On Conformal Structure in Space-Time and Nets of Local Algebras of Observables

In this paper we continue the study of the question of how to reconstruct the conformal structure (causality relation) of a space-time from a net of local algebras of observables on the underlying manifold.     

Note on Schramm-Loewner Evolution for Superconformal Algebras

Theoretical and Mathematical Physics - Using the group-theoretical formulation of Schramm-Loewner evolution (SLE), we propose variants of SLE related to superconformal algebras. The corresponding...     

基于Petri网的软件结构复杂性分析

本文从软件分析的工具数据流图入手 ,导出了基于 Petri网的软件结构模型 ,并借助于网论中的数学工具 ,定量地给出了软件结构的复杂性描述 ,该分析结果可以有效地用于大型系统软件的综合性能分析、设计方案的评价等工作过程中     

Topological超共形代数的Leibniz中心扩张

通过计算得到了Topological N=2超共形代数丁的Leibniz二上同调群,从而确定了此代数的Leibniz中心扩张.     

两类N=2超共形代数上的超双导子和超交换映射

确定广义Topological N=2超共形代数和Twisted N=2超共形代数上的超斜对称双导子.证明在这两类超代数上的所有超双导子都是超双内导子.应用此结论,得到在广义Topological N=2超共形代数上的线性超交换映射是非标准的,而Twisted N=2超共形代数上的线性超交换映射是标准的.     

Nets and generalized quadrangles

There is a new method of constructing generalized quadrangles (GQs) given by S. Löwe, which is based on covering of nets; all GQs with a regular point can be represented in this way. Here we give a method of constructing GQs with a regular point using the so-called content functions on nets. In the last part of the paper we lay the foundations for a research project aiming to use the more general notion of content to classify GQs and maybe to construct new ones.Both authors acknowledge the financial support by CRUI and DAAD in the frame of Programma Vigoni, which made this work possible.     

Nets and their codes

A finitek-net of ordern is an incidence structure ofnk lines andn ² points, with any two lines either meeting once or being parallel, havingk parallel classes ofn lines each, and havingn points on each line. Finite nets are important to the study of finite planes and Latin squares.In this paper finite nets will be studied using the following linear codes: the row space of the incidence vectors of lines, the intersection of this code with its orthogonal, the code generated by differences of parallel lines, and the orthogonal to these codes. Using these codes we are able to recast the Moorhouse conjecture in terms of subcodes of the codes he uses, determine coding-theoretic reasons for a net's being maximal, and generalize a theorem of Assmus and Key which uses codes to classify finite planes of prime order.     

交换群上Hopf路余代数的结构分类

设G是群, kG是域k上的群代数. 对任意Hopf箭向Q=(G, r), 利用右kZ_u(C) -模的直积范畴∏_C∈K(G) MkZ_u(C)与kG-Hopf双模范畴^kG_kG M^kG_kG之间的同构, 可由^u(C)(kQ₁)¹上的右kZ_u(C) -模结构导出在箭向余模kQ₁上的kG-Hopf双模结构. 该文讨论在群G分别是2阶循环群与克莱茵四元群时的Hopf路余代数kQ^c的同构分类及其子Hopf代数kG[kQ₁]结构.     

Transversal-Free Translation Nets

Translation planes of order q ² containing non-Desarguesian Baer subplanes are used to construct transversal-free translation nets with very small deficiencies. Also, a generalization of the ideas of Bruen shows that any non-Desarguesian spread in PG(3, q) produces a transversal-free net of small deficiency.     

Nets on manifolds

This paper is devoted to investigations on the geometry of multidimensional nets, connected with the thoery of distributions on smooth manifolds, and to the survey of some other papers on multidimensional nets, reviewed in RZh Matematika from 1964 to the present time.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 12, pp. 97–126, 1981.     

On Order Convergence of Nets

In this paper we show that any order continuous operator between two Riesz spaces is automatically order bounded. We also investigate different types of order convergence. Yuri Abramovich - Lived 1945 to 2003 Yuri Abramovich- Deceased     

KP Theory of Egorov Nets

The theory of multicomponent KP hierarchies is used to characterize explicit examples of Egorov nets. A dressing method for Cauchy propagators is found to be particularly efficient.     

Nets associated to multigroupoids

Aequationes mathematicae -     

On Optimal Random Nets

The possibility to approximate bounded linear mappings between Banach spaces depends on the degree of compactness. One way to measure this degree of compactness is the scale of entropy numbers, cf. (B. Carl and I. Stephani: 1990. "Entropy, Compactness and the Approximation of Operators," Cambridge Univ. Press, Cambridge). In the usual (worst-case) setting of numerical analysis this scale has been studied for a long time. Recent research is concerned with the study of the so-called average-case and randomized (Monte Carlo) settings. We propose the respective counterparts of the entropy numbers in these settings and obtain their behavior for Sobolev embeddings. It turns out that, at least in this situation, randomly chosen nets may not improve the approximability of operators in the Monte Carlo setting. However, we can use the results to improve previous estimates for average Kolmogorov numbers, as obtained in (P. Mathé, 1991, J. Complexity7, 261-281).     

Ovals and Hyperovals in Desarguesian Nets

We determine the Desarguesian planes which hold r-nets with ovals and those which hold r-nets with hyperovals for every r7.     

Nets associated to multigroupoids

Aequationes mathematicae -     

Sobriety in Terms of Nets

Sobriety is a subtle notion of completeness for topological spaces: A space is sober if it may be reconstructed from the lattice of its open subsets. The usual criterion to check sobriety involves either irreducible closed subsets or completely prime filters of open sets. This paper provides an alternative possibility, thus trying to make sobriety easier to understand. We define the notion of observative net, which, together with an appropriate convergence notion, characterizes sobriety. As the filter approach does not involve just usual (topological) convergence, this is not an instance of the classical net-filter translation in general topology.