Acyclic Heaps of Pieces, I

Heaps of pieces were introduced by Viennot and have applications to algebraic combinatorics, theoretical computer science and statistical physics. In this paper, we show how certain combinatorial properties of heaps studied by Fan and by Stembridge are closely related to the properties of a certain linear map _E associated to a heap E. We examine the relationship between _E and _F when F is a subheap of E. This approach allows neat statements and proofs of results on certain associative algebras (generalized Temperley–Lieb algebras) that are otherwise tricky to prove. The key to the proof is to interpret the structure constants of the aforementioned algebras in terms of the maps .     

On Structural and Asymptotic Properties of Some Classes of Distributions

We consider the two-parametric classes of distributions which comprise exponential dispersion models possessing a simple structure. Some of our models are related to Galton-Watson processes and branching diffusions. We study asymptotic properties of related classes of distributions emphasizing their convergence to Poisson-exponential law. We establish/refute infinite divisibility for certain classes of distributions. The critical value for the deflation of zeros from a geometric law which preserves infinite divisibility is determined. A class of distributions related to zero-modified geometric and logarithmic laws is considered.     

结构VAR的有向非循环图模型

研究用图模型方法辨识结构向量自回归(VAR)模型,图中的结点表示不同时刻的随机变量,结点间的边表示其所表示的随机变量之间存在的因果相依关系.针对建立有向非循环图的问题,提出了一种基于回归分析的判断方法,用回归方程的回归平方和之差作为统计量,确定当前变量之间相依关系的方向.与R ea le的逐一判别法和A lessio的图搜索方法相比,文中提出的基于统计分析的方法简单易行,且可获得唯一的当前变量有向非循环图.最后以两组模拟序列为例,验证了所提出的方法是可行且有效的.     

Technical Note: Some Structural Properties of a Newton-Type Method for Semidefinite Programs

Using the minimum function or the Fischer-Burmeister function, we obtain two reformulations of a semidefinite program as a nonlinear system of equations. Applying a Newton-type method to such a reformulation leads to a linear system of equations which has to be solved at each iteration. We discuss some properties of this linear system and show that the corresponding coefficient matrix is symmetric positive definite for the minimum function approach and positive definite but unsymmetric for the Fischer-Burmeister formulation.     

On Some Structural Properties of Banach Function Spaces and Boundedness of Certain Integral Operators

In this paper the notions of uniformly upper and uniformly lower -estimates for Banach function spaces are introduced. Further, the pair (X, Y) of Banach function spaces is characterized, where X and Y satisfy uniformly a lower -estimate and uniformly an upper -estimate, respectively. The integral operator from X into Y of the form

关于吸引子的某些性质

Conley在[1]中讨论拓扑空间X上动力系统的吸引子——排斥子对时,给出了吸引子存在的两个充分条件．本文证明这两个条件实际上也是必要的,进而证明Conley所定义的吸引子是渐近稳定的．     

Some Properties of Coronas

Recently Branko Grünbaum [3] introduced the concept of the corona of a tile in a tiling of Euclidean space. Here we survey all known results, establish some new properties, and highlight open problems in this area.     

HC-偏序集的若干性质

基于超连续格的内蕴式刻画,引入HC-偏序集的概念,讨论了HC-偏序集的一些性质.类似地,作为超代数格的推广,引入了HA-偏序集并讨论其相关性质.     

关于吸引子的某些性质

Conley在[1]中讨论拓扑空间X上动力系统的吸引子——排斥子对时,给出了吸引子存在的两个充分条件．本文证明这两个条件实际上也是必要的,进而证明Conley所定义的吸引子是渐近稳定的．     

弱^＊局部一致凸空间的一些性质

讨论了弱^*局部一致凸空间的一些等价定义和性质,以及乘积空间的弱^*凸部一致凸的传递性。     

Some Properties of Minimal Splines

S. G. Mikhlin was the first to construct systematically coordinate functions on an equidistant grid solving a system of approximate equations (called “fundamental relations”, see [5]; Goel discussed some special cases earlier in 1969; see also [1, 4, 6]). Further, the idea was developed in the case of irregular grids (which may have finite accumulation points, see [1] ). This paper is devoted to the investigation of A-minimal splines, introduced by the author; they include polynomial minimal splines which have been discussed earlier. Using the idea mentioned above, we give necessary and sufficient conditions for existence, uniqueness and g-continuity of these splines. The application of these results to polynomial splines of m-th degree on an equidistant grid leads us, in particular, to necessary and sufficient conditions for the continuity of their i-th derivative (i = 1, ?, m). These conditions do not exclude discontinuities of other derivatives (e.g. of order less than i). This allows us to give a certain classification of minimal spline spaces. It turns out that the spline classes are in one-to-one-correspondence with certain planes contained in a hyperplane.     

Some Properties of Residuated Lattices

We investigate some (universal algebraic) properties of residuated lattices--algebras which play the role of structures of truth values of various systems of fuzzy logic.     

W-Surfaces Having Some Properties

We investigate some characteristic properties of specific Weingarten surfaces in the Euclidean space E³ using the nets of the lines of curvature resp. the asymptotic lines on both central surfaces of them.     

关于TL子群的若干性质

引入拟正规的TL子群的概念,讨论一些重要性质。此外,在M．A．A．Mishref文献[7]和J-G Kim文献[8]的基础上,继续研究TL-p子群。     

Some New Transversality Properties

The theorems of Ceva and Menelaus are concerned with cyclic products of ratios of lengths of collinear segments of triangles or more general polygons. These segments have one endpoint at a vertex of the polygon and one at the intersection point of a side with a suitable line. To these classical results we have recently added a selftransversality theorem in which the suitable line is determined by two other vertices. Here we present additional transversality properties in which the suitable line is determined either by a vertex and the intersection point of two diagonals, or by the intersection points of two pairs of such diagonals. Unexpectedly it turns out that besides several infinite families of systematic cases there are also a few sporadic cases.