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 On the Maximization of Investment Portfolios with Returns of Contributions <p>In this work, how investment portfolios of a pension scheme can be maximized in the presence of the return clause of contributions is presented. This clause permits the return of accumulated contributions together with predetermined interest from risk-free assets to members’ families whenever death occurs to their family members. Also considered<br />herein are investments in cash, marketable security, and loan to increase the total accumulated funds of the pension scheme left to be distributed among the surviving members such that the price models of marketable security and loan follow geometric Brownian motions. The game-theoretic approach, separation of variable technique, and mean-variance utility are used to obtain closed-form solutions of the optimal control plans for the assets and the efficient frontier. Next, the consequence of some parameters on the optimal control plans with time is numerically analysed. Furthermore, a theoretical comparison of our result with an existing result is given.</p> Edikan E. Akpanibah Bright O. Osu Ben I. Oruh Okonkwo C. Ukwuoma and Everestus O. Eze Copyright (c) 2020 Edikan E. Akpanibah, Bright O. Osu, Ben I. Oruh, Okonkwo C. Ukwuoma, and Everestus O. Eze 2020-08-31 2020-08-31 6 1 16 Characterization of Maps on Positive Semidefinite Choi Matrices <p>Several investigations have been done on positive maps on their algebraic structures with more emphasis on completely positive maps. In this study, we have described the structure of the Choi matrices for 2-positive maps on positive semidefinite matrices and the conditions for complete positivity of positive linear maps from n to n+1. The motivation behind these objectives is work done by Majewski and Marciniak on the structure of positive maps ф from M<sub>n</sub> to M<sub>n</sub> + 1(2 ≥ 2) between matrix algebras.</p> C. A. Winda N. B. Okelo Omolo Ongati Copyright (c) 2020 C. A. Winda, N. B. Okelo, Omolo Ongati 2020-08-31 2020-08-31 6 17 27 On new classes of some nano closed sets <p>The aim of this paper is to introduce a new class of sets called N*<sub>μ</sub>-closed sets in Nano topological spaces and to study some of its basic properties. As applications of N*<sub>μ</sub>-closed sets, we introduce T<sub>N*</sub><sub>μ</sub> -spaces, <sub>g</sub>T<sub>N*</sub><sub>μ</sub> -spaces, and <sub>α</sub>T<sub>N*</sub><sub>μ</sub> -spaces. Moreover, we obtain certain new characterizations for the T<sub>N*</sub><sub>μ</sub> -spaces, <sub>g</sub>T <sub>N*</sub><sub>μ</sub> -spaces, and <sub>α</sub>T<sub>N*</sub><sub>μ</sub> -spaces.</p> S. Ganesan C. Alexander M. Sugapriya A. Aishwarya Copyright (c) 2020 S. Ganesan, C. Alexander, M. Sugapriya, A. Aishwarya 2020-08-31 2020-08-31 6 28 44 A Simple Approximation for the Normal Distribution Function via Variational Iteration Method <p>In this paper, we obtain some new approximations for the cumulative distribution function of the standard normal distribution via the He’s Variational Iteration Method. For this end, we consider the cumulative distribution function as the unknown function to be determined by solving a certain differential equation of the second-order that the cumulative distribution function satisfied subjected with the certain initial conditions. The correction functional in this approach is constructed here in such a manner that we have one real numerical parameter to be tuned for the best result. Our approximations to the cumulative distribution function are comparable to other approximations found in the literature and has the advantage of being a simple expression, that may have potential applications in several areas of applied sciences. Numerical comparison shows that our approximations are very accurate.</p> V. K. Shchigolev Copyright (c) 2020 V. K. Shchigolev 2020-08-31 2020-08-31 6 45 52 On Newton’s Method for Convex Functions and Operators and its Relationship with Contraction Principle <p>In this review paper, generally known results on a version of global Newton’s method for convex increasing or decreasing functions and operators, as well as afferent examples and applications, are recalled. Connection with the contraction principle is discussed in detail and applied to approximate , Where is a positive invertible symmetric operator acting on a finite-dimensional Hilbert space, and is a real number. Two numerical examples for symmetric matrices with real coefficients are given. Some other nonlinear matrix or scalar equations are solved approximately.</p> Octav Olteanu Copyright (c) 2020 Octav Olteanu 2020-08-31 2020-08-31 6 53 61 A Generalized Summation Formula <p>In this paper, we have developed the generalized expression of <img src="" /></p> <p>and it’s corresponding integral form.</p> Salahuddin Vinti Copyright (c) 2020 Salahuddin, Vinti 2020-08-31 2020-08-31 6 62 64 Pythagorean Neutrosophic Pre-Open Sets <p>The purpose of this paper is to introduce and study the notion of Pythagorean neutrosophic pre-open sets by using the notion of Pythagorean neutrosophic open set. Besides, we define the concepts of Pythagorean neutrosophic pre-open function, Pythagorean neutrosophic pre-continuous function, and Pythagorean neutrosophic pre-homeomorphism. Moreover, some of their properties are proved.</p> Carlos Granados Copyright (c) 2020 Carlos Granados 2020-08-31 2020-08-31 6 65 74 On Semi-$ + $-Open Sets in Topological Spaces <p>In this paper, we used the notion of operator A<sup>+</sup> for defining a new class of set which will be called semi-+-open set, besides we de fine the concepts of generalized semi-+-closed sets and regular generalized semi-+-closed sets. Moreover, some of their properties are shown.</p> Carlos Granados Copyright (c) 2020 Carlos Granados 2020-08-31 2020-08-31 6 75 80 Contra nIg μ-continuity <p>In this paper, nIgμ-closed sets and nIgμ-open sets are used to define and investigate a new class of maps called nIgμ-continuous, nIgμ-irresolute map and contra nIgμ-continuous maps in nano ideal topological spaces. We discuss the relationship with some other related maps.</p> Selvaraj Ganesan Copyright (c) 2020 Selvaraj Ganesan 2020-08-31 2020-08-31 6 81 91 On ngμ-closed sets <p>The aim of this paper, we offer a new class of sets called ngμ-closed sets in nano topological spaces and we study some of its basic properties. We introduce and study ng μ-continuous, ng μ-irresolute and contra ng μ-continuous. Moreover, we obtain their properties and characterizations.</p> S. Ganesan C. Alexander A. Aishwarya M. Sugapriya Copyright (c) 2020 S. Ganesan, C. Alexander, A. Aishwarya, M. Sugapriya 2020-08-31 2020-08-31 6 92 104