University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
1
2021
03
01
Gordon-Scantlebury and Platt Indices of Random Plane-oriented Recursive Trees
1
10
EN
Ramin
Kazemi
Department of Statistics,
Imam Khomeini International University, Qazvin, I. R. Iran
r.kazemi@sci.ikiu.ac.ir
10.22052/mir.2020.231250.1213
For a simple graph <em>G</em>, the Gordon-Scantlebury index of <em>G</em> is equal to the number of paths of length two in <em>G</em>, and the Platt index is equal to the total sum of the degrees of all edges in <em>G</em>. In this paper, we study these indices in random plane-oriented recursive trees through a recurrence equation for the first Zagreb index. As n ∊ ∞, the asymptotic normality of these indices are given.
Gordon-Scantlebury index,Platt index,the first Zagreb index,plane-oriented recursive tree,asymptotic normality
https://mir.kashanu.ac.ir/article_110787.html
https://mir.kashanu.ac.ir/article_110787_44ba1fd905ac99274f659196098a164d.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
1
2021
03
01
DE Sinc-Collocation Method for Solving a Class of Second-Order Nonlinear BVPs
11
22
EN
Ali
Eftekhari
Department of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Kashan,
Kashan, Iran
eftekhari@kashanu.ac.ir
Abbas
Saadatmandi
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
saadatmandi@kashanu.ac.ir
10.22052/mir.2020.220050.1195
In this work, we develop the Sinc-collocation method coupled with a Double exponential transformation for solving a special class of nonlinear second-order multi-point boundary value problems (MBVP). This method attains a convergence rate of exponential order. Four numerical examples are also examined to demonstrate the efficiency and functionality of the newly proposed approach.
Double Exponential transformation,Collocation points,Multi-point boundary value problem,Sinc methods
https://mir.kashanu.ac.ir/article_107701.html
https://mir.kashanu.ac.ir/article_107701_d8d78cde3127e17364f9e1b9d0b67eff.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
1
2021
03
01
Adjointness of Suspension and Shape Path Functors
23
33
EN
Tayyebe
Nasri
Department of Pure Mathematics,
Faculty of Basic Sciences,
University of Bojnord, Bojnord, Iran
t.nasri@ub.ac.ir
Behrooz
Mashayekhy
0000-0001-5243-0641
Department of Pure Mathematics,
Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad,
Iran
bmashf@um.ac.ir
Hanieh
Mirebrahimi
0000-0002-4212-9465
Department of Pure Mathematics,
Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad,
Iran
h_mirebrahimi@um.ac.ir
10.22052/mir.2021.240322.1246
In this paper, we introduce a subcategory ∼<em>Sh</em><sub>*</sub> of Sh<sub>*</sub> and obtain some results in this subcategory. First we show that there is a natural bijection Sh(∑(X, x), (Y,y))≅Sh((X,x),Sh((I, Ī),(Y,y))), for every (Y,y)∈ ~Sh<sub>*</sub> and (X,x)∈ Sh<sub>*</sub>. By this fact, we prove that for any pointed topological space (X,x) in ∼<em>Sh</em><sub>*</sub>,π<sub>n</sub><sup>top</sup>(X,x)≅ π<sub>n-k</sub><sup>top</sup>(Sh((S<sup>k</sup>, *),(X,x)), e<sub>x</sub>), for all 1≤k ≤n-1.
Shape category,Topological shape homotopy group,Shape group,Suspensions
https://mir.kashanu.ac.ir/article_111348.html
https://mir.kashanu.ac.ir/article_111348_a639434f373b5e2c1e63558d731d8772.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
1
2021
03
01
Schwinger Pair Creation by a Time-Dependent Electric Field in de Sitter Space with the Energy Density E_μ E^μ=E^2 a^2(τ)
35
61
EN
Fatemeh
Monemi
Department of Physics, University of Kashan, 87317-53135, I. R. Iran
f-monemi@grad.kashanu.ac.ir
Farhad
Zamani
0000-0003-1851-1223
Department of Physics, University of Kashan, 87317-53135, I. R. Iran
zamani@kashanu.ac.ir
10.22052/mir.2020.204420.1167
We investigate Schwinger pair creation of charged scalar particles from a time-dependent electric field background in (1+3)-dimensional de Sitter spacetime. Since the field's equation of motion has no exact analytical solution, we employ emph{Olver's uniform asymptotic approximation method} to find its analytical approximate solutions. Depending on the value of the electric field <em>E</em>, and the particle's mass <em>m</em>, and wave vector <em><strong>k</strong></em>, the equation of motion has two turning points, whose different natures (real, complex, or double) lead to different pair production probability. More precisely, we find that for the turning points to be real and single, <em>m</em> and <em><strong>k</strong></em> should be small, and the more smaller are the easier to create the particles. On the other hand, when <em>m</em> or <em><strong>k</strong></em> is large enough, both turning points are complex, and the pair creation is exponentially suppressed. In addition, we study the pair creation in the weak electric field limit, and find that the semi-classical electric current responds as E<sup>1-2√μ²</sup>, where μ<sup>²</sup>=(9/4)-(m<sup>2</sup><sub>ds</sub>/ H<sup>2</sup>). Thus, below a critical mass m<sub>cr</sub>=√2 H, the current exhibits the infrared hyperconductivity.
Schwinger mechanism,electromagnetic processes,time-dependent electric field,uniform asymptotic approximation
https://mir.kashanu.ac.ir/article_111349.html
https://mir.kashanu.ac.ir/article_111349_ca34fec44c952148702bac12fa527227.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
1
2021
03
01
Auto-Engel Polygroups
63
83
EN
Ali
Mosayebi-Dorcheh
Department of Mathematics, Payame Noor, University, Tehran, Iran
alimosayebi@pnu.ac.ir
Mohammad
Hamidi
Department of Mathematics, Payame Noor, University, Tehran, Iran
m.hamidi@pnu.ac.ir
Reza
Ameri
0000-0001-5760-1788
School of Mathematics,
Statistics and Computer Sciences,
University of Tehran,
Tehran, I. R. Iran
rameri@ut.ac.ir
10.22052/mir.2020.237037.1218
This paper introduces the concept of auto–Engel polygroups via the heart of hypergroups and investigates the relation between of auto–Engel polygroups and auto–nilpotent polygroups. Indeed, we show that the concept of heart of hypergroups plays an important role on construction of auto–Engel polygroups. This study considers the notation of characteristic set in hypergroups with respect to automorphism of hypergroups and shows that the heart of hypergroups is a characteristic set in hypergroups.
Auto–Engel polygroup,characteristic(-closure) set,general fundamental relation
https://mir.kashanu.ac.ir/article_111522.html
https://mir.kashanu.ac.ir/article_111522_26aefb3680a000cee94cf14b3e61aabc.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
1
2021
03
01
On n-A-con-cos Groups and Determination of some 3-A-con-cos Groups
85
95
EN
Ahmad
Gholami
Department of Mathematics,
Faculty of Science,
University of Qom,
Qom, I. R. Iran
a.gholami@qom.ac.ir
Fatemeh
Mahmudi
Department of Mathematics,
Faculty of Science,
University of Qom,
Qom, I. R. Iran
mahmodi.fateme64@gmail.com
10.22052/mir.2019.120428.1093
In this paper, we introduce the concept of n-A-con-cos groups, n ≥ 2, mention some properties of them and determine all finite abelian groups with at most two direct factors. As a consequence, it is proved that dihedral groups D<sub>2m</sub> in which m has at most two prime factors are n-A-con-cos.
n th−autocommutator subgroup,finite abelian groups,dihedral groups,n-A-con-cos groups
https://mir.kashanu.ac.ir/article_102140.html
https://mir.kashanu.ac.ir/article_102140_501ddd5549ad4d06d5b489e8d7ef1a0b.pdf