University of KashanMathematics Interdisciplinary Research2538-36397420221201The Applications of Algebraic Polynomial Rings in Satellite Coding and Cryptography30132911208310.22052/mir.2022.246273.1345ENAmirBagheriDepartment of Fundamental Sciences
Marand Faculty of Engineering
University of Tabriz
Tabriz, I. R. Iran0000-0001-6503-0508HassanEmamiDepartment of Geomatics Engineering
Marand Faculty of Engineering
University of Tabriz
Tabriz, I. R. IranJournal Article20220412This 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.https://mir.kashanu.ac.ir/article_112083_9a2af93515b1634dc49420f544c841a4.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36397420221201Sombor Index Under Some Graph Products33134211289810.22052/mir.2022.246533.1362ENIrandokhtRezaee AbdolhosseinzadehDepartment of Applied Mathematics,
Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad,
P.O. Box 1159,
Mashhad 91775, IranFreydoonRahbarniaDepartment of Applied Mathematics,
Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad,
P.O. Box 1159,
Mashhad 91775, IranMostafaTavakoliDepartment of Applied Mathematics,
Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad,
P.O. Box 1159,
Mashhad 91775, Iran0000-0002-3315-1759Journal Article20220628Let G=(V, E) be a graph with vertex set V(G) and edge set E(G). The Sombor index of a graph G, SO(G), is defined as ∑<sub>uv∈ E(G)</sub> √(d<sup>2</sup><sub>u</sub>+d<sup>2</sup><sub>v</sub>), where d<sub>u</sub> is the degree of vertex u in V(G). In the present paper, we determine the lower bound for the Sombor index of edge corona, R-edge and R-vertex corona products of two graphs. We also compute the exact value for the Sombor index of the line graphs of subdivision of tadpol, ladder and wheel graphs.https://mir.kashanu.ac.ir/article_112898_a6e0c8632e3ff18c00a444bd12f57f03.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36397420221201The Role of Ordinary Bessel and Hankel Functions in Simulation of Plasma Valve Mechanism in a Loss-Free Metallic Cylindrical Waveguide34335511205310.22052/mir.2022.243283.1321ENAsgharKaramianDepartment of Laser and Photonics,
Faculty of Physics,
University of Kashan,
Kashan, I. R. IranBahramJaziDepartment of Laser and Photonics,
Faculty of Physics,
University of Kashan,
Kashan, I. R. Iran0000-0002-8880-0605SamanehNajariDepartment of Laser and Photonics,
Faculty of Physics,
University of Kashan,
Kashan, I. R. IranJournal Article20211113In 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.https://mir.kashanu.ac.ir/article_112053_ce851ff7603f55b504dd542fb8c8538c.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36397420221201Some Results on Asymptotic Behavior of the Recalls of Random Median Quicksort35737511289710.22052/mir.2022.246282.1347ENMehriJavanianDepartment of Statistics,
University of Zanjan,
Zanjan, I. R. Iran0000-0002-5737-3663Ali MohammadianMosammamDepartment of Statistics,
University of Zanjan,
Zanjan, I. R. Iran0000-0001-8094-7517Journal Article20220414This paper investigates the asymptotic behavior of the number of recalls <em>X<sub>n</sub></em> of the Random Median Quicksort algorithm in order to sort a list of <em>n</em> distinct numbers. As n→∞, 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 <em>X<sub>n</sub></em> correctly normalized is Gaussian. The theoretical results are demonstrated by a simulation study.https://mir.kashanu.ac.ir/article_112897_7cbf053bfc8461d645caeecc6edf1000.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36397420221201S-Acts with Finitely Generated Universal Congruence37738411290510.22052/mir.2022.246505.1357ENAli AsgharGholipourDepartment of Mathematics,
Science and Research Branch,
Islamic Azad University,
Tehran, Iran0000-0002-8473-2246HasanBarzegarDepartment of Mathematics,
Tafresh University, 39518-79611, Tafresh, Iran0000-0002-8916-7733HamidRasoliDepartment of Mathematics,
Science and Research Branch,
Islamic Azad University,
Tehran, IranAbolfazlTehranianDepartment of Mathematics,
Science and Research Branch,
Islamic Azad University,
Tehran, IranJournal Article20220619Universal left congruences on semigroups were studied in “Y. Dandan, V. Gould, T. Quinn-Gregson and R. Zenab, Semigroups with finitely generated universal left congruence, Monat. Math. 190 (2019) 689−724”. We consider universal congruences on acts over monoids and extend the results from semigroups to acts. Among other things, for an S-act A<sub>S</sub> with zero over a monoid S, we prove that being finitely generated of the universal congruence ω<sub>A</sub> and being pseudofinite of A<sub>S</sub> coincide.https://mir.kashanu.ac.ir/article_112905_d254330567fbf36eaca6f1309f1c9f77.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36397420221201The Non-Coprime Graph of Finite Groups3853948741410.22052/mir.2019.172393.1117ENGholamrezaAghababaei-BeniDepartment of Pure Mathematics,
International Campus of Ferdowsi University of Mashhad,
Mashhad, IranAbbasJafarzadehDepartment of Mathematics,
Quchan University of Technology,
Quchan, IranJournal Article20190217The non-coprime graph Π_G of a finite group G is a graph with the vertex<br />set G-{e}, where two distinct vertices u and v are adjacent if they have<br />non-coprime orders. In this paper, the main properties of the Cartesian and<br />tensor product of the non-coprime graph of two finite groups are investigated.<br />We also describe the non-coprime graph of some special groups including the<br />dihedral and semi-dihedral groups. Some open questions are also proposed.https://mir.kashanu.ac.ir/article_87414_f4e8b2a7b27daf1345a4bdf277419ede.pdf