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KHALSA PUBLICATIONS en-US JOURNAL OF ADVANCES IN MATHEMATICS 2347-1921 <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> Congruences on *-Simple Type A I-Semigroups https://cirworld.com/index.php/jam/article/view/7980 <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> Ugochukwu Ndubuisi Asibong-Ibe U.I Udoaka O.G ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2019-01-31 2019-01-31 16 8199 8207 10.24297/jam.v16i0.7980 Some Techniques to Compute Multiplicative Inverses for Advanced Encryption Standard https://cirworld.com/index.php/jam/article/view/8016 <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> Waleed Eltayeb Ahmed ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2019-01-31 2019-01-31 16 8208 8212 10.24297/jam.v16i0.8016 Some modifications on RCAM for getting accurate closed-form approximate solutions of Duffing- and Lienard-type equations https://cirworld.com/index.php/jam/article/view/8017 <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> Prakash Kumar Das Debabrata Singh Madan Mohan Panja ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2019-01-31 2019-01-31 16 8213 8225 10.24297/jam.v16i0.8017 A Unique Solution of Stochastic Partial Differential Equations with Non-Local Initial condition https://cirworld.com/index.php/jam/article/view/8018 <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> Mahmoud Mohammed Mostafa El-Borai A. Tarek S.A. ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2019-01-31 2019-01-31 16 8226 8233 10.24297/jam.v16i0.8018 The Hermite Hadamard Inequality on Hypercuboid https://cirworld.com/index.php/jam/article/view/8053 <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> Mohammad W Alomari ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2019-01-31 2019-01-31 16 8234 8246 10.24297/jam.v16i0.8053 Solutions of Some Difference Equations Systems and Periodicity https://cirworld.com/index.php/jam/article/view/8057 <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> Elsayed M. Elsayed Faris Alzahrani Ibrahim Abbas N. H. Alotaibi ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2019-01-31 2019-01-31 16 8247 8261 10.24297/jam.v16i0.8057 On the Navier-Stokes problem https://cirworld.com/index.php/jam/article/view/8088 <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> Alexander G. Ramm ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2019-01-31 2019-01-31 16 8262 8266 10.24297/jam.v16i0.8088 Inverse Scattering with Non-Over-Determined Data https://cirworld.com/index.php/jam/article/view/8089 <p>The results of the author’s theory of the inverse scattering with non-over-determined&nbsp;data are described.</p> Alexander G. Ramm ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2019-01-31 2019-01-31 16 8267 8271 10.24297/jam.v16i0.8089 Intransitive Permutation Groups with Bounded Movement Having Maximum Degree https://cirworld.com/index.php/jam/article/view/8091 <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> Behnam Razzagh ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2019-01-31 2019-01-31 16 8272 8279 10.24297/jam.v16i0.8091 Existence and Uniqueness of Abstract Stochastic Fractional-Order Differential Equation https://cirworld.com/index.php/jam/article/view/8097 <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> Mahmoud Mohammed Mostafa El-Borai A. Tarek S.A. ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2019-01-31 2019-01-31 16 8280 8287 10.24297/jam.v16i0.8097