Compatible relations on filters and stability of local topological properties under supremum and product

An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Fréchetness, strong Fréchetness, countable tightness and countable fan-tightness, some of which recover or refine classical results, some of which are new. The reader may find other applications as well.     

Fuzzy序列紧性,可数Fuzzy紧性和Fuzzy列紧性

本文引进了Fuzzy序列紧性、可数Fuzzy紧性和Fuzzy列紧性,它们是一般拓扑学中相应概念的“良扩张”(R. Lowen意义下),文中讨论了这些fts的主要性质,以及它们之间的联系。     

Bruck nets,codes, and characters of loops

Numerous computational examples suggest that if _{k-1 k} are (k- 1)- and k-nets of order n, then rank _{p k} - rank _{p k-1} n - k + 1 for any prime p dividing n at most once. We conjecture that this inequality always holds. Using characters of loops, we verify the conjecture in case k = 3, proving in fact that if p ^e n, then rank _{p 3} 3n - 2 - e, where equality holds if and only if the loop G coordinatizing ₃ has a normal subloop K such that G/K is an elementary abelian group of order p ^e . Furthermore if n is squarefree, then rank _p = 3n - 3 for every prime p ¦ n, if and only if ₃ is cyclic (i.e., ₃ is coordinated by a cyclic group of order n).The validity of our conjectured lower bound would imply that any projective plane of squarefree order, or of order n 2 mod 4, is in fact desarguesian of prime order.     

紧－凸性与紧－光滑性

本文首先通过暴露集和暴露泛函的概念引入了闭凸集的紧－严格凸、紧－强凸、紧－一致凸及紧－非常凸等概念。并用对偶映射给出了Ｂａｎａｃｈ空间的两种新光滑性—紧－一致光滑与紧－非常光滑。然后特别研究了Ｂａｎａｃｈ空间的紧－非常凸与紧－非常光滑。此外还得到关于对偶映射的两个新结果。     

Actions of Compact Groups on Compact (4,m)-Quadrangles

We establish sharp upper bounds for the dimensions of compact groups which act effectively on finite-dimensional compact generalized quadrangles with four-dimensional point rows. These bounds are attained, or indeed approached, only for explicitly known actions of Lie groups on Moufang quadrangles.     

Compact and Weakly Compact Composition Operators on BMOA

Any analytic map φ of the unit disc ${\mathbb{D}}$ into itself induces a composition operator C _φ on BMOA, mapping ${f \mapsto f \circ \varphi}$ , where BMOA is the Banach space of analytic functions ${f\colon \mathbb{D} \to \mathbb{C}}$ whose boundary values have bounded mean oscillation on the unit circle. We show that C _φ is weakly compact on BMOA precisely when it is compact on BMOA, thus solving a question initially posed by Tjani and by Bourdon, Cima and Matheson in the special case of VMOA. As a crucial step of our argument we simplify the compactness criterion due to Smith for C _φ on BMOA and show that his condition on the Nevanlinna counting function alone characterizes compactness. Additional equivalent compactness criteria are established. Furthermore, we prove the unexpected result that compactness of C _φ on VMOA implies compactness even from the Bloch space into VMOA.     

Fluid stochastic Petri nets: Theory,applications, and solution techniques

In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold fluid rather than discrete tokens. We define a class of fluid stochastic Petri nets in such a way that the discrete and continuous portions may affect each other. Following this definition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented and evidence of the accuracy of the fluid approximation is given.     

Compact disconnected planes,inverse limits and homomorphisms

Every compact disconnected projective plane can be written as an inverse limit of finite discrete incidence structures. Every finite projective plane is a continuous epimorphic image of some compact disconnected projective plane. There exist compact disconnected projective planes of Lenz type V which do not admit any continuous epimorphism onto a finite projective plane.Supported in part by a travel grant of the Deutsche Forschungsgemeinschaft.     

Inversion relations, reciprocity and polyominoes

We derive self-reciprocity properties for a number of polyomino generating functions, including several families of column-convex polygons, three-choice polygons, and staircase polygons with a staircase hole. In so doing, we establish a connection between the reciprocity results known to combinatorialists and the inversion relations used by physicists to solve models in statistical mechanics. For several classes of convex polygons, the inversion (reciprocity) relation, augmented by certain symmetry and analyticity properties, completely determines the anisotropic perimeter generating function.     

Matrices, graphs and equivalence relations

A suitable equivalence relation is introduced on the set of square matrices with entries of any kind. This allows us to associate to every equivalence class an infinite family of graphs and determine their topological properties. When a given square matrix is the multiplication table of a finite groupoid, some connections between algebraic properties of the groupoid and topological properties of these graphs are proved. Received: May 4, 1999 Published online: December 19, 2001     

Extensible hyperplane nets

Extensible (polynomial) lattice point sets have the property that the number N of points in the node set of a quasi-Monte Carlo algorithm may be increased while retaining the existing points. Explicit constructions for extensible (polynomial) lattice point sets have been presented recently by Niederreiter and Pillichshammer. It is the aim of this paper to establish extensibility for a powerful generalization of polynomial lattice point sets, the so-called hyperplane nets.     

Scrambling non-uniform nets

In this paper, we consider Owen’s scrambling of an (m−1, m, d)-net in base b which consists of d copies of a (0, m, 1)-net in base b, and derive an exact formula for the gain coefficients of these nets. This formula leads us to a necessary and sufficient condition for scrambled (m − 1, m, d)-nets to have smaller variance than simple Monte Carlo methods for the class of L ₂ functions on [0, 1] ^d . Secondly, from the viewpoint of the Latin hypercube scrambling, we compare scrambled non-uniform nets with scrambled uniform nets. An important consequence is that in the case of base two, many more gain coefficients are equal to zero in scrambled (m − 1, m, d)-nets than in scrambled Sobol’ points for practical size of samples and dimensions.      

Commutation relations,homomorphisms, and differential equations

We present an algebraic approach to the theory of ordinary differential equations and indicate a method for constructing first integrals of such equations.     

Distributivity,binary relations,and standard bases

In the author’s previous papers, the connection between generating syzygy modules by binary relations, the property of a commutative ring to be arithmetical (that is to have a distributive ideal lattice), and the use of the so-called S-polynomials in the standard basis theory were discussed. In this note, these connections are considered in a more general context. As an illustration of the usefulness of these considerations, a simple proof of some well-known fact from commutative algebra is given.     

BL代数的fantastic滤子和normal滤子

滤子是研究逻辑代数的有效工具.本文研究了BL代数的fantastic和normal滤子的等价条件,得到了在MV-代数中两种滤子之间的等价性,给出了两个公开问题:"在什么样的合适条件下,一个normal滤子成为一个fantastic滤子?"和"在什么合适的条件下,normal滤子的拓展性成立?"结论成立的一种条件.     

Blocking sets, k-arcs and nets of order ten

Our first main objective here is to unify two important theories in finite geometries, namely, the theories of k-arcs and blocking sets. This has a number of consequences, which we develop elsewhere. However, one consequence that we do discuss here is an improvement of Bruck's bound [1] concerning the possibility of embedment of finite nets of order n, in the controversial case when n = 10. The argument also makes use of a recent computer result of Denniston [5]. The second (related) main result involves a new combinatorial bound concerning blocking sets (Theorem 5). We are able to show that the bound is sharp by constructing a new class of geometrical examples of blocking sets in Theorem 6. See also the note added in proof.     

Infinite Baer nets

In this article, the structure of the collineation groups which fix point-Baer subplanes in vector space nets over skewfields is completely determined. The theory depends on whether there are one, two, or at least three point-Baer subplanes sharing the same parallel classes and a common point.The authors are indebted to the referee for helpful suggestions.