JOURNAL OF ADVANCES IN MATHEMATICS 2019-10-04T07:03:15+00:00 Gurpal Kaur Open Journal Systems Interested in submitting to this journal? We recommend that you review the About the Journal page for the journal's section policies, as well as the Author Guidelines. Authors need to register with the journal prior to submitting or, if already registered, can simply log in and begin the five-step process. A Lie Symmetry Solutions of Sawada-Kotera Equation 2019-09-30T18:04:32+00:00 Winny Chepngetich Bor Owino M. Oduor John K. Rotich <p>In this article, the Lie Symmetry Analysis is applied in finding the symmetry solutions of the fifth order Sawada-Kotera equation. The technique is among the most powerful approaches currently used to achieveprecise solutions of the partial differential equations that are nonlinear. We systematically show the procedure to obtain the solution which is achieved by developing infinitesimal transformation, prolongations, infinitesimal generatorsand invariant transformations hence symmetry solutions of the fifth order Sawada-Kotera equation.</p> <p><strong><em>Key Words</em></strong>- Lie symmetry analysis. Sawada-Kotera equation. Symmetry groups. Prolongations. Invariant solutions. Power series solutions. Symmetry solutions.</p> 2019-07-30T09:35:48+00:00 Copyright (c) 2019 Winny Chepngetich Bor, Owino M. Oduor, John K. Rotich Breaking Boundaries: Discovering the Impossible Counterproof of Beal’s Conjecture 2019-09-30T18:05:37+00:00 Halima Jibril Mohamed Adela Zyfi Ghedlawit Futzum <p>This paper will attempt to logically differentiate between two types of fractions and discuss the idea of Zero as a neutral integer. This logic can then be followed to create a counterexample and a proof for Beal’s conjecture.</p> 2019-07-23T00:00:00+00:00 Copyright (c) 2019 Halima Jibril Convergence of the Collatz Sequence 2019-09-30T18:04:53+00:00 Anatoliy Nikolaychuk <p>For any natural number was created the supplement sequence, that is convergent together with the original Collatz sequence. The numerical parameter - index was defined, that is the same for both sequences. This new method provides the following results:</p> <ol> <li>All natural numbers were distributed into six different classes;</li> <li>The properties of index were found for the different classes;</li> <li>For any natural number was constructed the bounded sequence of increasing numbers,</li> </ol> <p>&nbsp;&nbsp;&nbsp; that is convergent together with the regular Collatz sequence.</p> 2019-07-23T00:00:00+00:00 Copyright (c) 2019 Anatoliy Nikolaychuk Karp's Theorem in Inverse Obstacle Scattering Problems 2019-09-30T18:04:12+00:00 Jaemin Shin <p>In this work, we provide a proof of the so-called Karp's theorem in a different approach. We&nbsp;use the unique continuation principle together with the monotonicity of eigenvalues for the&nbsp;negative Laplace operator. This method is new and would be applicable to other types of&nbsp;inverse scattering problems.</p> 2019-08-14T09:22:01+00:00 Copyright (c) 2019 Jaemin Shin Division And Combination In Linear Algebra 2019-09-30T18:03:50+00:00 Liang Fang Rui Chena <p>In this paper, the relationship between matrix operation, linear equations, linear representation of vector groups and linear correlation is discussed, and the idea of division and combination in linear algebra is discussed to help learners understand the connections between various knowledge points of linear algebra from multiple angles, deep levels, and high dimensions.</p> 2019-09-06T00:00:00+00:00 Copyright (c) 2019 Liang Fang, Rui Chena Numerical Solutions of Nonlinear Ordinary Differential Equations by Using Adaptive Runge-Kutta Method 2019-09-30T18:03:05+00:00 Abhinandan Chowdhury Sammie Clayton Mulatu Lemma <p>We present a study on numerical solutions of nonlinear ordinary differential equations by applying Runge-Kutta-Fehlberg (RKF) method, a well-known adaptive Runge-kutta method. The adaptive Runge-kutta methods use embedded&nbsp;integration formulas which appear in pairs. Typically adaptive methods monitor the truncation error at each integration&nbsp;step and automatically adjust the step size to keep the error within prescribed limit. Numerical solutions to different&nbsp;nonlinear initial value problems (IVPs) attained by RKF method are compared with corresponding classical Runge-Kutta&nbsp;(RK4) approximations in order to investigate the computational superiority of the former. The resulting gain in efficiency is compatible with the theoretical prediction. Moreover, with the aid of a suitable time-stepping scheme, we&nbsp;show that the RKF method invariably requires less number of steps to arrive at the right endpoint of the finite interval&nbsp;where the IVP is being considered.</p> 2019-09-16T04:56:12+00:00 Copyright (c) 2019 Abhinandan Chowdhury A Parametric Approach for Solving Interval–Valued fractional Continuous Static Games 2019-09-30T18:03:29+00:00 Mervat Elshafei <p>The aim of this paper is to show that a parametric approach can be used to solve fractional continuous static games with interval-valued in the objective function and in the constraints. In this game, cooperation among all the players is possible, and each player helps the others up to the point of disadvantage to himself, so we use the Pareto-minimal solution concept to solve this type of game. The Dinkelbach method is used to transform fractional continuous static games into non- fractional continuous static games. Moreover, an algorithm with the corresponding flowchart to explain the suggested approach is introduced. Finally, a numerical example to illustrate the algorithm’s steps is given.</p> 2019-09-16T04:42:34+00:00 Copyright (c) 2019 Mervat Elshafei Angle Trisection 2019-09-30T18:02:45+00:00 Mehryar Husyan Pour Shad <p>We seek to increase the development of science, but there are several fundamental questions about what is. Without solving the question is a false reflection of the history of science and the beginning of cognition. We know that their investigation and resolution, with the exception of rooting and knowledge of morphophonemic, do not come. Research on certain natural or pure mathematical phenomena is an example of my fundamental research that will lead to the definition of general principles and scientific theories.</p> 2019-09-16T04:59:03+00:00 Copyright (c) 2019 Mehryar Husyan Pour Shad Fuzzy Graphs 2019-10-04T07:03:15+00:00 Huda Mutab Al Mutab <p>In this paper, neighbourly irregular fuzzy graphs, neighbourly total irregular fuzzy graphs, highly irregular fuzzy graphs and highly total irregular fuzzy graphs are introduced. A necessary and sufficient condition under which neighbourly irregular and highly irregular fuzzy graphs are equivalent is provided. We define d2 degree of a vertex in fuzzy graphs and total d2 -degree of a vertex in fuzzy graphs and (2, k)-regular fuzzy graphs, totally (2, k)- regular fuzzy graphs are introduced. (2, k)- regular fuzzy graphs and totally (2, k)-regular fuzzy graphs are compared through various examples.</p> 2019-10-03T04:39:14+00:00 Copyright (c) 2019 Huda Mutab Al Mutab