Mathematics Interdisciplinary Research
https://mir.kashanu.ac.ir/
Mathematics Interdisciplinary Researchendaily1Sat, 01 Dec 2018 00:00:00 +0330Sat, 01 Dec 2018 00:00:00 +0330The Non-Coprime Graph of Finite Groups
https://mir.kashanu.ac.ir/article_87414.html
The non-coprime graph &Pi;_G of a finite group G is a graph with the vertex set G-{e}, where two distinct vertices u and v are adjacent if they have non-coprime orders. In this paper, the main properties of the Cartesian and tensor product of the non-coprime graph of two finite groups are investigated. We also describe the non-coprime graph of some special groups including the dihedral and semi-dihedral groups. Some open questions are also proposed.Golden Ratio: The Mathematics of Beauty
https://mir.kashanu.ac.ir/article_89245.html
&lrm;Historically, mathematics and architecture have been associated with one another. Ratios are good example of this interconnections. The origin of ratios can be found in nature, which makes the nature so attractive. As an example, consider the architecture inspired by flowers which seems so harmonic to us. In the same way, the architectural plan of many well-known historical buildings such as mosques and bridges show a rhythmic balance which according to most experts the reason lies in using the ratios. The golden ratio has been used to analyze the proportions of natural objects as well as building&rsquo;s harmony. In this paper, after recalling the (mathematical) definition of the golden ratio, its ability to describe the harmony in the nature are discussed. When teaching mathematics in the schools, one may refer to this interconnection to encourage students to feel better with mathematics and deepen their understanding of proportion. At the end, the golden ratio has been statistically examined using its first 100000 decimal digits to show that the golden ratio decimals can be used as a random number generator.On n-A-con-cos Groups and Determination of some 3-A-con-cos Groups
https://mir.kashanu.ac.ir/article_102140.html
We introduced the notion of 2-A-con-cos group in [5]. In this paper, we generalize&nbsp;this concept to n-A-con-cos group, also we mention some properties of it and&nbsp;determine all finite abelian groups with at most 2 direct factors and dihedral&nbsp;groups, D2n where n has at most 2 prime factors which are 3-A-con-cos.Gordon-Scantlebury and Platt Indices of Random Plane-oriented Recursive Trees
https://mir.kashanu.ac.ir/article_110787.html
&lrm;For a simple graph G&lrm;, &lrm;the Gordon-Scantlebury index of&nbsp;G is equal to the number of paths of length two in G&lrm;, &lrm;and the Platt index is equal to the total sum of the degrees of all edges in G&lrm;. &lrm;In this paper&lrm;, &lrm;we study these indices in random plane-oriented recursive trees through a recurrence equation for the first Zagreb index&lrm;. &lrm;As n ∊ &infin;, &lrm;the asymptotic normality of these indices are given&lrm;.DE Sinc-Collocation Method for Solving a Class of Second-Order Nonlinear BVPs
https://mir.kashanu.ac.ir/article_107701.html
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.Adjointness of Suspension and Shape Path Functors
https://mir.kashanu.ac.ir/article_111348.html
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 $1\leq k \leq n-1$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)
https://mir.kashanu.ac.ir/article_111349.html
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 $E^{1-2\sqrt{\mu^2}}\!\left(1-\ln E\right)$, 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.Auto-Engel Polygroups
https://mir.kashanu.ac.ir/article_111522.html
This paper introduces the concept of auto&ndash;Engel polygroups via the heart of hypergroups and investigates the relation between of auto&ndash;Engel polygroups and auto&ndash;nilpotent polygroups. Indeed, we show that the concept of heart of hypergroups plays an important role on construction of auto&ndash;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.On Finding a Relative Interior Point of a Polyhedral Set
https://mir.kashanu.ac.ir/article_111476.html
This paper proposes a new linear program for finding a relative interior point of a polyhedral set. Based on characterizing the relative interior of a polyhedral set through its polyhedral&nbsp;representing sets, two main contributions are made. First, we complete the existing results in the literature that require the non-negativity of the given polyhedral set. Then, we deal with the general case where this requirement may not be met.Weakly Compatible Maps and Fixed Points
https://mir.kashanu.ac.ir/article_111477.html
Here, the existence of fixed points for weakly compatible maps is studied. The results are new generalization of the results of [5]. Finally, we study the new common fixed point theorems.On Eccentricity Version of Zagreb Coindices
https://mir.kashanu.ac.ir/article_111483.html
The eccentric connectivity coindex has recently been introduced (Hua and Miao, 2019) as the total eccentricity sum of all pairs of non-adjacent vertices in a graph. Considering the total eccentricity product of non-adjacent vertex pairs, we introduce here another invariant of connected graphs called the second Zagreb eccentricity coindex. We study some mathematical properties of the eccentric connectivity coindex and second Zagreb eccentricity coindex. We also determine the extremal values of the second Zagreb eccentricity coindex over some specific families of graphs such as trees, unicyclic graphs, connected graphs, and connected bipartite graphs and describe the extremal graphs. Moreover, we compare the second Zagreb eccentricity coindex with the eccentric connectivity coindex and give directions for further studies.Big Finitistic Dimensions for Categories of Quiver Representations
https://mir.kashanu.ac.ir/article_111485.html
Assume that A is a Grothendieck category and R is the category of all A-representations of a given quiver Q. If Q is left rooted and A has a projective generator, we prove that the big finitistic flat (resp. projective) dimension FFD(A) (resp. FPD(A)) of A is finite if and only if the big&nbsp;finitistic flat (resp. projective) dimension of R is finite. When A is the Grothendieck category of left modules over a unitary ring R, we prove that if FPD(R) &lt; +&infin;&nbsp;then any representation of Q of finite flat dimension has finite projective dimension. Moreover, if R is n-perfect then we show that&nbsp;FFD(R) &lt; +&infin;&nbsp;&nbsp;if and only if FPD(R) &lt; +&infin;. &nbsp;On the Maximal Graph of a Commutative Ring
https://mir.kashanu.ac.ir/article_111486.html
Let R be a commutative ring with nonzero identity. Throughout this paper we explore some properties of two subgraphs of the maximal graph of R.Three Constructions on Graphs and Distance-Based Invariants
https://mir.kashanu.ac.ir/article_111491.html
Many graphs are constructed from simpler ones by the use of operations on graphs, and as a consequence, the properties of the resulting constructions are strongly related to the properties of their constituents. This paper is concerned with computing some distance-based graph invariants for three constructions on graphs namely double graph, extended double cover, and strong double graph.Scaling Symmetry and a New Conservation Law of the Harry Dym Equation
https://mir.kashanu.ac.ir/article_111506.html
In this paper, we obtain a new conservation law for the Harry Dym equation by using the scaling method. This method is algorithmic and based on variational calculus and linear algebra. In this method, the density of the conservation law is constructed by considering the scaling symmetry of the equation and the associated flux is obtained by the homotopy operator. This density-flux pair gives a conservation law for the equation. A conservation law of rank 7 is constructed for the Harry Dym equation.On the Hosoya Index of Some Families of Graph
https://mir.kashanu.ac.ir/article_111532.html
&lrm;We obtain the exact relations of the Hosoya index that is defined as the sum of the number of all the matching sets&lrm;, &lrm;on some classes of cycle-related graphs&lrm;. &lrm;Moreover&lrm;, &lrm;this index of three graph families&lrm;, &lrm;namely&lrm;, &lrm;chain triangular cactus&lrm;, &lrm;Dutch windmill graph&lrm;, &lrm;and Barbell graph is determined&lrm;.A Note on the Lempel-Ziv Parsing Algorithm under Asymmetric Bernoulli Model
https://mir.kashanu.ac.ir/article_111540.html
&lrm;In this paper&lrm;, &lrm;by applying analytic&lrm; &lrm;combinatorics&lrm;, &lrm;we obtain an asymptotics for the t-th moment&lrm;&lrm;of the number of phrases of length l in the Lempel-Ziv parsing algorithms built over a string generated by an asymmetric Bernoulli&lrm; &lrm;model&lrm;. We show that the t-th moment is approximated by its Poisson transform&lrm;.