Bulletin of The Iranian Mathematical Society最新文献

We characterize the matrix-weighted Triebel–Lizorkin spaces and Besov spaces by Peetre maximal function and approximation. Using these characterizations, we obtain the boundedness of pseudo-differential operators with symbol in Hörmander’s class on matrix weighted Besov and Triebel–Lizorkin spaces.

In the present paper, we propose a new approach on ‘distributed systems’: the processes are represented through total orders and the communications are characterized by means of biorders. The resulting distributed systems capture situations met in various fields (such as computer science, economics and decision theory). We investigate questions associated to the numerical representability of order structures, relating concepts of economics and computing to each other. The concept of ‘quasi-finite partial orders’ is introduced as a finite family of chains with a communication between them. The representability of this kind of structure is studied, achieving a construction method for a finite (continuous) Richter–Peleg multi-utility representation.

For a prime p, we show that uniqueness of factorization into irreducible (Sigma _{p^2})-invariant representations of ({mathbb Z}/p wr {mathbb Z}/p) holds if and only if (p=2). We also show nonuniqueness of factorization for (Sigma _8)-invariant representations of (D_8 wr {mathbb Z}/2). The representation ring of (Sigma _{p^2})-invariant representations of ({mathbb Z}/p wr {mathbb Z}/p) is determined completely when p equals two or three.

The Riccati equation method is used to establish some global solvability criteria for a classes of Lane–Emdem–Fowler and Van der Pol type equations. Two oscillation theorems are proved. The results obtained are applied to the Emden–Fowler equation and to the Van der Pol type equation.

Abstract

Let (V, 0) be a hypersurface with an isolated singularity at the origin defined by the holomorphic function (f: (mathbb {C}^n, 0)rightarrow (mathbb {C}, 0)) . We introduce a new derivation Lie algebra associated to (V, 0). The new Lie algebra is defined by the ideal of antiderivatives with respect to the Tjurina ideal of (V, 0). More precisely, let (I = (f, frac{partial f}{partial x_1},ldots , frac{partial f}{partial x_n})) and (Delta (I):= {gmid g,frac{partial g}{partial x_1},ldots , frac{partial g}{partial x_n}in I}) , then (A^Delta (V):= mathcal O_n/Delta (I)) and (L^Delta (V):= textrm{Der}(A^Delta (V),A^Delta (V))) . Their dimensions as a complex vector space are denoted as (beta (V)) and (delta (V)) , respectively. (delta (V)) is a new invariant of singularities. In this paper we study the new local algebra (A^Delta (V)) and the derivation Lie algebra (L^Delta (V)) , and also compute them for fewnomial isolated singularities. Moreover, we formulate sharp lower estimation conjectures for (beta (V)) and (delta (V)) when (V, 0) are weighted homogeneous isolated hypersurface singularities. We verify these conjectures for a large class of singularities. Lastly, we provide an application of (beta (V)) and (delta (V)) to distinguishing contact classes of singularities.

Abstract

In 2016, Beeler et al. defined the double Roman domination as a variation of Roman domination. Sometime later, in 2021, Ahangar et al. introduced the concept of [k]-Roman domination in graphs and settled some results on the triple Roman domination case. In 2022, Amjadi et al. studied the quadruple version of this Roman-domination-type problem. Given any labeling of the vertices of a graph, AN(v) stands for the set of neighbors of a vertex v having a positive label. In this paper we continue the study of the [k]-Roman domination functions ([k]-RDF) in graphs which coincides with the previous versions when (2le k le 4) . Namely, f is a [k]-RDF if (f(N[v])ge k+|AN(v)|) for all v. We prove that the associate decision problem is NP-complete even when restricted to star convex and comb convex bipartite graphs and we also give sharp bounds and exact values for several classes of graphs.

We present conditions under which the Gel’fand transform (E^{wedge },) of locally m-convex algebra E, is a dense subalgebra of ( mathcal {C}_{c}(mathfrak M(E))). The partition of unity and the local theorem are given for a commutative unital locally m-convex algebra.

Thomassen (J. Combin. Theory Ser B 128:192–218, 2018) showed that every subcubic planar graph has 2-distance chromatic number at most 7, which was originally conjectured by Wegner (graphs with given diameter and a coloring problem, University of Dortmund, preprint, 1977). In this note, we consider 3-distance colorings of this family of graphs, and prove that every subcubic planar graph has 3-distance chromatic number at most 17, and we conjecture that this number can be reduced to 12. In addition, we show that every planar graph with maximum degree at most (Delta ) has 3-distance chromatic number at most ((6+o(1))Delta ).

In this research paper, we undertake an investigation into Cesàro (mathfrak {q})-difference sequence spaces (mathfrak {X}(mathfrak {C}_1^{delta ;mathfrak {q}})), where (mathfrak {X} in {ell _{infty },c,c_0}.) These spaces are generated using the matrix (mathfrak {C}_1^{delta ,mathfrak {q}}), which is a product of the Cesàro matrix (mathfrak {C}_1) of the first-order and the second-order (mathfrak {q})-difference operator (nabla ^2_mathfrak {q}) defined by

where (mathfrak {q}in (0,1)) and (mathfrak {f}_k=0) for (k<0.) Our endeavor includes the establishment of significant inclusion relationships, the determination of bases for these spaces, the investigation of their (alpha )-, (beta )-, and (gamma )-duals, and the formulation of characterization results pertaining to matrix classes ((mathfrak {X},mathfrak {Y})), with (mathfrak {X}) chosen from the set ({ell _{infty }(mathfrak {C}_1^{delta ;mathfrak {q}}), c(mathfrak {C_1^{delta ;mathfrak {q}}}), c_0(mathfrak {C}_1^{delta ;mathfrak {q}})}) and (mathfrak {Y}) chosen from the set ({ell _{infty },c,c_0,ell _{1}}.) The final section of our study is dedicated to the meticulous spectral analysis of the weighted (mathfrak {q})-difference operator (nabla ^{2;mathfrak {z}}_{mathfrak {q}}) over the space (c_0) of null sequences.

Global and local existence results for the solutions of systems of stochastic Schrödinger equations with multiplicative noise and quadratic nonlinear terms are discussed in this paper. The same system in the deterministic treatment was studied in [23] where the mass and energy are conserved. In our stochastic situation, those are not conserved.