University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
4
2021
12
01
New Oscillation Results for a Nonlinear Generalization of Euler Differential Equation
243
256
EN
Vahid
Roomi
0000000221556433
Department of Mathematics,
Azarbaijan Shahid Madani University,
Tabriz, I. R. Iran
roomi@azaruniv.ac.ir
10.22052/mir.2021.240252.1237
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.
Oscillation,Lienard system,Euler Equations
https://mir.kashanu.ac.ir/article_111593.html
https://mir.kashanu.ac.ir/article_111593_b666b662939487695f9db8fd09f12023.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
4
2021
12
01
Hyperideals of (Finite) General Hyperrings
257
273
EN
Reza
Ameri
0000-0001-5760-1788
School of Mathematics,
Statistic and Computer Sciences,
University of Tehran,
Tehran, I. R. Iran
rameri@ut.ac.ir
Mohammad
Hamidi
Department of Mathematics,
Payame Noor University,
Tehran, I. R. Iran
m.hamidi20@gmail.com
Hoda
Mohammadi
Department of Mathematics,
Payame Noor University,
Tehran, I. R. Iran
hodamohamadi@student.pnu.ac.ir
10.22052/mir.2021.240436.1269
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.
General hyperring,Hyperideals,Krasner hyperring
https://mir.kashanu.ac.ir/article_111637.html
https://mir.kashanu.ac.ir/article_111637_7393b508a7b45a38ca94f4530cfee81c.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
4
2021
12
01
Integrals Involving Product of Polynomials and Daubechies Scale Functions
275
291
EN
Amjad
Alipanah
Department of Mathematics,
Faculty of Sciences,
University of Kurdistan,
Sanandaj, I. R. Iran
a.alipanah@uok.ac.ir
Masoud
Pendar
Department of Mathematics,
Faculty of Sciences,
University of Kurdistan,
Sanandaj, I. R. Iran
pendarmasoud@gmail.com
Kaveh
Sadeghi
Department of Mathematics,
Faculty of Sciences,
University of Kurdistan,
Sanandaj, I. R. Iran
k.sadeghi225@gmail.com
10.22052/mir.2021.239849.1225
In 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.
Daubechies wavelets,Scaling functions,Dyadic points,Diagonal dominant,Well-condition
https://mir.kashanu.ac.ir/article_111636.html
https://mir.kashanu.ac.ir/article_111636_a547b374a73ddef86196027b70d3ce18.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
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
EN
Zeinab
Rahmani
000000033311092
Department of Laser and Photonics, Faculty
of Physics, University of Kashan, Kashan, I.R. of Iran
z.rahmani@kashanu.ac.ir
10.22052/mir.2021.240214.1229
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.
Combinatorial dielectric-plasma waveguide,Relativistic pencil electron beam,Time growth rate,Finite element method
https://mir.kashanu.ac.ir/article_111588.html
https://mir.kashanu.ac.ir/article_111588_4fe49fb43801092cd65e9f44742ab673.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
4
2021
12
01
Commutativity Degree of Certain Finite AC-Groups
309
317
EN
Azizollah
Azad
0000-0002-7950-0977
Department of Mathematics,
Faculty of Sciences,
Arak University,
Arak, I. R. Iran
a-azad@araku.ac.ir
Sakineh
Rahbariyan
0000-0001-7193-3850
Department of Mathematics,
Faculty of Sciences,
Arak University,
Arak, I. R. Iran
s-rahbariyan@araku.ac.ir
10.22052/mir.2022.243081.1307
<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>
AC-group,Commutativity degree,Minimal non-abelian group
https://mir.kashanu.ac.ir/article_111898.html
https://mir.kashanu.ac.ir/article_111898_11db00fbda8eb7ea52a810a86b84a058.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
4
2021
12
01
Optimal Solution for the System of Differential Inclusion in Hilbert Space
319
327
EN
Zeinab
Soltani
Department of Pure Mathematics,
University of Kashan,
Kashan, 87317-53153, I. R. Iran
z.soltani@kashanu.ac.ir
Marzie
Darabi
Basic Science Group,
Golpayegan College of Engineering,
Isfahan University of Technology,
Golpayegan, 87717-67498, Iran
m.darabi@iut.ac.ir
10.22052/mir.2021.243050.1303
In 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.
Differential inclusion,Best proximity point,Selection theorem
https://mir.kashanu.ac.ir/article_111905.html
https://mir.kashanu.ac.ir/article_111905_9d81f269f8871bf246b843eb39cf360d.pdf