University of KashanMathematics Interdisciplinary Research2476-49656420211201New Oscillation Results for a Nonlinear Generalization of Euler Differential Equation24325611159310.22052/mir.2021.240252.1237ENVahid RoomiDepartment of Mathematics,
Azarbaijan Shahid Madani University,
Tabriz, I. R. Iran0000000221556433Journal Article20200822In the present work the oscillatory behavior of the solutions of a nonlinear generalization of Euler equation will be considered in which the nonlinearities satisfy the smoothness conditions which guarantee the uniqueness of solutions of initial value problems. However, no conditions of sub(super)linearity are assumed. Some new sufficient conditions are established ensuring oscillation of all solutions of this equation. Examples are also provided to illustrate the relevance of the main results.https://mir.kashanu.ac.ir/article_111593_b666b662939487695f9db8fd09f12023.pdfUniversity of KashanMathematics Interdisciplinary Research2476-49656420211201Hyperideals of (Finite) General Hyperrings25727311163710.22052/mir.2021.240436.1269ENReza AmeriSchool of Mathematics,
Statistic and Computer Sciences,
University of Tehran,
Tehran, I. R. Iran0000-0001-5760-1788Mohammad HamidiDepartment of Mathematics,
Payame Noor University,
Tehran, I. R. IranHoda MohammadiDepartment of Mathematics,
Payame Noor University,
Tehran, I. R. IranJournal Article20210119A general hyperring is an algebraic hypercompositional system (R,+,·) with two hyperoperations ”+" and ” · ”, such that for all x,y ∈ R, x + y and x · y are non-empty subsets of R, and R satisfies the axioms similar to a ring. We introduce and study hyperideals of a general hyperring. In this regards, we construct a connection between classical rings and general hyperrings, specifically, we extend a ring to a general hyperring in nontrivial way. Moreover, a way to construct a general hyperring from set are given. Also, we concentrate on an important class of general hyperrings, which is called Krasner hyperrings, and discuss on their hyperideals. Finally, the set of all hyperideals of a finite general (resp. Krasner) hyperring are considered and its hyperideals are investigated.https://mir.kashanu.ac.ir/article_111637_7393b508a7b45a38ca94f4530cfee81c.pdfUniversity of KashanMathematics Interdisciplinary Research2476-49656420211201Integrals Involving Product of Polynomials and Daubechies Scale Functions27529111163610.22052/mir.2021.239849.1225ENAmjad AlipanahDepartment of Mathematics,
Faculty of Sciences,
University of Kurdistan,
Sanandaj, I. R. IranMasoud PendarDepartment of Mathematics,
Faculty of Sciences,
University of Kurdistan,
Sanandaj, I. R. IranKaveh SadeghiDepartment of Mathematics,
Faculty of Sciences,
University of Kurdistan,
Sanandaj, I. R. IranJournal Article20200716In this paper, we will introduce an algorithm for obtaining integrals of the form ∫<sup>x</sup><sub>0 </sub>t<sup>m</sup> φ(t)dt, m ∈ N ∪ {0}, where φ is the scaling functions of Daubechies wavelet. In order to obtain these integrals in dyadic points for x’s, we have to solve a linear system. We will investigate, sparseness, well-conditioning and strictly diagonal dominant of matrices of these systems.https://mir.kashanu.ac.ir/article_111636_a547b374a73ddef86196027b70d3ce18.pdfUniversity of KashanMathematics Interdisciplinary Research2476-49656420211201The Use of Mathematical Finite Element Method to find the Optimum Waves Amplification by a Novel Elliptical Waveguide29330711158810.22052/mir.2021.240214.1229ENZeinab RahmaniDepartment of Laser and Photonics, Faculty
of Physics, University of Kashan, Kashan, I.R. of Iran000000033311092Journal Article20200724In this paper, a combinatorial elliptic-circular waveguide is introduced to amplify electromagnetic waves. The cross-section of this waveguide is elliptic and filled by a dielectric material, whereas two axial circular hollows have been created in it. One of the hollows has been filled by an unmagnetized cold plasma and a relativistic pencil electron beam(RPEB) is injected inside other hollow. By applying an adaptive finite element method(FEM), electromagnetic slow waves amplification in the waveguide is investigated. We study variations of growth rate of excited microwaves under influence of different factors. The purpose of investigating the effect of various parameters of this waveguide such as plasma and electron beam radiuses, the RPEB location, dielectric constant and beam current intensity; is to introduce the waveguide with optimal configuration and parameters to obtain the highest wave growth rate.https://mir.kashanu.ac.ir/article_111588_4fe49fb43801092cd65e9f44742ab673.pdfUniversity of KashanMathematics Interdisciplinary Research2476-49656420211201Commutativity Degree of Certain Finite AC-Groups30931711189810.22052/mir.2022.243081.1307ENAzizollah AzadDepartment of Mathematics,
Faculty of Sciences,
Arak University,
Arak, I. R. Iran0000-0002-7950-0977Sakineh RahbariyanDepartment of Mathematics,
Faculty of Sciences,
Arak University,
Arak, I. R. Iran0000-0001-7193-3850Journal Article20210909 <span class="fontstyle0">For a finite group </span><span class="fontstyle2">G</span><span class="fontstyle0">, the probability of two elements of </span><span class="fontstyle2">G </span><span class="fontstyle0">that commute is the commutativity degree of </span><span class="fontstyle2">G </span><span class="fontstyle0">denoted by </span><span class="fontstyle2">P</span><span class="fontstyle3">(</span><span class="fontstyle2">G</span><span class="fontstyle3">)</span><span class="fontstyle0">. As a matter of fact, if </span><span class="fontstyle4">C </span><span class="fontstyle3">= </span><span class="fontstyle4">{</span><span class="fontstyle3">(</span><span class="fontstyle2">a; b</span><span class="fontstyle3">) ∈</span> <span class="fontstyle2">G</span><span class="fontstyle4">×</span><span class="fontstyle2">G </span><span class="fontstyle4">| </span><span class="fontstyle2">ab </span><span class="fontstyle3">= </span><span class="fontstyle2">ba</span><span class="fontstyle4">}</span><span class="fontstyle0">, then </span><span class="fontstyle2">P</span><span class="fontstyle3">(</span><span class="fontstyle2">G</span><span class="fontstyle3">) = </span><span class="fontstyle5">|</span><span class="fontstyle6">C</span><span class="fontstyle5">|/|G|</span><span class="fontstyle7"><sup>2</sup> </span><span class="fontstyle0">. In this paper, we are going to find few formulas for </span><span class="fontstyle2">P</span><span class="fontstyle3">(</span><span class="fontstyle2">G</span><span class="fontstyle3">) </span><span class="fontstyle0">independent of </span> <span class="fontstyle5">|</span><span class="fontstyle6">C</span><span class="fontstyle5">|</span><span class="fontstyle0">; for some </span><span class="fontstyle3">AC</span><span class="fontstyle0">-groups, and also in some special cases of finite minimal non-abelian groups. Moreover, the study will present implications for certain qualified finite groups.</span>https://mir.kashanu.ac.ir/article_111898_11db00fbda8eb7ea52a810a86b84a058.pdfUniversity of KashanMathematics Interdisciplinary Research2476-49656420211201Optimal Solution for the System of Differential Inclusion in Hilbert Space31932711190510.22052/mir.2021.243050.1303ENZeinab SoltaniDepartment of Pure Mathematics,
University of Kashan,
Kashan, 87317-53153, I. R. IranMarzie DarabiBasic Science Group,
Golpayegan College of Engineering,
Isfahan University of Technology,
Golpayegan, 87717-67498, IranJournal Article20210830In this paper, we study the existence of the following optimal solution for the system of differential inclusion<br />y′ ∈ Φ(t,y(t)) a.e. t ∈ I = [t<sub>0</sub>,b] and y(t<sub>0</sub>) = u<sub>2</sub>,<br />y′ ∈ Ψ(t,y(t)) a.e. t ∈ I = [t<sub>0</sub>,b] and y(t<sub>0</sub>) = u<sub>1</sub>.<br />in a Hilbert space, where Φ and Ψ are multivalued maps. Our existence result is obtained via selection technique and the best proximity point methods reducing the problem to a differential inclusion.https://mir.kashanu.ac.ir/article_111905_9d81f269f8871bf246b843eb39cf360d.pdf