MathLAB Journal https://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 2582-0389 Level subsets and translations of QFST(G) https://purkh.com/index.php/mathlab/article/view/707 <p>First, we introduce level subsets and translations of <em>QFST(G)</em> and study their properties. Secondly, we prove that the union and intersection of two-level subsets of <em>QTST(G)</em> are subgroups of <em>G</em>. Also we prove that translations of <em>QTST(G)</em> are also <em>QFST(G)</em>. Finally, we define fuzzy image and fuzzy pre-image of translations of <em>QFST(G)</em> under group homomorphisms and anti group homomorphisms and investigate properties of them.</p> Rasul Copyright (c) 2020 rasul rasuli http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 1 11 Norms of Self-Adjoint Two-Sided Multiplication Operators in Norm-Attainable Classes https://purkh.com/index.php/mathlab/article/view/704 <p>Let <em>B(H)</em> be the algebra of all bounded linear operators on a complex Hilbert space H. In this note, we give characterizations when the elementary operator <em>T<sub>A,B</sub>: B(H)→B(H)</em> defined by <em>T<sub>A,B</sub>(X) =AX B + BX A, ∀ X ∈ B(H)</em> and <em>A, B</em> fixed in <em>B(H)</em> is self adjoint and implemented by norm-attainable operators. We extend our work by showing that the norm of the adjoint of T<sub>A, B </sub>is equal to the norm of T<sub>A,B</sub> when it is implemented by normal operators.</p> Benard Okelo Copyright (c) 2020 Benard Okelo http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 12 22 nIg-Closed Sets https://purkh.com/index.php/mathlab/article/view/696 <p>Characterizations and properties of <em>nI<sub>g</sub></em>-closed sets and <em>nI<sub>g</sub></em>-open sets are given. The main purpose of this paper is to introduce the concepts of<em> sg-nI</em>-locally closed sets, n∧<sub>sg</sub>-sets, <em>η<sub>sg</sub>-nI</em>-closed sets, <em>nI<sub>g</sub></em>-continuous,<em> sg-nI-LC-</em>continuous,<em> η<sub>sg</sub>-nI</em>-continuous and to obtain decompositions of <em>n*</em>-continuity in nano ideal topological spaces.</p> S. Ganesan C. Alexander Jeyashri S. M. Sandhya Copyright (c) 2020 S. Ganesan, C. Alexander, Jeyashri, S. M. Sandhya http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 23 34 Global Solution and Asymptotic Behaviour for a Wave Equation Type p-Laplacian with p-Laplacian Damping https://purkh.com/index.php/mathlab/article/view/687 <p>In this work we study the global solution, uniqueness and asymptotic behaviour of the nonlinear equation</p> <p><em>u<sub>tt </sub>− ∆<sub>p</sub>u − ∆<sub>p</sub>u<sub>t </sub>=|u|<sup>r−1</sup>u</em></p> <p>where ∆<sub>p</sub>u is the nonlinear <em>p</em>-Laplacian operator, 2 ≤ p &lt; ∞. The global solutions are constructed by means of the Faedo-Galerkin approximations and the asymptotic behavior is obtained by Nakao method. Keywords: p-Laplacian, global solution, asymptotic behaviour, p-Laplacian damping.</p> Ducival Pereira Carlos Raposo Celsa Maranhão Copyright (c) 2020 Carlos Raposo, Ducival Pereira, Celsa Maranhão http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 35 45 Generalized Fibonacci Numbers: Sum Formulas of the Squares of Terms https://purkh.com/index.php/mathlab/article/view/732 <p>In this paper, closed forms of the sum formulas <em>∑<sub>n</sub><sup>k=1</sup>kW<sub>k</sub><sup>2</sup></em> and <em>∑<sup>n</sup><sub>k=1</sub>kW<sup>2</sup><sub>−k</sub></em> for the squares of generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal and Jacobsthal-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery. Our work generalize second order recurrence relations.</p> Yüksel Soykan Copyright (c) 2020 Yüksel Soykan http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 46 62 Tripolar fuzzy sub implicative ideals of KU-Algebras https://purkh.com/index.php/mathlab/article/view/655 <p>The concept Tripolar fuzzy set is a generalization of bipolar fuzzy set, intuitionistic fuzzy set and fuzzy set. In this paper, the concept Tripolar fuzzy sub implicative ideals of KU-algebras are introduced and several properties are investigated. Also, the relations between Tripolar fuzzy sub implicative ideals and Tripolar fuzzy ideals are given. The image and the preimage of Tripolar fuzzy sub implicative ideals under homomorphism of KU-algebras are defined and how the image and the preimage of Tripolar fuzzy sub implicative ideals under homomorphism of KU-algebras become Tripolar fuzzy sub implicative ideals are studied. Moreover, the Cartesian product of Tripolar fuzzy sub implicative ideals in Cartesian product KU-algebras is established.</p> Samy Mohammed Mostafa Copyright (c) 2020 Samy Mohammed Mostafa http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 63 81 Markov Moment Problem in Concrete Spaces Revisited https://purkh.com/index.php/mathlab/article/view/663 <p>This review paper starts by recalling two main results on abstract Markov moment problem. Corresponding applications to problems involving concrete spaces of functions and self-adjoint operators are proved in detail. Some modified versions of such results are discussed. In the end, using polynomial approximation on special unbounded closed subsets, some multidimensional Markov moment problem on such subsets are recalled, without repeating the proofs. Our approximation results solve the difficulty arising from the fact that there exist positive polynomials on , &nbsp;which cannot be written as sums of squares of polynomials. However, the upper constraint of the solution is written in terms of products of quadratic forms. The solution are operators having as codomain an order complete Banach lattice. The latter space might be a commutative algebra of self-adjoint operators. All solutions obtained in this paper are continuous, and thanks to the density of polynomials in the involved domain function spaces, their uniqueness follows too. Operator valued solutions for classical moment problem are pointed out.</p> Octav Olteanu Janina Mihaela Mihaila Copyright (c) 2020 Octav Olteanu, Janina Mihaela Mihaila http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 82 91 Novel Alternative Methods to Romberg Integration and Richardson’s Extrapolation with Matlab Package:Integral_Calculator https://purkh.com/index.php/mathlab/article/view/676 <p>This paper introduces new integration methods for numerical integration problems in science and engineering applications. It is shown that the exact results of these integrals can be obtained by these methods with the use of only 2 segments. So no additional function and integrand evaluations are required for different levels of computation. This situation overcomes the computational inefficiency. A new Matlab Package; Integral_Calculator is presented. Integral_Calculator provides a user-friendly computational platform which requires only 3 data entries from the user and performs the integration and give the results for any functions to be integrated. This package has been tested for each numerical example considered below</p> Çiğdem Copyright (c) 2020 çiğdem http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 92 101 Shapes of the Transmuted Kumaraswamy Pareto Distribution for Varying Parameter Values https://purkh.com/index.php/mathlab/article/view/692 <p>In this study, a new generalization of the Pareto distribution is undertaken, by first generalizing the Pareto distribution using the Kumaraswamy method and thereafter transmuting the resulting Kumaraswamy Pareto distribution. A detailed account of the general mathematical properties of the new generalized distribution is presented. The shapes of the Transmuted Kumaraswamy Pareto Density were plotted using R-program. The results show the superiority of the Transmuted Kumaraswamy Pareto distribution over the one parameter Pareto distribution.</p> Francis Eze Kenny Urama Sidney Onyeagu Copyright (c) 2020 Francis Eze, Urama, K. U, S. I. Omyeagu http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 102 109 UFSD Test with Proton Beam and Signal Analysis by Using CFD Method https://purkh.com/index.php/mathlab/article/view/711 <p>Detecting the charge particles at Giga hertz rate is one of the applications of UFSD (Ultra- Fast Silicon Detectors). The UFSD test in front of the proton beam to count the beam particles and use it for more precise in Dose Delivery System for treatment the cancerous tumor by charge particles can become an effective step for development of cancer treatment. After choosing the best time measurement method which was constant fraction discriminator (CFD) method, by our previous experience, we used MATLAB software to analyze the UFSD signals. The results of many different runs of programs in MATLAB for many registered signals shows: 1- These sensors are reliable to count the proton particles in giga hertz rate. 2-The CFD devices could be used to record the UFSD output signals.</p> Mohammad Fadavi Mazinani Ali asghar Mowlavi Copyright (c) 2020 Mohammad Fadavi Mazinani, Ali asghar Mowlavi http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 110 116 A Rigorous Geometrical Proof on Constructability of Magnitudes (A Classical Geometric Solution for the Factors: √2 and √(3&2)) https://purkh.com/index.php/mathlab/article/view/730 <p>In the absence of a comprehensive geometrical perceptive on the nature of rational (commensurate) and irrational (incommensurate) geometric magnitudes, a solution to the ages-old problem on the constructability of magnitudes of the forms and (the square root of two and the cube root of two as used in modern mathematics and sciences) would remain a mystery. The primary goal of this paper is to reveal a pure geometrical proof for solving the construction of rational and irrational geometric magnitudes (those based on straight lines) and refute the established notion that magnitudes of form are not geometrically constructible. The work also establishes a rigorous relationship between geometrical methods of proof as applied in Euclidean geometry, and the non-Euclidean methods of proof, to correct a misconception governing the geometrical understanding of irrational magnitudes (expressions). The established proof is based on a philosophical certainty that "the algebraic notion of irrationality" is not a geometrical concept but rather, a misrepresentative language used as a means of proof that a certain problem is geometrically impossible.</p> Munyambu .C. June Kimuya Alex Copyright (c) 2020 Munyambu .C. June, Kimuya Alex http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 117 142 New Results on Extension of Linear Operators and Markov Moment Problem https://purkh.com/index.php/mathlab/article/view/728 <p>One recalls earlier applications of extension of linear operators with two constraints to the abstract Markov moment problem and Mazur-Orlicz theorem. Next we generalize one of our previous results on the characterization for the existence of a linear extension preserving the sandwich condition on the positive cone of the domain (where are given linear operators). Precisely, a similar characterization is obtained, when the sandwich condition on the extension is on , where are sublinear operators, and is an arbitrary convex cone (that might be the entire domain space). In the end, solutions of moment and Mazur-Orlicz problems are discussed, pointing out evaluation of their norms. All these solutions are obtained from the theorems previously stated or proved in this work. Some of the solutions are Markov operators.</p> Octav Olteanu Copyright (c) 2020 Octav Olteanu http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 143 154 On Decomposition of Continuity Via *μ-Closed Sets https://purkh.com/index.php/mathlab/article/view/685 <p>There are various types of generalization of continuous functions in the development of topology. Recently some decompositions of continuity are obtained by various authors with the help of generalized continuous functions in topological spaces. In this paper we obtain a decomposition of continuity using a generalized continuity called *u-continuity in topology.</p> Ganesan Selvaraj Copyright (c) 2020 Ganesan Selvaraj http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 155 158 On special FCn-cell modules https://purkh.com/index.php/mathlab/article/view/706 <p>In this paper, we study a speci ed family of Fuss-Catalan algebra cell modules. We defi ne the set of the basis diagrams and we give the general form for the Gram matrix related to this family. In addition, we state when these modules are irreducible by finding the determinant of the Gram matrices. Finally, we define a homomorphism between certain cell modules.</p> Ahmed B. Hussein Copyright (c) 2020 Ahmed B. Hussein http://creativecommons.org/licenses/by/4.0 2020-04-30 2020-04-30 5 159 172