JOURNAL OF ADVANCES IN MATHEMATICS 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. 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="">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 <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## 2019-01-31 2019-01-31 16 8199 8207 10.24297/jam.v16i0.7980 Some Techniques to Compute Multiplicative Inverses for Advanced Encryption Standard <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## 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 <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## 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 <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## 2019-01-31 2019-01-31 16 8226 8233 10.24297/jam.v16i0.8018 The Hermite Hadamard Inequality on Hypercuboid <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## 2019-01-31 2019-01-31 16 8234 8246 10.24297/jam.v16i0.8053 Solutions of Some Difference Equations Systems and Periodicity <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## 2019-01-31 2019-01-31 16 8247 8261 10.24297/jam.v16i0.8057 On the Navier-Stokes problem <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## 2019-01-31 2019-01-31 16 8262 8266 10.24297/jam.v16i0.8088 Inverse Scattering with Non-Over-Determined Data <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## 2019-01-31 2019-01-31 16 8267 8271 10.24297/jam.v16i0.8089 Intransitive Permutation Groups with Bounded Movement Having Maximum Degree <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## 2019-01-31 2019-01-31 16 8272 8279 10.24297/jam.v16i0.8091 Existence and Uniqueness of Abstract Stochastic Fractional-Order Differential Equation <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## 2019-01-31 2019-01-31 16 8280 8287 10.24297/jam.v16i0.8097 Initial Value Problem for Stochastic Hyprid Hadamard Fractional Differential Equation <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> Mahmoud Mohammed Mostafa El-Borai Wagdy G. El-sayed A. A. Badr Ahmed Tarek Sayed ##submission.copyrightStatement## 2019-02-28 2019-02-28 16 8288 8296 10.24297/jam.v16i0.8113 A New Inexact Non-Interior Continuation Algorithm for Second-Order Cone Programming <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> Liang Fang ##submission.copyrightStatement## 2019-02-28 2019-02-28 16 8297 8316 10.24297/jam.v16i0.8152 A way to compute a greatest common divisor in the Galois field (GF (2^n )) <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> Waleed Eltayeb Ahmed ##submission.copyrightStatement## 2019-02-28 2019-02-28 16 8317 8321 10.24297/jam.v16i0.8167 On the Mixed Dirichlet--Farwig biharmonic problem in exterior domains <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> Hovik A. Matevossian ##submission.copyrightStatement## 2019-02-28 2019-02-28 16 8322 8329 10.24297/jam.v16i0.8124 Comparison of Halley-Chebyshev Method with Several Nonlinear equation Solving Methods Methods <p>In this paper, we present one of the most important numerical analysis problems that we find in the roots of the nonlinear equation. In numerical analysis and numerical computing, there are many methods that we can approximate the roots of this equation. We present here several different methods, such as Halley's method, Chebyshev's method, Newton's method, and other new methods presented in papers and journals, and compare them. In the end, we get a good and attractive result.</p> Hamideh Eskandari ##submission.copyrightStatement## 2019-03-29 2019-03-29 16 8330 8333 10.24297/jam.v16i0.8169 For some boundary Value Problems in Distributions <p>In this paper we give a result concerning convergent sequences of functions that give convergent sequence of distributions in &nbsp;and find the analytic representation of the distribution obtained by their boundary values. Also, we present two examples.</p> Vasko Reckovski Vesna Manova Erkovikj Bedrije Bedjeti Egzona Iseni ##submission.copyrightStatement## 2019-03-29 2019-03-29 16 83331 8339 10.24297/jam.v16i0.7958 Intransitive Permutation Groups with Bounded Movement Having Maximum Degree <p>Let G be a permutation group on a set with<img src="/public/site/images/editor/Untitled4.png" width="15" height="14">no fixed points&nbsp;in <img src="/public/site/images/editor/Untitled5.png" width="17" height="15">and let m be a positive integer. If for each subset T of <img src="/public/site/images/editor/Untitled6.png" width="18" height="16">the&nbsp;&nbsp;size |T<sup>g</sup>\T| is bounded, for gEG, we define the movement of g as the&nbsp;max|T<sup>g</sup>\T| over all subsets T of <img src="/public/site/images/editor/Untitled6.png" width="18" height="16"> . In this paper we classified all of&nbsp;permutation groups on set&nbsp;<img src="/public/site/images/editor/Untitled6.png" width="18" height="16">&nbsp; &nbsp;of size 3m + 1 with 2 orbits such that&nbsp;has movement m .&nbsp;2000 AMS classification subjects: 20B25</p> Behnam Razzagh ##submission.copyrightStatement## 2019-03-29 2019-03-29 16 8340 8347 10.24297/jam.v16i0.8136 Approximation of The Lower Operator in Nonlinear Differential Games with Non-Fixed Time <p>Approximate properties of the lower operator in nonlinear differential games with&nbsp;non-fixed time are studied.</p> I.M. Iskanadjiev ##submission.copyrightStatement## 2019-03-29 2019-03-29 16 8348 8358 10.24297/jam.v16i0.8220 The Computational Approach for Recommendation System Based on Tagging Data <p>Recommendation approaches like a platform for learning algorithm. We can use some predicted values to put them in the data pipeline forlearning. There is a hard nuance of how to calculate the similarity measurewhen we have a small number of actions at all, its not a new user or item to use cold start methods, we just have not enough quantity to say it may be interpreted like regularity. The frequency of tags what we would have fromusers will have a huge impact to predict his future taste. The article describes created a computational approach using as explicit and as implicit feedbacks from users and evaluates tags by Jaccard distance to resolve this issue. To compare results with existed numerical methods there is a comparison table that shows the high quality of the proposed approach.</p> Kateryna Nesvit ##submission.copyrightStatement## 2019-03-29 2019-03-29 16 8359 8367 10.24297/jam.v16i0.8212 The Primitive and Imprimitive Soluble Subgroups of GL(4,Pk) <p>In this paper we will determined all of the primitive and imprimitive Soluble Subgroups of GL(4,p<sup>k</sup>). It turns out that the number of types of the irreducible Soluble Subgroups in GL(4,p<sup>k</sup>)are 10 types and are M<sub>i</sub>,i=1,…,10. moreover we find these subgroups.</p> Behnam Razzagh ##submission.copyrightStatement## 2019-03-30 2019-03-30 16 8368 8375 10.24297/jam.v16i0.8217 Supra Soft b-Compact and Supra Soft b-Lindle÷F Spaces <p>The purpose of this paper is to introduce and study the concepts of supra soft&nbsp;b-compact and supra soft b-Lindelˆf spaces. Also we study several of their properties and&nbsp;characterizations in details. Furthermore, the invariance of these kinds of spaces under&nbsp;some types of supra soft mappings and their hereditary properties are also investigated</p> Jamal Mustafa ##submission.copyrightStatement## 2019-04-03 2019-04-03 16 8376 8383 10.24297/jam.v16i0.8175 New Numerical Methods for Solving Differential Equations <p>In this paper, we present new numerical methods to solve ordinary differential equations in both linear and nonlinear cases. we apply Daftardar-Gejji technique on theta-method to derive anew family of numerical method. It is shown that the method may be formulated in an equivalent way as a RungeKutta method. The stability of the methods is analyzed.</p> Osama. Y. Ababneh ##submission.copyrightStatement## 2019-01-31 2019-01-31 16 8384 8390 10.24297/jam.v16i0.8280 Influence of Mathematics in The Desertion of Higher Education <p>In the present work the different models of university desertion are analyzed, identifying the factors that have influence in the continuation of the studies of the students. These factors are essentials to defining what will be understood by university desertion and to elaborate the profile of the deserter. In the case of the Universidad de Las Américas (Quito, Ecuador), the main factors that influence the desertion are corroborated with those that have been established according to the existing bibliography and a descriptive study of these data is carried out, in order to elaborate indicators that allow us to predict the behavior of the student population with a higher risk of dropping out. An analysis is made relating the area of Mathematics and the desertion, seeing how this area influences the possibility of a student dropping out.</p> <p>&nbsp;</p> Johan Ceballos Scarlett Abalco Daniel González Guido Saltos Ximena Suquillo Mauricio Angel ##submission.copyrightStatement## 2019-04-30 2019-04-30 16 8391 8406 10.24297/jam.v16i0.8249 Aanalytical Solution for Motion Around Radiated Varying Mass Body <p>In this work we will add the radiation pressure effect of varying mass body to the model of varying mass Hamiltonian function, including Periastron effect. The problem was formulated in terms of Delaunay variables. The solution of the problem was constructed based on Delava – Hansilmair perturbation techniques. Finally we find the first order solution for the problem as time series by calculating the desired order for the D operator and variables.</p> Marwa Abdullah Bin Humaidan ##submission.copyrightStatement## 2019-04-30 2019-04-30 16 8407 8419 10.24297/jam.v16i0.8228 Calculations on a Class of Candidate Solutions for the Distortion Problem on l 2 <p>In 1994 E. Odell and Th. Schlumprecht showed that the Hilbert space (` 2 ) was arbitrarily distortable.<br>However, we do not have a defined sequence of norms that would perform this distortion. G. An-<br>droulakis and the author defined a class of norms equivalent to the Hilbert space norm. These norms<br>are candidate sequences of norms that might distort ` 2 . These norms are recursively defined and<br>calculations with these norms are quite difficult. Here we present a tool, a Python program, that<br>calculates the norms defined by G. Androulakis and the author.</p> Frank Sanacory ##submission.copyrightStatement## 2019-05-13 2019-05-13 16 8420 8422 10.24297/jam.v16i0.8223 Third Order Hamiltonian for a Binary System with Varying Masses Including Preastron Effect <p>This work concerns of the effects of the variation in the masses for two attracting bodies on the orbiter orbital elements. The formulation of the problem was done in different kind of mechanics, Newtonian, Lagrangian, and Hamiltonian. Moreover, constructing the Hamiltonian function of the varying masses of a binary system including, periastron effect, in canonical form in the extended phase space, up to third order of the small parameter ?, to be able to solve using canonical perturbation techniques. Canonical perturbation method based on Lee transformation was developed by Kamel used to remove the short periodic terms from the Hamiltonian to be able to solve the system of equations. The Hamiltonian of the system was transformed to the extended phase space by introducing two variable represents the variation of the masses and their conjugate momenta. Finally, Hamilton's equation of motions was used to drive general formula to calculate the variations in the elements due to the variations in their masses and what so called periastron effects.</p> Doaa Saleh Al-Johani M. I. El-Saftawy ##submission.copyrightStatement## 2019-05-30 2019-05-30 16 8423 8429 10.24297/jam.v16i0.8299 Spectacular Exponents: A semi modular Approach to Fast Exponentiation <p>This paper introduces a computational scheme for calculating the exponential <em>b</em><em>w</em>&nbsp;where <em>b</em> and <em>w</em> are positive integers. This two-step method is based on elementary number theory that is used routinely in this and similar contexts, especially the Chinese remainder theorem (CRT), Lagrange’s theorem, and a variation on Garner’s algorithm for inverting the CRT isomorphism. We compare the performance of the new method to the standard fast algorithm and show that for a certain class of exponents it is significantly more efficient as measured by the number of required extended multiplications.&nbsp;&nbsp; &nbsp;</p> Robert Valenza ##submission.copyrightStatement## 2019-06-04 2019-06-04 16 8430 8448 10.24297/jam.v16i0.8301