MathLAB Journal http://purkh.com/index.php/mathlab <p>MathLAB is an&nbsp;open access, peer-reviewed, international journal publishing original research works of high standard in all areas of pure and applied mathematics. Publication Frequency MathLAB publishes one volume per year. Usually a volume consists of three issues with about 200 pages each.</p> en-US <p>Authors retain the copyright of their manuscripts, and all Open Access articles are distributed under the terms of the&nbsp;<a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License</a>, which permits unrestricted use, distribution, and reproduction in any medium, provided that the original work is properly cited.</p> <p>&nbsp;</p> rajinderpal@khalsacollege.edu.in (Rajinderpal Kaur) editor@purkh.com (Gurdev Singh) Tue, 30 Apr 2019 00:00:00 +0000 OJS 3.1.2.1 http://blogs.law.harvard.edu/tech/rss 60 Garay’s Condition of Deformed Cylindrical and Translation Surfaces in E3 http://purkh.com/index.php/mathlab/article/view/98 <p>The motivation of the present work is to develop the finiteness property in our work [1, 2, 3, 4] by using Garay’s condition [5]. The mean curvature flow and the finiteness property of the cylindrical surfaces in E3 are investigated. Additionally, the linear deformation of such surfaces is studied. Finally, the translation surfaces are discussed.</p> Hamdy N. Abd-Ellah, M. A. Soliman, S. A. Hassan, S. Q. Saleh Copyright (c) 2019 Hamdy N. Abd-Ellah, M. A. Soliman, S. A. Hassan, S. Q. Saleh https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/98 Tue, 30 Apr 2019 10:51:45 +0000 Permutation Groups with Bounded Movement having Maximum Orbits http://purkh.com/index.php/mathlab/article/view/248 <p>Let G be a permutation group on a set with no fixed points in and let m be a positive integer.If no element of G moves any subset of by more than m points (that is, if |</p> behnam razzaghmaneshi Copyright (c) 2019 behnam razzaghmaneshi https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/248 Tue, 30 Apr 2019 10:54:11 +0000 Approximation of Solutions of Monotone Variational Inequality Problems with Applications in Real Hilbert Spaces http://purkh.com/index.php/mathlab/article/view/253 <p>In this paper, variational inequality problem which hinges on operators of monotone type is studied, and an iterative algorithm which is a modification of extragradient method is proposed for approximation of solution (assuming existence) of the variational inequality problem. Weak and strong convergence theorems are obtained and as applications, the iterative scheme proposed is shown to also approximate fixed points of pseudocontractive mappings, zeros of monotone mappings and solutions of equilibrium problems. A numerical example is given to show the functionality of the scheme studied. The results obtained improve and unify the corresponding results of several authors.</p> Eric Uwadiegwu Ofoedu, Bona Chimezie Osigwe, Kingsley Obinna Ibeh, Genevieve Chinenye Ezeamama Copyright (c) 2019 Eric Uwadiegwu Ofoedu, Bona Chimezie Osigwe, Kingsley Obinna Ibeh, Genevieve Chinenye Ezeamama https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/253 Thu, 18 Apr 2019 00:00:00 +0000 Nonlinear Vibration of Piezoelectric Nano Biological Sensor Based on Non-Classical Mathematical Approach http://purkh.com/index.php/mathlab/article/view/256 <p>In this study, nonlinear vibration analysis of a parametrically excited piezoelectric nano beam subjected to DC and AC voltages is investigated for biological sensor applications on the basis of the non-local continuum theory. Equations of the motion and boundary conditions of the nano beam are obtained by implementation of Hamilton’s principle and the Galerkin approach. Hamiltonian solution namely Frequency-Amplitude approach is used for natural frequencies and mode shapes as a function of the piezo-layered nano beam characteristic non-local size scale parameter. The size effects on the vibration behavior (frequency and harmonic response) of the beam are studied and it is found that the non-local parameter has significant effects on the free vibration of system.</p> Sayyid H. Hashemi Kachapi, S.GH. Hashemi Kachapi Copyright (c) 2019 Sayyid H. Hashemi Kachapi, S.GH. Hashemi Kachapi https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/256 Tue, 30 Apr 2019 11:24:54 +0000 The Norms Over Anti Fuzzy G-submodules http://purkh.com/index.php/mathlab/article/view/270 <p>In this study, we define anti fuzzy-submodules with respect to investigate some of their algebraic properties. Later we introduce the union and direct sum of&nbsp;them and finally, we prove that the union, direct sum, homomorphic images and pre images of&nbsp;them are also anti fuzzy</p> rasul rasuli Copyright (c) 2019 rasul rasuli https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/270 Thu, 18 Apr 2019 00:00:00 +0000 Extending the Applicability of an Efficient Fifth Order Method Under Weak Conditions in Banach Space http://purkh.com/index.php/mathlab/article/view/289 <p>We extend the applicability of an efficient fifth order method for solving Banach space valued equations. To achieve this we use weaker Lipschitz-type conditions in combination with our idea of the restricted convergence region. Numerical examples are used to compare our results favorably to the ones in earlier works.</p> Santhosh George, Ioannis K. Argyros Copyright (c) 2019 Santhosh George, Ioannis K. Argyros https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/289 Thu, 18 Apr 2019 00:00:00 +0000 Impulsive Control for Exponential Stability of Neural Networks with Time-varying Delay http://purkh.com/index.php/mathlab/article/view/291 <p>In this paper we investigate the exponential stability of impulsive control for neural networks with time-varying delay by using a Lyapunov-Krasovskii functional. One numerical example is given to demonstrate the effectiveness of the obtained results.</p> Jianli Li, Xinni Tu Copyright (c) 2019 Jianli Li, Xinni Tu https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/291 Thu, 18 Apr 2019 00:00:00 +0000 An Introduction To Complex Arithmetic and an Original Reformulation of the Goldbach Conjecture http://purkh.com/index.php/mathlab/article/view/296 <p>In this paper, we give an original reformulation of the Goldbach conjecture via complex arithmetic calculus. This reformulation shows that the Goldbach conjecture can be attacked without using strong investigations that have been on this conjecture in the past.</p> Ikorong Annouk Copyright (c) 2019 Ikorong Annouk https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/296 Tue, 30 Apr 2019 11:08:25 +0000 A Robust Mantel-Haenszel Test using Probabilistic Approach http://purkh.com/index.php/mathlab/article/view/303 <p>Mantel-Haenszel test statistic is one of the common test statistics for test of significance variation between/among factors and its application is similar to One-way Analysis of Variance and Kruskal-Wallis test statistics. The method can be categorized as non-parametric and robust in nature. It has been used over time by researchers for test of significance variation among factors. Critical look at the test statistic reveals it weakness which is inability to remove variation among factors in terms of sample size or weight. To remove biasness in the test of hypothesis with Mantel-Haenszel test as the statistic, there is need for proper and appropriate modification. This paper addressed the noticed short fall of the test statistic with illustrative example for easy computation by users. Similar data used by researchers in the past was also used in the study using the propose method called modified Mantel-Haenszel test statistic.</p> Awopeju K. Abidemi, Umeh Edith Uzoma, Ajibade Bright F. Copyright (c) 2019 Awopeju K. Abidemi, Umeh Edith Uzoma, Dr., Ajibade Bright F., Dr. https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/303 Tue, 30 Apr 2019 11:10:28 +0000 Extension of Linear Operators and Polynomial Approximation, with Applications to Markov Moment Problem and Mazur-Orlicz Theorem http://purkh.com/index.php/mathlab/article/view/307 <p>One recalls the relationship between the Markov moment problem and extension of linear functionals (or operators), with two constraints. One states necessary and sufficient conditions for the existence of solutions of some abstract vector-valued Markov moment problems, by means of a general Hahn-Banach principle. The classical moment problem is discussed as a particular important case. A short section is devoted to applications of polynomial approximation in studying the existence and uniqueness of the solutions for two types of Markov moment problems. Mazur-Orlicz theorem is also recalled and applied. We use general type results in studying related problems which involve concrete spaces of functions and self-adjoint operators. Sometimes, the uniqueness of the solution follows too. Most of our solutions are operator-valued or function-valued.</p> Octav Olteanu Copyright (c) 2019 Octav Olteanu https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/307 Tue, 30 Apr 2019 11:12:43 +0000 Some New Results on the Curvatures of the Spherical Indicatrices of the Involutes of a Spacelike Curve with a Spacelike Binormal in Minkowski 3-Space http://purkh.com/index.php/mathlab/article/view/310 <p>In the present paper, we deal with the spherical indicatrices of involutes of a given spacelike curve with spacelike binormal. Then we give some important relationships between arc lengths and geodesic curvatures of the base curve and its involutes in Minkowski 3-sapace. Also, some important results are given for these curves.</p> Mustafa Bilici, Mustafa Çalışkan Copyright (c) 2019 Mustafa Bilici, Mustafa Çalışkan https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/310 Tue, 30 Apr 2019 11:19:11 +0000 Lie-B¨acklund Transformations and Symmetries approach to exactly solvable evolution For Soliton Equation http://purkh.com/index.php/mathlab/article/view/322 <p><span class="fontstyle0">In this paper, we obtain well-known B¨acklund transformations of several equationsv by applying Symmetries methods . We indicate by examples how symmetries of a system of differential equations . Also, these equations may be combined with a B¨acklund&nbsp;map for the system to produce another B¨acklund map.&nbsp;Finally we show that one can obtain Symmetries of Soliton equations from their B¨acklund&nbsp;Transformations.We explain briefly the conceptsof LB trasformation group,infinitesimal&nbsp;LB symmetries and the associated evolution equations and the methods of obtaining&nbsp;them.</span></p> Manal S.I. Zaki Copyright (c) 2019 Manal S.I. Zaki https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/322 Tue, 30 Apr 2019 00:00:00 +0000 Invariant Solutions of Generalized Fisher-KPP Equation http://purkh.com/index.php/mathlab/article/view/324 <p>‎In this paper‎, ‎we consider a hyperbolic generalized Fisher-KPP equation‎: ‎$\varepsilon^2 u_{tt}‎ + ‎g(u) u_t = ( k(u) u_x )_x‎ +‎f(u)$ where $f$‎, ‎$g$ ‎‎‎and $k$ are arbitrary smooth functions of variable $u$ and $\varepsilon$ is a speed parameter‎. ‎We find invariant solutions by Lie method‎. ‎Also‎, ‎we study standard and weak conditional and approximate symmetries‎.</p> Mehdi Nadjafikhah Copyright (c) 2019 Mehdi Nadjafikhah https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/324 Tue, 30 Apr 2019 00:00:00 +0000 Study of Einstein Solutions And Symmetries of Type N Pure Radiation Field http://purkh.com/index.php/mathlab/article/view/336 <p>In the present research paper, we study Einstein solitons with a physical interpretation of the notion of the vector field associated with Einstein solitons. We investigate the geometrical symmetries of Petrov type <em>N</em> pure radiation fields along the vector field also associated with Einstein solitons.</p> Mohd Anall Ali Copyright (c) 2019 Mohd Anall Ali https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/336 Tue, 30 Apr 2019 00:00:00 +0000 Analysis of Qualitative Behavior of Fifth Order Difference Equations http://purkh.com/index.php/mathlab/article/view/338 <p>The main aim of this paper is to investigate the stability, global attractivity and periodic nature of the solutions of the difference equationsThe main aim of this paper is to investigate the stability, global attractivity and periodic nature of the solutions of the difference equations<br> x_{n+1}=ax_{n-1}±((bx_{n-1}x_{n-2})/(cx_{n-2}±dx_{n-4})),&nbsp; &nbsp; n=0,1,2,...,&nbsp;<br>where the initial conditions x₋₄, x₋₃ ,x₋₂, x₋₁ and x₀ are arbitrary positive real numbers and a, b, c, d are constants.</p> Marwa Mohammed Alzubaidi Copyright (c) 2019 Marwa Mohammed Alzubaidi https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/338 Tue, 30 Apr 2019 00:00:00 +0000 Wilf's Formula and a Generalization of the Choi-Lee-Srivastava Identities http://purkh.com/index.php/mathlab/article/view/343 <p>The identities of Choi, Lee, and Srivastava imply a formula proposed by Wilf. We show that these identities are immediate consequences of the well-known product formulas for the sine function and the cosine function. Moreover, we prove a generalization.</p> Ulrich Abel Copyright (c) 2019 Ulrich Abel https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/343 Tue, 30 Apr 2019 00:00:00 +0000 Markov Moment Problems and Mazur-Orlicz Theorems in Concrete Spaces http://purkh.com/index.php/mathlab/article/view/351 <p>One solves Markov moment and Mazur-Orlicz problems in concrete spaces of functions and respectively operators. One uses earlier results, as well as recent theorems on the subject. One characterizes the existence of a solution, or one gives sufficient conditions for it does exist. Sometimes the uniqueness of the solution of some moment problems follows too. Spaces of continuous, of integrable and respectively analytic functions are considered as domain space of the solution. Usually, an order complete Banach lattice of self-adjoint operators (the bicommutant) is the target-space. Results on the abstract Markov moment problem, the abstract version of Mazur-Orlicz theorem and appropriate knowledge in functional analysis are applied. Basic elements of measure theory and Cauchy inequalities are used as well.</p> Octav Olteanu Copyright (c) 2019 Octav Olteanu https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/351 Tue, 30 Apr 2019 00:00:00 +0000 On Markov Moment Problem and Related Inverse Problems http://purkh.com/index.php/mathlab/article/view/352 <p>Existence and construction of the solutions of some Markov moment problems are discussed. Starting from the moments of a solution, one recalls a method of recovering this solution, also solving approximately related systems with infinite many nonlinear equations and infinite unknowns. This is the first aim of this work. Extension of linear forms with two constraints, as well as measure theory results is applied. Secondly, existence of the solutions of special Markov moment problems is studied. &nbsp;</p> Octav Olteanu Copyright (c) 2019 Octav Olteanu https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/352 Tue, 30 Apr 2019 00:00:00 +0000 Distribution of Decision Power among the Parties and Coalitions in the 44th Bulgarian Parliament as a Weighted Voting Game http://purkh.com/index.php/mathlab/article/view/356 <p>Weighted voting games are a class of cooperative games that model group decision making systems in various domains, such as parliaments. One of the main challenges in a weighted voting game is to measure of player influence in decision making. This problem is fundamental in game theory and political science. In this paper we consider the 2017 Bulgarian Election and the distribution of decision power among the parties and coalitions in the 44<sup>th</sup> Bulgarian Parliament.</p> Zdravko Dimitrov Slavov Copyright (c) 2019 Zdravko Dimitrov Slavov https://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/356 Tue, 30 Apr 2019 00:00:00 +0000