After consideration, we have decided to cease publication of this journal at the end of 2022. This journal will no longer accept submissions and subscriptions from 2023. All published articles will remain available in Archive at https://www.hrpub.org/journals/jour_archive.php?id=24]]>

Araceli Giménez Lorente

It presents a mathematical modeling of a biological system, this is a particular case of two fractal sets, an attractor repeller pair, according to the definition given by the Morse-Smalle theory; these are complementary fractal sets, since the complementary of the fractal repeller set is the attractor set, as we can see in the demonstration. The existence of this model in Nature is found in the flight of starlings. This dynamic system works like a beat of a heart, where the movement of the systole is equivalent to the contraction (attractor set) of the flight trajectory of birds and the diastole movement to its expansion (repeller set).The modeling is presented with differential equations written in Matlab code, and several images of the fractal sets associated with the flight pattern of the starlings are generated, so that we can see this model more clearly. We will begin with a definition and its subsequent mathematical demonstration to study this complex system of complementary fractals.

]]>V. K. Shchigolev

In this paper, some new approximations to the cumulative distribution function of the standard normal distribution via the He's homotopy perturbation method are proposed. There are several methods which provide an approximation of the integral in the formula for the cumulative distribution function by different numerical methods. For the same purpose, we first establish a differential equation of the second order that the cumulative distribution function satisfied subjected with the certain initial conditions. Then we apply the Homotopy Perturbation Method to solve the Cauchy problem for the governing equation. As well known, the result of solving an equation by this method and the convergence rate greatly depend on the choice of homotopy applied. Therefore, we consider two cases in this work. In one case, we construct the homotopy from the idea of simplicity. In the next case, we just follow the procedure of the general approach proposed early. As a result, we obtain several approximations which can be are easily calculated and are better than some other approximations. Numerical comparison shows that our approximations are very accurate.

]]>Maryam Mazdarani Ali Asghar Khakpoor and Bahare Agahi Keshe

In the future molecular electronic is substitute the silicon electronic by the organic molecules. Due to p orbital's, upper and lower electron clouds, and resonance phenomenon, the aromatic hydrocarbon from the root of benzene can provide suitable environments for electron transition. A useful approach for this purpose is an appropriate pattern to predict electronic properties by topological indices method (TIM). Therefore, it is first tried to produce a relationship between the topological indices based on the number of rings; then F index values are measured for Circumacenes family. The gap energy changes in the family of C_{8(n+2)/3}H_{(2n+22)/3} was calculated using Gaussian 09 Software by Hartree–Fock method. The relationships described the gap energy changes in the Circumacenes family achieved by F index. Finally, some heavier members of Circumacenes family are exposed to TIM to predict of Gap energy.

N.M. Alrasheedi and I.A. Alsubiahi

Solving nonlinear equations is one of the most important problems in numerical analysis, and has a wide range of application in various aspects, as well as many branches of science, engineering, physics, computing, astronomy, finance, .. . Generally, it is difficult to find the exact root of the nonlinear equations, and so iterative methods become the efficient way to obtain approximate solutions. Recently Kou et. al. presented a class of new variants of Ostrowski's method with order of convergence equals seven (OSM7) for solving simple roots of nonlinear equations proposed in [7]. Ostrowski's method (OSM7) has efficiency index equals to ∜7≈1.626, it has four functions per iteration but its order of convergence is seven that means it's not optimal method. In this paper, we have proposed new two improvements of Ostrowski's method (OSM7) to make it an optimal eight family and to increase its efficiency index. The first improvement has obtained by multiplied the third step of (OSM7) by product of two weight functions with some special conditions and the second improvement has obtained by multiplied the third step of (OSM7) by summation of two others weigh functions with special conditions, too. Using weight functions in every improvement helped us to improve the order of convergence of (OSM7) from seven to eight without changing the number of function evaluations to be an optimal family. New two optimal families have efficiency index equals to ∜8≈1.682. Some numerical examples are provided to show the good performance of the new methods.

]]>Ayda Valinezhad Orang and Hassan Hajimohammadi

Wireless sensor networks (WSNs) consist of a number of nodes and one or two base stations (BS). Each node has limited energy. Therefore, the energy each node is very important parameter in network since accessing the nodes and re-charging them are difficult or in some cases, are impossible. Thus, the main purpose of this article is to increase the lifetime of the wireless sensor networks by finding the optimal route to send the data to the base station in order to save the energy of each node. In this paper, a hybrid clustering method called Hybrid based on Bayesian Networks (HBN) is proposed based on Bayesian network which considers the radio range of each nodes. In this algorithm, four different parameters are considered including residual energy, the distance to the base station, distance to the neighbor nodes and the radio range of the sensor nodes. According to the simulation results, this algorithm enables an increase in network lifetime in comparison to other similar algorithms.

]]>Alma Braimllari

Online reviews are used by customers as an important source of information during the travel and tourism decision-making process. This research main objective is to analyze the online ratings of hotels in Tirana and Durrës, Albania. Data from Booking.com were collected for 132 hotels with 30 or more online reviews during the period of time 29 November - 2 December 2017. Mean of the overall online rating of hotels was 8.65 with a standard deviation of 0.636. About 62.4% of online reviewers of hotels in Tirana have scored from 9 to 10, and 44% of online reviewers of hotels in Durrës have scored from 9 to 10. Results of two econometric models indicated that hotel's size and location negatively impact the overall online rating of the hotels, whereas the hotel's category, the number of online reviews and year the hotel was welcomed by Booking.com positively impact the overall online rating of hotels. These findings are useful for hotel guests and potential customers, and also for hotels' managers in developing appropriate marketing strategies.

]]>I. B. Olenych and A.F. Gukaliuk

The expert system of the fuzzy inference of the Sugeno's type with three inputs and one output for the choice of optimal routes of the transport network is proposed in the work. The developed system involves the formation of a fuzzy production rules base, the fuzzification of the values of the input parameters, the aggregation of the truth of the sub-conditions of each rule, activating the conclusions and defuzzification the output variable. An algorithm for finding quantitative values of coefficients that corrects the weight of the edges of the graph in optimization problems under conditions of approximate input data is implemented. In particular, the proposed model takes into account the condition of the road surface, the urgency of delivery and the caution of transportation of cargoes during the formation of transport routes, which allows minimizing costs and improving the efficiency of the logistics system.

]]>Kolade M. Owolabi and Ayodeji A. Adejola

In this paper, we have studied a new fractional reaction-diffusion two-species system as an extension to the Rosenzweig-MacArthur reaction-diffusion di-trophic food chain system which models the spatial interactions between a prey and predator. To guarantee good working guidelines when numerically simulating the model, we first show that the system is locally asymptotically stable, as it provides good conditions and correct choice of ecological parameters to enhance a biologically meaningful result. We propose a fast and accurate method for numerical solutions of space fractional reaction-diffusion equations. The technique is based on Fourier spectral method in space and exponential integrator scheme in time. The complexity of fractional derivative index in fractional reaction diffusion model is numerically formulated and graphically displayed in one-, two- and three-dimensions.

]]>V. K. Shchigolev

This work deals with a new approach in the approximate analytical representation of the luminosity distance in a homogenous Friedmann-Lemaître-Robertson-Walker (FLRW) model of the Universes by means of the variational iteration method (VIM). For the analytical calculation of the luminosity distance, we obtain the approximate solution of the differential equation which the luminosity distance obeys, using the corresponding initial conditions. On the basis of this approximate solution, a simple analytic formula for the luminosity distance as a function of redshift is obtained and compared with a numerical solution from the general integral formula.

]]>Alisher Matyakubov

The property of a finite speed of a perturbation distribution to the Cauchy problem for a parabolic system not in divergence form based on comparison method and an asymptotic behavior of a self-similar solution for both slow and fast diffusion cases are established. It is shown that the coefficients of the main term of the asymptotic of solution satisfy some system of nonlinear algebraic equations. It is found the Zeldovich-Kompaneets-Barenblatt type solution to the parabolic system.

]]>Armen Avagyan and Gurgen Dallakyan

In the current paper we are seeking P_{1}(y); P_{2}(y); P_{3}(y) with the highest possible degree polynomials with integer coefficients, and Q(y) via the lowest possible degree polynomial, such that = Q(y). Actually, the solution of this problem has close relation with the problem of the sum of three cubes a^{3} + b^{3} + c^{3} = d, since degQ(y) = 0 case coincides with above mentioned problem. It has been considered estimation of possibility of minimization of degQ(y). As a conclusion, for specific values of d we survey a new algorithm for finding integer solutions of a^{3} + b^{3} + c^{3} = d.

Yusupov Y. and Khaldjigitov A.A.

Using the strain space and deformation thermoplasticity theories the coupled dynamic thermoplastic boundary value problems are formulated. Strain space thermoplasticity theory, in contrast to the deformation one, allows formulating the coupled thermoplastic boundary value problems for the displacement and temperature increments. As an example, in one-dimensional case, the explicit and implicit types of finite difference equations are constructed. The numerical solution of the explicit finite difference equations reduced to the application of the recurrent formulas, whereas the implicit scheme reduced to the application of the elimination method. Comparison shows that the numerical results obtained using explicit and implicit scheme coincides.

]]>S. M. Atiqur Rahman Chowdhury Ashish Barmon Sharmin Alam and Maria Akter

So far, so many works have been done in a different way to find the exact track that can grasp the true solution for the one-dimensional porous media equation (PME). For instance, Monika studied using relaxation [1], Q. Zhang and Z. Wu. have already done the similar work by local degenerate Galarkin (LDG) method [12] and so on. Still, this is a challenge to find an appropriate scheme that can track the true solution when adiabatic exponent increases monotonically. In this paper, we have studied numerical result for where we have used Explicit-Implicit Finite Difference Method (EIFDM). Since so far PME is a degenerate parabolic equation and analytically the existence and uniqueness occur weakly only in the Sobolev sense, it is very hard to track the true solution numerically. Our main objective is to study numerically the PME with mixed boundary conditions and shown the result is helpful to track the Barenblatt's self similar solution and its interface when adiabatic exponent larger than 3 that provides much less error. This paper will show a possibility that Finite Difference Method (FDM) is also helpful rather the Finite Elements Method to track the interface in the simulation with an appropriate initial guess. Also checked L_{1}, L_{2} and L_{∞}-error for Boussinesq's equation which is a fundamental equation of ground- water flow, hopefully, the simulated results can help when this equation is useful in the practical world. Finally, all studied results are given to show the advantage of the θ-scheme method in the simulation of the PME and its capability to capture accurately sharp interfaces without oscillation.

Rowa E.E. Omer Eihab B.M. Bashier and Arbab I. Arbab

In the present paper, we consider a first-order exponential splitting method (or exponential Lie-Trotter splitting) and second order exponential splitting method (or exponential Strang splitting method) for the Cauchy problem. Then we compare the errors between Lie-Trotter splitting and Strang splitting by discretizing the space into N sub-intervals, and compute the convergence rate for both Lie-Trotter splitting and Strang splitting methods.

]]>K. Prudhvi

In this paper, we prove fixed point theorems on c-distance in ordered cone metric spaces. Our results generalize, extend and improve the recent results existing in the literature.

]]>R. A. Rashwan and H. A. Hammad

In this paper, we establish a unique common random fixed point theorem in cone random metric spaces for four weakly compatible mappings by using an implicit relation. Some corollaries of this theorem for two and three random weakly compatible mappings are obtained. Some examples are given to support our generalization. Our results presented in this paper extend and improve several recent results in the setting of cone random metric spaces.

]]>Mirsaid Aripov and Alisher Matyakubov

The Zeldovich-Barenblatt type solution of the Cauchy problem for a cross-diffusion parabolic system not in divergence form with a source and a variable density is obtained. Based on comparison method the property of finite speed perturbation of distribution is considered. An asymptotic behavior of self-similar solutions, both for slow and fast diffusion cases, is established. It is obtained the system of the nonlinear algebraic equations with the coefficients of the main terms of the asymptotical solution.

]]>Rozana Liko and Artion Kashuri

The aim of this paper is to investigate the volatility of USD/ALL daily exchange rate using generalized autoregressive conditional heteroscedasticity model. The data set used in this study cover a period from 5 January 2010 to 30 April 2015. Autoregressive conditional heteroscedasticity (ARCH), generalized autoregressive conditional heteroscedasticity (GARCH), threshold generalized autoregressive conditional heteroscedasticity (TGARCH), and exponential GARCH (EGARCH) model are applied to model the volatility of daily exchange rate return. The main result is that volatility of exchange rate return is affected by past volatility, and exchange return of USD/ALL is well modeled by this model.

]]>R. A. Rashwan and H. A. Hammad

In this paper, we prove a unique common random fixed point theorem in the framework of cone random metric spaces for four weakly random compatible mappings under strict contractive condition. Some corollaries of this theorem for three and two weakly random compatible mappings and for one random mapping are derived. Two examples to justify our theorem are given. Our results extend some previous work related to cone random metric spaces from the current existing literature.

]]>Fayazov K.S. and Khajiev I.O.

In this paper, we consider a system of equations of mixed type and with changing time direction. It is proved that solution of the system is not stable depend from the variation of the data. Theorems of uniqueness and conditional stability proved. The approximate solution constructed and numerical results are given.

]]>Peter Uchenna Okoye Peter Emenike Ogunoh and Chinwendu Christopher Mbakwe

This study analysed pre and post re-basing economic performance of Nigeria construction sector with a view to ascertaining if significant improvements have been achieved in terms of construction output, construction growth rate, contribution to Gross Domestic Product (GDP) and economic development. Data were obtained from the publications of the Central Bank of Nigeria and the National Bureau of Statistics from 1981 to 2015, and analysed using Z test and Pearson correlation. Statistically, the study found that there was significant improvement in the construction sector outputs and contribution to GDP after re-basing as the computed Z scores (-8.0381) and (-5.4647) were greater than the critical value (1.96) at 5% significance difference respectively. The correlation coefficients (0.706) and (0.561) and the p-values (<0.00001) indicated a strong and significant correlations. However, there was no significant difference in the growth rate of construction sector and GDP after re-basing as the computed Z scores (-0.2388) and (0.2835) were less than the critical value (1.96). The correlation coefficient (0.030) and (0.036) and p-values (0.81126) and (0.776794) also showed a very weak and non-significant correlation. This implied that Nigeria economic re-basing has triggered improvement in construction output and contribution to GDP but not in construction growth rate and GDP growth rate as previously believed.

]]>Kolade M. Owolabi

Evolution systems containing fractional derivatives can result to suitable mathematical models for describing better and important physical phenomena. In this paper, we consider a multi-components nonlinear fractional-in-space reaction-diffusion equations consisting of an improved deterministic model which describe the spread of Hepatitis B virus disease in areas of high endemic communities. The model is analyzed. We give some useful biological results to show that the disease-free equilibrium is both locally and globally asymptotically stable when the basic reproduction number is less than unity. Our findings of this paper strongly recommend a combination of effective treatment and vaccination as a good control measure, is important to record the success of HBV disease control through a careful choice of parameters. Some simulation results are presented to support the analytical findings.

]]>Annalakshmi Harikrishna Dennis Effah Osei Magdalena Weronika Kamińska and Sarangam Majumdar

Parkinson's disease and Parkinson's tremor are the two most common movement disorders, nor do we fully understand the origin of one of the disease's cardinal symptom: the Parkinsonian tremor. We study one mathematical model involved in Parkinson's disease and in the Parkinsonian tremor. In this paper, we use the Van der Pol equation to further understand this tremor as well as investigate different numerical approaches to solve the system and compare them.

]]>K. Prudhvi

In this paper, we obtain a common fixed point theorem for four self-mappings with the property (C) in cone metric spaces without assuming the regular cone. These results are extends, improves and generalization of some known results existing in the literature.

]]>Jamshad Ahmad and Nida Fatima

In this paper, we introduce a well-known technique Differential Transform method (DTM) which is very effective to control the convergence region of the approximate solution. The Differential Transform Method is applied to neutral functional-differential equation with proportional delays. The DTM produces an approximate solution with few hand computations without rounding off the error. Obtained solution of Neutral functional-differential equation with proportional delays reveals that DTM is one of the efficient and accurate methods.

]]>Andri Lopez

In this article I demonstrate the method for solve Galois's equations, is applying simply arithmetic in his coefficients.

]]>Andri Lopez

In this article the why and how of the prime numbers were shown; to be more specific, I present the pattern that was defined, i.e. every prime number is in the interval between (30a + (p)) and (42a + (p1)); p = (11;17;23;29); p1 = (13; 19; 25; 31; 37; 43). This verifies the accuracy of the series of Dirichelet, and improvement, because any series that of a prime number matches the prime number of this pattern. Another contribution of this work is to know whether a number is prime; both for a small number, as for one he is infinitely large, without applying the process of factorization.

]]>K. Prudhvi

In this paper, we study the existence of coincidence points and common fixed point theorem for three self - mappings in cone metric spaces and relaxing the completeness of the space. This result extends and improves the results of M. Abbas and B. E. Rhoades [M. Abbas and B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett., 22(2009) 511-515] who proved fixed point theorems for two self-mappings without assuming commutativity conditions in cone metric spaces and using the completeness of the space.

]]>Mirsaid Aripov and Zafar Rakhmonov

In this paper we study the global solvability or nosolvability of a nonlinear ﬁltration problem with nonlinear ﬂux boundary condition in the fast diffusion case. The critical global existence and critical Fujita exponent by constructing various self-similar supersolutions and subsolutions are obtained.

]]>Sharif Mozumder ABM Shahadat Hossain Sadia Tasnim and Arafatur Rahman

This paper comparatively investigates some iterative methods and Monte Carlo simulation technique for the dynamics underlying the celebrated Black and Scholes (BS) model. In particular we attempt to answer the question: 'How many Monte Carlo replications can yield prices, for plain vanilla type European derivatives on a stock, which are similar to those obtained by solving the BS PDE using iterative numerical schemes?' We confine to three frequently referred iterative schemes such as Successive over Relaxation (SOR), Gauss-Seidel (GS) and Jacobi (JC). This information together with the information of 'differences in time requirements' will help to guess the similar trade-offs for complex derivatives(exotic) pricing for which there are no analytic pricing formulas.

]]>V. K. Shchigolev

We propose a new approach in studying the planetary orbits and the perihelion precession in General Relativity by means of the Homotopy Perturbation Method (HPM).For this purpose, we give a brief review of the nonlinear geodesic equations in the spherical symmetry spacetime which are to be studied in our work. On the basis of the main idea of HPM, we construct the appropriate homotopy what leads to the problem of solving the set of linear equations. First of all, we consider the simple example of the Schwarzschild metric for which the approximate geodesics solutions are known, in order to compare the HPM solution for orbits with those obtained earlier. Moreover, we obtain an approximate HPM solution for the Reissner-Nordstorm spacetime of a charged star.

]]>Andri Lopez

In this article I demonstrate the Collatz conjecture that there are infinitely because there are infinitely many values of (a) magic in set of the integers numbers that lead directly to the cycle 4,2,1. With the algorithm (3a + 1) we have always one of the (a) magic. Another contribution of this paper is the demonstration for existing two equations for polynomial time of all 2^{n}. Finally the existence of another algorithm for 4,2,1 cycle; as is the (7a + 1).

Abdellatif Agouzal Karam Allali and Siham Binna

In this paper, we will study the fully discretized finite element approximation for an incompressible flow in porous media. The model consists of the heat equation, the equation for the concentration and the equations of motion under the Darcy law. The model is rewritten using the stream function-vorticity formulation. The Stability of the fully discrete problem is established. Optimal a priori error estimates are given.

]]>Andri Lopez

In this article I present the of demonstration Goldbach conjecture: every pair number is the sum of two primes. As only reference: the logic mathematical and also, the enunciate of Euclides in his proof for the existence of infinitely many primes.

]]>K. Prudhvi

In this paper, we prove two fixed point theorems in S-metric spaces. Our results extend and improve some known results.

]]>Jamshad Ahmad and Mariyam Mushtaq

In this research paper, we applied the Adomian’s decomposition method to determine the analytical exact solutions of linear and nonlinear Goursat problems which play very important part in applied and engineering sciences. The proposed technique is fully compatible with the complexity of these problems and obtained results are highly encouraging. Some examples with closed form solutions are studied in detail to further illustrate the proposed technique, and the results obtained indicate this approach is indeed practical and efficient.

]]>Atif Nazir and Mohammad Shafique

The steady flow of a micropolar fluid, due to a stretching cylinder, is considered. The equations of motion are reduced to a system of ordinary differential equations, which in turn are solved numerically using SOR iterative procedure and Simpson's (1/3) rule, for three different combinations of the three dimensionless parameters involved. Results are calculated, for the range 0.1 to 100 of the parameter R. The accuracy of the results was checked by comparing them on different grid sizes and with the previous results where possible.

]]>R Kayastha V Krishna Murthy and P R Adhikary

The purpose of this paper was to extend the existing body of knowledge on the occupational stress index among executive officers into the context of governmental and non-governmental organizations of Nepal, as limited research has been conducted with respect to this field in Nepal. A conceptual framework was developed to study the occupational stress index among executive officers in the governmental and nongovernmental sectors in Nepal. Occupational stress index questionnaire was used to collect data. The overall response rate from the employees of governmental organizations and nongovernmental organizations were encouraging. The statistical approaches used and analysis done brought out many finer aspects and the realistic picture of the stress felt by the employees. The stressors, the different types of stress and its role, the effects on the individual and the organization, the natural effect, the possible stresses including the stressors have a direct bearing on executive officers have been investigated through this battery of statistical methods attempted by Factor analysis. The study also has revealed association of some of the stressors as independent variables and one of them being considered as a dependent variable.

]]>Essam. R. El-Zahar Ehab. A. El-Sayed and Hamza. M. Habib

In this paper, the differential transform method is used to find approximate analytical and numerical solutions of singular perturbation problems. The principle of the method is briefly introduced and then applied for solving two mathematical models of stiff initial value singular perturbation problems. The results are then compared with the exact solutions to demonstrate the reliability and efficiency of the method in solving the considered problems.

]]>Kasani Prudhvi

In this paper, we prove a coincidence point theorem for two self-mappings in an ordered cone metric spaces, without using normality and continuity. Our result extends and improves some recent results existing in the literature.

]]>M. S. Pukhta

In this paper we obtain results concerning the bound for the number of zeros for the polynomial p(z) which generalizes well known result due to A.Ebadian ,M.Bidkham and M.Eshaghi Gordji [Number of zeros of a polynomial in a given domain, Tamkang Jour, of Mathematics, Vol 42, No.4,(2011), 531-536] and also improves upon some well-known results.

]]>R. A. Rashwan and H. A. Hammad

In this paper, we prove three common fixed point theorems for weak contraction map- pings of integral type in modular spaces. In the first theorem we prove a common fixed point of ρ−compatible mappings satisfying a (φ − Ψ)−weak contraction. The second theorem is another version of the first theorem. In the third theorem we study a common fixed point of ρ−compatible mappings in modular spaces involving altering distances of integral type. The results extended several similar results in metric and Banach spaces.

]]>V. Amarendra Babu and P.Koteswara Rao

For given p (= prime), a p-ring as first introduced by Mc Coy and Montgomery [2]. The concept of p-ring is an evident generalization of that of Boolean ring (p = 2). The well known result of Stone [7], each Boolean ring is isomorphically representable as a ring of classes or what is equivalent, is isomorphic with a sub ring of some direct power of Z_{2} ( 2-element Boolean ring = field of residues mod 2) was generalized by Mc Coy and Montgomery [2] to: each p-ring is a isomorphic with a sub ring of some direct power of Z_{P} (field of residues mod p) and they showed that each finite p-ring is isomorphic with a sub ring of some direct power of Z_{P}. The present communication concerned with a further study of p-rings. In particular we study the topological properties of p-rings and proved a Stone duality theorem.

B. Satyanarayana L. Krishna and R. Durga Prasad

The notion of intuitionistic fuzzy positive implicative hyper BCK-ideals of type-1, 2... 8 of hyper BCK-algebras was introduced in 2012 by Durga Prasad, Satyanarayana and Ramesh. In this paper, we investigate some related properties of intuitionistic fuzzy positive implicative hyper BCK-ideals of types-1. We characterize positive implicative Artinian (shortly, PI-Artinian) hyper BCK-algebras of type-1 and positive implicative Noetherian (shortly, PI-Noetherian) hyper BCK-algebra of type-1.

]]>Shakir Ali Basudeb Dhara and Mohammad Salahuddin Khan

Let R be an associative ring. A mapping f : R → R is said to be additive if f(x+y) = f(x)+f(y) holds for all x; y ∈ R: An additive mapping d : R → R is called a derivation if d(xy) = d(x)y + xd(y) holds for all x; y ∈ R: In this paper, we investigate commutativity of prime and semiprime rings satisfying certain identities involving additive mappings and derivations. Moreover, some results have also been discussed.

]]>Chii-Huei Yu and Bing-Huei Chen

This paper uses the mathematical software Maple for the auxiliary tool to study six types of integrals. We can obtain the infinite series forms of these six types of integrals by using integration term by term theorem. In addition, 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. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. Therefore, Maple provides insights and guidance regarding problem-solving methods.

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

A new extended (G’/G)-expansion method is presented in this paper to construct more general type and new traveling wave solutions of nonlinear partial differential equations. To illustrate the novelty and advantage of the proposed method, we solve the (3+1)-dimensional Jimbo-Miwa equation. Abundant exact traveling wave solutions of this equation is obtained, which successfully recover most of the previously published solutions. Many of those solutions are found for the first time. Furthermore, the results reveal that the proposed method is very elementary, effective and can be used for many other nonlinear partial differential equations.

]]>T. Som A Choudhury B. S Choudhury and Amaresh Kundu

The aim of this present work is to generalize the notion of weakly isotone increasing mappings and prove an α- fixed point theorems for α -weakly isotone increasing self mappings which satisfy some inequality in complete metric spaces endow with partially ordering.

]]>Chii-Huei Yu

This paper takes the mathematical software Maple as the auxiliary tool to study the partial differential problem of two types of three variables functions. We can obtain the infinite series forms of any order partial derivatives of these two types of functions by using differentiation term by term theorem, and hence greatly reduce the difficulty of calculating higher order partial derivative values of these functions. On the other hand, we propose two examples to do calculation practically.

]]>A.C. Paul and Ayesha Nazneen

Let M be a Γ- ring and U a Lie ideal of M. Let d : M → M and k :Γ → Γ be additive mappings. Then d is a k- derivation on U of M if d(uαv) = d(u)αv + uk(α)v + uαd(v) is satisfied for all u, v ∈ U and α ∈ Γ. And d is a Jordan k- derivation on U of M if d(uαu) = d(u)αu + uk(α)u + uαd(u) holds for all u ∈ U and α ∈ Γ. It is well-known that every k- derivation on U of M is a Jordan k- derivation on U of M but the converse is not true in general. In this article we prove that every Jordan k- derivation on U of M is a k- derivation on U of M if , M is a 2- torsion free prime Γ- ring and U is a Lie ideal of M such that uαu ∈ U for all u ∈ U and α ∈ Γ.

]]>T.I. Serezhnikova

In the paper, we propose a new regularization algorithm based on the generalized Tikhonov regularization method. In the paper proposed technique treats problems in the form of Fredholm first kind integral equations which must be inverted. In classical regularization functionals we propose put in the specialize summand, which allows to distribution control of points of approximate solutions. The best additional summand one can get with using more information about solutions. There are six model numerical results in the paper. Numerical experiments prove, that our technique does a better job of preserving functions jumps. As result in the case of the image reconstructions problems, we obtain approximate solutions of better accuracy and images become more blur-free images.

]]>Bandhu Prasad

In this paper, we define (h(x); g(y))-extension of the Fibonacci p-numbers. We also define golden (p; h(x); g(y))-proportions where p (p = 0; 1; 2; 3; ) and h(x)(> 0), g(y)(> 0) are polynomials with real coefficients. The relations among the code elements of a new Fibonacci matrix, Gp;h;g, (p = 0; 1; 2; 3; ), h(x) (> 0), g(y) (> 0) coincide with the relations among the code matrix for all values of p and h(x) = m(> 0) and g(y) = t(> 0) [8]. Also, the relations among the code matrix elements for h(x) = 1 and g(y) = 1, coincide with the generalized relations among the code matrix elements for Fibonacci coding theory [6]. By suitable selection for the initial terms in (h(x); g(y))-extension of the Fibonacci p-numbers, a new Fibonacci matrix, Gp;h;g is applicable for Fibonacci coding/decoding. The correct ability of this method, increases as p increases but it is independent of h(x) and g(y). But h(x) and g(y) being polynomials, improves the cryptography protection. And complexity of this method increases as the degree of the polynomials h(x) and g(y) increases. We have also find a relation among golden (p; h(x); g(y))-proportion, golden (p; h(x))-proportion and golden p-proportion.

]]>Ilgar G. Mamedov

In the paper, we consider the Cauchy problem for a fifth order pseudoparabolic equation that appears in studying the issues of fluid filtration in fissured media, the moisture transfer in soils and etc. The Cauchy problem with non-classic conditions not requiring the agreement conditions are studied for a discontinuous coefficient pseudoparabolic equation. The equivalence of these conditions with the Cauchy classic condition is substantiated in the case when the solution of the stated problem is sought in S.L.Sobolev anisotropic space

]]>Md. Nur Alam and M. Ali Akbar

The exact solutions of nonlinear evolution equations (NLEEs) play a crucial role to make known the internal mechanism of compound physical phenomena. In this article, we implement the new generalized (G’/G)-expansion method for seeking the exact solutions of NLEEs via the Benjamin-Ono equation and achieve exact solutions involving parameters. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized G’/G -expansion method is a powerful and concise mathematical tool for solving nonlinear evolution equations.

]]>A. S. Yakimov

On the basis of the Laplace integral transform, locally one-dimensional scheme of cleavage and quasi-linearization method to obtain an approximate analytical solution of the three-dimensional nonlinear hyperbolic equation of second order. The assessment of the accuracy of analytical formulas when compared with the exact solution of the first boundary value problem and numerical solution by a known method.

]]>Boris M. Shumilov and Ulukbek S. Ymanov

In this article two new types of wavelet bases for Hermite quintic splines are offered. The algorithm of wavelet decomposition as the solution of three systems of the linear equations, from which one system is three-diagonal with strict diagonal domination and two other systems are four-diagonal, is received.

]]>Elisabete Alberdi Celaya and Juan Jose Anza

When solving numerically the stiff second order ODE system obtained after semidiscretizing the wave-type partial differential equation (PDE) with the finite element method (FEM), and similarly to the HHT-α method, which allows the numerical damping of the undesirable high frequency modes associated to FEM semidiscretization, we have constructed a modification of the 2-order BDF method (the BDF2 method), which we have called BDF-α. This new method is second-order accurate and with a smaller local truncation error than the BDF2, it is unconditionally stable for some values of α and it permits a parametric control of numerical dissipation.

]]>J. P. JAISWAL and SUNIL PANDAY

In this paper we established a new eighth-order iterative method, consisting of three steps, for solving nonlinear equations. Per iteration the method requires four evaluations (three function evaluations and one evaluation of the first derivative). Convergence analysis shows that this method is eighth-order convergent which is also substantiated through the numerical works. Computational results ascertain that our method is efficient and demonstrate almost better performance as compared to the other well known eighth-order methods.

]]>Andri Lopez

with this work the equation is defined for the primes numbers; this one work is based on additive theory number and arithmetical progressions.

]]>Mikheev Serge E.

Cycling in Newton’s method for systems of nonlinear equations in multi-dimensional spaces is researched. The functions of the system have most favorable for convergence properties such as convexity or concavity, no singularity of Jacobi’s matrix for the functions and of course existence of the root. It was shown by the counterexample that these properties do not prevent cycling in pure Newton’s method while various relaxations of the method have good convergence.

]]>Lauretta O. Osho Francisca Ogwueleka and Oluwafemi Osho

This paper considers a formal method, known as axiomatic semantics, used to prove the correctness of a computer program. This formal method extracts, using some proof rules, the mathematical verification conditions from a computer program. The axioms of program flow, including, sequential flow, iteration, and alternation flows are presented. Using the axiomatic basis the completeness of two variants of integer multiplication program is proved. Results show that computer programs can actually be verified sufficiently for correctness without necessarily testing them, or more practically put, to complement their testing.

]]>M. A. Kumbhalkar Umesh Nawghare Rupesh Ghode Yogesh Deshmukh and Bhushan Armarkar

Biomechanics is the study of the structure and function of biological systems by means of the methods of “mechanics” which is the branch of physics involving analysis of the actions of forces. Knee joint is the complex structure of the human body acquires the critical loads in various moving conditions. This paper discusses the loads acting on the joint during different motions such as steady, walking and lifting. A 3d modeling software PRO/E is used to prepare a CAD model of knee prosthesis and evaluate the results in the form of stresses by applying the calculated loads in the finite element analysis software ANSYS. The stresses are evaluated by considering several cases of loading. The aim is to study and evaluate the loads and stresses acting on knee joint and compared with the implant results.

]]>Mark A. Pinsky

This paper describes a novel approach to predicting time-series which blends techniques developed in the areas of observer design and numerical solvers for ODEs. The developed predictor is based on a novel feedback control architecture which leads to computationally efficient and a fairly accurate forecast even for volatile economic series. Application to series of various kinds shows that the developed forecaster possesses some basic properties of numerical solvers for ODE. In the same time it prediction horizon is favorably compared with a time step attaining in numerical simulations for the series with precisely known models whereas no knowledge of the series’ global model is assumed in our forecast. We demonstrate that for noisy series the accuracy of prediction reduces to the level of noise to signal ratio as well as that reduction of noise by smoothing the series comparably increases the accuracy of prediction. It is also shown that the developed approach provides practically valuable forecast in application to volatile economic series.

]]>Abdellatif Agouzal and Karam Allali

In this paper we suggest a fully discretized problem of a model describing two-step chemical kinetics. The model considered is a system of equations coupling Navier-Stokes equations with three non-linear reaction-diffusion equations. A space-time finite elements approximations are presented. The stability of the fully discretized problem is studied. Optimal error estimates are given.

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

In this paper we prove a triple coincidence point theorem for multi - valued and single-valued mappings in a partially ordered metric space based on the concepts of [5]. Also we give an example which supports our main result. Our result generalizes several results relating to coupled fixed point theorems.

]]>Ilgar G. Mamedov

In this paper substantiated for a differential equation of pseudoparabolic type with discontinuous coefficients a Goursat problem with non-classical boundary conditions is considered, which requires no matching conditions. Equivalence of these conditions boundary condition is substantiated classical, in the case if the solution of the problem in the anisotropic S. L. Sobolev's space is found. The considered equation as a pseudoparabolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller's equation , moisture transfer generalized equation, Manjeron equation, Boussinesq - Love equation and etc.). It is grounded that the Goursat boundary conditions in the classic and non-classic treatment are equivalent to each other, and such boundary conditions are demonstrated in geometric form. Even from geometric interpretation can see that the grounded non-classic treatment doesn't require any additional conditions of agreement type. Thus, namely in this paper, the non-classic problem with Goursat conditions is grounded for a pseudoparabolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev anisotropic space .

]]>Matej Mencinger

Groebner basis are an important theoretical building block of modern (polynomial) ring theory. The origin of Groebner basis theory goes back to solving some theoretical problems concerning the ideals in polynomial rings, as well as solving polynomial systems of equations. In this article four practical applications of Groebner basis theory are considered; we use Groebner basis to solve the systems of nonlinear polynomial equations, to solve an integer programming problem, to solve the problem of chromatic number of a graph, and finally we consider an original example from the theory of systems of ordinary (polynomial) differential equations. For practical computations we use systems »MATHEMATICA« and »SINGULAR«.

]]>Enfer Diez

this aim of this article is simply to present the process to define the equation that allows to know if a elliptical curve has solution and which is y^{2}=x^{3}+ax^{2}+bx+c