L-fuzzy矩形带

给出了L-fuzzy子矩形带的概念,并给出了L-fuzzy子半群与L-fuzzy子矩形带L-fuzzy同构的条件.     

正则半群上的矩形群同余

文[1]中PetrichM定义了同余的核与迹，用它们描述了逆半群上的同余，Gomes在文[2]中定义了同余的核与超迹并描述了正则半群上的R-幂单(R-unipo-tent)同余，本文利用同余的核与超迹描述正则半群上的另一类重要同余，即矩形群同余．     

逆半群的基本矩形带的同余完备性

本文讨论了逆半群的基本矩形带上的完备同余，就若干特殊情形给出了这类半群是完备的充分必要条件。     

对边简支矩形薄板方程的算子半群方法

考虑弹性理论中对边简支矩形薄板方程,用算子半群方法求解问题.首先,将方程转换成抽象Cauchy问题.其次,构造空间框架并证明对应的算子矩阵生成压缩半群.最后,经Fourier变换,采用一致连续半群做逼近,进而给出对边简支矩形薄板方程的解析解.该方法自然蕴含着解的存在唯一性.     

π-纯正半群的r-半素矩形群同余

主要讨论π-纯正半群的r-半素矩形群同余和同余对之间的关系,并且找到了在r-半素矩形群同余的集合到r-半素矩形群同余对的集合之间的一一对应.     

带簇及矩形带簇的推广

本将带簇和矩形带簇的概念推广到了n-带簇εn=[x^n 1=x^n]和n-矩形带簇εn=[x^nyx^n=x^n]，讨论了这两种半群簇之间的关系，特别对所有n-带簇的并集ε=∪εn和所有n-矩形带簇的并集Rε=∪Rεn进行了研究．     

半群的子半群上的同余扩张

设ρ是半群Ｓ上的一个同余,如果Ｓ／ρ是矩形带,则称ρ是矩形同余,本文刻画了半群上的最小矩形带同余,设Ｔ是半群Ｓ的子半群,本文给出了Ｔ上每个矩形带同余能扩张成Ｓ上矩形带同余的充分必要条件。     

具有Clifford断面的纯正半群

本文研究有Clifford断面的纯正半群.为了获得主要的结构定理，证明了纯正半群有群断面当且仅当它是矩形群;利用半格和矩形带，建立了有Clifford断面的纯正半群的结构.     

E-矩形性拟正则半群

本文定义了一类拟正则半群,所谓E-矩形性拟正则半群,给出了它的若干特征和特例,特别地,给出了它在Green关系上的特征,讨论了它具左、右E-矩形性的特殊情形,并建立了它的结构.     

矩形板的侧屈

本文研究矩形板的侧向屈曲问题.文中分别讨论了有集中力,均布荷载及集中力偶作用之下矩形板发生侧向屈曲时的最小临界荷载.文中使用了能量法.     

On rectangular products of topological spaces

Several results on rectangular products in the sense of B.A. Pasynkov will be obtained, one of which asserts that for a Tychonoff space X, X × Y is rectangular for any space Y iff X is locally compact and paracompact.     

Proper forcing and rectangular ramsey theorems

I prove forcing preservation theorems for products of definable partial orders preserving cofinality of the meager or null ideal. Rectangular Ramsey theorems for the related ideals follow from the proofs. Partially supported by grant GA ČR 201-03-0933, NSF grants DMS 0071437 and DMS 0300201, and a visiting appointment at CRM, Universitat Autònoma de Barcelona.     

On the free vibration response of rectangular plates,partially supported on elastic foundation

Rectangular plates on distributed elastic foundations are widely employed in footings and raft foundations of variety of structures. In particular, mounted columns and single footings may partially occupy the rectangular plate of any kind.     

Bessel capacities and rectangular differentiation in Besov spaces

We consider the differentiation of integrals of functions in Besov spaces with respect to the basis of arbitrarily oriented rectangular parallelepipeds in Rn. We study almost everywhere convergence with respect to Bessel capacities. These outer measures are more sensitive than n-dimensional Lebesgue measure, and therefore we improve the positive results in [H. Aimar, L. Forzani, V. Naibo, Rectangular differentiation of integrals of Besov functions, Math. Res. Lett. 9 (2-3) (2002) 173-189].     

Pseudospectra of rectangular matrices

Pseudospectra of rectangular matrices vary continuously withthe matrix entries, a feature that eigenvalues of these matricesdo not have. Some properties of eigenvalues and pseudospectraof rectangular matrices are explored, and an efficient algorithmfor the computation of pseudospectra is proposed. Applicationsare given in (square) eigenvalue computation (Lanczos iteration),square pseudospectra approximation (Arnoldi iteration), controltheory (nearest uncontrollable system) and game theory.     

The Hamiltonian connectivity of rectangular supergrid graphs

A Hamiltonian path of a graph is a simple path which visits each vertex of the graph exactly once. The Hamiltonian path problem is to determine whether a graph contains a Hamiltonian path. A graph is called Hamiltonian connected if there exists a Hamiltonian path between any two distinct vertices. In this paper, we will study the Hamiltonian connectivity of rectangular supergrid graphs. Supergrid graphs were first introduced by us and include grid graphs and triangular grid graphs as subgraphs. The Hamiltonian path problem for grid graphs and triangular grid graphs was known to be NP-complete. Recently, we have proved that the Hamiltonian path problem for supergrid graphs is also NP-complete. The Hamiltonian paths on supergrid graphs can be applied to compute the stitching traces of computer sewing machines. Rectangular supergrid graphs form a popular subclass of supergrid graphs, and they have strong structure. In this paper, we provide a constructive proof to show that rectangular supergrid graphs are Hamiltonian connected except one trivial forbidden condition. Based on the constructive proof, we present a linear-time algorithm to construct a longest path between any two given vertices in a rectangular supergrid graph.     

Superconvergence for rectangular serendipity finite elements

Based on an orthogonal expansion and orthogonality correction in an element, superconvergence at symmetric points for any degree rectangular serendipity finite element approximation to second order elliptic problem is proved, and its behaviour up to the boundary is also discussed.     

On area-efficient drawings of rectangular duals for VLSI floor-plan

In this paper, we consider a problem to seek a rectangular dual and its area-efficient drawing such that can be drawn in the smallest area among all rectangular duals under the constraints imposed not only on the area and the minimum dimension of each face but also on the length of abutment between two adjacent faces. Since the problem is hard to solve, we tackle this problem in an exhaustive manner by using an algorithm to enumerate all the rectangular duals. In order to make this exhaustive method efficient, we propose the following two algorithms working under the constraints stated above; an algorithm to find an area-efficient drawing of a given rectangular dual, and an algorithm to estimate a lower bound to the area required to draw a given rectangular dual. We also show some esperimental results to demonstrate the effectiveness of the lower bound. The area-efficient drawing of can be used as a VLSI floor-plan by regarding each inner face of as an area for a block to be placed.     

Singular values of nonnegative rectangular tensors

The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. Some properties concerning the singular values of a real rectangular tensor were discussed by K. C. Chang et al. [J. Math. Anal. Appl., 2010, 370: 284–294]. In this paper, we give some new results on the Perron-Frobenius Theorem for nonnegative rectangular tensors. We show that the weak Perron-Frobenius keeps valid and the largest singular value is really geometrically simple under some conditions. In addition, we establish the convergence of an algorithm proposed by K. C. Chang et al. for finding the largest singular value of nonnegative primitive rectangular tensors.     

An efficient deterministic optimization approach for rectangular packing problems

The rectangular packing problem aims to seek the best way of placing a given set of rectangular pieces within a large rectangle of minimal area. Such a problem is often constructed as a quadratic mixed-integer program. To find the global optimum of a rectangular packing problem, this study transforms the original problem as a mixed-integer linear programming problem by logarithmic transformations and an efficient piecewise linearization approach that uses a number of binary variables and constraints logarithmic in the number of piecewise line segments. The reformulated problem can be solved to obtain an optimal solution within a tolerable error. Numerical examples demonstrate the computational efficiency of the proposed method in globally solving rectangular packing problems.