University of Kashan Mathematics Interdisciplinary Research 2538-3639 6 4 2021 12 01 New Oscillation Results for a Nonlinear Generalization of Euler Differential Equation 243 256 111593 10.22052/mir.2021.240252.1237 EN Vahid Roomi Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I. R. Iran Journal Article 2020 08 22 ‎‎‎‎In 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.pdf

University of Kashan Mathematics Interdisciplinary Research 2538-3639 6 4 2021 12 01 Hyperideals of (Finite) General Hyperrings 257 273 111637 10.22052/mir.2021.240436.1269 EN Reza Ameri School of Mathematics, Statistic and Computer Sciences, University of Tehran, Tehran, I. R. Iran 0000-0001-5760-1788 Mohammad Hamidi Department of Mathematics, Payame Noor University, Tehran, I. R. Iran Hoda Mohammadi Department of Mathematics, Payame Noor University, Tehran, I. R. Iran Journal Article 2021 01 19 A 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.pdf

University of Kashan Mathematics Interdisciplinary Research 2538-3639 6 4 2021 12 01 Integrals Involving Product of Polynomials and Daubechies Scale Functions 275 291 111636 10.22052/mir.2021.239849.1225 EN Amjad Alipanah Department of Mathematics, Faculty of Sciences, University of Kurdistan, Sanandaj, I. R. Iran Masoud Pendar Department of Mathematics, Faculty of Sciences, University of Kurdistan, Sanandaj, I. R. Iran Kaveh Sadeghi Department of Mathematics, Faculty of Sciences, University of Kurdistan, Sanandaj, I. R. Iran Journal Article 2020 07 16 In this paper, we will introduce an algorithm for obtaining integrals of the form ∫x0 tm 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.pdf

University of Kashan Mathematics Interdisciplinary Research 2538-3639 6 4 2021 12 01 The Use of Mathematical Finite Element Method to find the Optimum Waves Amplification by a Novel Elliptical Waveguide 293 307 111588 10.22052/mir.2021.240214.1229 EN Zeinab Rahmani Department of Laser and Photonics, Faculty of Physics, University of Kashan, Kashan, I.R. of Iran Journal Article 2020 07 24 In 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.pdf

University of Kashan Mathematics Interdisciplinary Research 2538-3639 6 4 2021 12 01 Commutativity Degree of Certain Finite AC-Groups 309 317 111898 10.22052/mir.2022.243081.1307 EN Azizollah Azad Department of Mathematics, Faculty of Sciences, Arak University, Arak, I. R. Iran Sakineh Rahbariyan Department of Mathematics, Faculty of Sciences, Arak University, Arak, I. R. Iran Journal Article 2021 09 09 For a finite group G, the probability of two elements of G that commute is the commutativity degree of G denoted by P(G). As a matter of fact, if C = {(a; b) ∈ G×G | ab = ba}, then P(G) = |C|/|G|2 . In this paper, we are going to find few formulas for P(G) independent of |C|; for some AC-groups, and also in some special cases of finite minimal non-abelian groups. Moreover, the study will present implications for certain qualified finite groups.

https://mir.kashanu.ac.ir/article_111898_11db00fbda8eb7ea52a810a86b84a058.pdf

University of Kashan Mathematics Interdisciplinary Research 2538-3639 6 4 2021 12 01 Optimal Solution for the System of Differential Inclusion in Hilbert Space 319 327 111905 10.22052/mir.2021.243050.1303 EN Zeinab Soltani Department of Pure Mathematics, University of Kashan, Kashan, 87317-53153, I. R. Iran Marzie Darabi Basic Science Group, Golpayegan College of Engineering, Isfahan University of Technology, Golpayegan, 87717-67498, Iran Journal Article 2021 08 30 In this paper, we study the existence of the following optimal solution for the system of differential inclusion y′ ∈ Φ(t,y(t)) a.e. t ∈ I = [t0,b] and y(t0) = u2, y′ ∈ Ψ(t,y(t)) a.e. t ∈ I = [t0,b] and y(t0) = u1. 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