Mathematics Interdisciplinary Research
https://mir.kashanu.ac.ir/
Mathematics Interdisciplinary Researchendaily1Thu, 01 Dec 2022 00:00:00 +0330Thu, 01 Dec 2022 00:00:00 +0330The Applications of Algebraic Polynomial Rings in Satellite Coding and Cryptography
https://mir.kashanu.ac.ir/article_112083.html
This survey illustrates and investigates the application of polynomial rings over finite fields to generate PRN codes for Global Navigation Satellite System (GNSS) satellites. In GNSS, satellites continually broadcast signals at two or more frequencies, including pseudo-random noise (PRN) codes. Each GNSS satellite has its own PRN code, and due to the unique mathematical properties of PRN codes, all satellites can communicate at the same frequency without interfering with another one. Although PRN code appears to be devoid of any discernible structure, it is composed of a deterministic series of pulses that will repeat itself after its period. The PRN code generator employs two shift registers known as Gold polynomials, and the suitable polynomial is decided by the number of satellites. The approach used in satellites is based on the usage of two primitive polynomials, with the output of the first polynomial being used as input for the second polynomial.Sombor Index Under Some Graph Products
https://mir.kashanu.ac.ir/article_112898.html
&lrm;Let G=(V&lrm;, &lrm;E) be a graph with vertex set V(G) and edge set E(G)&lrm;. &lrm;The Sombor index of a graph G&lrm;, &lrm;SO(G)&lrm;, &lrm;is defined as &sum;uv&isin; E(G) &radic;(d2u+d2v), &lrm;where du is the degree of vertex u in V(G)&lrm;. &lrm;In the present paper&lrm;, &lrm;we determine the lower bound for the Sombor index of edge corona&lrm;, &lrm;R-edge and R-vertex corona products of two graphs&lrm;. &lrm;We also compute the exact value for the Sombor index of the line graphs of subdivision of tadpol&lrm;, &lrm;ladder and wheel graphs&lrm;.On the Maximal Graph of a Commutative Ring
https://mir.kashanu.ac.ir/article_111486.html
Let R be a commutative ring with nonzero identity. Throughout this paper we explore some properties of two subgraphs of the maximal graph of R.The Role of Ordinary Bessel and Hankel Functions in Simulation of Plasma Valve Mechanism in a Loss-Free Metallic Cylindrical Waveguide
https://mir.kashanu.ac.ir/article_112053.html
In this paper, a finite cylindrical plasma waveguide is investigated as a plasma valve in the path of a non-dissipative cylindrical waveguide with metal walls. Theoretical simulation to investigate the effect of the main parameters of this plasma valve on the transmission coefficients and reflection coefficients of the symmetric modes is the main part of this paper. The transmittance coefficients of electromagnetic waves in each symmetric mode are introduced in terms of Henkel functions and ordinary Bessel functions, and the role of these functions in the purification of some modes is investigated. Taking into account the boundary conditions, the transmission coefficient of the output wave modes from the plasma valve are obtained. The diagrams of the mentioned coefficient versus the incident wave frequency, geometry dimensions and the type of the used plasma in the valve are studied.Some Results on Asymptotic Behavior of the Recalls of Random Median Quicksort
https://mir.kashanu.ac.ir/article_112897.html
This paper investigates the asymptotic behavior of the number of recalls &nbsp;Xn of the Random Median Quicksort algorithm in order to sort a list of n distinct numbers. As&nbsp; n&rarr;&infin;, we provide the asymptotics of the expectation and variance of the recalls. Furthermore, by utilizing a refined version of the contraction method for degenerate limits, we show the limiting distribution of Xn correctly normalized is Gaussian. The theoretical results are demonstrated by a simulation study.S-Acts with Finitely Generated Universal Congruence
https://mir.kashanu.ac.ir/article_112905.html
Universal left congruences on semigroups were studied in &ldquo;Y. Dandan, V. Gould, T. Quinn-Gregson and R. Zenab, Semigroups with finitely generated universal left congruence, Monat. Math. 190 (2019) 689&minus;724&rdquo;. We consider universal congruences on acts over monoids and extend the results from semigroups to acts. Among other things, for an S-act AS with zero over a monoid S, we prove that being finitely generated of the universal congruence &omega;A and being pseudofinite of AS coincide.Exact Solution of SchrÃ¶dinger Equation for Pentaquark Systems
https://mir.kashanu.ac.ir/article_112796.html
In this paper we present an exact analytical solution for five interacting quarks. We solve Schr&ouml;dinger equation for pentaquarks in the framework of five-body and two-body problems. For this purpose, we utilize Yukawa potential in Jacobi coordinates. Also finding the relation between the reduced masses and coupling constants of pentaquarks, we obtain the coupling constant of Yukawa potential for pentaquark systems. We calculate the energy of these systems in their ground state. The results are well consistent with the theoretical results. Our procedure to obtain these results is appropriate for other potentials and n-body systems.The Non-Coprime Graph of Finite Groups
https://mir.kashanu.ac.ir/article_87414.html
The non-coprime graph &Pi;_G of a finite group G is a graph with the vertexset G-{e}, where two distinct vertices u and v are adjacent if they havenon-coprime orders. In this paper, the main properties of the Cartesian andtensor product of the non-coprime graph of two finite groups are investigated.We also describe the non-coprime graph of some special groups including thedihedral and semi-dihedral groups. Some open questions are also proposed.The Effect of the Caputo Fractional Derivative on Polynomiography
https://mir.kashanu.ac.ir/article_112883.html
This paper presents the visualization process of finding the roots of a complex polynomial - which is called polynomiography - by the Caputo fractional derivative. In this work, we substitute the variable-order Caputo fractional derivative for classic derivative in Newton&rsquo;s iterative method. To investigate the proposed root-finding method, we apply it for two polynomials p(z) = z5 &minus;1 and p(z) = &minus;2z4 + z3 + z2 &minus;2z&minus;1 on the complex plan and compute the MNI and CAI parameters. Presented examples show that through the expressed process, we can obtain very interesting fractal patterns. The obtained patterns show that the proposed method has potential artistic application.