MathLAB Journal http://purkh.com/index.php/mathlab <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 <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> Annual Reviewer Acknowledgement http://purkh.com/index.php/mathlab/article/view/147 <p>The Editorial team of the would like to thank the following reviewers for their work in refereeing manuscripts during 2018.</p> Chief Editor ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-29 2018-08-29 1 2 Operational Representations for The Quadruple Hypergeometric Function (4)^F30 http://purkh.com/index.php/mathlab/article/view/93 <p>Based upon the classical derivative and integral operators we introduce a new symbolic operational representations for the hypergeometric function of four variables (4)^F30. By means of these symbolic operational representations number of generating functions (4)^F30 involving the hypergeometric function &nbsp;are then found. Some special cases of the main result here are also considered.</p> Maged G. Bin-Saad Jihad Ahmed Younis ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-29 2018-08-29 1 2 180 185 Strong Insertion of a Contra-Continuous Function Between Two Comparable Contra-B−Continuous Functions http://purkh.com/index.php/mathlab/article/view/96 <p>Enough condition in terms of lower cut sets are given for the strong insertion of a contra-continuous&nbsp;&nbsp; function between two comparable contra-b−continuous real-valued functions on such topological spaces that kernel of sets is open.</p> Majid Mirmiran ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-29 2018-08-29 1 2 186 191 Thermoelastic Problem for An Infinitely Long Annular Cylinder Without Energy Dissipation (GN Theory) http://purkh.com/index.php/mathlab/article/view/99 <p>In this paper we consider the problem of an infinitely long annular cylinder whose inner and outer surfaces are subjected to known surrounding temperatures and are traction free. The problem is in the context of the theory of thermoelasticity without energy dissipation. The Laplace transform with respect to time is used. The inversion process is carried out using a numerical method based on a Fourier series expansion. Numerical results are computed for the temperature, displacement and stress distributions. The numerical results are represented graphically. Comparison is made between the predictions here and those of the theory of thermoelasticity with one relaxation time.</p> Shaaban Khader ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-29 2018-08-29 1 2 192 201 An Improved Poisson Distribution and Its Application in Option Pricing http://purkh.com/index.php/mathlab/article/view/102 <p>This work, introduces an improve Poisson distribution function. This improved Poisson is equipped with some financial terms, which generate a model for determining the prices of a European call and put option for two period models. Some of its important statistical properties like the mean, variance are given. It was found that the problem of option for non-dividend paying stock can be approached using an improved Poisson distribution function equipped with some financial terms. In comparison it gives exactly the numerical results with the CRR binomial model using the numerical data. An empirical example is given in a concrete setting.</p> Samson Ogu- Egege Bright Okore Osu Chigozie Chibuisi ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-29 2018-08-29 1 2 202 212 Certain Integral Representations for Hypergeometric Functions of Four Variables http://purkh.com/index.php/mathlab/article/view/104 <p>In the present work, we first introduce five new quadruple hypergeometric series and then we give integral representations of Euler type and Laplace type for these new hypergeometric series, which we denote by <img src="/public/site/images/editor/Untitled.jpg"></p> Jihad A. Younis Maged G. Bin-Saad ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-29 2018-08-29 1 2 213 223 On The Gould’s Formula for Stirling Numbers of The Second Kind http://purkh.com/index.php/mathlab/article/view/107 <p>We present an alternative deduction of the Gould’s relation for Stirling numbers of the second kind. Our approach is based in the Nörlund polynomials and in the duality property between the Stirling numbers.</p> A. Zuniga-Segundo Jose Luis Lopez Bonilla S. Vidal-Beltran ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-29 2018-08-29 1 2 224 226 Full-Rank Factorization and Moore-Penrose’s Inverse http://purkh.com/index.php/mathlab/article/view/108 <p>C. MacDuffee apparently was the first to point out, in private communications, that a full-rank factorization of a matrix <em>A</em> leads to an explicit formula for its Moore-Penrose’s inverse <em>A</em><strong><sup>+</sup></strong>. Here we apply this idea of MacDuffee and the Singular Value Decomposition to construct <em>A</em><strong><sup>+</sup></strong>.</p> Jose Luis Lopez Bonilla ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-29 2018-08-29 1 2 227 230 Analysis of nonlinear neutral pantograph differential equations with Hilfer fractional derivative http://purkh.com/index.php/mathlab/article/view/85 <p>In this paper, we discuss the existence, uniqueness and stability of nonlinear&nbsp;neutral pantograph equation with ?-Hilfer fractional derivative. The arguments are&nbsp;based upon Schauder fixed point theorem and Banach contraction principle. Moreover&nbsp;we discuss the Ulam-Hyers type stability.</p> Elsayed M. Elsayed S. Harikrishnan K. Kanagarajan ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2018-08-29 2018-08-29 1 2 231 240