Gordon-Scantlebury and Platt Indices of Random Plane-oriented Recursive Trees
Ramin
Kazemi
Department of Statistics,
Imam Khomeini International University, Qazvin, I. R. Iran
author
text
article
2021
eng
For a simple graph G, the Gordon-Scantlebury index of G is equal to the number of paths of length two in G, and the Platt index is equal to the total sum of the degrees of all edges in G. 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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
6
v.
1
no.
2021
1
10
https://mir.kashanu.ac.ir/article_110787_44ba1fd905ac99274f659196098a164d.pdf
dx.doi.org/10.22052/mir.2020.231250.1213
DE Sinc-Collocation Method for Solving a Class of Second-Order Nonlinear BVPs
Ali
Eftekhari
Department of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Kashan,
Kashan, Iran
author
Abbas
Saadatmandi
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
author
text
article
2021
eng
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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
6
v.
1
no.
2021
11
22
https://mir.kashanu.ac.ir/article_107701_d8d78cde3127e17364f9e1b9d0b67eff.pdf
dx.doi.org/10.22052/mir.2020.220050.1195
Adjointness of Suspension and Shape Path Functors
Tayyebe
Nasri
Department of Pure Mathematics,
Faculty of Basic Sciences,
University of Bojnord, Bojnord, Iran
author
Behrooz
Mashayekhy
Department of Pure Mathematics,
Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad,
Iran
author
Hanieh
Mirebrahimi
Department of Pure Mathematics,
Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad,
Iran
author
text
article
2021
eng
In this paper, we introduce a subcategory ∼Sh* of Sh* 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* and (X,x)∈ Sh*. By this fact, we prove that for any pointed topological space (X,x) in ∼Sh*,πntop(X,x)≅ πn-ktop(Sh((Sk, *),(X,x)), ex), for all 1≤k ≤n-1.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
6
v.
1
no.
2021
23
33
https://mir.kashanu.ac.ir/article_111348_a639434f373b5e2c1e63558d731d8772.pdf
dx.doi.org/10.22052/mir.2021.240322.1246
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)
Fatemeh
Monemi
Department of Physics, University of Kashan, 87317-53135, I. R. Iran
author
Farhad
Zamani
Department of Physics, University of Kashan, 87317-53135, I. R. Iran
author
text
article
2021
eng
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 E, and the particle's mass m, and wave vector k, 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, m and k should be small, and the more smaller are the easier to create the particles. On the other hand, when m or k 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 E1-2√μ², where μ²=(9/4)-(m2ds/ H2). Thus, below a critical mass mcr=√2 H, the current exhibits the infrared hyperconductivity.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
6
v.
1
no.
2021
35
61
https://mir.kashanu.ac.ir/article_111349_ca34fec44c952148702bac12fa527227.pdf
dx.doi.org/10.22052/mir.2020.204420.1167
Auto-Engel Polygroups
Ali
Mosayebi-Dorcheh
Department of Mathematics, Payame Noor, University, Tehran, Iran
author
Mohammad
Hamidi
Department of Mathematics, Payame Noor, University, Tehran, Iran
author
Reza
Ameri
School of Mathematics,
Statistics and Computer Sciences,
University of Tehran,
Tehran, I. R. Iran
author
text
article
2021
eng
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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
6
v.
1
no.
2021
63
83
https://mir.kashanu.ac.ir/article_111522_26aefb3680a000cee94cf14b3e61aabc.pdf
dx.doi.org/10.22052/mir.2020.237037.1218
On n-A-con-cos Groups and Determination of some 3-A-con-cos Groups
Ahmad
Gholami
Department of Mathematics,
Faculty of Science,
University of Qom,
Qom, I. R. Iran
author
Fatemeh
Mahmudi
Department of Mathematics,
Faculty of Science,
University of Qom,
Qom, I. R. Iran
author
text
article
2021
eng
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 D2m in which m has at most two prime factors are n-A-con-cos.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
6
v.
1
no.
2021
85
95
https://mir.kashanu.ac.ir/article_102140_501ddd5549ad4d06d5b489e8d7ef1a0b.pdf
dx.doi.org/10.22052/mir.2019.120428.1093