MathLAB Journal <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> PURKH en-US MathLAB Journal 2582-0389 <p>The author warrants that the article is original, written by stated author(s), has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author(s).</p> Editorial, Volume 4 (2019) <p>On behalf of the Editorial Board, it is with great pride and sincere privilege that I am writing this message to present the volume 4 (2019) of the&nbsp;<em>MathLAB JOURNAL</em>. The issue comes from a long process, and we took all the necessary steps to make it a high-caliber scientific publication. We are relying on the collaboration of all our Editors, reviewers, and contributors to make it a contemporary, lively, and relevant publication.</p> Rajinderpal Kaur Copyright (c) 2019-12-30 2019-12-30 4 Annual Reviewer Acknowledgement <p>The Editorial team of the journal would like to thank the following reviewers for their work in refereeing manuscripts during 2019</p> Rajinderpal Kaur Copyright (c) 2019 Chief Editor 2019-12-21 2019-12-21 4 A Riccati-Bernoulli Sub-ODE Method for the Resonant Nonlinear Schrödinger Equation with Both Spatio-Temporal Dispersions and Inter-Modal <p>This work uses the Riccati-Bernoulli sub-ODE method in constructing various new optical soliton solutions<br>to the resonant nonlinear Schrodinger equation with both Spatio-temporal dispersion and inter-modal dispersion. Actually, the proposed method is effective tool to solve many other nonlinear partial differential equations in mathematical physics. Moreover this method can give a new infinite sequence of solutions. These solutions are expressed by hyperbolic functions, trigonometric functions and rational functions. Finally, with the aid of Matlab release 15, some graphical simulations were designed to see the behavior of these solutions.</p> Mahmoud Abdelrahman Yasmin Omar Copyright (c) 2019 Mahmoud Abdelrahman, Yasmin Omar 2019-12-17 2019-12-17 4 1 10 Some Fractional Variational Problems Involving Caputo Derivatives <p>In this paper, we study some fractional variational problems with functionals that involve some unknown functions and their Caputo derivatives. We also consider Caputo iso-perimetric problems. Generalized fractional Euler-Lagrange equations for the problems are presented. Furthermore, we study the optimality conditions for functionals depending on the unknown functions and the optimal time T. In addition, some examples are discussed.</p> Amele Taieb Zoubir Dahmani Copyright (c) 2019 Amele TAÏEB, Zoubir DAHMANI 2019-12-21 2019-12-21 4 11 24 Some Results of Anti Fuzzy Subrings Over t-Conorms <div>In this paper, we define anti fuzzy subrings by using t-conorm&nbsp;C and study some of their algebraic properties. We consider properties of intersection, direct product and homomorphisms for anti fuzzy subbrings with respect to t-conorm C. Thereafter, we define anti fuzzy quotient subrings over t-conorm C.</div> Rasul Rasuli Copyright (c) 2019 Rasul Rasuli 2019-12-18 2019-12-18 4 25 32 Inverse Source Problem with Many Frequencies and Attenuation for One-Dimensional Domain <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <div>In this article, we consider the one-dimensional inverse source problem for Helmholtz equation with attenuation (damping) factor in a one layer medium. We establish a stability by using multiple frequencies at the two end points of the domain which contains the compact support of the source functions. The main result is an estimate which consists of two parts: the data discrepancy and the high frequency tail. We show that increasing stability possible using multi-frequency wave at the two endpoints.</div> </div> </div> </div> Elham Sohrabi Shahah Almutairi Copyright (c) 2019 Elham Sohrabi 2019-12-18 2019-12-18 4 33 40 Weak and Strong Convergence of Implicit and Explicit Algorithms for Total Asymptotically Nonexpansive Mappings <p>In this paper, we prove weak and strong convergence of implicit and explicit iterative algorithms for approximation of common fixed point of a finite family of total asymptotically nonexpansive mappings. Our recursion formulas seem more efficient than those recently announced by several authors for the same problem. Our theorems improve, generalize and extend several recently announced results.</p> Eric Uwadiegwu Ofoedu L. O. Madu Copyright (c) 2019 Eric Uwadiegwu Ofoedu, L. O. MADU 2019-12-18 2019-12-18 4 41 57 Comparisons of Alternative Axial Distances for Cuboidal Regions of Central Composite Designs Using D and G Efficiencies <p>In this study, three axial distances are proposed as alternatives to the existing axial distances of the Central Composite Design (CCD) in cuboidal design regions with the aim of providing formidable alternatives to the existing axial distances of the CCD whose prediction properties are less extreme and more stable in the cuboidal design regions. The three alternative axial distances, namely the arithmetic, harmonic and geometric axial distances for cuboidal regions, were developed algebraically based on the concepts of the three Pythagorean means. The strengths and weaknesses of the alternative axial distances were validated by comparing their performances with the existing axial distances in the cuboidal regions. The D- and G-efficiencies are used for comparison. The cuboidal region shows that the three alternative axial distances are consistently better in terms of the D- and G-efficiencies</p> Francis Eze Linus Ifeanyi Onyishi M. E. Nja E. O. Effanga Copyright (c) 2019 Francis Eze, Linus Onyishi 2019-12-18 2019-12-18 4 58 66 Giving Birth to Vectorial Coordinate Geometry II <p>This paper is an extension of the earlier work titled “Giving birth to vectorial coordinate geometry”, which appeared in volume 3 of MathLab journal in 2019. While the novel concept of vectorial coordinates has been applied in the said work for the derivation of some useful results of two-dimensional Cartesian coordinate geometry, the concept of novel vectorial coordinates has been employed in the present scheme for the derivation of some standard results of three-dimensional Cartesian coordinate geometry. The fact that Vector algebra is a more powerful mathematical tool gets justified from this study. The vectorial treatments offered are novel, simple and straight forward. Furthermore, they will enhance the deepening of thought and understanding about Vector algebra and its application. Thus this contribution will enrich the relevant literature. At the same time, it increases the range of applicability of Vector algebra as well &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</p> Pramode Ranjan Bhattacharjee Copyright (c) 2019 Pramode Ranjan Bhattacharjee 2019-12-18 2019-12-18 4 67 76 Minimizing and Evaluating Weighted Means of Special Mappings <p>A constrained optimization problem is solved, as an application of minimum principle for a sum of strictly concave continuous functions, subject to a linear constraint, firstly for finite sums of elementary such functions. The motivation of solving such problems is minimizing and evaluating the (unknown) mean of a random variable, in terms of the (known) mean of another related random variable. The corresponding result for infinite sums of the such type of functions follows as a consequence, passing to the limit. Note that in our statements and proofs the condition &nbsp;on the positive numbers &nbsp;is not essential for the interesting part of the results. So, our work refers not only to means of random variables, but to more general weighted means. A related example is given. A corresponding result for special concave mappings taking values into an order-complete Banach lattice of self-adjoint operators is also proved. Namely, one finds a lower bound for a sum of special concave mappings with ranges in the above mention order-complete Banach lattice, under a suitable linear constraint.</p> Octav Olteanu Janina Mihaela Mihăilă Copyright (c) 2019 Octav Olteanu, Janina Mihaela Mihăilă 2019-12-18 2019-12-18 4 77 86 Product of Polycyclic-By-Finite Groups (PPFG) <p>In this paper we show that If the soluble-by-finite group G=AB is the product of two polycyclic-by-finite subgroups A and B, then G is polycyclic-by-finite</p> Behnam Razzaghmaneshi Copyright (c) 2019 behnam razzaghmaneshi 2019-12-18 2019-12-18 4 87 94 Exponent of Convergence of Solutions to Linear Differential Equations in the Unit Disc <p><img src="/public/site/images/editor/abstract.PNG"></p> Saada Hamouda Somia Yssaad Copyright (c) 2019 Saada Hamouda, Somia Yssaad 2019-12-18 2019-12-18 4 95 110 On Modified Picard−S−AK Hybrid Iterative Algorithm for Approximating Fixed Point of Banach Contraction Map <p>The purpose of this work is to introduce a new iteration called the modified Picard-S-AK hybrid iterative scheme for approximating fixed point for Banach contractive maps. We show that our scheme converges to a unique fixed point p at a rate faster than the recent AK iterative scheme for Banach contractive maps. Furthermore, using Java programming language, we give some numerical examples to justify our claim. Stability and data dependence of the proposed scheme are also explored.</p> Joshua Olilima Hudson Akewe Adefemi Adeniran Copyright (c) 2019 Joshua Olilima, Hudson Akewe, Adefemi Adeniran 2019-12-18 2019-12-18 4 111 125 Differentıal Transform Method for Solvıng a Boundary Value Problem Arısıng in Chemıcal Reactor Theory <p>In this study, we deal with the numerical solution of the mathematical model for an adiabatic tubular chemical reactor which processes an irreversible exothermic chemical reaction. For steady state solutions, the model can be reduced to the following nonlinear ordinary differential equation [1]:</p> <table> <tbody> <tr> <td width="584"><img src="/public/site/images/vserturk/gif.gif"></td> <td width="30"> <p>(1)</p> </td> </tr> </tbody> </table> <p>where lambda, mu and beta are Péclet number, Damköhler number and adiabatic temperature rise, respectively.</p> <p>Boundary conditions of Eq. (1) are</p> <table> <tbody> <tr> <td width="584"><img src="/public/site/images/vserturk/gif2.gif"></td> <td width="33"> <p>(2)</p> </td> </tr> </tbody> </table> <p>Differential transform method [2] is used to solve the problem (1)-(2) for some values of the considered parameters. Residual error computation is adopted to confirm the accuracy of the results. In addition, the obtained results are compared with those obtained by other existing numerical approach [3].</p> Vedat Suat Erturk Mahmud Awolijo Chirko Copyright (c) 2019 Vedat Suat ERTURK, Mahmud Awolijo Chirko 2019-12-18 2019-12-18 4 126 136 On Roots of Apolar Polynomials <p>This article continues the exploration of methods based on that of Gian-Carlo Rota that involve apolar invariants used for solving cubic and quintic polynomial equations. These polynomial invariants were disclosed previously as an alternative to and to clarify the umbral method of Rota. Theorems are proved regarding quintic, cubic, and<br>quadratic polynomials that are pairwise apolar in that they satisfy particular polynomial apolar invariants</p> Kristofer Jorgenson Copyright (c) 2019 Kristofer Jorgenson 2019-12-21 2019-12-21 4 137 152 On A Chain Involving the Multivariable I-Transform I <p>In the present paper, we first establish an interesting new chain interconnecting a number of multivariable I-transform of Prathima et al. [6] by the method of mathematical induction. Full care has been taken of all the convergence and existence conditions for the validity of the chain. The chain established herein has been put in a very compact form and it exhibits an interesting relationship existing between images and originals of a series of related functions in several multidimensional I-function. The importance of our findings lies in the fact that it involves the multivariable I-function which is sufficiently general in nature and so a large number of chains involving other simpler and useful integral transforms of one and more variables follow as special ceses of our chain merely by specializing the parameters. In the end, we shall see several corollaries.</p> Frédéric Ayant Dr Gulshan Chand Gupta Dr. Vinod Gill Copyright (c) 2019 Frédéric Ayant, Dr Gulshan Chand Gupta, Dr. Vinod Gill 2019-12-21 2019-12-21 4 153 162 Chelyshkov Collocation Method for Solving Three-Dimensional linear Fredholm Integral Equations <p>The main purpose of this work is to use the Chelyshkov-collocation method for the solution of three- dimensional Fredholm integral equations. The method is based on the approximate solution in terms of Chelyshkov polynomials with unknown coefficients. This method transforms the integral equation to a system of linear algebraic equations by means of collocation points. Finally, numerical results are included to show the validity and applicability of the method and comparisons are made with existing results.</p> Doaa Shokry Mohamed Copyright (c) 2019 Doaa shokry 2019-12-21 2019-12-21 4 163 171 Precise Asymptotics in Wichura's Law of Iterated Logarithm <p>Let {X<sub>n</sub>, n ≥ 1} be a sequence of independent and identically distributed random variables with a common distribution function F = P(X ≤ x) in the domain of attraction of an asymmetric stable law, with index α, 1 &lt; α &lt; 2 and set S<sub>n</sub>=∑<sup>n</sup><sub>K=1</sub>X<sub>K.</sub> We prove</p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; lim<sub>ε-&gt;0</sub>(√ε) ∑<sub>n≥3</sub>(1/n)P(Sn≤(θ<sub>α</sub>-ε)A<sub>n</sub> )=1/(2√2α),</p> <p>where A<sub>n</sub> = n<sup>1/α</sup>(<em>log log</em><em>&nbsp;</em>n)<sup>((α-1)/α)</sup> θ<sub>α</sub> =(B(α))<sup>((α-1)/α)</sup> and B(α) = (1 − α)α<sup>(α/(1-α))</sup> (cos (πα/2)) <sup>(α/α-1)</sup></p> Divanji Gooty Vidyalaxmi Kokkada K. N. Raviprakash Copyright (c) 2019 Divanji Gooty, Vidyalaxmi Kokkada, K. N. Raviprakash 2019-12-21 2019-12-21 4 172 181 CnIg-Continuous Maps in Nano Ideal Topological Spaces <p>The aim of in this paper, we introduced nIg-interior, nIg-closure and study some of its basic properties. we introduced and studied nIg-continuous map, nIg-irresolute map and study their properties in nano ideal topological spaces</p> Ganesan Selvaraj Copyright (c) 2019 Ganesan Selvaraj 2019-12-21 2019-12-21 4 182 190 a-Dot Interval Valued Fuzzy New Ideal of Pu-Algebra <p>In this paper, our aim is to introduce and study the notion of an α-dot interval valued fuzzy new-ideal of a PU-algebra. The homomorphic images (pre images) of α-dot interval valued fuzzy new-ideal under homomorphism of a PU-algebras have been obtained and some related results have been derived. Finally, we give the properties of the concept of Cartesian product of an α-dot interval valued fuzzy new-ideal of a PU-algebra..</p> Rodyna A. Hosny Samy M. Mostafa Copyright (c) 2019 rodyna, Samy mostafa 2019-12-18 2019-12-18 4 191 205