2022-05-20T15:09:54Z
https://mir.kashanu.ac.ir/?_action=export&rf=summon&issue=15269
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2021
6
1
Gordon-Scantlebury and Platt Indices of Random Plane-oriented Recursive Trees
Ramin
Kazemi
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.
Gordon-Scantlebury index
Platt index
the first Zagreb index
plane-oriented recursive tree
asymptotic normality
2021
03
01
1
10
https://mir.kashanu.ac.ir/article_110787_44ba1fd905ac99274f659196098a164d.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2021
6
1
DE Sinc-Collocation Method for Solving a Class of Second-Order Nonlinear BVPs
Ali
Eftekhari
Abbas
Saadatmandi
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
2021
03
01
11
22
https://mir.kashanu.ac.ir/article_107701_d8d78cde3127e17364f9e1b9d0b67eff.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2021
6
1
Adjointness of Suspension and Shape Path Functors
Tayyebe
Nasri
Behrooz
Mashayekhy
Hanieh
Mirebrahimi
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.
Shape category
Topological shape homotopy group
Shape group
Suspensions
2021
03
01
23
33
https://mir.kashanu.ac.ir/article_111348_a639434f373b5e2c1e63558d731d8772.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2021
6
1
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
Farhad
Zamani
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.
Schwinger mechanism
electromagnetic processes
time-dependent electric field
uniform asymptotic approximation
2021
03
01
35
61
https://mir.kashanu.ac.ir/article_111349_ca34fec44c952148702bac12fa527227.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2021
6
1
Auto-Engel Polygroups
Ali
Mosayebi-Dorcheh
Mohammad
Hamidi
Reza
Ameri
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
2021
03
01
63
83
https://mir.kashanu.ac.ir/article_111522_26aefb3680a000cee94cf14b3e61aabc.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2021
6
1
On n-A-con-cos Groups and Determination of some 3-A-con-cos Groups
Ahmad
Gholami
Fatemeh
Mahmudi
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.
n th−autocommutator subgroup
finite abelian groups
dihedral groups
n-A-con-cos groups
2021
03
01
85
95
https://mir.kashanu.ac.ir/article_102140_501ddd5549ad4d06d5b489e8d7ef1a0b.pdf