University of KashanMathematics Interdisciplinary Research2538-36396120210301Gordon-Scantlebury and Platt Indices of Random Plane-oriented Recursive Trees11011078710.22052/mir.2020.231250.1213ENRaminKazemiDepartment 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.2020.220050.1195ENAliEftekhariDepartment of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Kashan,
Kashan, IranAbbasSaadatmandiDepartment 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.2021.240322.1246ENTayyebeNasriDepartment of Pure Mathematics,
Faculty of Basic Sciences,
University of Bojnord, Bojnord, IranBehroozMashayekhyDepartment of Pure Mathematics,
Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad,
Iran0000-0001-5243-0641HaniehMirebrahimiDepartment 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 $widetilde{Sh}_*$ of Sh$_*$ and obtain some results in this subcategory. First we show that there is a natural bijection $Sh (Sigma (X, x), (Y,y))cong Sh((X,x),Sh((I, dot{I}),(Y,y)))$, for every $(Y,y)in widetilde{Sh}_*$ and $(X,x)in Sh_*$. By this fact, we prove that for any pointed topological space $(X,x)$ in $widetilde{Sh}_*$, $check{pi}_n^{top}(X,x)cong check{pi}_{n-k}^{top}(Sh((S^k, *),(X,x)), e_x)$, for all $1leq k leq n-1$https://mir.kashanu.ac.ir/article_111348_667a50fe5ef11868ed6c038d281de25e.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)255111134910.22052/mir.2020.204420.1167ENFatemehMonemiDepartment of Physics, University of Kashan, 87317-53135, I. R. IranFarhadZamaniDepartment 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 $E$, and the particle's mass $m$, and wave vector $bfk$, 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 $bfk$ should be small, and the more smaller are the easier to create the particles. On the other hand, when $m$ or $bfk$ 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 $E^{1-2sqrt{mu^2}}!left(1-ln Eright)$, where $mu^2=frac94-frac{mds^2}{H^2}$. Thus, below a critical mass $m_{mathrm{cr}}=sqrt{2} H$, the current exhibits the infrared hyperconductivity.https://mir.kashanu.ac.ir/article_111349_7d53493d7e73d1843cedb566a01fb5dd.pdf