Abstract: Publication date: Jan 2018 Source:Universal Journal of Applied Mathematics Volume 6 Number 1 Cansel Yormaz Serife Naz Elmas and Simge Simsek In this article, firstly we study about geometrical applications of split quaternions. Then, we obtain Hamitonian mechanical systems with Split quaternions. Quaternionic and Coquaternionic (split analoque of quaternions) extensions of Hamiltonian mechanics are introduced and are shown as offer a unifying framework for quantum mechanics. This study leads to the possibility of employing algebraic techniques of quaternions and coquaternions to absorbing in quantum mechanics. The founded equations are compared with the Hamiltonian energy equations generally are known and the Hamilton energy equations are obtained in Minkowski space. PubDate: Jan 2018

Abstract: Publication date: Jan 2018 Source:Universal Journal of Applied Mathematics Volume 6 Number 1 Aydin Teymourifar and Gurkan Ozturk In this paper, a hybrid method is proposed to generate feasible neighbors for the flexible job shop scheduling problem. Many of the optimization and artificial intelligence methods have been used to solve this important and NP-hard combinatorial problem which provides the basis for solving real-life problems. It is well-known that for such problems the hybrid methods obtain better results than the other approaches. For instance, the applied non-hybrid neural networks for the combinatorial problems, as the Hopfield neural network, usually converge early. Also, their results almost always contain large gaps. These shortcomings prevent them to find good results. Another necessity for a quality search is to find suitable neighbors of the obtained solutions; however, it is possible to create infeasible neighbors during the optimization process. The aim of this study is to overcome these deficiencies. In the suggested approach, at first, an initial solution is generated and then using the left shift heuristics, its gaps are removed. Based on the critical path and critical block concepts, 6 neighbors are constructed for the obtained solution. After the generation of each neighbor, a neural network runs and controls the constraints of the problem. If the achieved neighbor is feasible it is saved. Else if it is infeasible, the neural network tries to transform it into a feasible solution. This is done by applying penalties to the start time of the operations on the violated constraints, which shifts them to the right or the left. During this process, if there are not any violated constraints, the neural network reaches the stable condition so it stops and the obtained solution is saved as a feasible neighbor. Otherwise, after a certain number of the iterations, it stops without any feasible neighbors. Then these steps are repeated for the other created neighbors. This constraint-based process provides an effective and diverse search. Finally, the obtained neighbors, are improved using the left shift heuristics. Also to demonstrate the importance of the initial solutions, they are generated randomly and also using the Giffler and Thompson's heuristic. The comparison between the proposed approach and the methods from the literature shows that it constructs better neighbors. However, using the Giffler and Thompson heuristic to create the initial solution improves the results significantly. PubDate: Jan 2018

Abstract: Publication date: Sep 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 4 M. Z. I. Bangalee Roushanara Begum M. Ferdows Md. Matiar Rahman and Mir Shariful Islam The buoyancy driven natural convection flow in an open cavity has become an important issue to study. In this study, the difficulties of computing natural convection flow in open cavity with an extended computational domain around the cavity are reported. The κ-ε turbulence model is used for the computation to capture the turbulence nature of the air flow inside the cavity. ANSYS CFX software is used to solve the governing equations in this study. Effects of different aspect ratio and different temperature at the left wall and thus the temperature difference between the left and the right walls are analyzed numerically as well. Average mass flow, temperature, velocity etc. at different location in the cavity for different boundary conditions are studied and reported. A comparison between the present work and a previous work is also reported here to validate the methodology. Finally, relations among non-dimensional parameters (e.g. Ra, Re, Pr, Nu numbers) are also presented. PubDate: Sep 2017

Abstract: Publication date: Sep 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 4 Souida Boukrioua Adel Aissaoui and Nacerdine Hemici We consider a quasistatic contact problem between two viscoelastic bodies with long-term memory and damage. The contact is bilateral and the tangential shear due to the bonding field is included. The adhesion of the contact surfaces is taken into account and modelled by a surface variable, the bonding field. We prove the existence of a unique weak solution to the problem. The proof is based on arguments of time-dependent variational inequalities, parabolic inequalities, differential equations and fixed point. PubDate: Sep 2017

Abstract: Publication date: Jun 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 3 V. A. Meshkoff On the ground of Prime Numbers Classification it is generalized approach to Composite Numbers Factorization presented. The resulting task goes to the different Diophantine equations reducing. Some methods of reducing and its practical application, in particular for Fermat numbers, are demonstrated. PubDate: Jun 2017

Abstract: Publication date: Jun 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 3 Said Elkassimi Said Safi and B. Manaut This paper proposes an algorithm based on ZF and MMSE methods for blind channel equalization, which is compared with adaptive filter algorithms which are Constant Modulus Algorithm (CMA), Fractional Space CMA (FSCMA) and Sign Kurtosis Maximization Adaptive Algorithm (SKMAA). The simulations show that the proposed algorithm gives satisfied result versus CMA, FSCMA and SKMAA algorithms. The study is done under certain conditions, it is implemented in noisy environment, for different number of symbols and different SNR values with QPSK modulation. Equalization of channel is more performing if we use the proposed algorithms. PubDate: Jun 2017

Abstract: Publication date: Feb 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 1 Seiji Tomita and Oliver Couto Historically equation ( pan+qbn+rcn=pun+qvn+rwn ) has been studied for degree 2, 3, 4 etc., and equation (pan+qbn=pcn+qdn ) herein called equation (1) has been published for n=4 ,p=1,q=4 (Ref.no. 1) by Ajai Choudhry. Also Tito Piezas & others has discussed about equation (1) (Ref. no. 3 & 2). While Ref. no. (1, 2 & 3) deals with equation no. (1) for degree n=4 this paper has provided parametric solutions for degree n=2, 3, 4, 5, 6, 7, 8 & 9. Also there are instances in this paper where parametric solutions have been arrived at using different methods. PubDate: Feb 2017

Abstract: Publication date: Feb 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 1 Igor Ya. Subbotin and Michael Gr. Voskoglou The Generalized Rectangular Fuzzy Assessment Model (GRFAM) is applied for the evaluation of student group acquisition of the van Hiele levels of geometric reasoning and an example is presented illustrating our results. The GRFAM is a variation of the Center of Gravity defuzzification technique created in an effort to treat better the ambiguous assessment cases being at the boundaries between any two successive assessment grades. PubDate: Feb 2017

Abstract: Publication date: Dec 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 5 Simge Simsek and Cansel Yormaz The aim of this paper is to apply the necessary and sufficient conditions of well-known Lagrangian equations with time dependent case for Minkowski 4-space. Many fundamental geometrical properties for time dependent Minkowski 4-space have been obtained in this paper. The energy equations have been applied to the numerical example in order to test its performance. In the numerical examples, we have studied with two time parameters (earth and space time) for accordance to Minkowski 4-space coordinates. This idea is an interesting approach to energy function with Earth-time and Space-time in physical comment. Moreover, velocity and two time dimensions for energy movement equations have been presented a new concept. This study show some physical application of those equations and interpretations are made in Minkowski space too. Results showed that Lagrangian functions for any surface are same type and depend on time coordinates. PubDate: Dec 2017

Abstract: Publication date: Dec 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 5 Mihail Cocos and Kent Kidman A necessary condition for a connection in a vector bundle to be locally metric is for its curvature matrix, which consists of 2 forms, to be skew symmetric with respect to some local frame. In this paper we give a simple algorithm that can be used to decide when a matrix of 2 forms is equivalent to a skew symmetric matrix. We apply this algorithm to verify whether a full rank curvature connection is locally metric. PubDate: Dec 2017

Abstract: Publication date: Dec 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 5 Naeem Salem and Said Beloul The aim of this paper is to establish some common fixed point results for two weakly subsequentially continuous and compatible of type (E) pairs of self mappings via implicit relation in modified intuitionistic fuzzy metric spaces, also we give an example to illustrate our results. PubDate: Dec 2017

Abstract: Publication date: Dec 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 5 R. Marta García Fernández and Miguel V. Carriegos Linear systems with constant real coefficients are completely described in terms of feedback actions. In this paper the problem is studied in the framework of linear systems where coefficients depending continuously on a set of parameters. Some invariants are given as well as criteria to find a complete classification in low dimension. PubDate: Dec 2017

Abstract: Publication date: Apr 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 2 András Simonovits In van Groezen, Leers and Meijdam (2003) (for short, GLM), the government pays child support and pensions to raise fertility and replace the insufficient old-age saving of myopic workers, respectively. Concentrating on the equilibrium core of GLM, we analyze its simplest possible versions. We impose credit constraint on workers, and extend GLM's analysis to heterogeneous rearing costs and preferences for enjoying children. Two major results: (i) the infusion of public transfers only raises social welfare when the bulk of private savings has been crowded out; (ii) the introduction of fertility-dependent pensions raises average fertility but diminishes welfare. PubDate: Apr 2017

Abstract: Publication date: Apr 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 2 Michael Scarinci Katherine Encarnacion Angel R. Pineda and Lance S. Evans Plants of the many subspecies of Artemisia tridentata are dominant shrubs of the Great Basin Desert of the United States. Many subspecies of Artemisia tridentata show extensive eccentric growth in which vascular cambium dies and no longer produces secondary xylem in stems. The purpose of this study was to create three-dimensional images of xylary rings from stem segments so that characteristics of individual xylary rings among successive segments could be accurately represented. Four stem segments from a branch were sized and aligned in MATLAB. Three xylary rings were given a unique color for visualization. All portions of images were removed so only the xylary rings were visible. Rings of the four segments were aligned to make a three-dimensional visualization. The images were analyzed to determine the locations of complete rings, locations of partial rings, percentages of arcs of rings of individual rings, and calculations of ring areas. Eccentric growth is localized. For example, on one stem segment all three rings were complete while the next segment 20 mm along the stem had two incomplete rings. The visualization and resulting data generated provide information about eccentric growth which, in turn, reflects the overall health and mechanical stability of stems. PubDate: Apr 2017

Abstract: Publication date: Apr 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 2 Andrei Zelenyy and Alexey Bunyakin This article presents numerical simulation of planar potential flow around an airfoil with possibility of changing its shape. Two-dimensional unsteady flow model with scalar velocity potential, which allows us to calculate pressure distribution along an airfoil from Cauchy-Lagrange integral, is used. For this purpose, an airfoil contour is approximated by a complex cubic spline with possibility of displacement its vertices. This algorithm has been used in the context of fluid-structure interaction and has been applied successfully to determination of stability of an elastic airfoil segment interacting with a flow stream, so-called panel flutter problem. Calculation of external flow is carried out by vortex panel method with Kutta-Joukowski trailing edge condition, which makes mathematical solution unique. Using this method of approximation of an airfoil in combination with the method of discrete vortices provides a semi-analytical solution for complex potential for whole computational domain of air flow. This solution significantly accelerates process of numerical computation of time-averaged aerodynamic force as well as the dynamic stability problem for aeroelastic wing design and temporal evolution of its natural disturbances. PubDate: Apr 2017

Abstract: Publication date: Apr 2017 Source:Universal Journal of Applied Mathematics Volume 5 Number 2 Yasar Pala and Mutlu Ozgur Ertas In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method doesn't require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at a first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples. PubDate: Apr 2017