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> en-US <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> editor@purkh.com (Gurdev Singh) tomathlab@purkh.com (Bavneet Kaur) Sat, 31 Aug 2019 08:05:53 +0000 OJS 3.1.2.1 http://blogs.law.harvard.edu/tech/rss 60 Various Bounds of Group of Autocentral Automorphisms http://purkh.com/index.php/mathlab/article/view/328 <p>In this paper, we find various bounds for the group of all autocentral automorphisms of a finite group $G$. We consider the cases, where the group of all autocentral automorphisms coincides with its upper bound, that is, the group of all central automorphisms and also where it coincides with its lower bound, that is, the group of all inner automorphisms.</p> Harsha Arora Copyright (c) 2019 Harsha Arora http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/328 Fri, 30 Aug 2019 05:34:54 +0000 Increasing Stability of The Inverse Source Problem for One Dimensional Domain http://purkh.com/index.php/mathlab/article/view/431 <p>In this paper, we are investigating the one-dimensional inverse source problem for the Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two endpoints. Our main result is to obtain a stability estimate consists of two parts: the data discrepancy and the high-frequency tail.</p> Ajith Gunaratne, Shahah Almutairia Copyright (c) 2019 Ajith Gunaratne, Shahah Almutairia http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/431 Fri, 30 Aug 2019 05:37:03 +0000 Some Properties of Strictly Quasi-Fredholm Linear Relations http://purkh.com/index.php/mathlab/article/view/366 <p>In this paper we rst give some properties of strictly quasi-Fredholm linear relations. Next we investigate the perturbation of this class under nite rank operators.</p> Mnif Maher, Bouaniza Hafsa Copyright (c) 2019 Mnif Maher, Bouaniza Hafsa http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/366 Fri, 30 Aug 2019 05:35:34 +0000 Existence of Positive Solutions for Higher Order Boundary Value Problems on Time Scales http://purkh.com/index.php/mathlab/article/view/386 <p>In this paper, we establish the existence of at least one positive solution for the higher order boundary value problems on time scales by using the Krasnosel’skii fixed point theorem.</p> Fatma Serap Topal, Buse Eralp Copyright (c) 2019 Fatma Serap Topal, Buse Eralp http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/386 Fri, 30 Aug 2019 05:36:02 +0000 Weinstein Transform Generalized Weinstein Transform in Quantum Calculus http://purkh.com/index.php/mathlab/article/view/419 <p>In this paper, we introduce a q-analogue of the Weinstein operator and we investigate its eigenfunction. Next, we<br>define and study its associated Fourier transform which is a q-analogue of the Weinstein transform. In addition to<br>several properties, we establish an inversion formula and prove a Plancheral theorem for this q-Weinstein transform.</p> Youssef Bettaibi, Hassen Ben Mohamed Copyright (c) 2019 Youssef Bettaibi, Hassen Ben Mohamed http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/419 Fri, 30 Aug 2019 05:36:22 +0000 b js maximal http://purkh.com/index.php/mathlab/article/view/424 <p>in this paper</p> behnam razzaghmaneshi Copyright (c) 2019 behnam razzaghmaneshi http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/424 Fri, 30 Aug 2019 05:36:45 +0000 Increasing Stability of The Inverse Source Problem For One Dimensional Domain http://purkh.com/index.php/mathlab/article/view/346 <p>In this paper, we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two endpoints. Our main result is to obtain a stability estimate consists of two parts: the data discrepancy and the high frequency tail.</p> Manal S.I. Zaki, Hind Hashem Copyright (c) 2019 Manal S.I. Zaki, Hind Hashem http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/346 Fri, 30 Aug 2019 05:35:12 +0000 Reference Temperature Dependent Thermoelastic Solid with Voids Subjected to Continuous Heat Sources http://purkh.com/index.php/mathlab/article/view/436 <p>In the present article, the reference temperature dependency Lord--Shulman model of generalized thermoelasticity with voids subjected to a continuous heat source in a half-space is discussed. The Laplace transform together with eigenvalue approach technique is applied to find a closed-form solution for the physical variables viz. distribution of temperature, volume fraction field, deformation and stress field in the Laplace transform domain. The numerical inversions of those physical variables in the space-time domain are carried out by using the Zakian algorithm for the inversion of the Laplace transform. Numerical results are shown graphically and the results obtained are analyzed.</p> Sudip Mondal Copyright (c) 2019 Sudip Mondal http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/436 Fri, 30 Aug 2019 05:37:36 +0000 Permutation Groups with Bounded Movement having Maximum Orbits http://purkh.com/index.php/mathlab/article/view/442 <p><img src="/public/site/images/editor/abstract.JPG" width="718" height="170"></p> Behname Razzaghmaneshi, Mehdi Alaeiyan Copyright (c) 2019 Behname Razzaghmaneshi, Mehdi Alaeiyan http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/442 Fri, 30 Aug 2019 06:31:46 +0000 Analysis of Exact Solutions to Some Systems of Difference Equations http://purkh.com/index.php/mathlab/article/view/478 <pre>Some nonlinear difference equations can be sometimes solved analytically using</pre> <pre>manual iteration which begins with some given initial conditions. Obtaining next iterations always depends on the previous ones. Through this paper, we utilize the manual iteration in investigating the exact</pre> <pre>solutions of the following recursive sequences</pre> <pre>&nbsp;</pre> <pre>$x_{n+1}=\frac{y_{n-5}x_{n-8}}{y_{n-2}(-1-y_{n-5}x_{n-8})},\ \ \ \ \ y_{n+1}%</pre> <pre>=\frac{x_{n-5}y_{n-8}}{x_{n-2}\left( \pm1\pm x_{n-5}y_{n-8}\right) },$</pre> <pre>&nbsp;</pre> <pre>where the initial conditions $x_{\delta},\ y_{\delta},\ \delta\in</pre> <pre>\{0,1,...,8\}$ are non-zero real numbers. Some numerical solutions are also</pre> <pre>presented in some figures to show the behaviour of the solutions.</pre> <pre>&nbsp;</pre> Mohammed Almatrafi, Marwa M. Alzubaidi Copyright (c) 2019 Mohammed Almatrafi, Marwa M. Alzubaidi http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/478 Fri, 30 Aug 2019 06:32:18 +0000 Seventh Convergence Order Solvers Free Of Derivatives For Solving Equations In Banach Space http://purkh.com/index.php/mathlab/article/view/445 <p>We study a seventh convergence order solver introduced earlier on the&nbsp;j−dimensional Euclidean space for solving systems of equations. We use hypotheses only on the divided differences of order one in contrast to the earlier study using hypotheses on derivatives reaching up to order eight although these derivatives do not appear on the solver. This way we expand the applicability of the solver, and in the more general setting of Banach space valued operators. Numerical examples complement the theoretical results.</p> Santhosh George, Ioannis K. Argyros Copyright (c) 2019 Santhosh George, Ioannis K. Argyros http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/445 Fri, 30 Aug 2019 08:26:44 +0000 Giving Birth to Vectorial Coordinate Geometry http://purkh.com/index.php/mathlab/article/view/363 <p>This paper deals with certain foundational questions about the adequacy of the long- running Cartesian coordinate geometry which is based on the abstract concept of “sign convention” for the study of the physical world. To establish a bridge between theory and practice, the present paper purports to introduce the “Vectorial coordinate geometry” that makes use of a modern notational system to work as an alternative for the long-running historical system. The proposed scheme will be equally applicable to the “Pure mathematical world” as well as to the “Real physical world” and is much clearer leaving no room for confusion.</p> Pramode Ranjan Bhattacharjee Copyright (c) 2019 Pramode Ranjan Bhattacharjee http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/363 Fri, 30 Aug 2019 11:24:01 +0000 Construction of Codes By Hyper KU-Valued Functions http://purkh.com/index.php/mathlab/article/view/365 <p>Coding Theory is a mathematical domain with many applications in Information theory. Various type of codes and their connections with other mathematical objects have been intensively studied. One of these applications, namely connections between binary block codes and BCK-algebras, was recently studied in (Jun, Song,&nbsp; Flaut ).In this paper, we will focus to one of the recent applications of KU-algebras in the coding theory, namely the Construction of codes by hyper KU-valued functions. First, we shall introduce the notion of hyper KU -valued functions, on a set and&nbsp; investigate some of it’s related properties. Moreover the codes generated by a hyper&nbsp; K U- valued function are constructed and several Examples are given. Furthermore, Example with graphs of binary block code constructed from a hyper&nbsp; KU-algebra and hyper KU-algebra are constructed.</p> Samy Mohammed Mostafa, Rodyna A. Hosny, Reham A. Ghanem Copyright (c) 2019 Samy Mohammed Mostafa, Rodyna A. Hosny, Reham A. Ghanem http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/365 Fri, 30 Aug 2019 11:24:27 +0000 Increasing Velocity, Determining the Values at Equilibrium and Remarkable Rate Constants in Inter–Conversion Processes Revisited http://purkh.com/index.php/mathlab/article/view/373 <p>Inter-conversion processes of labile molecules obey similar laws to those of reversible chemical reactions. The main purpose of this review article is to recall and improve and correct previous results on this subject. Namely, one corrects a result on the relationship between two rate constants, in the case when an intermediate state is involved. One proves that by increasing velocity, the concentrations of the main species at equilibrium are equal. This assertion seems to be true in both cases: when an intermediate state is involved and in the opposite case. In the latter case, one characterizes the property of being a projector for the linear transform defined by the matrix of the differential system which governs the process. Namely, one proves that this transform is a projector if and only if the rate constants have a common value. This value is ½ and equals the equal values of the concentrations at equilibrium.</p> Octav Olteanu Copyright (c) 2019 Octav Olteanu http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/373 Fri, 30 Aug 2019 11:25:15 +0000 Nonlinear Forced Vibration of Piezoelectric and Electrostatically Actuated Nano/Micro Piezoelectric Beam http://purkh.com/index.php/mathlab/article/view/377 <p>In this study, the nonlinear vibration analysis of nano/micro electromechanical (NEMS/MEMS) piezoelectric beam exposed to simultaneous electrostatic and piezoelectric actuation. NEMS/MEMS beam actuate with combined DC and AC electrostatic actuation on the through two upper and lower electrodes. An axial force proportional to the applied DC voltage is produced by piezoelectric layers present via a DC electric voltage applied in the direction of the height of the piezoelectric layers. The governing differential equation of the motion is derived using Hamiltonian principle based on the Eulere-Bernoilli hypothesis and then this partial differential equation (PDE) problem is simplified into an ordinary differential equation (ODE) problem by using the Galerkin approach. Hamiltonian approach has been used to solve the problem and introduce a design strategy. Phase plane diagram of piezoelectric and electrostatically actuated beam has plotted to show the stability of presented nonlinear system and natural frequencies are calculated to use for resonator design. The result compare with the numerical results (fourth-order Runge-Kutta method), and approximate is more acceptable and results show that one could obtain a predesign strategy by prediction of effects of mechanical properties and electrical coefficients on the stability and forced vibration of common electrostatically actuated micro beam.</p> Sayyid H. Hashemi Kachapi, S.GH. Hashemi Kachapi Copyright (c) 2019 Sayyid H. Hashemi Kachapi, S.GH. Hashemi Kachapi http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/377 Fri, 30 Aug 2019 11:25:28 +0000 Definition Of Derivative Function:Logical Error In Mathematics http://purkh.com/index.php/mathlab/article/view/446 <p>The critical analysis of the foundations of the differential calculus is proposed. Methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is shown that differential calculus is fictitious mathematical theory because the concept of the limiting process is the starting point for definition of the derivative function. The passage to the limit “zero” in the definition of the derivative function signifies that the variable quantity takes the only essential value “zero”. This fact leads to the following errors. (1) The definition of the derivative function is based on the violation of the necessary and sufficient condition for the validity of the relationship between the increment of the function argument and the increment of the function because the increment of the function is divided by the zero increment of the argument in the case of the limiting process. (2) The definition of the derivative function is based on the contradiction which is that the increment of the argument is both zero and not zero in the same relationship. This contradiction represents a violation of the formal-logical law of identity and of the formal-logical law of the lack of contradiction. (3) The definition of the differential of function is based on two contradictory (mutually exclusive) features: the differential of the argument is not zero while the increment of the argument in the definition of the derivative function is zero.</p> Temur Kalanov Copyright (c) 2019 Temur Kalanov http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/446 Sat, 31 Aug 2019 07:15:59 +0000 Earlier and Recent Results on Convex Mappings and Convex Optimization http://purkh.com/index.php/mathlab/article/view/495 <p>The main purpose of this review-paper is to recall and partially prove earlier, as well as recent results on convex optimization, published by the author in the last decades. Examples are given along the article. Some of these results have been published recently. Most of theorems have a clear geometric meaning. Minimum norm elements are characterized in normed vector spaces framework. Distanced convex subsets and related parallel hyperplanes preserving the distance are also discussed. The convex involved objective-mappings are real valued or take values in an order-complete vector lattice. On the other side, an optimization problem related to Markov moment problem is solved in the end.</p> Octav Olteanu Copyright (c) 2019 Octav Olteanu http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/495 Sat, 31 Aug 2019 00:00:00 +0000 Insertion of Factors Property in Boolean Like Semi Rings http://purkh.com/index.php/mathlab/article/view/501 <p>In this paper, Insertion of factors property is introduced in a Boolean like semi ring (shortly BLSR) and also<br>study some of its properties. Denote IFP Boolean like semi ring by shortly IFPBLSR. Also, prove that the<br>collection of nilpotent elements forms a sub ring in IFPBLSR. Further prove that annihilator of x, denotes A(x) is<br>an ideal in IFPBLSR Ɍ and also any sub sets of Ɍ, A(Ѕ) is an ideal of Ɍ.</p> BVN Murthy Bhagavathula Copyright (c) 2019 BVN Murthy Bhagavathula http://creativecommons.org/licenses/by/4.0 http://purkh.com/index.php/mathlab/article/view/501 Sat, 31 Aug 2019 08:10:58 +0000