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 \$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\$ Shape category,Topological shape homotopy group,Shape group,Suspensions https://mir.kashanu.ac.ir/article_111348.html https://mir.kashanu.ac.ir/article_111348_667a50fe5ef11868ed6c038d281de25e.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 \$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. 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