Mathematics Interdisciplinary Research
https://mir.kashanu.ac.ir/
Mathematics Interdisciplinary Researchendaily1Thu, 01 Sep 2022 00:00:00 +0430Thu, 01 Sep 2022 00:00:00 +0430On a Maximal Subgroup 2^6:(3^. S6) of M24
https://mir.kashanu.ac.ir/article_112777.html
The Mathieu group M24 has a maximal subgroup of the form G ̅=N:G, where N=26 and G=3. S6 &cong; 3. PGL2 (9). Using Atlas, we can see that M24 has only one maximal subgroup of type 26:(3. S6). The group is a split extension of an elementary abelian group, N=26 by a non-split extensionmgroup, G=3. S6. The Fischer matrices for each class representative of G are computed which together with character tables of inertia factor groups of G lead to the full character table of G ̅. The complete fusion of G ̅ into the parent group M24 has been determined using the technique of set intersections of characters.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 vertex set G-{e}, where two distinct vertices u and v are adjacent if they have non-coprime orders. In this paper, the main properties of the Cartesian and tensor product of the non-coprime graph of two finite groups are investigated. We also describe the non-coprime graph of some special groups including the dihedral and semi-dihedral groups. Some open questions are also proposed.More on the Enumeration of Some Kind of Dominating Sets in Cactus Chains
https://mir.kashanu.ac.ir/article_112056.html
A non-empty set S &sube; V is a dominating set, if every vertex not in S is adjacent to at least one vertex in S, and S is a total dominating set, if every vertex of V is adjacent to some vertices of S. We enumerate dominating sets, non-split dominating sets and total dominating sets in several classes of cactus chains.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.Efficient Generation 1.5THz Pulses Using DASC/GaAs and DASB/GaAs Multilayer Structures via Difference Frequency Generation 1.5 µm Femtosecond Laser Pulses
https://mir.kashanu.ac.ir/article_112092.html
We present a study of high efficient terahertz (THz) wave generation in DASB/GaAs, DASC/GaAs, and DAST/GaAs multilayer structures at 1.5THz via difference frequency generation (DFG) process with 1.5&micro;m femtosecond laser pulses. We also compare the conversion efficiency in proposed structures with DASB/SiO2, DASC/SiO2, and DAST/SiO2 multilayer structures and bulk crystals DASB, DASC, and DAST. These structures compensate for phase mismatching in bulk crystals DASB, DASC, and DAST and increase conversion efficiency from 10-5 in bulk organic crystals up to 10-3 in multilayer structures. We show that DASC/GaAs is the best structure to generate 1.5THz waves.Continuity and Differentiability of Solutions with Respect to Initial Conditions and Peano Theorem for Uncertain Differential Equations
https://mir.kashanu.ac.ir/article_112082.html
&nbsp;In this paper we study the dependence of solutions of uncertain initial value problems (UIVP) on the initial values. Introducing a contraction mapping and using Banach Fixed Point Theorem (BFPT), the existence and uniqueness (EaU) of solutions of the UIVP will be proven. We show that under appropriate assumptions, the solutions of UIVP are continues and differentiable with respect to initial conditions (ICs). The paper will be ended by proving a theorem about the existence of solutions of an autonomous UIVP under weaker conditions. This theorem is a generalization of PeanoTheorem to UDEs.The Role of Ordinary Bessel Function and Hankel Function 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.Providing a Framework for Increasing Security in Digital Document Management Systems
https://mir.kashanu.ac.ir/article_112060.html
In the era of information technology and the expansion of global networks, digital document management systems play a crucial role in providing services. The use of digital instead of paper documents has become more common to reduce the administrative costs in small and large organizations. One of the most significant concerns of such systems, though, is the security of documents against alteration or distortion. There are various ways to increase the security of digital documents and this paper is aimed at providing a new framework of the combination of steganography and cryptography to increase the security of digital documents.The proposed method first has been tested and reviewed with MATLAB 2018 software on standard images such as Lena, Baboon and Pepper. Then, it has been tested on digital documents of the Social Security Organization through the proposed conceptual model which utilizes a combination of unique image features to generate messages. The evaluation of results indicates the effectiveness of the proposed method and its applicability in digital document management systems.Chebyshev Cardinal Wavelets for Nonlinear Volterra Integral Equations of the Second Kind
https://mir.kashanu.ac.ir/article_112483.html
This study concentrated on the numerical solution of a nonlinear Volterra integral equation. The approach is accorded to a type of orthogonal wavelets named the Chebyshev cardinal wavelets. The undetermined solution is extended concerning the Chebyshev cardinal wavelets involving unknown coefficients. Hence, a system of nonlinear algebraic equations is drawn out by changing the introduced expansion to the predetermined problem, applying the generated operational matrix, and supposing the cardinality of the basis functions. Conclusively, the estimated solution is achieved by figuring out the mentioned system. Relatively, the convergence of the founded procedure process is reviewed in the Sobolev space. In addition, the results achieved from utilizing the method in some instances display the applicability and validity of the method.Exact Solution of Schrödinger 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 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.