JOURNAL OF ADVANCES IN MATHEMATICS 2019-03-21T11:46:54+00:00 Gurdev Singh 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. Congruences on *-Simple Type A I-Semigroups 2019-03-21T11:46:44+00:00 Ugochukwu Ndubuisi Asibong-Ibe U.I Udoaka O.G <p>This paper obtains a characterisation of the congruences on *-simple type A I-semigroups. The *-locally idempotent-separating congruences, strictly *-locally idempotent-separating congruences and minimum cancellative monoid congruences, are characterised.</p> 2019-01-31T04:25:40+00:00 ##submission.copyrightStatement## Some Techniques to Compute Multiplicative Inverses for Advanced Encryption Standard 2019-03-21T11:46:42+00:00 Waleed Eltayeb Ahmed <p>This paper gives some techniques to compute the set of multiplicative inverses, which uses in the Advanced Encryption Standard (AES).</p> <p>&nbsp;</p> 2019-01-31T04:25:51+00:00 ##submission.copyrightStatement## Some modifications on RCAM for getting accurate closed-form approximate solutions of Duffing- and Lienard-type equations 2019-03-21T11:46:40+00:00 Prakash Kumar Das Debabrata Singh Madan Mohan Panja <p>In this work, authors propose some modifications Adomian decomposition method to get some accurate closed form&nbsp;approximate or exact solutions of Duffing- and Li´enard-type nonlinear ordinary differential equations.<br>Results obtained by the revised scheme have been exploited subsequently to derive constraints among parameters&nbsp;to get the solutions to be bounded. The present scheme appears to be efficient and may be regarded as&nbsp;the confluence of apparently different methods for getting exact solutions for a variety of nonlinear ordinary&nbsp;differential equations appearing as mathematical models in several physical processes.</p> 2019-01-31T04:26:04+00:00 ##submission.copyrightStatement## A Unique Solution of Stochastic Partial Differential Equations with Non-Local Initial condition 2019-03-21T11:46:37+00:00 Mahmoud Mohammed Mostafa El-Borai A. Tarek S.A. <p>In this paper, we shall discuss the uniqueness ”pathwise uniqueness”&nbsp;of the solutions of stochastic partial differential equations (SPDEs) with&nbsp;non-local initial condition,<br><img src="/public/site/images/mel-borai/222.JPG"><br>We shall use the Yamada-Watanabe condition for ”pathwise uniqueness”&nbsp;of the solutions of the stochastic differential equation; this condition is&nbsp;weaker than the usual Lipschitz condition. The proof is based on Bihari’s<br>inequality.</p> 2019-01-31T04:26:15+00:00 ##submission.copyrightStatement## The Hermite Hadamard Inequality on Hypercuboid 2019-03-21T11:46:35+00:00 Mohammad W Alomari <p>Given any a := (a1; a2,... ; an) and b := (b1; b2;... ; bn) in Rn.&nbsp;The n-fold convex function dened on [a; b], a; b 2 Rn with a &lt; b is a convex&nbsp;function in each variable separately. In this work we prove an inequality of&nbsp;Hermite-Hadamard type for n-fold convex functions. Namely, we establish the&nbsp;inequality</p> <p><img src="/public/site/images/editor/Untitled_11112.png"></p> <p><img src="/public/site/images/editor/Untitled_32.png"></p> 2019-01-31T04:26:19+00:00 ##submission.copyrightStatement## Solutions of Some Difference Equations Systems and Periodicity 2019-03-21T11:46:33+00:00 Elsayed M. Elsayed Faris Alzahrani Ibrahim Abbas N. H. Alotaibi <p>In this article, analysis and investigation have been conducted on the periodic&nbsp;nature as well as the type of the solutions of the subsequent schemes of&nbsp;rational difference equations</p> <p><img src="/public/site/images/editor/Untitled1.png" width="336" height="58"><br>with a nonzero real numbers initial conditions.</p> 2019-01-31T04:26:23+00:00 ##submission.copyrightStatement## On the Navier-Stokes problem 2019-03-21T11:46:54+00:00 Alexander G. Ramm <p>One of the millennium problems is discussed. The results of the author’s solution to&nbsp;this problem are explained. The problem discussed is the Navier-Stokes problem in the&nbsp;whole space.</p> 2019-01-31T00:00:00+00:00 ##submission.copyrightStatement## Inverse Scattering with Non-Over-Determined Data 2019-03-21T11:46:52+00:00 Alexander G. Ramm <p>The results of the author’s theory of the inverse scattering with non-over-determined&nbsp;data are described.</p> 2019-01-31T00:00:00+00:00 ##submission.copyrightStatement## Intransitive Permutation Groups with Bounded Movement Having Maximum Degree 2019-03-21T11:46:49+00:00 Behnam Razzagh <p>Let G be a permutation group on a set <img src="/public/site/images/editor/CaptureO.PNG">with no fixed points&nbsp;in <img src="/public/site/images/editor/CaptureO1.PNG">and let m be a positive integer. If for each subset <img src="/public/site/images/editor/Capture_ell.PNG">of&nbsp;<img src="/public/site/images/editor/CaptureO2.PNG"> the&nbsp;size&nbsp;<img src="/public/site/images/editor/Capture_ell2.PNG"> is bounded, for <img src="/public/site/images/editor/Captureg.PNG">, we define the movement of g as the&nbsp;max&nbsp;<img src="/public/site/images/editor/Capture_ell21.PNG"> over all subsets <img src="/public/site/images/editor/Capture_ell1.PNG">of <img src="/public/site/images/editor/CaptureO3.PNG">. In this paper we classified all of&nbsp;permutation groups on set <img src="/public/site/images/editor/CaptureO4.PNG">of size 3m + 1 with 2 orbits such that&nbsp;has movement m .&nbsp;2000 AMS classification subjects: 20B25</p> 2019-01-31T00:00:00+00:00 ##submission.copyrightStatement## Existence and Uniqueness of Abstract Stochastic Fractional-Order Differential Equation 2019-03-21T11:46:47+00:00 Mahmoud Mohammed Mostafa El-Borai A. Tarek S.A. <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">In this paper, the existence and uniqueness about the solution for a class of abstract stochastic fractional-order differential equations</p> <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<img src="/public/site/images/editor/Capture_new1.PNG"></p> <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">where&nbsp;<img src="/public/site/images/editor/Capture_new2.PNG"> in and&nbsp;<img src="/public/site/images/editor/Capture_new31.PNG"> are given functions, are investigated, where the fractional derivative is described in Caputo sense. The fractional calculus, stochastic analysis techniques and the standard $Picard's$ iteration method are used to obtain the required.</p> 2019-01-31T00:00:00+00:00 ##submission.copyrightStatement## Initial Value Problem for Stochastic Hyprid Hadamard Fractional Differential Equation 2019-03-21T11:46:30+00:00 Mahmoud Mohammed Mostafa El-Borai Wagdy G. El-sayed A. A. Badr Ahmed Tarek Sayed <p>In this paper, we discuss the existence of solutions for a stochastic initial value problem of Hyprid fractional dierential equations of Hadamard&nbsp;type given by&nbsp;</p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<img src="/public/site/images/editor/Capture_jam.PNG"></p> <p>where HD is the Hadamard fractional derivative, <img src="/public/site/images/editor/Capturejam2.PNG"><img src="/public/site/images/editor/Capturejam3.PNG">and <img src="/public/site/images/editor/Capture111.PNG">is the Hadamard fractional&nbsp;integral and <img src="/public/site/images/editor/Capture.PNG">be such that <img src="/public/site/images/editor/Capture222.PNG">are investigated. The&nbsp;fractional calculus and stochastic analysis techniques are used to obtain&nbsp;the required results.&nbsp;</p> 2019-02-28T00:00:00+00:00 ##submission.copyrightStatement## A New Inexact Non-Interior Continuation Algorithm for Second-Order Cone Programming 2019-03-21T11:46:23+00:00 Liang Fang <p>Second-order cone programming has received considerable attention in the past decades because of its wide range of applications. Non-interior continuation method is one of the most popular and efficient methods for solving second-order cone programming partially due to its superior numerical performances. In this paper, a new smoothing form of the well-known Fischer-Burmeister function is given. Based on the new smoothing function, an inexact non-interior continuation algorithm is proposed. Attractively, the new algorithm can start from an arbitrary point, and it solves only one system of linear equations inexactly and performs only one line search at each iteration. Moreover, under a mild assumption, the new algorithm has a globally linear and locally Q-quadratical convergence. Finally, some preliminary numerical results are reported which show the effectiveness of the presented algorithm.</p> 2019-02-28T06:21:39+00:00 ##submission.copyrightStatement## A way to compute a greatest common divisor in the Galois field (GF (2^n )) 2019-03-21T11:46:25+00:00 Waleed Eltayeb Ahmed <p>This paper presents how the steps that used to determine a multiplicative inverse by method based on the Euclidean algorithm, can be used to find a greatest common divisor for polynomials in the Galois field (2^n ).</p> 2019-02-28T00:00:00+00:00 ##submission.copyrightStatement## On the Mixed Dirichlet--Farwig biharmonic problem in exterior domains 2019-03-21T11:46:28+00:00 Hovik A. Matevossian <p>We study the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Moreover, we study the unique solvability of the mixed Dirichlet--Farwig biharmonic problem in the exterior of a compact set under the assumption that generalized solutions of these problems has a bounded Dirichlet integral with weight $|x|^a$. Admitting different boundary conditions, we used the variation principle and depending on the value of the parameter $a$, we obtained uniqueness (non-uniqueness) theorems of the problem or present exact formulas for the dimension of the space of solutions.</p> 2019-02-28T00:00:00+00:00 ##submission.copyrightStatement##