singular and hypersingular integrals with respect to Chebyshev polynomials of third and forth kind with corresponding weights allows us to obtain high accurate approximate solution. Gauss-Chebyshev quadrature formula is extended for regular kernel integrals. Three examples are provided to verify the validity and accuracy of the proposed method. Numerical examples reveal that approximate solutions are exact if solution of HSIEs is of the polynomial forms with corresponding weights.

]]>Nurazlina Abdul Rashid Norashikin Nasaruddin Kartini Kassim and Amirah Hazwani Abdul Rahim

Classification studies are widely applied in many areas of research. In our study, we are using classification analysis to explore approaches for tackling the classification problem for a large number of measures using partial least square discriminant analysis (PLS-DA) and decision trees (DT). The performance for both methods was compared using a sample data of breast tissues from the University of Wisconsin Hospital. A partial least square discriminant analysis (PLS-DA) and decision trees (DT) predict the diagnosis of breast tissues (M = malignant, B = benign). A total of 699 patients diagnose (458 benign and 241 malignant) are used in this study. The performance of PLS-DA and DT has been evaluated based on the misclassification error and accuracy rate. The results show PLS-DA can be considered as a good and reliable technique to be used when dealing with a large dataset for the classification task and have good prediction accuracy.

]]>Nurul Shazwani Mohamed Sharifah Kartini Said Husain and Faridah Yunos

Given two algebras and , if lies in the Zariski closure of the orbit , we say that is a degeneration of . We denote this by . Degenerations (or contractions) were widely applied to a range of physical and mathematical point of view. The most well-known example oriented to the application on degenerations is limiting process from quantum mechanics to classical mechanics under that corresponds to the contraction of the Heisenberg algebras to the abelian ones of the same dimension. Research on degenerations of Lie, Leibniz and other classes of algebras are very active. Throughout the paper we are dealing with mathematical background with abstract algebraic structures. The present paper is devoted to the degenerations of low-dimensional nilpotent Leibniz algebras over the field of complex numbers. Particularly, we focus on the classification of three-dimensional nilpotent Leibniz algebras. List of invariance arguments are provided and its dimensions are calculated in order to find the possible degenerations between each pair of algebras. We show that for each possible degenerations, there exists construction of parameterized basis on parameter We proof the non-degeneration case for mentioned classes of algebras by providing some reasons to reject the degenerations. As a result, we give complete list of degenerations and non-degenerations of low-dimensional complex nilpotent Leibniz algebras. In future research, from this result we can find its rigidity and irreducible components.

]]>Busyra Latif Mat Salim Selamat Ainnur Nasreen Rosli Alifah Ilyana Yusoff and Nur Munirah Hasan

Newell-Whitehead-Segel (NWS) equation is a nonlinear partial differential equation used in modeling various phenomena arising in fluid mechanics. In recent years, various methods have been used to solve the NWS equation such as Adomian Decomposition method (ADM), Homotopy Perturbation method (HPM), New Iterative method (NIM), Laplace Adomian Decomposition method (LADM) and Reduced Differential Transform method (RDTM). In this study, the NWS equation is solved approximately using the Semi Analytical Iterative method (SAIM) to determine the accuracy and effectiveness of this method. Comparisons of the results obtained by SAIM with the exact solution and other existing results obtained by other methods such as ADM, LADM, NIM and RDTM reveal the accuracy and effectiveness of the method. The solution obtained by SAIM is close to the exact solution and the error function is close to zero compared to the other methods mentioned above. The results have been executed using Maple 17. For future use, SAIM is accurate, reliable, and easier in solving the nonlinear problems since this method is simple, straightforward, and derivative free and does not require calculating multiple integrals and demands less computational work.

]]>Patricia Abelairas-Etxebarria and Inma Astorkiza

The Exploratory Data Analysis raised by Tuckey [19] has been used in multiple research in many areas but, especially, in the area of the social sciences. This technique searches behavioral patterns of the variables of the study, establishing a hypothesis with the least possible structure. However, in recent times, the inclusion of the spatial perspective in this type of analysis has been revealed as essential because, in many analyses, the observations are spatially autocorrelated and/or they present spatial heterogeneity. The presence of these spatial effects makes necessary to include spatial statistics and spatial tools in the Exploratory Data Analysis. Exploratory Spatial Data Analysis includes a set of techniques that describe and visualize those spatial effects: spatial dependence and spatial heterogeneity. It describes and visualizes spatial distributions, identifies outliers, finds distribution patterns, clusters and hot spots and suggests spatial regimes or other forms of spatial heterogeneity and, it is being increasingly used. With the objective of reviewing the last applications of this technique, this paper, firstly, shows the tools used in Exploratory Spatial Data Analysis and, secondly, reviews the latest Exploratory Spatial Data Analysis applications focused on different areas in the social sciences particularly. As conclusion, it should be noted the growing interest in the use of this spatial technique to analyze different aspects of the social sciences including the spatial dimension.

]]>Agung Prabowo Agus Sugandha Agustini Tripena Mustafa Mamat Sukono and Ruly Budiono

Linear regression is widely used in various fields. Research on linear regression uses the OLS and ML method in estimating its parameters. OLS and ML method require many assumptions to complete. It is frequently found there is an unconditional assumption that both methods are not successfully used. This paper proposes a new method which does not require any assumption with a condition. The new method is called SAM (Simple Averaging Method) to estimate parameters in the simple linear regression model. The method may be used without fulfilling assumptions in the regression model. Three new theorems are formulated to simplify the estimation of parameters in the simple linear regression model with SAM. By using the same data, the simple linear regression model parameter estimation is conducted using SAM. The result shows that the obtained regression parameter is not quite far different. However, to measure the accuracy of both methods, a comparison of errors made by each method is conducted using Root Mean Square Error (RMSE) and Mean Averaged Error (MAE). By comparing the values of RMSE and MAE for both methods, SAM method may be used to estimate parameters in the regression equation. The advantage of SAM is free from all assumptions required by regression, such as error normality assumption while the data should be from the normal distribution.

]]>Jirapud Limthanakul and Nopparat Pochai

A source of contaminated groundwater is governed by the disposal of waste material on a land fill. There are many people in rural areas where the primary source of drinking water is well water. This well water may be contaminated with groundwater from landfills. In this research, a two-dimensional mathematical model for long-term contaminated groundwater pollution measurement around a land fill is proposed. The model is governed by a combination of two models. The first model is a transient two-dimensional groundwater flow model that provides the hydraulic head of the groundwater. The second model is a transient twodimensional advection-diffusion equation that provides the groundwater pollutant concentration. The proposed explicit finite difference techniques are used to approximate the hydraulic head and the groundwater pollutant concentration. The simulations can be used to indicate when each simulated zone becomes a hazardous zone or a protection zone.

]]>Nor Asmaa Alyaa Nor Azlan Effendi Mohamad Mohd Rizal Salleh Oyong Novareza Dani Yuniawan Muhamad Arfauz A Rahman Adi Saptari and Mohd Amri Sulaiman

The purpose of this review paper is to set an augmentation approach and exemplify distribution of augmentation works in Simplex method. The augmentation approach is classified into three forms whereby it comprises addition, substitution and integration. From the diversity study, the result shows that substitution approach appeared to be the highest usage frequency, which is about 45.2% from the total of percentage. This is then followed by addition approach which makes up 32.3% of usage frequency and integration approach for about 22.6% of usage frequency which makes it the least percentage of the overall usage frequency approach. Since it is being the least usage percentage, the paper is then interested to foresee a future study of integration approach that can be performed from the executed distribution of the augmentation works according to Simplex's computation stages. A theme screening is then conducted with a set of criteria and themes to come out with a proposal of new integration approach of augmentation of Simplex method.

]]>Arif Rahman Oke Oktavianty Ratih Ardia Sari Wifqi Azlia and Lavestya Dina Anggreni

Some researches need data homogeneity. The dispersion of data causes research towards an absurd direction. The outlier makes unrealistic homogeneity. The research can reject the extreme data as outlier to estimate trimmed arithmetic mean. Because of the wide data dispersion, it will fail to identify the outliers. The study will evaluate the confidence interval and compare it with the acceptance tolerance. There are three types of invalidity of data gathering: outliers, too wide dispersion, distracted central tendency.

]]>Zahari Md Rodzi and Abd Ghafur Ahmad

The purpose of this work is to present a new theory namely fuzzy parameterized dual hesitant fuzzy soft sets (FPDHFSSs). This theory is an extension of the existing dual hesitant fuzzy soft set whereby the set of parameters have been assigned with respective weightage accordingly. We also introduced the basic operation functions for instance intersection, union, addition and product operations of FPDHFSSs. Then, we proposed the concept of score function of FPDHFSSs of which these scores function were determined based on average mean, geometry mean and fractional score. The said scores function then were divided into the membership and non-membership elements where the distance of FPDHFSSs was introduced. The proposed distance of FPDHFSSs has been applied in TOPSIS which will be able to solve the problem of fuzzy dual hesitant fuzzy soft set environment.

]]>Alec John Villamar Marionne Gayagoy Flerida Matalang and Karen Joy Catacutan

This study aimed to determine the usefulness of Mathematics subjects in the accounting courses for Bachelor of Science in Accountancy. Mathematics subjects, which include College Algebra, Mathematics of Investment, Business Calculus and Quantitative Techniques, were evaluated through its Course Learning Objectives, while its usefulness for accounting courses which include Financial Accounting, Advance Accounting, Cost Accounting, Management Advisory Services, Auditing and Taxation, was evaluated by the students. Descriptive research was employed among all students in their 5^{th}-year in BS-Accountancy who were done with all the Accounting Subjects in the Accountancy Program and they all passed the different Mathematics subjects prerequisite to their courses. A survey questionnaire was used to gather data. Using descriptive statistics, results showed that Mathematics of Investment is the most useful subject in the different accounting courses particularly in Financial Accounting, Advance Accounting and Auditing. Further, by using Mean, the results showed that several skills that can be acquired in the Mathematics subjects are found to be useful in accounting courses and the use of the fundamental operations is the most useful skill in all accounting subjects.

Rafid S. A. Alshkaki

Differential equations are used in modelling many disciplines, in engineering, chemistry, physics, biology, economics, and other fields of sciences, hence can be used to understand and to determine the underlying probabilistic behavior of phenomena through their probability distributions. This paper came to use a simple form of differential equations, namely, the linear form, to determine the probabilistic distributions of some of the most important and popular sub class of discrete distributions used in real-life, the Poisson, the binomial, the negative binomial, and the logarithmic series distributions. A class of finite number of inflated points power series distributions, that contains the Poisson, the binomial, the negative binomial, and the logarithmic series distributions as some of its members, was defined and some of its characteristics properties, along with characterization of the 3-points inflated of these four distributions, through a linear differential equation for their probability generating functions were given. Further, some previous known results were shown to be special cases of our results.

]]>Hasibun Naher Humayra Shafia Md. Emran Ali and Gour Chandra Paul

In this article, the nonlinear partial fractional differential equation, namely the KdV equation is renewed with the help of modified Riemann- Liouville fractional derivative. The equation is transformed into the nonlinear ordinary differential equation by using the fractional complex transformation. The goal of this paper is to construct new analytical solutions of the space and time fractional nonlinear KdV equation through the extended -expansion method. The work produces abundant exact solutions in terms of hyperbolic, trigonometric, rational, exponential, and complex forms, which are new and more general than existing results in literature. The newly generated solutions show that the executed method is a well-organized and competent mathematical tool to investigate a class of nonlinear evolution fractional order equations.

]]>Llesh Lleshaj and Alban Korbi

In this study analyzed 20 different countries that are the origin state of foreign investors, which have invested in Albania (this sample represents 95% of FDI (Foreign Direct Investments) stocks, 2007 - 2014). The analysis technic used is the gravity model of FDI stocks in Albania. The main independent variables in this analysis are GDP, the level of business taxes, the difference of GDP per capita, the similarity economies, etc. The result of this study: The level of FDI stocks in Albania is lower than its potential compare with FDI stock average in the States of the Balkan Region.

]]>Anuradha Seema Mehra and Said Broumi

Motivated by the concepts of fuzzy metric and m-metric spaces, we introduced the notion of Non- Archimedean fuzzy m-metric space which is an extension of partial fuzzy metric space. We present some examples in support of this new notion. Regarding this notion, its topological structure and some properties are specified simultaneously. At the end, some fixed point results are also provided.

]]>Igor Sinitsyn and Vladimir Sinitsyn

Analytical methods of the mathematical statistics of random vectors and matrices based on the parametrization of the distributions are widely used. These methods permit to design practically simple software when it is possible to have the definite information about analytical properties of the distributions under research. The main difficulty in practical applications of the methods based on the parametrization of the distributions is the rapid increase of the number of equations for the moments, the semiinvariants or the coefficients of the truncated orthogonal expansions of the dimension or the state vector (extended in the general case) and the maximal order of the moments involved. The number of equations for the parameters becomes exceedingly large in such cases. For structural parametrization and/or approximation of the probability densities of the random vectors we shall apply the ellipsoidal densities, i.e. the densities whose planes of the levels of equal probability are similar concentric ellipsoids (the ellipses for two-dimensional vectors, the ellipsoids for three-dimensional vectors, the hyperellipsoids for the vectors of the dimension more than three). In particular, a normal distribution in any finite-dimensional space has an ellipsoidal structure. The distinctive characteristics of such distributions consists in the fact that their probability densities are the functions of positively determined quadratic form where is an expectation of the random vector is some positively determined matrix. Ellipsoidal approximation method (EAM) cardinally reduces the number of parameters till () where being the number of probabilistic moments. While using ellipsoidal linearization method (ELM) we get Basic EAM and ELM foundations and applications to problems of mathematical statistics and ellipsoidal distributions with invariant measure in populational Volterra differential stochastic nonlinear systems are considered.

]]>Aripov M. Mukimov A. and Mirzayev B.

We study the asymptotic behavior (for ) of solutions of the Cauchy problem for a nonlinear parabolic equation with a double nonlinearity, describing the diffusion of heat with nonlinear heat absorption at the critical value of the parameter ᵝ. For numerical computations as an initial approximation we used founded the long time asymptotic of the solution. Numerical experiments and visualization were carried for one and two dimensional case.

]]>Emil V. Veitsman

This paper is aimed to find a connection between i-dimensional spaces (i=0,…, ‘n') and the long-range j-dimensional attractive forces (j=0,…, ‘m') creating these spaces. The connection is fundamental and unrelated to any processes going in the spaces being studied. A theorem is formulated and strictly proved showing in which cases the long-ranged attractive forces can form real spaces of different dimensions ( i=0,…,n). The existence of the attraction between masses is defined by divergence of the vector of interaction between masses. Weak anisotropic real spaces are studied by rotating an ellipsoid for (3ζ)D-cases when its eccentricity ε<<1. Such spaces cannot be in equilibrium, the time of their existence is substantially limited. The greater is anisotropy, the shorter is the lifetime of such substance. The latter cannot be in equilibrium, the time of their existence is substantially limited.

]]>Taehan Bae and Maral Mazjini

Recent studies on correlated Poisson processes show that the backward simulation methods are computationally efficient, and incorporate flexible and extremal correlation structures in a multivariate risk system. These methods rely on the fact that the past arrival times of a Poisson process given the number of events over a time interval, [0; T], are the order statistics of uniform random variables on [0; T]. In this paper, we discuss an extension of the backward methods to a correlated negative binomial L´evy process which is an appealing model for over-dispersed count data such as operational losses. To obtain the conditional uniformity for the negative binomial L´evy process, we consider a particular setting in which the time interval is partitioned into equally spaced sub-intervals with unit length and the terminal time T is set to be the number of sub-intervals. Under this setting, the resulting joint probability of the increment series, conditional on the number of events over [0; T], say l, is uniform for any points in the support of a [T; l]-simplex lattice. Based on this result, we establish a backward simulation method similar to that of Poisson process. Both the conditional independence and conditional dependence cases are discussed with illustrations of the corresponding time correlation patterns.

]]>Mykola Bokalo and Olha Sus

In this paper, we consider the initial-value problem for parabolic variational inequalities (subdifferential inclusions) with Volterra type operators. We prove the existence and the uniqueness of the solution. Furthermore, the estimates of the solution are obtained. The results are achieved using the Banach's fixed point theorem (the principle of compression mappings). The motivation for this work comes from the evolutionary variational inequalities arising in the study of frictionless contact problems for linear viscoelastic materials with long-term memory. Also, such kind of problems have their application in constructing different models of the injection molding processes.

]]>Benjamin Kedem Lemeng Pan and Paul J. Smith Chen Wang

It is shown how to estimate any threshold probability from data below or even far below the threshold through repeated fusion of the data with externally generated random samples. This is referred to as repeated out of sample fusion (ROSF). A comparison of the approach with peaks-over-threshold (POT) across different tail types shows that ROSF provides more precise point and interval estimates based on moderately large samples.

]]>Sh. A. Dildabayev and G. K. Zakir'yanova

Up to now remains open the question of constructing fundamental solutions of the two-dimensional statics of an elastic body with arbitrary anisotropy. Also in the scope of BEM method, the question of calculating stresses in boundary points and points located close to the boundary of the region still remains actual. In this work, fundamental solutions of the static problem for elastic plane with arbitrary anisotropic properties are obtained as the sum of residues with complex variable function. The assessments of fundamental solution and theirs derivatives are presented in closed form. In the distribution space obtained are the regular representations for the Somigliana formulas and the stress calculation formulas. The numerical implementation of the BIE method in direct formulation has been realized in standard way. The test results performed for circular hole in anisotropic plane of rhombic system show a higher compliance with the boundary values of displacements and stresses and with nodes placed close to boundary. The results of analysis of the stress-strain state in the vicinity of rectangular mining chambers located deep from day surface are presented in tables and pictures of isolines.

]]>D. A. Karpov and V. I. Struchenkov

This article deals with the problem of approximation of plane curves defined by a sequence of points by a spline of a given type. This task arises when developing methods for computer-aided design of linear structures: railways and roads, trenches for laying pipelines, canals, etc. Its fundamental differences from the problems are considered in the theory of splines and its applications are as follows: spline elements are of various types (straight line segments and circles joined by clothoids), the boundaries of the elements and even their number is unknown; also there are restrictions - inequalities on the parameters of the elements. Continuity of the curve, the tangent, and the curvature is provided. Clothoids are missing if curvature continuity is not required, for example, when designing pipelines. The above mentioned features of the task do not allow using the achievements of the theory of splines and nonlinear programming. We cannot recognize the individual elements of the desired spline by a given sequence of points. Therefore, it is not possible to implement their selection separately. We must search for the spline as a whole. The article presents a mathematical model and a new algorithm for solving the problem using dynamic programming.

]]>Afif Shihabuddin Norhaslinda Ali and Mohd Bakri Adam

Air pollution index (API) is a common tool used to describe the air quality in the environment. High level of API indicates the greater level of air pollution which will gives bad impact on human health. Statistical model for high level of API is important for the purpose of forecasting the level of API so that the public can be warned. In this study, extremes of API are modelled using Generalized Pareto Distribution (GPD). Since the values of API are determined by the value of five pollutants namely sulphur dioxide, nitrogen dioxide, carbon monoxide, ozone and suspended particulate matter, data on API exhibit non-stationarity. Standard method for modelling the non-stationary extremes using GPD is by fixing the high constant threshold and incorporating the covariate model in the GPD parameters for data above the threshold to account for the non-stationarity. However, high constant threshold value might be high enough on certain covariate for GPD approximation to be a valid model for extreme values, but not on the other covariates which leads to the violation of the asymptotic basis of GPD model. New method for the threshold selection in non-stationary extremes modelling using regression tree is proposed to the API data. Regression tree is used to partition the API data into a stationary group with similar covariate condition. Then, a high threshold value can be applied within a group. Study shows that model for extremes of API using tree-based threshold gives a good fit and provides an alternative to the model based on standard method.

]]>Norin Rahayu Shamsuddin and Nor Idayu Mahat

Clustering with heterogeneous variables in a dataset is no doubt a challenging process owing to different scales in a data. The paper introduced a SimMultiCorrData package in R to generate the artificial dataset for clustering. The construction of artificial dataset with various distribution helps to mimic the scenario of nature of real datasets. Our experiments shows that the clusterability of a dataset are influenced by various factors such as overlapping clusters, noise, sub-cluster, and unbalance objects within the clusters.

]]>F. Z. Che Rose M. T. Ismail and N. A. K. Rosili

The existence of outliers in financial time series may affect the estimation of economic indicators. Detection of outliers in structural time series framework by using indicator saturation approach has become our main interest in this study. The reference model used is local level model. We apply Monte Carlo simulations to assess the performance of impulse indicator saturation for detecting additive outliers in the reference model. It is found that the significance level, α = 0.001 (tiny) outperformed the other target size in detecting various size of additive outliers. Further, we apply the impulse indicator saturation to detection of outliers in FTSE Bursa Malaysia Emas (FBMEMAS) index. We discover that there were 14 outliers identified corresponding to several economic and financial events.

]]>Ling, A. S. C. Darmesah, G. Chong, K. P. and Ho, C. M.

The losses caused by cocoa black pod disease around the world exceeded $400 million due to inaccurate forecasting of cocoa black pod disease incidence which leads to inappropriate spraying timing. The weekly cocoa black pod disease incidence is affected by external factors, such as climatic variables. In order to overcome this inaccuracy of spraying timing, the forecasting disease incidence should consider the influencing external factors such as temperature, rainfall and relative humidity. The objective of this study is to develop a Autoregressive Integrated Moving Average with external variables (ARIMAX) model which tries to account the effects due to the climatic influencing factors, to forecast the weekly cocoa black pod disease incidence. With respect to performance measures, it is found that the proposed ARIMAX model improves the traditional Autoregressive Integrated Moving Average (ARIMA) model. The results of this forecasting can provide benefits especially for the development of decision support system in determine the right timing of action to be taken in controlling the cocoa black pod disease.

]]>Nurazlina Abdul Rashid Wan Siti Esah Che Hussain Abd Razak Ahmad and Fatihah Norazami Abdullah

Classification methods are fundamental techniques designed to find mathematical models that are able to recognize the membership of each object to its proper class on the basis of a set of measurements. The issue of classifying objects into groups when variables in an experiment are large will cause the misclassification problems. This study explores the approaches for tackling the classification problem of a large number of independent variables using parametric method namely PLS-DA and PCA+LDA. Data are generated using data simulator; Azure Machine Learning (AML) studio through custom R module. The performance analysis of the PLS-DA was conducted and compared with PCA+LDA model using different number of variables (p) and different sample sizes (n). The performance of PLS-DA and PCA+LDA has been evaluated based on minimum misclassification rate. The results demonstrated that PLS-DA performed better than the PCA+LDA for large sample size. PLS-DA can be considered to have a good and reliable technique to be used when dealing with large datasets for classification task.

]]>Noor Hidayah Mohd Zaki Aqilah Nadirah Saliman Nur Atikah Abdullah Nur Su Ain Abu Hussain and Norani Amit

A queuing system is a process to measure the efficiency of a model by underlying the concepts of queue models: arrival and service time distributions, queue disciplines and queue behaviour. The main aim of this study is to compare the behaviour of a queuing system at check-in counters using the Queuing Theory Model and Fuzzy Queuing Model. The Queuing Theory Model gives performance measures of a single value while the Fuzzy Queuing Model has a range of values. The Dong, Shah and Wong (DSW) algorithm is used to define the membership function of performance measures in the Fuzzy Queuing Model. Based on the observation, the problem often occurs when customers are required to wait in the queue for a long time, thus indicating that the service systems are inefficient. Data including the variables were collected, such as arrival time in the queue (server) and service time. Results show that the performance measures of the Queuing Theory Model lie in the range of the computed performance measures of the Fuzzy Queuing Model. Hence, the results obtained from the Fuzzy Queuing Model are consistent to measure the queuing performance of an airline company in order to solve the problem in waiting line and will improve the quality of services provided by airline company.

]]>Zakiah I. Kalantan and Faten Alrewely

Mixture distributions have received considerable attention in life applications. This paper presents a finite Laplace mixture model with two components. We discuss the model properties and derive the parameters estimations using the method of moments and maximum likelihood estimation. We study the relationship between the parameters and the shape of the proposed distribution. The simulation study discusses the effectiveness of parameters estimations of Laplace mixture distribution.

]]>Hafizah Bahaludin Mimi Hafizah Abdullah Lam Weng Siew and Lam Weng Hoe

In recent years, there has been a growing interest in financial network. The financial network helps to visualize the complex relationship between stocks traded in the market. This paper investigates the stock market network in Bursa Malaysia during the 2008 global financial crisis. The financial network is based on the top hundred companies listed on Bursa Malaysia. Minimal spanning tree (MST) is employed to construct the financial network and uses cross-correlation as an input. The impact of the global financial crisis on the companies is evaluated using centrality measurements such as degree, betweenness, closeness and eigenvector centrality. The results indicate that there are some changes on the linkages between securities after the financial crisis, that can have some significant effect in investment decision making.

]]>Mihail Cocos

The Fundamental Theorem of Riemannian geometry states that on a Riemannian manifold there exist a unique symmetric connection compatible with the metric tensor. There are numerous examples of connections that even locally do not admit any compatible metrics. A very important class of symmetric connections in the tangent bundle of a certain manifolds (afinnely flat) are the ones for which the curvature tensor vanishes. Those connections are locally metric. S.S. Chern conjectured that the Euler characteristic of an affinely at manifold is zero. A possible proof of this long outstanding conjecture of S.S. Chern would be by verifying that the space of locally metric connections is path connected. In order to do so one needs to have practical criteria for the metrizability of a connection. In this paper, we give necessary and sufficient conditions for a connection in a plane bundle above a surface to be locally metric. These conditions are easy to be veri ed using any local frame. Also, as a global result we give a necessary condition for two connections to be metric equivalent in terms of their Euler class.

]]>Zurab Kvatadze and Beqnu Pharjiani

On the probabilistic space (Ω ,F , P ) we consider a given two-component stationary (in the narrow sense) sequence , where is the controlling sequence and the members of the sequence are the observations of some random variable which are used in the construction of kernel estimates of Rosenblatt-Parzen type for an unknown density of the variable . The cases of conditional independence and chain dependence of these observations are considered. The upper bounds are established for mathematical expectations of the square of deviation of the obtained estimates from .

]]>Roselaine Neves Machado and Luiz Guerreiro Lopes

There are many simultaneous iterative methods for approximating complex polynomial zeros, from more traditional numerical algorithms, such as the well-known third order Ehrlich–Aberth method, to the more recent ones. In this paper, we present a new family of combined iterative methods for the simultaneous determination of simple complex zeros of a polynomial, which uses the Ehrlich iteration and a correction based on King's family of iterative methods for nonlinear equations. The use of King's correction allows increasing the convergence order of the basic method from three to six. Some numerical examples are given to illustrate the convergence behaviour and effectiveness of the proposed sixth order Ehrlich-like family of combined iterative methods for the simultaneous approximation of simple complex polynomial zeros.

]]>Norazaliza Mohd Jamil

The material of pipelines transporting water is usually polymers. Chlorine as oxidant agent is added into the water system to prevent the spread of some disease. However, exposure to a chlorinated environment could lead to polymer pipe degradation and crack formation which ultimately reaches a complete failure for the pipes. To save labor, time and operating cost for predicting a failure time for a polymer pipe, we focus on its modeling and simulation. A current kinetic model for the corrosion process of polymers due to the action of chlorine is extensively analyzed from the mathematical point of view. By using the nondimensionalization method, the number of parameters in the original governing equations of the kinetic model has been reduced. Then, the dimensionless set of differential equations is numerically solved by the Runge Kutta method. There are two sets of simulations which are low chlorine concentration and high chlorine concentration, and we captured some essential characteristics for both types. This approach enables us to obtain better predictive capabilities, hence increasing our understanding of the corrosion process.

]]>Reem Allogmany Fudziah Ismail and Zarina Bibi Ibrahim

In this paper, we present an implicit two-point block method for solving directly the general second order ordinary differential equations (ODEs). The method incorporates the first and second derivatives of f(x; y; y'), which are the third and fourth derivatives of the solution. The method is derived using Hermite Interpolating Polynomial as the basic function. A performance comparison of the two-point block method is compared in term of accuracy to several existing methods, which have order almost equal or higher than that of the new method. Numerical results interpret the accuracy and efficacy of the new method. Application of the new method is discussed.

]]>A. Artykbaev and B. M. Sultanov

The linear transformation of the plane is considered, whose matrix belongs to the Heisenberg group. The transformation matrix is neither symmetric nor orthogonal. But the determinant is one. The class of the second-order curves is studied, which is obtained from each other by the transformation under consideration. The invariant values of curves of this class are proved. In particular, the conservation of the product of semi-axes of curves in this class is proved, as well as the equality of the areas for the ellipses of the class under consideration. The obtained invariants of the second order curves are applied to curves of the second order, which is the indicatrix of the surface. Conclusion: a theorem is obtained which proves the invariance of the total curvature of a surface in a Euclidean space of the class under consideration is a transformation, which is a deformation.

]]>Abdussakir

The concept of the topological index of a graph is increasingly diverse because researchers continue to introduce new concepts of topological indices. Researches on the topological indices of a graph which initially only examines graphs related to chemical structures begin to examine graphs in general. On the other hand, the concept of graphs obtained from an algebraic structure is also increasingly being introduced. Thus, studying the topological indices of a graph obtained from an algebraic structure such as a group is very interesting to do. One concept of graph obtained from a group is subgroup graph introduced by Anderson et al in 2012 and there is no research on the topology index of the subgroup graph of the symmetric group until now. This article examines several topological indices of the subgroup graphs of the symmetric group for trivial normal subgroups. This article focuses on determining the formulae of various Zagreb indices such as first and second Zagreb indices and co-indices, reduced second Zagreb index and first and second multiplicatively Zagreb indices and several eccentricity-based topological indices such as first and second Zagreb eccentricity indices, eccentric connectivity, connective eccentricity, eccentric distance sum and adjacent eccentric distance sum indices of these graphs.

]]>Lucy Twumwaah Afriyie Bashiru I. I. Saeed and Abukari Alhassan

Statistical surveys are conducted to estimate population parameters where there are reasons restricting the use of the total population. In practice, there are two different survey strategies (i.e. simple and complex survey designs) to be implemented and the choice of a strategy depends on several factors including the characteristics of the population, the nature of the research questions, etc. However, when the complex survey design is used, standard statistical methods that do not take into account the complex nature of the survey design may lead to inaccurate estimates. In Ghana, living standard surveys are conducted using complex survey design involving stratifications, clustering and estimation of survey weights. In this study, bootstrap resampling methods are used to explore the effect of complex survey design in the analysis of child labour prevalence rate. The relative efficiency of the complex survey design approach was determined by using design effect (deff). Data from the Ghana Living Standard Survey Round 6 (GLSS 6) conducted by the Ghana Statistical Service in 2012 was used for the analysis and the target population was children aged 5–17 years. The results from the simulation study shows that relative efficient estimates are obtained when the complex survey design characteristics are considered in the analysis. Thus, ignoring the characteristics of complex survey design could lead to unrealistic estimates.

]]>Aloev R. D. Eshkuvatov Z. K. Khudoyberganov M. U. and Nematova D. E.

In the paper, we propose a systematic approach to design and investigate the adequacy of the computational models for a mixed dissipative boundary value problem posed for the symmetric t-hyperbolic systems. We consider a two-dimensional linear hyperbolic system with variable coefficients and with the lower order term in dissipative boundary conditions. We construct the difference splitting scheme for the numerical calculation of stable solutions for this system. A discrete analogue of the Lyapunov's function is constructed for the numerical verification of stability of solutions for the considered problem. A priori estimate is obtained for the discrete analogue of the Lyapunov's function. This estimate allows us to assert the exponential stability of the numerical solution. A theorem on the exponential stability of the solution of the boundary value problem for linear hyperbolic system and on stability of difference splitting scheme in the Sobolev spaces was proved. These stability theorems give us the opportunity to prove the convergence of the numerical solution.

]]>Renz Jimwel S. Mina and Jerico B. Bacani

Numerous researches have been devoted in finding the solutions , in the set of non-negative integers, of Diophantine equations of type (1), where the values p and q are fixed. In this paper, we also deal with a more generalized form, that is, equations of type (2), where n is a positive integer. We will present results that will guarantee the non-existence of solutions of such Diophantine equations in the set of positive integers. We will use the concepts of the Legendre symbol and Jacobi symbol, which were also used in the study of other types of Diophantine equations. Here, we assume that one of the exponents is odd. With these results, the problem of solving Diophantine equations of this type will become relatively easier as compared to the previous works of several authors. Moreover, we can extend the results by considering the Diophantine equations (3) in the set of positive integers.

]]>Nurulkamal Masseran Lai Hoi Yee Muhammad Aslam Mohd Safari and Kamarulzaman Ibrahim

Poverty is an important issue that needs to be addressed by all countries. Poverty is related to a group of people earning a low income (lower-tail of the income distribution). In Malaysia, low-income earners are classified as the B40 group. This study aims to describe the behavior of the low-income distribution using the power law model. For this purpose, an inverse Pareto model was applied for describing the lower tail data of Malaysian household income. A robust and efficient estimator, called the probability integral transform statistic estimator, was utilized for estimating the shape parameter of the inverse Pareto distribution. Based on the fitted inverse Pareto model, not all households in the B40 group complied with the power law behavior. However, the power law was able to provide a good description for the group of B40 that was below the poverty line. Based on the inverse Pareto model, the parametric Lorenz curve and the Gini index were derived to provide a robust measure of the income inequality of poor households in Malaysia.

]]>Xin Yi Kh'ng Su Yean Teh and Hock Lye Koh

Low-lying atoll islands that depend heavily on fresh groundwater for survival are particularly vulnerable to sea level rise (SLR), which calls for appropriate climate action SDG 13. As the sea level rises, the associated increase in surface seawater inundation and subsurface saltwater intrusion will reduce the availability of fresh groundwater due to permanent salinization of groundwater with corresponding thinning of freshwater lens. This paper provides scientific insights on how freshwater lens in atoll islands respond to SLR. Simulations on saturated-unsaturated variable-density groundwater flow with salt transport are performed by the groundwater flow and solute transport model SUTRA (Saturated-Unsaturated Transport) developed by the U.S. Geological Survey. Model simulations and statistical analyses suggest that freshwater lens thickness depends mainly on groundwater recharge rate, island size and aquifer hydraulic conductivity. The impact of various geo-hydrologic parameters on fresh groundwater sustainability is then analyzed to explore feasibility of increasing groundwater recharge through rainwater harvesting, as a mitigation measure. The implication to the achievement of sustainable clean water and sanitation for all (SDG 6) is also discussed.

]]>Shahryar Sorooshian and Yasaman Parsia

Multi Attribute Decision Making (MADM) is an asset to provide solutions for our todays' complex issues and problems. The fact of the matter is that the main source of information in many MADMs is a panel of experts. However, in some cases, there is a possibility of lack of knowledge by the panel to rank or weight one or a few particular criterion/criteria for the decision making. Therefore, the decision maker needs an altered source of information to complete the decision making process. Hence, WSM (Weighted Sum Method) by means of the most popular MADM techniques is selected; and as a prior aim of this article, a modified version of the WSM is proposed as a solution for multiple criteria decision makers by way of a solution for the cases when there is a need for another source of information to rank or weight the particular criterion/criteria. The modified WSM is presented in five stages. The validity, through feasibility, of the modified WSM is tested and verified in a numerical example. Additionally, following this article, future researches could use the same approach for modification of other MADMs to deal with two or more sources of information.

]]>Swasti Maharani Toto Nusantara Abdur Rahman As'ari and Abdul Qohar

Critical thinking is a skill needed for education. Critical thinking has two main components i.e. ability and critical thinking disposition. The purpose of this research is to describe the disposition of critical thinking of mathematics education students especially analyticity and systematicity component when solving non-routine problem (the problem that is not logical and incomplete). This research is a qualitative descriptive study. The stages in this study are first, students are given three non-routine questions. The second stage, the researchers observed directly and recorded the subject when working on the problem. Third, interviewing the subject related to non-routine problem resolution. Fourth, concluded by describing the disposition of critical thinking of mathematics teacher candidate students, especially analyticity and systematicity components. The results showed that the disposition of critical thinking of first-year college students in mathematics education major is still low. They have not analyzed the problems and answers well and have not written the answers in order and lack of focus when solving non-routine problems. They not yet have a high sense about the irregularities of the problem. It is highly recommended for further research that there is a need for advanced development to improve the disposition of critical thinking students.

]]>Beshimov R. B. and Zhuraev R. M.

In this paper, we study some topological properties of connected topological groups. From a logical point of view, the concept of a topological group arises as a simple combination of the concepts of a group and a topological space. In the same set G, operations multiplication and topological closure are specified simultaneously.

]]>Ivy Barley Gabriel Asare Okyere Henry Man’tieebe Kpamma James Baah Achamfour David Kweku and Godfred Zaachi

Economic trade amongst the various West African economies can either lead to mutual gains or losses. It is therefore important to assess the extent to which dependence amongst these countries can have on their economies. The linear correlation coefficient is normally used as a measure of dependence between random variables. However, there are some limitations when used for economic variables like the stock market; as they do not follow the elliptical distribution. Copulas, however are scale-free methods of constructing dependence structures amongst the stock markets, even in cases of data perturbations. The aim of this study is to assess the impact of data perturbations on the copula models. The maximum likelihood estimation method was the parameter estimation method used for the Archimedean copulas. The Clayton, Joe, Frank and Gumbel copulas were estimated. The Gumbel copula was the most robust copula in all the cases of data perturbations.

]]>Ruggero Ferro

An analogy with how life would be evolving in a town where one is moving in, may help us to understand what could be meant by discovery, insight and invention in mathematics. The relevant key common features of these two environments (life in an another town and mathematics) are: 1) the involved mental abilities to deal with the situation, 2) the realization that anything observed is contingent, 3) the discovery of the motivations of what has been done and of their influence up to the present via insight, 4) the need to understand the motivations and the manners of realization of what was done to continue the development, 5) the continuous evolution of needs and requirements that opens new problems that demand insight and invention for their solutions, 6) not every solution meets the goals and requirements with the same short range and long range convenience, thus a preventive evaluation is convenient according to criteria to be established, though a conclusive evaluation can be done only afterward. What observed will justify the support of a dynamic attitude toward mathematics and the refusal of the one claiming that everything can't be but the way it is, according to a priori mental evidence which is unduly assumed.

]]>Young Whan Lee and Gwang Hui Kim

In 2001, Maksa and P´ales [12] introduced a new type’s stability: hyperstability for a class of linear functional equation. Riedel and Sahoo [14] have generalized a functional equation associated with the distance between the probability distributions, which is . Elfen etc. [7] obtained the solution of the functional equation on semigroup G. The aim of this paper is to investigate the hyperstability and the Hyers-Ulam stability for the above Logarithm-type functional equation considered by Elfen, etc. Namely, if f is an approximative equation related to the above equation, then it is a solution of this equation which exists within " bound of a given approximative function f.

]]>Ana Vivas-Barber and Sunmi Lee

Influenza infection shows a wide range of severity and it is well known that a significant proportion of individuals is asymptomatic or experience mild infections. Also, It is widely accepted that influenza transmission dynamics depends on age distributions. An integro-partial differential system is considered for influenza transmission dynamics, which includes the standard Susceptible-Infected-Recovered (SIR) classes with a quarantine (Q) class and an asymptomatic class (A). In this work, we extend the previous model to an integro-partial differential model by including age-structure. We establish the existence of an endemic steady state distribution and its explicit expression. Then, an analytic expression for the basic reproduction number is obtained. Furthermore, we prove the local and global stability of the disease-free equilibrium. Some numerical simulations of the basic reproduction number have been carried out using age-dependent influenza parameter values. This study can provide effective interventions and implementing age-dependent countermeasures.

]]>Barbara Abraham-Shrauner

Exact traveling (solitary) wave solutions of nonlinear partial differential equations (NLPDEs) are analyzed for third-order nonlinear evolution equations. These equations have indeterminant homogenous balance and therefore cannot be solved by the Power Index Method (PIM). Some evolution equations are linearizable where solutions are transferred from those of a linear PDE. For other evolution equations transforming to a NLPDE which has a homogenous balance gives rise to possible solutions by the PIM. The solutions for evolution equations that are not linearizable are developed here.

]]>Cem Onat and Mahmut Daskin

Excess air coefficient (λ) is the most important parameter characterizing the combustion efficiency. Conventional measurement of λ is practiced by way of the flue analyze device with high market priced. Estimating of the λ from flame images is crucial in perspective of the combustion control because of decreasing structural dead time of the combustion process. Beside, estimation systems can be used continuously in a closed loop control system, unlike conventional analyzers. This paper represents a basic λ prediction system with a neural network for small scale nut coal burner equipped with a CCD camera. The proposed estimation system has two inputs. First input is stack gas temperature simply measuring from the flue. To choose the second input, eleven different matrix parameters have been evaluated together with flue gas temperature values and performed by matrix-based multiple linear regression analysis. As a result of these analyses, it has been seen that the trace of image matrix obtained from the flame image provides higher accuracy than the other matrix parameters. This instantaneous trace value of image source matrix is then filtered from high frequency dynamics by means of a low pass filter. Experimental data of the inputs and λ are synchronously matched by a neural network. Trained algorithm has reached R=0.984 in terms of accuracy. It is seen from the result that proposed estimating system using flame image with assistance of the stack gas temperature can be preferred in combustion control systems.

]]>Pierpaolo Angelini

I realized that it is possible to construct an original and well-organized theory of multiple random quantities by accepting the principles of the theory of concordance into the domain of subjective probability. A very important point relevant to such a construction is consequently treated in this paper by showing that a coherent prevision of a bivariate random quantity coincides with the notion of -product of two vectors while a coherent prevision of a quadruple random quantity coincides with the notion of -product of two affine tensors. Metric properties of the notion of -product mathematically characterize both the notion of coherent prevision of a generic bivariate random quantity and the notion of coherent prevision of a generic quadruple random quantity. Coherent previsions of bivariate and quadruple random quantities can be used in order to obtain fundamental metric expressions of bivariate and quadruple random quantities.

]]>Medhat Edous and Omar Eidous

This paper proposes an approximation to the standard normal distribution function. The introduced approximation formula is very simple and it has a very acceptable accurate. By comparing the proposed approximation with other existing approximations, it can be observed that the proposed one has a simple, easily computable formula and it gives a good accurate with maximum absolute error equals 0.000444.

]]>Samuel Bertrand Liyimbeme Mouchili

Since Galois rings are the generalization of Galois fields, the question we tried to answer is: How to move from the discrete logarithm in Galois fields to the one in Galois rings? That concept of the discrete logarithm in Galois rings is a little bit different from the one in Galois fields. Here, the discrete logarithm of an element is the tuple, which is not the case in Galois fields. However, thanks to the multiplicative representation of elements in Galois rings, each element can be uniquely represented in the form: ; where k is a nonnegative integer, is a generator of the Galois ring (the definition of a generator in a Galois ring will be given later on). Then the tuple will be called: the discrete logarithm of . The notion of generators in Galois rings comes from the one in the group theory. The Knowledge of the generators in multiplicative groups allows, as well to determine the generators in Galois rings ; p is a prime number and m is a nonnegative integer greater than or equal to two. These new concepts of discrete logarithm and generators in Galois rings will help to securely share common information and to perform ElGamal encryption in Galois rings.

]]>Md. Jahurul Islam Md. Shahidul Islam and Md. Shafiqul Islam

In this paper, we discuss Hausdorff measure and Hausdorff dimension. We also discuss iterated function systems (IFS) of the generalized Cantor sets and higher dimensional fractals such as the square fractal, the Menger sponge and the Sierpinski tetrahedron and show the Hausdorff measures and Hausdorff dimensions of the invariant sets for IFS of these fractals.

]]>Marian Anton and Landon Renzullo

The field of computational topology is evolving rapidly and new algorithms are updated and released at a rapid pace. A good reference for currently available opensource libraries with peer-review publication can be found in [7]. In this paper we examine the descriptive potential of a combinatorial data structure known as Generating Set in constructing the boundary maps of a simplicial complex. By refining the approach of [1] in generating these maps, we provide algorithms that allow for relations among simplices to be easily accounted for. In this way we explicitly generate faces of a complex only once, even if a face is shared among multiple simplices. The result is a useful interface for constructing complexes with many relations and for extending our algorithms to ∆-complexes. Once we efficiently retrieve the representatives of "living" simplices i.e., of those that have not been related away, the construction of the boundary maps scales well with the number of relations and provides a simpler alternative to JavaPlex [8]. We note that the generating data of a complex is equivalent in information to its incidence matrix and provide efficient algorithms for converting from an incidence matrix to a Generating Set.

]]>Chun P.B Ibrahim A.A and Kamoh N.M

The use of the adjacency matrix of a graph as a generator matrix for some classes of binary codes had been reported and studied. This paper concerns the utilization of the stable variety of Cayley regular graphs of odd order for efficient interconnection networks as studied, in the area of Codes Generation and Analysis. The Use of some succession scheme in the construction of a stable variety of the Cayley regular graph had been considered. We shall enumerate the adjacency matrices of the regular Cayley graphs so constructed which are of odd order (2m+1), for m≥3 as in [1]. Next, we would show that the Matrices are cyclic and can be used in the generation of cyclic codes of odd lengths.

]]>Pokutnyi Oleksandr

Sufficient conditions for the existence of solutions for a weakly linear perturbed boundary value problem are obtained in the so called resonance (critical) case. Iterative process for finding solutions has been presented. Necessary and sufficient conditions of the existence of solutions, bounded solutions, generalized solutions and quasi solutions are obtained.

]]>Siloko, I. U. Ishiekwene, C. C. and Oyegue, F. O.

The bivariate kernel density estimator is fundamental in data smoothing methods especially for data exploration and visualization purposes due to its ease of graphical interpretation of results. The crucial factor which determines its performance is the bandwidth. We present new methods for bandwidth selection in bivariate kernel density estimation based on the principle of gradient method and compare the result with the biased cross-validation method. The results show that the new methods are reliable and they provide improved methods for a choice of smoothing parameter. The asymptotic mean integrated squared error is used as the measure of performance of the new methods.

]]>Nora Dörmann

Let X_{i}, i ≥ 1, describe the lifetimes of items with finite mean μ = E (X_{i}) which are successively placed in service. In order to estimate the replacement rate ^{1}/_{μ} or related quantities, the random variables X_{i} are usually assumed to be independent and identically distributed. It is shown that a nonparametric estimation of the replacement rate and other reciprocal functions of renewal theory is possible while using a delta method with weakened requirements upon the global growth of f which also allows dependent observations and respects the unboundedness of the analyzed reciprocal functions. Moreover, results on the moments and, furthermore, on corresponding simulations are included.

Yulia Koroleva

The paper deals with study of Stokes-Brinkman system with varying viscosity that describes the fluid flow along an ensemble of partially porous cylindrical particles using the cell approach. Existence and uniqueness of the solution to the system is proved for an arbitrary varying viscosity. Some uniform estimates on the velocity of flow are derived. Moreover, an axillary weighted Friedrichs inequality was proved for the solution of the considered system. The numerical illustration of the obtained results is given.

]]>C. Filosa J. H. M. Thije Boonkkamp and W. L. IJzerman

Ray tracing is a technique used in geometric optics for calculating the light distribution at the target of an optical system. Monte Carlo (MC) ray tracing is very common in non-imaging optics. We propose a new ray tracing method that employs the phase space of the source and the target of the system. The new method gives a more accurate target distribution than classical MC ray tracing and requires less computational time. It is tested for two-dimensional optical systems. The results for the paraboloid reflector are provided.

]]>Gülistan Kaya Gök

Let M_{2,m} be a free metabelian nilpotent Lie algebra of rank 2 and nilpotency class m-1. It is shown that M_{2,m} admits a minimal presentation whose set of defining relators consists of certain types of basic commutators of length at most m.

Dhouha Mejri Mohamed Limam and Claus Weihs

Combining methods from Statistical Process Control (SPC) in order to benefit from more than one method's efficiency has been recently challenged. One of the reasons is that real life problems change overtime and a small improvement can lead to a very big profit. Ensemble methods from data mining domain have recently shown their effectiveness when used with SPC. The first combined control chart based on dynamic ensemble method, called Dynamic weighted control chart, is designed especially for monitoring concept drift in online processes. This article presents a new model of combining more than two control charts based on ensemble methods as well as error rates classifications to optimize the shift identification and control. This method can be applied for offline and online processes. It is based on a three step learning model: first a preprocessing step to prepare the data for classification. Second, an ensemble method based on Dynamic Weighted Majority (DWM) is applied to aggregate the decisions of the different charts at the end of the each batch. Finally, shifts are identified based on the misclassification error rates of DWM. Dynamic Ensemble Control chart model benefits from the knowledge from classification and control to give a most precise information about the process. Experiments have shown that the latter is better than the use of individual charts and classifies the variable which is responsible for the out of control.

]]>V. A. Meshkoff

«Shnoll effect» proved to be at the histograms study of a wide variety of processes. This paper examines the effect mainly for the examples of radioactive decay and chemical reactions. S.E. Shnoll supposed that the observed processes are caused by unknown Cosmophysical effects. In this article, we suggested not only a qualitative explanation of the effect, but also its mathematical model. It allows to get some quantitative estimation and to optimize the process of observation and data handling. To this end, we developed a quantitative method of estimation «similarity of histograms» that allows the use of standard computer programs. As far as «Shnoll effect» at present is not currently recognized by the scientific community, we suppose that the use of mathematical model and adequate methods of data handling allow synonymously solving that problem.

]]>Huriye Kadakal Mahir Kadakal and İmdat İşcan

In this article, by using an integral identity together with both the Hölder, Power-Mean integral inequalities and Hermite-Hadamard's inequality, we establish several new inequalities for n-time differentiable s-convex and s-concave functions in the second sense.

]]>Otakar Kříž

An algorithm SP (= Symptom Proximity) is suggested for solving discrete diagnostic problem. It is based on probabilistic approach to decision-making under uncertainty, however, it does not use knowledge integration from marginal distributions.

]]>Hisham Mahdi and Fadwa Nasser

The purpose of this paper is to investigate the concepts of minimal and maximal regular open sets and their relations with minimal and maximal open sets. We study several properties of such concepts in a semi-regular space. It is mainly shown that if X is a semi-regular space, then m_{i}O(X) = m_{i}RO(X). We introduce and study new type of sets called minimal regular generalized closed. A special interest type of topological space called rT_{min} space is studied and obtain some of its basic properties.

Peter Kopanov and Miroslav Marinov

We examine the properties of a cumulative distribution function which is related to the Bernoulli process. Results figuring in a paper ^{[1]} are shown and new ones are included. Most of them are connected to the behaviour of the probability density function (derivative) of the given distribution.

Fiaz Hussain and Saima Zainab

In this paper, we establish strong convergence and Δ-convergence theorems for the class of generalized non-expansive multi-valued maps in a CAT(0) space. Our work extends and improves some recent results announced in the current literature.

]]>L. Rob Verdooren

The most popular designs for fitting the second-order polynomial model are the central composite designs of Box and Wilson [2] and the designs of Box and Behnken [1]. For k = 2, 4, 6 and 8, the uniform shell designs of Doehlert [4] require fewer experimental runs than the central composite or Box-Behnken designs. In analytic chemistry the Doehlert designs are widely used. The uniform shell designs are based on a regular simplex, this is the geometric figure formed by k + 1 equally spaced points in a k -dimensional space; an equilateral triangle is a two-dimensional regular simplex. The shell designs are used for fitting a response surface to k independent factors over a spherical region. Doehlert (1930 - 1999) proposed in 1970 the design for k = 2 factors starting from an equilateral triangle with sides of length 1, to construct a regular hexagon with a centre point at (0, 0). The n = 7 experimental points are (1, 0), (0.5, 0.866), (0, 0), (-0.5, 0.866), (-1, 0), (-0.5, -0.866) and (0.5, -0.866).The 6 outer points lie on a circle with a radius 1 and centre (0, 0). This Doehlert design has an equally spaced distribution of points over the experimental region, a so-called uniform space filler, where the distances between neighboring experiments are equal. Response surface designs are usually applied by scaling the coded factor ranges to the ranges of the experimental factors. The first factor covers the interval [-1, + 1], the second factor covers the interval [-0.866, + 0.866]. Doehlert design for four factors needs only 21 trials. Doehlert and Klee [5] show how to rotate the uniform shell designs to minimize the number of levels of the factors. Most of the rotated uniform shell designs have no more than five levels of any factor; the central composite design has five levels of every factor. The D-Optimality determinant criterion of the variance matrix of Doehlert designs will be compared with central composite designs and Box-Behnken designs, see Rasch et al. [6].

]]>Katia Vigo Ingar and Maria José Ferreira da Silva

The objective of this article is to present part of a doctoral thesis, which deals with an extension of Duval's study in relation to apprehensions in the graphic register of a two-variable function. Its relevance is extensive in teaching and learning Differential Calculus of two variables since the information the graph of this type of functions may provide is important to build knowledge on two-variable functions and for its applications. For graphic representation and knowledge building, we rely on CAS Mathematica, given that its dynamism allows performing operations in the graphic register. Because of this, we ask ourselves, how do apprehensions take place in the CAS graphic register of two-variable functions? Our research is qualitative and exploratory since the proposed object of study has not been studied a lot. We believe the interaction of apprehensions in the CAS graphic register allows students to conjecture properties of the two-variable functions when, for instance, a student applies those notions to optimization problems.

]]>Emrah Hanifi Firat

In economies that are open to foreign markets the numerical value of the currencies as a macroeconomic variable is of great importance especially when the mutual dependency among the economies is concerned. When it is considered in terms of political economy, the targeted level of the currencies have vital importance especially in economies that have the characteristics of export-driven growth and in economies that struggle not to disrupt the picture in macroeconomic design. When it is considered that each time series has a structure that is sensitive to its own internal dynamics (sometimes these dynamics are expressed as the time series components), these dynamics provide us with coordinates for estimations and may eliminate the compulsory dependency on the outsourced variables at a serious level. This is exactly what has been done in this study. First of all, the non-linear time series analyses are examined in terms of linearity tests, and the linearity tests are applied for all parties and for different time periods. Then, the SETAR Modelling, which is the title of the study, has been applied in order to explain the non-linear pattern in detail. The SETAR Modelling process and other definitions statistical analyses of this model have been applied in relevant parities for separate time periods. The SETAR model, which is one of the TAR Group modeling, shows a better performance than many other linear and non-linear modeling. In this study, the secondary purpose is to express that the SETAR model performance is superior to the other models by considering the observation values of the parities.

]]>Iftikhar I. M. Naqash

Inequitable distribution of investment funds on governorates and the autonomy of the Kurdistan Region with own investment policy are often mentioned as the main causes of the huge regional differences in social development in Iraq. In this paper, the differences in social development among 18 Iraqi governorates will be analyzed by using two different methods: first, 12 indicators of education, health and economic level are given equal weights and the length of the distance between every governorate and the governorate with the maximum standardized score for each individual indicator is combined into a Composite Regional Social Development Index (CRSDI_{equal}); second, unequal weights are given for each indicator depending on the indicator's loading in the first principal component to identify the weight of that indicator in a Composite Regional Social Development Index (CRSDI_{unequal}). Both methods will result in the same ranking of the 18 governorates with respect to their social development level.

Victor Chulaevsky

Exponential decay of eigenfunctions and of their correlators is shown to occur in two Anderson models on the lattice of arbitrary dimension, with summable decay of infinite-range correlations of the random potential. For the proof, we check the applicability of the Fractional Moment Method.

]]>Öznur Kulak and A. Turan Gürkanlı

Let ω_{1}, ω_{2} be slowly increasing functions and let ω_{3} be weight function on ℝ^{n}. In section 2 we define a bilinear multiplier from L(p_{1}, q_{1}, ω_{1}dμ) (ℝ^{n}) × L(p_{2}, q_{2}, ω_{2}dμ) (ℝ^{n}) to L(p_{3}, q_{3}, ω_{3}dμ) (ℝ^{n}) by a bounded operator B_{m}, where 1≤ p_{1}, p_{2}, p_{3}, q_{1}, q_{2}, q_{3} < ∞ and m (ξ,η) is a bounded, measurable function on ℝ^{n} × ℝ^{n}. We denote the space of bilinear multipliers of this type by BM (L(p_{1}, q_{1}, ω_{1}dμ) × L(p_{2}, q_{2}, ω_{2}dμ), L(p_{3}, q_{3}, ω_{3}dμ)), and study of the basic properties of this space. We give methods of construction examples of bilinear multipliers. Similarly in section 3, by using variable exponent Lorentz space, we define the bilinear multipliers from L( p_{1} (x), q_{1} (x)) × L( p_{2} (x), q_{2} (x)) to L( p_{3} (x), q_{3} (x)) and discuss basic properties of the space of bilinear multipliers BM (L( p_{1} (x), q_{1} (x)) × L( p_{2} (x), q_{2} (x)), L( p_{3} (x), q_{3} (x))).

Fahid Al Eibood and Omar Eidous

This paper considers a parametric model for grouped data collected via line transect technique. The weighted exponential model is studied and investigated when the data are assumed to be grouped in the intervals. The maximum likelihood method is adopted for purpose of estimation. The resultant estimator of the population abundance is compared with the corresponding estimator that developed for ungrouped data by using the Laake stakes real data.

]]>Quay van der Hoff and Temple H. Fay

In this article, a new predator-prey model having predator saturation is proposed. The model resembles a classical Rosenzweig-MacArthur type model, but comes with an added function, the population saturation function of the predator. This function of the predator population is a factor in the predator fertility term in the model. Consequently the model behaves better than the Rosenzweig-MacArthur model since all solutions are bounded within the population quadrant. An invariant region arises where the Poincaré-Bendixon theorem can be applied. In most cases there is but a single critical value, either an attracting spiral point suggesting a stable population pair or an unstable node, resulting in a unique limit cycle. This model is fully described and an analysis of the stability of critical values is provided. The robustness of the model is demonstrated based on the classification of Gunawardena [8].

]]>Nitaya Jantakoon

The key atmospheric variables that impact crops are weather and rainfall. Extreme rainfall or drought at critical periods of a crop's development can have dramatic influences on productivity and yields. The analysis of effect of rainfall is needed to evaluate crop production in Northeastern Thailand. Two operations were performed on the Fuzzy Logic model; the fuzzification operation and defuzzification operation. The model predicted outputs were compared with the actual rainfall data. Simulation results reveal that predicted results are in good agreement with measured data. Prediction Error and Root Mean Square Error (RMSE) were calculated, and on the basis of the results obtained, it can be suggested that fuzzy methodology is efficiently capable of handling scattered data.

]]>Simona Gozzo and Venera Tomaselli

This paper proposes an innovative methodological approach to measure sociometric status in small groups of pupils. Although it uses indirect data collected by interview, in this study the sociometric status is analysed by direct observation. This method is specifically suitable when the target population concerns pre-school children. Their cognitive competence, in fact, is not as well developed as their relational abilities. Hence, the indicators constructed are more reliable than the measures derived by the subjective perception of interviewed pupils. The Network Analysis methods allow for the definition of sociometric status by means of regular equivalence. Employing lambda sets and cliques, then, we specify further roles into distinctive small groups. The results show that sociometric status can be revealed by regular equivalence. Besides, the Network Analysis approach allows for the observation of further relational skills, not strictly associated with traditional social roles, detectable only through lambda sets and cliques.

]]>Helmut Vorkauf

A parsimonious and robust new method, based on information theory, to analyze multidimensional contingency tables is presented. It swiftly reveals the important relations between dependent and independent variables and casually detects confounding effects in a straightforward manner. The method in its simplicity could replace logistic regression and log-linear analysis that, in dealing with their limitations and defects, have grown complicated and convoluted.

]]>GÜlistan Kaya GÖk

Let M_{2,m,3} be a free solvable nilpotent Lie algebra of rank 2 and nilpotency class m - 1. We show that M_{2,m,3} admits a minimal presentation whose set of defining relators consists of certain types of basic commutators using techniques in Gröbner-Shirshov basis theory.

Adepoju K.A Shittu O.I and Chukwu A.U

The classical Fisher-Snedecor test which compares several population means depends on the underlined assumptions which include; independent of populations, constant variance and absence of outlier among others .Arguably the source of violation of some of these assumptions is the outlier which lead to unequal variances. Outlier leads to inequality in the variances of the populations which consequently leads to the failure of the classical-F to take correct decision in terms of the null hypothesis. A series of robust tests have been carried out to ameliorate these lapses with some degrees of inaccuracies and limitations in terms of inflating the type 1 error and the power of different combination of parameters at various sample sizes while still uses the conventional F-table. This study focuses on developing robust F-test called exponentiated F test with the introduction of one shape parameter to the conventional F-distribution capable of taking decisions on ANOVA that are robust to the existence of outlier. The performance of the robust F test was compared with the existing F-tests in the literature using the power of test. Real life and simulated data were used to illustrate the applicability and efficiency of the proposed distribution over the existing ones. Experimental data with balanced and unbalanced design were used with populations sizes k=3 and k=5 were simulated with 10000 replications and varying degrees of outliers were ejected randomly. The results obtained indicate that the Proposed Exponentiated-F test is uniformly most powerful than the conventional-F tests for analysis of variance in the presence of outlier and is therefore recommended for use by researchers.

]]>Sarbjit Singh

This paper presents an inventory model for perishable items with constant demand, for which holding cost increases with time, the items considered in the model are deteriorating items with a constant rate of deterioration θ. In the majority of the earlier studies the holding cost has been considered to be constant, which is not true in most of the practical situations as the insurance cost and record keeping costs or even cost of keeping the items in the cold storage increases with time. In this paper the time dependent linear holding cost has been considered, the holding cost for the items increases with time. The approximate optimal solution has been obtained. The results are illustrated with the help of numerical examples.

]]>O.V. Troshkin

2D-flows of an ideal incompressible fluid are treated in a rectangular. If analytical (resolved in series of powers of coordinates), the stationary flows are uniquely determined with the inflow vorticity. When excluded vortices of a spectral origin, such flows prove to be stable.

]]>Xiao Liu

There is the work by Bridges et al (1999) on the key features of a constructive proof of the implicit function theorem, including some applications to physics and mechanics. For mixtures of logistic distributions such information is lacking, although a special instance of the implicit function theorem prevails therein. The theorem is needed to see that the ridgeline function, which carries information about the topography and critical points of a general logistic mixture problem, is well-defined [2]. In this paper, we express the implicit function theorem and related constructive techniques in their multivariate extension and propose analogs of Bridges and colleagues' results for the multivariate logistic mixture setting. In particular, the techniques such as the inverse of Lagrange's mean value theorem [4] allow to prove that the key concept of a logistic ridgeline function is well-defined in proper vicinities of its arguments.

]]>Alexander D. Bruno

Here we present a way of computation of asymptotic expansions of solutions to algebraic and differential equations and present a survey of some of its applications. The way is based on ideas and algorithms of Power Geometry. Power Geometry has applications in Algebraic Geometry, Differential Algebra, Nonstandard Analysis, Microlocal Analysis, Group Analysis, Tropical/Idempotent Mathematics and so on. We also discuss a connection of Power Geometry with Idempotent Mathematics.

]]>Sibanee Sahu and Sarat Kumar Acharya

The paper is concerned with the study of change point problem in the inter-arrival time and service time of single server queues. Maximum likelihood estimators of the parameters are derived. A test statistics has been developed and its properties have been studied.

]]>Omar Eidous and Samar Al-Salman

This paper presents a one-term approximation to the cumulative normal distribution functions. The absolute maximum error of the proposed approximation is 0.0018 less than 0.003 of Polya's approximation. Comparisons between the proposed approximation and the different approximations with one-term that stated in the literature are given.

]]>Adepoju, K.A Chukwu, A.U and Shittu, O.I

We propose the Kumaraswamy-F (KUMAF) distribution which is a generalization of the conventional Fisher Snedecor (F-distribution). The new distribution can be used even when one or more of the regular assumptions are violated. It is obtained with the addition of two shape parameters to a continuous F-distribution which is commonly used to test the null hypothesis in the Analysis of Variance (ANOVA test).The statistical properties of the proposed distribution such as moments, moment generating function, the asymptotic behavior among others were investigated. The method of maximum likelihood is used to estimate the model parameters and the observed information matrix is derived. The distribution is found to be more flexible and robust to regular assumptions of the conventional F-distribution. In future research, the flexibility of this distribution as well as its robustness using a real data set will be examined. The new distribution is recommended for used in most applications where the assumption underlying the use of conventional F distribution for one-way analysis of variance are violated such as homogeneity of variance or normality assumption probably as result of the presence of outlier(s). It is instructive to note that the new distribution preserves the originality of the data without transformation.

]]>Arash Pourkia

First, referring to our previous work, 'Hopf cyclic cohomology in braided monoidal categories', we reduce the restriction of the ambient category C being symmetric. We let C to be non-symmetric but assume only the restriction, ψ^{2} = id, on the braid map correspond to the Hopf algebra H, which is the main player in the theory. We define a family of examples of such desired braided Hopf algebras, H, living in the category of anyonic vector spaces. Next, on one hand, we will prove that these anyonic Hopf algebras are the enveloping (Hopf) algebras of particular quantum Lie algebras, which we will construct. On the other hand, we will show that, analogous to the non-super and the super case, the well known relationship between the periodic Hopf cyclic cohomology of an enveloping (super) algebra and the (super) Lie algebra homology also holds for these particular quantum Lie algebras.

Robert Erdahl and Viacheslav Grishukhin

By a Voronoi parallelotope P(a) we mean a parallelotope determined by linear in normal vectors p inequalities with a non-negative quadratic form a(p) as right hand side. For a positive form a, it was studied by Voronoi in his famous memoir. For a set of vectors P, we call its dual a set of vectors P^{*} such that ∈ {0;±1} for all p ∈ P and q ∈ P^{*}. We prove that Minkowski sum of an irreducible Voronoi parallelotope P(a) and a segment z(u) is a Voronoi parallelotope if and only if u = we, where w > 0 and e is a vector of the dual of the set of normal vectors of all facets of P(a). Then the segment z(u) is described by the same set of inequalities with wa_{e}(p)=w as right hand side and P(a) + z(u) = P(a + wa_{e}). A similar assertion is true for Minkowski sum of a reducible Voronoi parallelotope with a segment.

Bhatt Milind B.

Independence of suitable function of order statistics, linear relation of conditional expectation, recurrence relations between expectations of function of order statistics, distributional properties of exponential distribution, record valves, lower record statistics, product of order statistics and Lorenz curve etc.. are various approaches available in the literature for the characterization of the power function distribution. In this research note different path breaking approach for the characterization of power function distribution through the expectation of function of order statistics is given and provides a method to characterize the power function distribution which needs any arbitrary non constant function only.

]]>Sergey Krylov

The paper shows meta-mathematical prerequisites for basic concepts of rigorous science called mathematics. These concepts explore a very simple idea concerning the hypothesis that all surrounding physical processes are basically algorithmic processes - as understandable as well as partially or fully incomprehensible ones. Mathematics is very successful in studying, formal describing and utilizing of such processes, because mathematics is based on similar algorithmic ideas, methods, and structures. These facts allow us to formulate more precisely useful mathematical (meta-scientific) concepts concerning some well-known scientific problems in various rigorous theories, including the theory of "object calculus", the theory of automatic cognition, the theory of biological evolution, the theory of heterogeneous electronic systems, the theory of logics in various chemical transformations, the basic architecture of completely programmable universal (multi-purpose) synthesizers-analyzers for various objects, and so on.

]]>Imdat Iscan Mustafa Aydin and Sema Dikmenoglu

In this paper, we establish some estimates, involving the Euler Beta function and the Hypergeometric function of the integral for the class of functions whose certain powers of the absolute value are harmonically convex.

]]>Beshimov R.B. and Mamadaliev N.K.

In the paper it is proved that if a covariant functor F : Comp → Comp is weakly normal, then for any infinite Tychonoff space X following inequalities hold: d( (X)) ≤ d(X), d( (X)) ≤ d(X), wd( (X)) ≤ wd(X), wd( (X)) ≤ wd(X).

]]>Molete Mokhele and Caston Sigauke

Electricity demand exhibits a large degree of randomness in South Africa, particularly in summer. Its description requires a detailed analysis using statistical methodologies, in particular stochastic processes. The paper presents a Markov chain analysis of peak electricity demand. The data used is from South Africa's power utility company Eskom, for the period 2000 to 2011. This modelling approach is important to decision makers in the electricity sector particularly in scheduling maintenance and refurbishments of power-plants. The randomness effect is accountable to meteorological factors and major electricity appliance usage. Aggregated data on daily electricity peak demand is used to develop the transition probability matrices, steady-state probabilities, mean return- and the first passage times. Such analysis is important to Eskom and other energy companies in planning load-shifting, load analysis and scheduling of electricity particularly during peak period in summer.

]]>Akram.H. Begmatov M.E. Muminov and Z.H. Ochilov

We study new problem of reconstruction of a function in a strip from their given integrals with known weight function along polygonal lines. We obtained two simply inversion formulas for the solution to the problem. We prove uniqueness and existence theorems for solutions and obtain stability estimates of a solution to the problem in Sobolev's spaces and thus show their weak ill-posedness. Then we consider integral geometry problems with perturbation. The uniqueness theorems are proved and stability estimates of solutions in Sobolev spaces are obtained.

]]>Victor Chulaevsky

We study the regularity of the conditional distribution of the empiric mean of a finite sample of IID random variables with a bounded common probability density, conditional on the sample "uctuations", and extend a prior result, proved for strictly positive smooth densities, to a larger class of smooth densities vanishing at one or more points of their support.

]]>Beshimov R. B. Mamadaliev N. K. and Mukhamadiev F. G.

In the paper the local density and the local weak density of topological spaces are investigated. It is proved that for stratifiable spaces the local density and the local weak density coincide, these cardinal numbers are preserved under open mappings, are inverse invariant of a class of closed irreducible mappings. Moreover, it is showed that the functor of probability measures of finite supports preserves the local density of compacts.

]]>Ye-zhi Xiao and Sha Fu

This study proposes a grey-correlation multi-attribute decision-making method based on intuitionistic trapezoidal fuzzy numbers to solve the problem that the attribute weight depends on the various statuses and the attribute values offer multi-attribute decision making in the form of intuitionistic trapezoidal fuzzy numbers. Firstly, this paper gives the definitions of intuitionistic trapezoidal fuzzy numbers, and the distance formula. Then, the grey-correlation coefficient about the intuitionistic trapezoidal fuzzy numbers is obtained through grey-correlation analysis. The correlation degree between different options is obtained through calculation based on the correlation coefficient. With that, the options are ranked based on the values to identify the optimal option. Finally, the result of analysis of examples demonstrates the feasibility and effectiveness of the proposed method.

]]>Sha Fu

This paper takes the time weight and attribute weight in different periods into consideration to propose a dynamic triangular fuzzy number type multi-attribute decision making method to solve the problem with multi-attribute decision making with triangular fuzzy number as the attribute value. This method utilizes the characteristics of the triangular fuzzy number in order to establish the correlation model between the evaluation scheme and the positive and negative ideal scheme, and obtain comprehensive ranking of the evaluation scheme, thus acquiring the decision making result. At last, this paper demonstrates the feasibility and validity of the proposed methods through instance analysis.

]]>Wun-Yi Shu(許文郁)

In the late 1990s, observations of type Ia supernovae led to the astounding discovery that the universe is expanding at an accelerating rate. The explanation of this anomalous acceleration has been one of the great problems in physics since that discovery. We propose cosmological models that can simply and elegantly explain the cosmic acceleration via the geometric structure of the spacetime continuum, without introducing a cosmological constant into the standard Einstein field equation, negating the necessity for the existence of dark energy. In this geometry, the three fundamental physical dimensions length, time, and mass are related in new kind of relativity. There are four conspicuous features of these models: 1) the speed of light and the gravitational "constant" are not constant, but vary with the evolution of the universe, 2) time has no beginning and no end; i.e., there is neither a big bang nor a big crunch singularity, 3) the spatial section of the universe is a 3-sphere, and 4) in the process of evolution, the universe experiences phases of both acceleration and deceleration. One of these models is selected and tested against current cosmological observations, and is found to fit the redshift- luminosity distance data quite well.

]]>Karwan H. F. Jwamer and Hawsar Ali HR

This paper deals with the behavior of the solution and asymptotic behaviors of eigenvalues of a fourth order boundary value problem, having the following definition: (1) with boundary conditions: Where and are real valued functions and ρ(χ)=1, and λ is a spectral parameter in which . Here it has been assumed that and .

]]>Zul Amry and Adam Baharum

The main purpose of this study is to find the Bayesian forecast of ARMA model under Jeffrey's prior assumption with quadratic loss function. The point forecast model is obtained based on the mean of the marginal conditional posterior predictive in mathematical expression. Furthermore, the point forecast model of the Bayesian forecasting compared to the traditional forecasting. The simulation shows that the forecast accuracy of Bayesian forecasting is better than the traditional forecasting and the descriptive statistics of Bayesian forecasting are closer to the true value than the traditional forecasting.

]]>Robert Bruner Khairia Mira Laura Stanley and Victor Snaith

Let p be a prime. We calculate the connective unitary K-theory of the smash product of two copies of the classifying space for the cyclic group of order p, using a Kunneth formula short exact sequence. As a corollary, using the Bott exact sequence and the mod 2 Hurewicz homomorphism we calculate the connective orthogonal K-theory of the smash product of two copies of the classifying space for the cyclic group of order two.

]]>V. Amarendra Babu and T. Anitha

We introduce the concept of vague implicative LI – ideals of lattice implication algebra and discuss some of their properties. We study the relationship between v-implicative filters, vague ILI - ideals and ILI – ideals. Extension property of a vague implicative LI – ideal is built.

]]>Victor Chulaevsky

We prove an optimized estimate for the regularity of the conditional distribution of the empiric mean of a finite sample of IID random variables, conditional on the sample "fluctuations". Prior results, based on bounds in probability, provided a Hölder-type regularity of the conditional distribution. We establish a Lipschitz regularity, using bounds in expectation. The new estimate, extending a well-known property of Gaussian IID samples, is a crucial ingredient of the Multi-Scale Analysis of multi-particle Anderson-type random Hamiltonians in a Euclidean space. In particular, the H¨older regularity of the multi-particle eigenvalue distribution, sufficient for the localization analysis of N-particle lattice Hamiltonians, with N ≥ 3, needs to be replaced by Lipschitz regularity for similar Hamiltonians in the Euclidean space.

]]>Ali M. Mosammam

The Kalman filter is a recursive estimator and plays a fundamental role in statistics for filtering, prediction and smoothing. The key element in any recursive estimator is the estimate of the current state, xk, at time k, based on observations up to and including observation k and the Kalman filter enables the estimate of the state to be updated as new observations become available. In this paper we have tried to derive the Kalman filter as simple as possible.

]]>Kwadwo Agyei Nyantakyi B. L. Peiris and L. H. P. Gunaratne

Change-point analysis is a powerful tool for determining whether a change has taken place or not. In this paper we study the structural changes in the Conditional Quantile Polynomial Distributed Lag (QPDL) model using change-point analysis. We employ both the Binary Segmentation (BinSeg) and Cumulative Sum (Cusum) methods for this analysis. We studied the structural changes in both correctly specified and misspecified QPDL models. As an economic application we considered the production of rubber and its price returns. We observe that both Cusum and BinSeg methods correctly detected the structural changes for both the correctly specified and the misspecified QPDL model. The Cusum method gave the exact positions where the structural changes occurred and the BinSeg gave the approximated positions where the changes occurred. Both methods were able to detect the shift in time for both the mean and variance for the missspecified QPDL model, hence both methods were better for predicting structural stability in a QPDL models. The impact of this is that, when there are changes made to a data knowingly or unknowingly, they can be detected, as well as when these changes were effected. We further observed that both methods were powerful tools that better characterizes the changes, controls the overall error rate, robust to outliers, more flexible and simple to use.

]]>Mohammad Shafique Fatima Abbas and Atif Nazir

The two dimensional stagnation flows towards a shrinking sheet of Newtonian fluids has been solved numerically by using SOR Iterative Procedure. The similarity transformations have been used to reduce the highly nonlinear partial differential equations to ordinary differential equations. The results have been calculated on three different grid sizes to check the accuracy of the results. The problem relates to the flows towards a shrinking sheet when and if the flows towards a stretching sheet. The numerical results for Newtonian fluids are found in good agreement with those obtained previously.

]]>Sorokin O.S.

The K-theoretical aspect of the commutative mophic rings is established using the arithmetical properties of the morphic rings in order to obtain a ring of all Smith normal forms of matrices over the morphic ring. The internal structure and basic properties of such rings are discussed as well as their presentations by the Witt vectors. In a case of a commutative von Neumann regular rings the famous Grothendieck group K_{0}(R) obtains the alternative description.

A. C. Paul and S. Chakraborty

Let U be a non-zero σ-square closed Lie ideal of a 2-torsion free σ-prime Τ-ring M satisfying the condition aαbβc = aβbαc for all a, b, c ∈ M and α, β ∈ Τ, and let d be a derivation of M such that dσ = σd. We prove here that (i) if d acts as a homomorphism on U, then d = 0 or U ⊆ Z(M), where Z(M) is the centre of M; and (ii) if d acts as an anti-homomorphism on U, then d = 0 or U⊆ Z(M).

]]>Mehsin Jabel Atteya

The main purpose of this paper is to study and investigate some results concerning generalized Jordan derivation and generalized derivation on semiprime ring R, where D an additive mapping on R such that for all and D acts as left centralizer.

]]>R. M. Dzhabarzadeh

In this paper we present two criteria for the existence of common eigen values of several operator pencils having discrete spectrum. One of the given criteria is proved by using analogs of resultant for several operator pencils; proof of the other criterion requires the use of the results of the multiparameter spectral theory. In both cases the number of operator pencils is finite, operator pencils act, generally speaking, in different Hilbert spaces.

]]>Mehsin Jabel Atteya and Dalal Ibraheem Rasen

The main purpose of this paper is study and investigate a skew-commuting and skew-centralizing d and g be a derivations on noncommutative prime ring and semiprime ring R, we obtain the derivation d(R)=0 (resp. g(R)=0 ) .

]]>K.N.S. Yadava Shruti and J.Pandey

Some models have been proposed for the projection of future size of population for short and long terms under the stability conditions with changed regime of fertility schedule. The main aim of this paper is to see the size of population if fertility is curtailed up to the level of replacement, especially in developing countries. Models have been illustrated taking a set of real and hypothetical data consistent with the current demographic scenario of India. It was found that the proposed models are the extended forms of the models developed by the previous researchers and the projected population is more or less consistent with them.

]]>Behnam Talaee

Let R be a ring and M an R−module. A module N ∈ [M] is called M-small if, N ≪ K for some K ∈ [M]. Torsion theory cogenerated by M−small modules is introduced and investigated in [9]. Also as a generalization of M−small modules, −M−small modules are studied in [6]. In this paper we will introduce M−delta (briefly M − D) modules and investigate the torsion theory cogenerated by such modules. We will get some equivalent conditions for when N is equal to its torsion theory submodule cogenerated by M − D modules. Especially we show that D(N;A) = 0 for all A ∈ [M] iff N = ReD[M](N). Some other important properties about this kind of modules will be obtained.

]]>N. Azimi and M. Amirabadi

A non-nilpotent finite group whose proper subgroups are all nilpotent (or a finite group without non-nilpotent proper subgroups) is well-known (called Schmidt group). O.Yu. Schmidt (1924) studied such groups and proved that such groups are solvable. More recently Zarrin generalized Schmidt's Theorem and proved that every finite group with less than 22 non-nilpotent subgroups is solvable. In this paper, we show that every locally graded group with less than 22 non-nilpotent subgroups is solvable.

]]>J. Venetis

In this paper, the author obtains an analytic exact form of the unit step function, which is also known as Heaviside function and constitutes a fundamental concept of the Operational Calculus. Particularly, this function is equivalently expressed in a closed form as the summation of two inverse trigonometric functions. The novelty of this work is that the exact representation which is proposed here is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Therefore it may be much more appropriate in the computational procedures which are inserted into Operational Calculus techniques.

]]>S. V. S. Girija A. V. Dattatreya Rao and G. V. L. N. Srihari

In this paper, a new discrete circular model, the Wrapped Binomial model is constructed by applying the method of wrapping a discrete linear model. The characteristic function of the Wrapped Binomial Distribution is also derived and the population characteristics are studied.

]]>Erhan Piskin

In this work, we consider the initial boundary value problem for the Kirchhoff-type equations with damping and source terms in a bounded domain. We prove the blow up of the solution with positive initial energy by using the technique of [26] with a modification in the energy functional due to the different nature of problems. This improves earlier results in the literature [3, 9, 13, 21].

]]>Swapnil Srivastava and Punish Kumar

In this paper, we have defined the concept of p-map and studied some properties of p-map. By using this map, we have shown that p(G) is a subgroup of G and S = {x : p(x) = e} is a right transversal (with identity) of p(G) in G which becomes group by using p-map and some more conditions. Finally, we have shown that G be an extension of p(G).

]]>Bhatt Milind B.

Normally the mass of a root has a uniform distribution but some of have different uniform distribution named generalized uniform distribution (GUD). The characterization result based on expectation of function of order statistics has been obtained for generalized uniform distribution. Applications are given for illustrative purpose.

]]>Chris Gilbert Waltzek

This paper builds on Goldbach’s weak conjecture, showing that all primes to infinity are composed of 3 smaller primes, suggesting that the modern definition of a prime number may be incomplete, requiring revision. The results indicate that prime numbers should include 1 as a prime number and 2 as a composite number, adding a new dimension to the most fundamental of all integers.

]]>Uri Itai

Generalization of subdivision schemes refining points to schemes refining more complex geometric objects has become popular in recent years. In this paper we generalize corner-cutting schemes in order to refine curves taking into account the geometry of the curves. We provide conditions guaranteeing that these schemes are well defined and converge to surfaces with contentious tangents.

]]>Sergey V. Sudoplatov

We apply a general approach for distributions of binary isolating and semi-isolating formulas to the class of strongly minimal theories. For this aim we introduce and use the notion of forcing of infinity. Structures associated with binary formulas, in strongly minimal theories, and containing compositions and Boolean combinations are characterized: a list of basic structural properties for these structures, including the forcing of infinity, is presented, and it is shown that structures satisfying this list of properties are realized in strongly minimal theories.

]]>Rustamova S.Mastura

In this paper, a formula for calculating the Martinelli-Bochner integral of functions from L^{p} in the half-space is obtained.

K.P. Samanta B. C. Chandra and C.S.Bera

In this paper we have obtained some novel generating functions of -a modification of Gegenbauer polynomials, by utilizing L. Wesiner’s grouptheoretic method. By giving suitable interpretations to both the index (n) and the parameter (λ) of the polynomial under consideration, we obtain, in section 2, a set of infinitesimal operators known as raising and the lowering operators which generates a four dimensional Lie algebra. Finally, in Section 3, a novel generating function of the modified Gegenbauer polynomials which in turn yields a number of new and known results on generating functions.

]]>Iryna Dubovets’ka Oleksandr Masyutka and Mikhail Moklyachuk

Spectral theory of isotropic random fields in Euclidean space developed by M. I. Yadrenko is exploited to find solution to the problem of optimal linear estimation of the functional which depends on unknown values of a periodically correlated (cyclostationary with period T) with respect to time isotropic on the sphere S_{n} in Euclidean space En random field ζ(j, x), j ∈ Z, x ∈ S_{n}. Estimates are based on observations of the field ζ(j, x) + θ(j, x) at points (j, x), j = 0,−1,−2, . . . , x ∈ S_{n}, where θ(j, x) is an uncorrelated with ζ(j, x) periodically correlated with respect to time isotropic on the sphere S_{n} random field. Formulas for computing the value of the mean-square error and the spectral characteristic of the optimal linear estimate of the functional Aζ are obtained. The least favorable spectral densities and the minimax (robust) spectral characteristics of the optimal estimates of the functional Aζ are determined for some special classes of spectral densities.

Chii-Huei Yu and Bing-Huei Chen

This paper uses the mathematical software Maple for the auxiliary tool to study two types of multiple integrals. We can obtain the infinite series forms of these two types of multiple integrals by using binomial series and integration term by term theorem. On the other hand, we propose some examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple.

]]>Dais George

Heavy-tailed distributions have wide applications in life-time contexts, especially in reliability and risk modeling. So we consider the estimation problem of reliability, R = P(X > Y ) for small samples, when X and Y are two independent but not identically distributed random variables belonging to the family of heavy-tailed distributions, using a robust estimator, namely the harmonic moment estimator. Extensive simulation studies are carried out to study the performance of this estimator. The relative efficiency of the estimator with the well known Hill estimator is studied. We obtain the sampling distribution of the parameters of the distribution as well as that of estimator of R which will help us to study the properties of the estimators. Also we find out the asymptotic confidence intervals of R and its performance is studied with respect to average width and the coverage probability, through simulations.

]]>Amit Choudhury

Of all statistical distributions, the standard normal is perhaps the most popular and widely used. Its use often involves computing the area under its probability curve. Unlike many other statistical distributions, there is no closed form theoretical expression for this area in case of the normal distribution. Consequently it has to be approximated. While there are a number of highly complex but accurate algorithms, some simple ones have also been proposed in literature. Even though the simple ones may not be very accurate, they are nevertheless useful as accuracy has to be gauged vis-à-vis simplicity. In this short paper, we present another simple approximation formula to the cumulative distribution function of standard normal distribution. This new formula is fairly good when judged vis-à-vis its simplicity.

]]>Alexander A. Butov

The optimal control problem for the intensity of observation events of the process of random walk is considered for the case of counting Poisson process in semimartingale terms. The linear function of the intensity as a cost of observations and the expected value of the quadratic form of errors of estimation as a cost of an error are reckoned in a loss function. The analogues result for the problem of the optimal intensity of stochastic approximation is presented.

]]>R. Subba Rao A. Naga Durgamamba and R.R.L. Kantam

In this paper, a hybrid group acceptance sampling plan is introduced for a truncated life test if life times of the items follow size biased Lomax model. The minimum number of testers and acceptance number are obtained when the consumer’s risk and the test termination time and group size are pre-specified. The operating characteristic values, minimum ratios of the true mean life to the specified mean life for the given producer’s risk are also derived. The results are discussed through an example, a comparative study of proposed sampling plan with existing sampling plan are elaborated.

]]>S.V.S. Girija A.J.V. Radhika and A.V. Dattatreya Rao

One of the available techniques of constructing circular models, offsetting has not been paid much attention, in particular for the construction of arc models. Here making use of the method of offsetting on bivariate distributions, l-arc models are constructed. The method of transforming a bivariate linear random variable to its directional component is called OFFSETTING and the respective distribution of directional component is called offset distribution which is a univariate circular model. By employing the concept of arc models, we obtain Offset Semicircular Cauchy model. Here we obtain Arc models directly by applying offsetting on a linear bivariate models such as Bivariate Beta and Bivariate Exponential models. Existence of these arc models occur in natural phenomenon. Some of the newly proposed semicircular/arc models are bimodal models and the population characteristics of the offset semicircular and arc models are studied.

]]>Said Broumi Florentin Smarandache and Pabitra Kumar Maji

S.Broumi and F.Smarandache introduced the concept of intuitionistic neutrosophic soft set as an extension of the soft set theory. In this paper we have applied the concept of intuitionistic neutrosophic soft set to rings theory .The notion of intuitionistic neutrosophic soft set over ring (INSSOR for short ) is introduced and their basic properties have been investigated.The definitions of intersection, union, AND, and OR operations over ring (INSSOR) have also been defined. Finally, we have defined the product of two intuitionistic neutrosophic soft set over ring.

]]>V. Amarendra Babu M. Srinivasa Reddy and P.V.Srinivasa Rao

A partial semiring is a structure possessing an infinitary partial addition and a binary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a partial semiring. In this paper we introduce the notions of ( R, S ) - partial bi-semimodule and ( R, S ) - homomorphism of ( R, S ) - partial bi-semimodules and extended the results on partial semimodules over partial semirings by P. V. Srinivasa Rao [8] to ( R, S ) - partial bi-semimodules.

]]>B. Satyanarayana R. Durga Prasad and L. Krishna

The notion of BCK-algebras was initiated by Imai and Iseki in 1966 as a genera-lization of both classical and non-classical posi-tional calculus. In 1999, Huang and Chen introduced the notion of n-fold positive implicative ideals in BCK-algebras. In 2011, Satyanarayana and Durga Prasad introduced foldness of intuitionistic fuzzy positive implicative ideals in BCK-algebras. In this paper, we introduce the notion of n-fold positive implicative ideals, n-fold positive implicative Artinian (shortly, PI^{n} -Artinian) and n-fold positive implicative Noe-therian (shortly, PI^{n}-Noetherian) BCK-algebras and study some of its properties.

Rachid Assel Mouez Dimassi and Claudio Fernandez

The main purpose of this note is to study spectral properties of the Stark magnetic Hamiltonian : , on the Hilbert space L^{2}(R^{2}). We show that if the potential V satisfies some mild regularity conditions and is sufficiently decaying at infinity, then the operator H(μ, ϵ) has possibly at most a finite number of eigenvalues.

Maddalena Cavicchioli

We present various formulae in closed form for the spectral density of multivariate or univariate ARMA models subject to Markov switching, and describe some new properties of them. Many examples and numerical applications are proposed to illustrate the behaviour of the spectral density. This turns out to be useful in order to investigate various concepts of stationarity via spectral analysis.

]]>Maksym Luz and Mikhail Moklyachuk

The problem of optimal estimation of the linear functionals and depending on the unknown values of stochastic process ξ(t), t ∈ R, with stationary nth increments from observations of the process at points t < 0 is considered. Formulas for calculating the mean square error and the spectral characteristic of optimal linear estimates of the functionals are derived in the case where the spectral density of the process is exactly known. Formulas that determine the least favorable spectral densities and the minimax (robust) spectral characteristic of the optimal linear estimates of the functionals are proposed in the case where the spectral density of the process is not exactly known, but a set of admissible spectral densities is given.

]]>Zhenmin Chen

Checking whether or not the population distribution, from which a random sample is drawn, is a specified distribution is a popular topic in statistical analysis. Such a problem is usually named as goodness-of-fit test. Numerous research papers have been published in this area. The purpose of this short paper is to provide a goodness-of-fit test statistic which works for many kinds of censored data formed by order statistics. This is an extension of the work presented in Chen and Ye (2009). The method can be used for censored samples that are commonly used in reliability analysis including left censored data, right censored data and doubly censored data.

]]>Said Broumi and Florentin Smarandache

Hesitancy is the most common problem in decision making, for which hesitant fuzzy set can be considered as a useful tool allowing several possible degrees of membership of an element to a set. Recently, another suitable means were defined by Zhiming Zhang [1], called interval valued intuitionistic hesitant fuzzy sets, dealing with uncertainty and vagueness, and which is more powerful than the hesitant fuzzy sets. In this paper, four new operations are introduced on interval-valued intuitionistic hesitant fuzzy sets and several important properties are also studied.

]]>Md.Jalilul Islam Mondal and Tapan Kumar Roy

The aim of this paper is to find multi criteria decision making problems to a selected project using intuitionistic fuzzy soft matrix based on generalized operators of t-norm and t-conorm. We use the concept of level operators of intuitionistic fuzzy sets [ K.T.Atanassov, On intuitionistic fuzzy sets theory , Springer – Verlag 2012 ] to define intuitionistic fuzzy soft level matrix. Finally, we give an application of decision making problem by using the operators of t-norm and t-conorm .

]]>Chien-Wei Chang Yen-Huang Hsu and H. T. Liu

Let p, q, T be positive real numbers, B = {x ∈ R^{n} : }, ∂B = {x ∈ R^{n} : }, x^{∗} ∈ B, △ be the Laplace operator in R^{n}. In this paper, the following the initial boundary value problem with localized reaction term is studied: , where u_{0} ≥ 0. The existence of the unique classical solution is established. When x^{∗} = 0, quenching criteria is given. Moreover, the rate of change of the solution at the quenching point near the quenching time is studied.

J Madhusudan Rao and P Sumati Kumari

This paper proves the existence of periodic and fixed points for self maps satisfying some contractive conditions in symmetric space and also we prove coincidence and fixed points without continuity requirement satisfying a slightly more general Seghal’s contractive conditions with suitable example.

]]>V. Kaviyarasu

This paper tries to study the designing of new attribute sampling plan towards Quick Switching Conditional Repetitive Group Sampling System (QSCRGSS)-3 indexed through Average Outgoing Quality (AOQ), Average Outgoing Quality Limit (AOQL) and its Operating Ratio (OR). Tables are provided with numerical illustrations for newly developed plan for its various plan parameters.

]]>Alexander G. Gein and Mikhail P. Shushpanov

We construct the system of 11 defining relations for the 3-generated free modular lattice. This system is proved to be minimal. Systems of defining relations for lattices close to modular one are studied.

]]>R.K. Saxena

The object of this article is to investigate the solutions of one-dimensional linear fractional diffusion equations defined by (2.1) and (4.1). The solutions are obtained in a closed and elegant forms in terms of the H-function and generalized Mittag - Leffler functions, which are suitable for numerical computation. The derived results include the results for the one-dimentional linear fractional telegraph equation due to Orsingher and Beghin [1], and recently derived results by Saxena ,Mathai and Haubold [2].

]]>Marian Matłoka

We consider and study a new class of convex functions that are called- (h_{1},h_{2})preinvex functions on the co-ordinates. Some Hermite-Hadamard inequalities for the (h_{1},h_{2})– preinvex functions on the co-ordinates and its variant forms are derived. Some our theorems are new and other generalize some results of Dragomir and Latif.

Chii-Huei Yu

This paper takes the mathematical software Maple as the auxiliary tool to study four types of integrals. We can obtain the Fourier series expansions of these four types of integrals by using integration term by term theorem. On the other hand, we provide two examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple.

]]>Alberto Cavicchioli Friedrich Hegenbarth Yurij V. Muranov and Fulvia Spaggiari

In this paper we describe some relations between various structure sets which arise naturally for a Browder-Livesay ltration of a closed topological mani- fold. We use the algebraic surgery theory of Ranicki for realizing the surgery groups and natural maps on the spectrum level. We obtain also new relations between Browder{Quinn surgery obstruction groups and structure sets. Finally we illustrate several examples and applications.

]]>R.F. Al Subaie and M.A. Mourou

We consider a singular differential operator Δ on the half line which generalizes the Bessel operator. Using harmonic analysis tools corresponding to Δ, we construct and investigate a new continuous wavelet transform on [0,∞[ tied to Δ. We apply this wavelet transform to invert an intertwining operator between Δ and the second derivative operator d^{2}/dx^{2}.

HAKAN OZTURK

The main interest of the present paper is to study α-cosymplectic manifolds that satisfy some certain tensor conditions. In particular, we consider α-cosymplectic manifolds with flatness conditions. We prove that there can not exist ϕ-projectively flat α-cosymplectic manifolds whose scalar curvature is zero for the dimension is greater than three. Furthermore, we work with special weakly Ricci-symmetric α-cosymplectic manifolds. We conclude the paper with an example on α-cosymplectic manifolds.

]]>Sergey Akimov and Olga Kvan

The article is about the problem of calculating the probability of discreteness and continuity sample from the general totality. There is a definition of discreteness. The main task of research is the definition of continuity or discreteness of unknown data. We consider the existing methodology as a method of finding the frequency of repetition of individual values variants of totality under test. The presented procedure is mathematically described. The basic disadvantage of this procedure: this procedure has great difficulties in interpreting the results. Based on the foregoing, the task of creating an algorithm determining the continuous or discrete becomes very important. The new algorithm is also based on the search for a match in the data array. However, now we use not only the array, but the quantity of changes between two successive values. To do it we need a sorting procedure of array from a minimum value to maximum one. In addition, we introduce the concept of "step" as a minimum amount of change between two values in the discrete series. An iterative method for detecting the matches in the array and defining the identity of the changes of the neighboring values is proposed in the article. Thus we have obtained three key values that define the continuity or discreteness. It has been found empirically that each of these values change its sensitivity based on the number of observations in the array. We also identified factors, which usage as (dependence on the number of values in the data) helps to attribute data array to the continuous or discrete distribution.

]]>Parivash Shams Derakhsh and Parisa Shams Derakhsh

The most famous classical variational principle is the so-called Brachistochroneproblem. In this work, Homotopy perturbation method (HPM) is applied to the Brachistochrone problem that arises invariational problems. The results reveal the efficiency and the accuracy of the proposed method. Homotopy perturbation method yields solutions in convergent series forms with easy computation

]]>M. R. Rismanchian S. Sedghi N. Shobkolaei and K.P.R. Rao

In this paper, we define the concept of almost generalized (S; T)-contractive condition, and prove some common fixed point results for four mappings satisfying almost generalized (S; T)− contractive condition in partially ordered fuzzy metric spaces.

]]>Tuncay Tunc

In this study, we have constructed a sequence of new positive linear operators with two variable by using Szasz-Mirakyan and Bernstein Operators, and investigated its approximation properties.

]]>Harun-Or-Roshid Md. Nur Alam M. F. Hoque and M. Ali Akbar

In this paper, we propose a new extended (G'/G)-expansion method to construct exact traveling wave solutions for nonlinear evolution equations. To check the validity and effectiveness of our method, we implement it to the (2+1)-dimensional typical breaking soliton equation. The results that we get are more general and successfully recover most of the previously known solutions which have been found by other sophisticated methods. Many of these solutions are found for the first time. Moreover, our method is direct, concise, elementary, effective and can be used for many other nonlinear evolution equations.

]]>Boris Shekhtman

It is well-known that the following properties of a matrix are equivalent: a matrix is non-derogatory if and only if is cyclic if and only if it is simple and if and only if it is 1-regular. In this article we attempt to extend these properties to a sequence of commuting matrices and examine the relation between them.

]]>Rovshan A. Bandaliev

In this paper a two-weight criterion for multidimensional Hardy type operator and its dual operator acting from weighted Lebesgue spaces into weighted Musielak-Orlicz spaces is proved. As application we prove the boundedness of multidimensional geometric mean operator in the weighted Musielak-Orlicz spaces. In particular, from obtained results implies the boundedness of multidimensional Hardy operator and its dual operator acting from usual weighted Lebesgue spaces into weighted variable Lebesgue spaces. In this paper we establish integral-type necessary and sufficient condition on weights, which provides the boundedness of the multidimensional Hardy type operator from weighted Lebesgue spaces into weighted Musielak-Orlicz spaces.

]]>Kevin K. H. Cheung

A classical result due to Steinitz states that a graph is isomorphic to the graph of some 3-dimensional polytope P if and only if it is planar and 3-connected. If a graph G is isomorphic to the graph of a 3-dimensional polytope inscribed in a sphere, it is said to be of inscribable type. The problem of determining which graphs are of inscribable type dates back to 1832 and was open until Rivin proved a characterization in terms of the existence of a strictly feasible solution to a system of linear equations and inequalities which we call sys(G), which, surprisingly, also appears in the context of the Traveling Salesman Problem. Using such a characterization, various classes of graphs of inscribable type can be described. Dillencourt and Smith gave a characterization of 3-connected 3-regular planar graphs that are of inscribable and a linear-time algorithm for recognizing such graphs. In this paper, their results are generalized to r-edge-connected r-regular graphs for odd r ≥ 3 in the context of the existence of strictly feasible solutions to sys(G). An answer to an open question raised by D. Eppstein concerning the inscribability of 4-regular graphs is also given.

]]>VICTOR CHULAEVSKY

We propose a new probabilistic approach to the analysis of decay of the Green’s functions and the eigenfunctions of the Anderson Hamiltonians on countable graphs. Our method is close in spirit to the Fractional Moment Method, but we show how the use of the fractional moments can be avoided, so that exponential decay of the Green’s functions can be established in some models where the fractional moments diverge, due to low regularity of the random potential. We elucidate the exceptional role of the Holder continuity condition, usual in the FMM, in terms of Cramer’s condition in the large deviations problem for a suitably constructed rigorous path expansion.

]]>Parivash Shams Derakhsh and Jafar Biazar

In this paper we develop a framework for necessary condition for the existence of noise terms for systems of partial differential and integral equations with (HPM) method. We show that the noise terms are conditional and are generated for inhomogeneous equations if specific criteria are justified. And to illustrate the capability and reliability of this method we numerically test our approach for a variety of systems of inhomogeneous problems.

]]>Md. Nur Alam M. Ali Akbar and Harun-Or-Roshid

Exact solutions of nonlinear evolution equations (NLEEs) play very important role to make known the inner mechanism of compound physical phenomena. In this paper, the new generalized (G'/G)-expansion method is used for constructing the new exact traveling wave solutions for some nonlinear evolution equations arising in mathematical physics namely, the (3+1)-dimensional Zakharov-Kuznetsov equation and the Burgers equation. As a result, the traveling wave solutions are expressed in terms of hyperbolic, trigonometric and rational functions. This method is very easy, direct, concise and simple to implement as compared with other existing methods. This method presents a wider applicability for handling nonlinear wave equations. Moreover, this procedure reduces the large volume of calculations.

]]>N.A. Aliev O.H. Asadova and A.M. Aliev

In this paper solution of mixed complex boundary value problem of first order is considered. The basic term in the problem with respect to space variables, has Cauchy-Riemann operator. We first use Laplace transformation to introduce spectral problem. Then we investigate for corresponding Fredholm’s type. The spectral problem here is different from classical boundary value problems. Here boundary conditions are nonlocal and global and in general linear. At the end we find asymptotic expansionfor the solution of spectral problemwhich depends on unknown complex parameter. With the help of this asymptotic expansion we prove existence and uniqueness of mixed problem.

]]>imdat İşcan

In this paper, some new integral inequalities of Hermite-Hadamard type related to the geometrically convex functions are established and some applications to special means of positive real numbers are also given.

]]>B. S. Trivedi and M. N. Patel

In this paper, we are concerned with the situations, where sometimes value two is reported erroneously as one in relation to size biased generalized negative binomial distribution (SBGNBD) with probability α. We have obtained the Maximum likelihood estimator and Bayes estimator under general entropy loss function. A simulated study is carried out to access the performance of the maximum likelihood estimators and Bayes estimators. Also comparison has been made between maximum likelihood estimator and Bayes estimator.

]]>Divo Dharma Silalahi Putri Aulia Wahyuningsih and Fahri Arief Siregar

The most popular nonparametric density estimates is kernel density estimate. This estimate depends on the bandwidth choice which was given the optimization to kernel optimality process. We proposed Epanechnikov kernel which is the most optimal kernel in the AMISE. The resample data as replicate samples has been obtained by using bootstrap mechanism to provide the information about the sampling distribution. Then the resample data was used in Epanechnikov kernel simulation to estimate the optimal solution. This study was simulated using oil contents (%) data at various periods after pollination. The oil contents (%) were obtained by extraction of oil palm mesocarp. The result show that, Epanechnikov kernel using resamples data from bootstrap could be used for nonparametric optimization cases such as oil content (%) of oil palm mesocarp.

]]>R. K. Saxena

In this paper , we derive the solutions of fractional master equation defined by (2.1) and fractional diffusion equation defined by (3.3). The method followed in deriving the solution is that of Laplace and Fourier transforms. The solutions are obtained in a neat and compact forms in terms of the generalized Mittag –Leffler function and Fox’ H-function. The results established are of general character and include some known results, as special cases.

]]>Sergey Gurov

Point and interval probability estimates for an event that has never been observed in a Bernoulli trial series (0-event) are proposed and validated. In this case, the classical statistical methods yield a zero point estimate, which is often unacceptable in practice. Nonzero point and interval probability estimates for a 0-event are proposed and validated. A classification of samples by size for the case of a 0-event is proposed.

]]>Guy Jumarie

In order to convince the sceptical reader, we herein give another proof of the fact that the Leibniz rule for fractional derivatives applies whenever we are dealing with non-differentiable functions, as they occur for instance, when one considers problems involving fractal space-time

]]>Md.Jalilul Islam Mondal and Tapan Kumar Roy

The purpose of this paper is to put forward the notion of intuitionistic fuzzy soft matrix theory and some basic results. In this paper, we define intuitionistic fuzzy soft matrices and have introduced some new operators with weights, some properties and their proofs and examples which make theoretical studies in intuitionistic fuzzy soft matrix theory more functional. Moreover, we have given one example on weighted arithmetic mean for decision making problem.

]]>M.S. Pukhta

If has all its zeros on K≤1, then it was recently proved by Dewan and Ahuja [3] that for every real or complex number where In this paper, we improve the above result and obtain new inequality for the polar derivative of a polynomial.

]]>Majid Mirmiran

Necessary and sufficient conditions in terms of lower cut sets are given for the strong insertion of a Baire-one function between two comparable real-valued functions on the topological spaces that sets are

]]>Erhan Pişkin

We study the system of nonlinear integro- differential equations with strong damping and weak damping terms, in a bounded domain with the initial and Dirich let boundary conditions. The existence of global solutions by using the potential well method, and the energy decay estimate by applying a lemma of Komornik [3]

]]>K.P.R. Rao G.N.V. Kishore and P.R.Sobhana Babu

In this paper, we obtain a unique common fixed point theorem for four self mappings satisfying Meir-Keeler type contractive condition in partial metric spaces, which is slightly different from the result of Aydi and Karapinar [5].

]]>M.S. Pukhta

Let p(z) be a polynomial of degree n which does not vanish in , k≧1, then for 1≦R≦k Bidkham and Dewan [J. Math. Anal. Appl. 166 (1992),191-193] proved In this paper we shall present several intersting generalizations and a re nement of this result which includes some results due to Malik, Govil and others. We also present a re nement of some other results.

]]>Mehdi Delkhosh

In many of applied sciences, various Self-adjoint differential equations are generated, where, methods for their solution is very complex. Usually, numerical methods used to solve them. Leighton et al were investigated oscillation properties of solutions of self-adjoint differential equations of the fourth order, with specific conditions. In this paper, we use a new method for the solving a class of Self-adjoint differential equations of the fourth order. We use a variable change in the equation, and then obtain an analytical solution for the equation with a specific condition. Because in this method, an analytical solution is obtained, therefore, it is not necessary to use numerical methods to solve the problem.

]]>MAJID MIRMIRAN

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a Baire-one function between two comparable real-valued functions on the topological spaces that are .

]]>Jinxia Ma and Rand R. Wilcox

The paper considers the problem of testing the hypothesis that J≧2 dependent groups have equal population measures of location when using a robust estimator and there are missing values. For J = 2, methods have been studied based on trimmed means. But the methods are not readily extended to the case J > 2. Here, two alternative test statistics were considered, one of which performed poorly in some situations. The one method that performed well in simulations is based on a very simple test statistic with the null distribution approximated via a basic bootstrap technique. The method uses all of the available data to estimate each of the marginal (population) trimmed means. Other robust measures of location were considered, for which imputation methods have been derived, but in simulations the actual Type I error probability was estimated to be substantially less than the nominal level, even when there are no missing values.

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