University of KashanMathematics Interdisciplinary Research2538-36396120210301Gordon-Scantlebury and Platt Indices of Random Plane-oriented Recursive Trees11011078710.22052/mir.2020.231250.1213ENRamin KazemiDepartment of Statistics,
Imam Khomeini International University, Qazvin, I. R. IranJournal Article20200514For 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.https://mir.kashanu.ac.ir/article_110787_44ba1fd905ac99274f659196098a164d.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36396120210301DE Sinc-Collocation Method for Solving a Class of Second-Order Nonlinear BVPs112210770110.22052/mir.2020.220050.1195ENAli EftekhariDepartment of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Kashan,
Kashan, IranAbbas SaadatmandiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, IranJournal Article20200215In 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.https://mir.kashanu.ac.ir/article_107701_d8d78cde3127e17364f9e1b9d0b67eff.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36396120210301Adjointness of Suspension and Shape Path Functors233311134810.22052/mir.2021.240322.1246ENTayyebe NasriDepartment of Pure Mathematics,
Faculty of Basic Sciences,
University of Bojnord, Bojnord, IranBehrooz MashayekhyDepartment of Pure Mathematics,
Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad,
Iran0000-0001-5243-0641Hanieh MirebrahimiDepartment of Pure Mathematics,
Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad,
Iran0000-0002-4212-9465Journal Article20201017In 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.https://mir.kashanu.ac.ir/article_111348_a639434f373b5e2c1e63558d731d8772.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36396120210301Schwinger 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)356111134910.22052/mir.2020.204420.1167ENFatemeh MonemiDepartment of Physics, University of Kashan, 87317-53135, I. R. IranFarhad ZamaniDepartment of Physics, University of Kashan, 87317-53135, I. R. Iran0000-0003-1851-1223Journal Article20191009We 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.https://mir.kashanu.ac.ir/article_111349_ca34fec44c952148702bac12fa527227.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36396120210301Auto-Engel Polygroups638311152210.22052/mir.2020.237037.1218ENAli Mosayebi-DorchehDepartment of Mathematics, Payame Noor, University, Tehran, IranMohammad HamidiDepartment of Mathematics, Payame Noor, University, Tehran, IranReza AmeriSchool of Mathematics,
Statistics and Computer Sciences,
University of Tehran,
Tehran, I. R. Iran0000-0001-5760-1788Journal Article20200627This 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.https://mir.kashanu.ac.ir/article_111522_26aefb3680a000cee94cf14b3e61aabc.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36396120210301On n-A-con-cos Groups and Determination of some 3-A-con-cos Groups859510214010.22052/mir.2019.120428.1093ENAhmad GholamiDepartment of Mathematics,
Faculty of Science,
University of Qom,
Qom, I. R. IranFatemeh MahmudiDepartment of Mathematics,
Faculty of Science,
University of Qom,
Qom, I. R. IranJournal Article20180223In 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.https://mir.kashanu.ac.ir/article_102140_501ddd5549ad4d06d5b489e8d7ef1a0b.pdf