Bulletin of The Iranian Mathematical Society最新文献

Abstract

A set of vertices X of a graph G is a strong edge geodetic set if, to any pair of vertices from X, we can assign one (or zero) shortest path between them, such that every edge of G is contained in at least one on these paths. The cardinality of a smallest strong edge geodetic set of G is the strong edge geodetic number (mathrm{sg_e}(G)) of G. In this paper, the strong edge geodetic number of complete multipartite graphs is determined. Graphs G with (mathrm{sg_e}(G) = n(G)) are characterized and (mathrm{sg_e}) is determined for Cartesian products (P_n,square , K_m) . The latter result in particular corrects an error from the literature.

Let (X=X_1cup cdots cup X_ssubset mathbb {P}^n), (nge 4), be a general union of smooth non-special curves with (X_i) of degree (d_i) and genus (g_i) and (d_ige max {2g_i-1,g_i+n}) if (g_i>0). We prove that X has maximal rank, i.e., for any (tin mathbb {N}) either (h^0(mathcal {I}_X(t))=0) or (h^1(mathcal {I}_X(t))=0) if it is so in a few explicit cases in (mathbb {P}^4). We also prove an unconditional weaker result, maximal rank up to a positive integer (delta _n).

This paper deals with a pseudo-parabolic equation with singular potential and variable exponents. First, we determine the existence and uniqueness of weak solutions in Sobolev spaces with variable exponents. Second, in the frame of variational methods, we classify the blow-up and the global existence of solutions completely using the initial energy. Third, we obtain lower and upper bounds of blow-up time for all possible initial energy. The results in this paper are compatible with the corresponding problems with constant exponents. Part results of the paper extend the recent ones in Lian et al. (J Differ Equ 269:4914–4959, 2020), Xu and Su (J Funct Anal 264:2732–2763, 2013), and Liu and Yu (J Funct Anal 274:1276–1283, 2018).

A weaker variant of the selection principle ({{,mathrm{U_{fin}},}}({mathcal {O}},Omega ),) namely ({{,mathrm{U_{fin}},}}({mathcal {O}},overline{Omega }),) is investigated in this article. We present situations where ({{,mathrm{U_{fin}},}}({mathcal {O}},Omega )) behaves differently from ({{,mathrm{U_{fin}},}}({mathcal {O}},overline{Omega }).) Few characterization results are obtained by considering mappings into the Baire space. Several results are presented concerning critical cardinalities. In particular, we perform investigations assuming near coherence of filters (NCF) and semifilter trichotomy. Besides, ({{,mathrm{U_{fin}},}}({mathcal {O}},overline{Omega })) is characterized using weakly groupable and related covers. We also exhibit certain game theoretic observations.

Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational matrix valued functions. An important source of linearizations are the so called Fiedler linearizations, which are generalizations of the classical companion forms. In this paper the concept of Fiedler linearization is extended from square regular to rectangular rational matrix valued functions. The approach is applied to Rosenbrock functions arising in mathematical system theory.

Let (Phi ) be a field of prime characteristic p and let G be a finite group. We develop an equivalence relation between the set of isomorphism types of indecomposable (simple) KG-modules, where K is any finite subfield of (Phi ), and relate the equivalence classes to the set of isomorphism types of indecomposable (resp. simple) (Phi G)-modules. When (Phi ) is the algebraic closure of a field F of order p, we study indecomposable (resp. simple) (Phi G-)modules and obtain a classification of the isomorphism types of simple (Phi G)-modules and a new formula for the number of such types in each equivalence class.

Abstract

A finite set of the Euclidean space is called an s-distance set provided that the number of Euclidean distances in the set is s. Determining the largest possible s-distance set for the Euclidean space of a given dimension is challenging. This problem was solved only when dealing with small values of s and dimensions. Lisoněk (J Combin Theory Ser A 77(2):318–338, 1997) achieved the classification of the largest 2-distance sets for dimensions up to 7, using computer assistance and graph representation theory. In this study, we consider a theory analogous to these results of Lisoněk for the pseudo-Euclidean space (mathbb {R}^{p,q}) . We consider an s-indefinite-distance set in a pseudo-Euclidean space that uses the value $$begin{aligned} || varvec{x}-varvec{y}||&=(x_1-y_1)^2 +cdots +(x_p -y_p)^2 &quad -(x_{p+1}-y_{p+1})^2-cdots -(x_{p+q}-y_{p+q})^2 end{aligned}$$ instead of the Euclidean distance. We develop a representation theory for symmetric matrices in the context of s-indefinite-distance sets, which includes or improves the results of Euclidean s-distance sets with large s values. Moreover, we classify the largest possible 2-indefinite-distance sets for small dimensions.

In this paper, we analyze various classes of multi-dimensional Stepanov almost automorphic type functions in general metric. We clarify the main structural properties for the introduced classes of metrically Stepanov almost automorphic type functions, providing also some applications to the abstract Volterra integro-differential equations.

In this work we prove, under symmetry and convexity assumptions on the domain (Omega ), the non- degeneracy at zero of the Hessian matrix of the Robin function for the spectral fractional Laplacian. This work extends to the fractional setting the results of M. Grossi concerning the classical Laplace operator.

In this article, we present a numerical analysis of the Korteweg-de Vries (KdV) and Regularized Long Wave (RLW) equations using a finite difference space-time method. The KdV and RLW equations are partial differential equations that describe the behavior of long shallow water waves. We show that the finite difference space-time method is an effective way to solve these equations numerically, and we compare the results with those obtained using explicit method and generalized finite difference (GFD) formulae. Our results indicate that the finite difference space-time method provides accurate and stable solutions for both the KdV and RLW equations.