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 <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> Some Characterizations of The Exponential Family <p>This paper introduces some characterizations concerning the exponential family. Recurrence relation between two consecutive conditional moments of h(z) given x&lt;z&lt;y&nbsp; is presented. In addition, an &nbsp;&nbsp;&nbsp;expression of V[h(Z]x&lt;Z&lt; y)as well as a closed form of E[h<sup>r</sup>(Z)x&lt;Z&lt; y] in terms of the failure rate and the reversed failure rate is deduced. Finally, the left r<sup>th</sup> truncated moment of h(Y<sub>k</sub>) ( where Y<sub>k</sub> is &nbsp;&nbsp;the K<sup>th</sup> order statistic) is expressed in terms of a polynomial,&nbsp; h(-) , of degree r. Some results concerning the exponentiated Pareto, exponentiated Weibull, the Modified Weibull, Weibull, generalized exponential, Linear failure rate,1<sup>st</sup> type Pearsonian distributions, Burr, power and the uniform distributions are obtained as special cases.</p> Ali Ahmed A-Rahman ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 241 250 A Semi-Analytical Method for The Solution of Linear And Nonlinear Newell-Whitehead-Segel Equations <p>The aim of this work is to use a semi-analytical method “Reduced Differential Transform Method (RDTM)” for the solution of linear and nonlinear Newell-Whitehead-Segel Equations (NWSE). RDTM does not require linearization, transformation, discretization, perturbation or restrictive assumptions. To determine the performance measure of the RDTM, two illustrative examples were considered. The comparative study of the results obtained via the RDTM was compared with that of the exact solution. Hence, RDTM offers solutions with easily computable components as convergent series and is an alternative approach that overcomes the shortcoming of complex calculations of differential transform method.</p> Sunday Emmanuel Fadugba ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 251 258 Modelling Stochastic Volatility of The Stock Market: A Nigerian Experience <p>In this paper, The GARCH (1,1)&nbsp; model is presented and some results for the existence and uniqueness outlined. Other extensions of the GARCH model including EGARCH, PARCH and TARCH models were presented. The daily stock price of Dangote Cement (Dangocem) was used to test the performance of the above named models with respect to some stylized facts of volatility of financial data: fat tail, volatility clustering, volatility persistence, mean reversion and leverage effect. The Akaike Information Criterion (AIC), Schwarz Information Criterion (SIC) and the Hannan-Quinn criterion (HQ) were used to rate the performance of the models. The results show that the return series are stationary. The summary statistics showed that the return series has a fat tail. From the Q-Q plot, it was seen that the assumption of normality was spurious. The parameter estimation result showed that the volatility of the return series has the mean reversion property.. News impact was asymmetric and there is the presence of leverage effect. It was also seen that the volatility process was driven more by negative innovation. Overall the GARCH(1,1) and the TARCH model outperform the other model.</p> Bright Okore Osu ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 259 267 The Basic Concepts On Distribution of Decision Power Between The Players and Manipulation in Weighted Voting Games <p>It is known that voting is a widely used method in social choice theory. In the present paper we consider some concepts of distribution of voting powers between the player and the process of manipulation in weighted voting games. The aim is to show some basic problems in social choice theory by studying the decision powers of players and the three processes of manipulation in weighted voting games: by merging of two players into a single player, by players splitting into a number of smaller units, and by annexation of a part or all of the voting weights of another player.</p> Zdravko Dimitrov Slavov ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 268 285 On Tensor Products and Elementary Operators <p>In This Paper We Describe Operator Systems And Elementary Operators Via Tensor Products. We Also Discuss Norms Of Elementary Operators.</p> Otieno E. Achieng, 397455 Benard Okelo Omolo Ongati ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 286 295 Identities of Choi-Lee-Srivastava involving the Euler-Mascheroni’s constant <p>We give an elementary deduction of the Choi-Lee-Srivastava’s identities involving the Euler Mascheroni’s constant, thus from them is immediate the identity of Wilf.</p> Jose Luis Lopez Bonilla C. Hernández Aguilar R. López Vázquez ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 396 298 Some identities for Stirling numbers <p>We study the identities for Stirling numbers obtained by Wildon, and Yuluklu <em>et al.</em></p> Jose Luis Lopez Bonilla ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 299 301 Some Notes on Neville’s Algorithm of Interpolation with Applications to Trigonometric Interpolation <p>&nbsp;In this paper is given a description of Neville’s algorithm which is generated from Lagrange interpolation polynomials. Given a summary of the properties of these polynomials with some applications. Then, using the Lagrange polynomials of lower degrees, Neville algorithm allows recursive computation of those of the larger degrees, including the adaption of Neville’s method to trigonometric interpolation. Furthermore, using a software application, such as in our case, <em>Matlab</em>, we will show the numerical experiments comparisons between the Lagrange interpolation and Neville`s interpolation methods and conclude for their advantages or disadvantages.</p> Shpetim Rexhepi Egzona Iseni Bilall I. Shaini Tetuta Zenku ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 302 313 Novel Artificial Human Optimization Field Algorithms – The Beginning <p>New Artificial Human Optimization (AHO) Field Algorithms can be created from scratch or by adding the concept of Artificial Humans into other existing Optimization Algorithms. Particle Swarm Optimization (PSO) has been very popular for solving complex optimization problems due to its simplicity. In this work, new Artificial Human Optimization Field Algorithms are created by modifying existing PSO algorithms with AHO Field Concepts. These Hybrid PSO Algorithms comes under PSO Field as well as AHO Field. There are Hybrid PSO research articles based on Human Behavior, Human Cognition and Human Thinking etc. But there are no Hybrid PSO articles which are based on concepts like Human Disease, Human Kindness and Human Relaxation. This paper proposes new AHO Field algorithms based on these research gaps. Some existing Hybrid PSO algorithms are given a new name in this work so that it will be easy for future AHO researchers to find these novel Artificial Human Optimization Field Algorithms. A total of 6 Artificial Human Optimization Field algorithms titled "Human Safety Particle Swarm Optimization (HuSaPSO)", “Human Kindness Particle Swarm Optimization (HKPSO)", “Human Relaxation Particle Swarm Optimization (HRPSO)", “Multiple Strategy Human Particle Swarm Optimization (MSHPSO)", “Human Thinking Particle Swarm Optimization (HTPSO)" and “Human Disease Particle Swarm Optimization (HDPSO)” are tested by applying these novel algorithms on Ackley, Beale, Bohachevsky, Booth and Three-Hump Camel Benchmark Functions. Results obtained are compared with PSO algorithm.</p> Satish Gajawada ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 314 335 Determination of the Order and the Error Constant of an Implicit Linear-Four Step Method <p>The aim of this work is to determine the order and the error constant of an implicit linear-four step method namely “The Quade’s method”. From the results generated, It is observed that the method is of order six and the error constant is obtained as . The Local Truncation Error (LTE) of the general implicit linear four-step is obtained.</p> Fadugba Sunday Emmanuel ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 336 342 The Parody of Mathematics <p>In this very brief paper by precise statement the author has shown that numbers are a continuum in mathematics( mathematics has to be a continuum), and numbers do define all non-linear space by a set configuration at the very base of mathematics. The author has separately both by published papers and now a book on created mathematics defined this very basic fact that as created <em>numbers and space</em> are connected by the Pythagoras 1:3 configuration. The paper itself is constrained to the observation of the 1,3 as base <em>ligands</em> in the mathematical sense.</p> Vinoo Cameron ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 343 345 η-Einstein Solitons In N(K)-Paracontact Metric Manifolds <p>The objective of the present paper is to study the η-Einstein soli-tons on N(k)-Paracontact metric manifolds. Also, admitting the Ricci Soli-tons under certain conditions.</p> Mohd Anall Ali ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 345 355 Solutions and Formulae for Some Systems of Difference Equations <p>This paper is written to provide some solutions to the following systems of difference equations:</p> <p><img src="/public/site/images/editor/000001.JPG"></p> <p>where the initial data <img src="/public/site/images/editor/111111.JPG">are arbitrary non zero real numbers.</p> Mohammed Almatrafi E. M. Elsayed ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 356 369 Solving Fractional Geometric Programming Problems via Relaxation approach <p style="-qt-block-indent: 0; text-indent: 0px; -qt-user-state: 0; margin: 0px;">In the optimization literature , Geometric Programming problems play a very important role rather than primary in engineering designs. The geometric programming problem is a nonconvex optimization problem that has received the attention of many researchers in the recent decades. Our main focus in this issue is to solve a Fractional Geometric Programming(FGP) problem via linearization technique[1]. Linearizing separately both the numerator and denominator of the fractional geometric programming problem in the objective function, causes the problem to be reduced to a Fractional Linear Programming problem (FLPP) and then the transformed linearized FGP is solved by Charnes and Cooper method which in fact gives a lower bound solution to the problem. To illustrate the accuracy of the final solution in this approach, we will compar our result with the LINGO software solution of the initial FGP problem and we shall see a close solution to the globally optimum. A numerical example is given in the end to illustrate the methodology and efficiency of the proposed approach.</p> Mansour Saraj ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 370 383 Missing at random in nonparametric regression for functional stationary ergodic data in the functional index model <p>The main objective of this paper is to estimate non-parametrically the the estimator for the regression function operator when the observations are linked with a single-index. The functional stationary ergodic data with missing at random (MAR) are considered.In particular, we construct the kernel type estimator of the regression operator, some asymptotic properties such as the convergence rate in probability as well as the asymptotic normality of the estimator are established under some mild conditions respectively. As an application, the asymptotic $(1 -\zeta)$ confidence interval of the regression operator is also presented for $0 &lt; \zeta &lt; 1.$</p> Fatima Akkal Mustapha Meghnafi Abbes Rabhi ##submission.copyrightStatement## 2018-12-30 2018-12-30 1 3 384 398