Uncovering Organizational Hierarchies

This paper adapts a procedure, canonical analysis of asymmetry,originally defined by Gower (1977) to the analysis of hierarchicalproperties in organizational structures. Its application is demonstratedusing two available data sets, Freeman and Freeman's (1980) data on computercommunication and Krackhardt's (1987) data on advice-giving and getting inan organization.     

Hilbert-Enskog-Chapman expansion in the turbulent kinetic theory of gases. I

Giving up the assumption of molecular chaos, we get a hierarchy of equations, instead of the Boltzmann equation, governing the motion of a dilute gas. The Hilbert-Enskog-Chapman expansion methods for the hierarchy are studied in this paper and its continuations.     

纯正半群上的同余扩张(一)

刻划半群上的同余及其扩张是半群的代数理论中的一个非常重要的课题．本文讨论了带上的同余的正规性和不变性以及在其Ｈａｌｌ半群上的扩张，从同余扩张的角度刻划了带上的同余的性质，给出了扩张的极大、极小同余的描述．     

Quantum statistical hierarchy equation in nonequilibrium systems

An extension is given for the Fourier expansion method with the contraction technique, which was introduced by Balescu for quantum statistical systems. This is attained by introducing a diagrammatic method with a concept of moving contraction. Then the hierarchy equation for the Contracted Fourier coefficient of the Wigner distribution function is obtained. As an application, a generalized master equation involvingn-body collision effects and quantum statistical effects is also derived.     

A simple proof of a curious congruence by Zhao

The author gives a simple proof of the following curious congruence for odd prime 3$"> which was established by Jianqiang Zhao:

0}}}\frac{1}{ijk}\equiv -2B_{p-3}(\text{mod} p).\end{displaymath}">

     

Some Categorical Algebraic Properties: Counter-Examples for Functor Categories

This work is a complement to the authors earlier papers, where it is shown that a functor category inherits from such properties as amalgamation, transferability and congruence extension if has either products or certain pushouts. A general scheme is given for constructing counter-examples which show that the latter condition on is essential. In particular, it is shown that the functor categories , , ( resp.) do not satisfy the amalgamation (congruence extension resp.) property in general. Moreover, one class of categories is described, where the condition of the existence of certain pushouts is not only sufficient, but also necessary for to preserve the considered properties of .Mathematics Subject Classifications (2000) 18A25, 18A32, 18B99, 08B26.Dali Zangurashvili: The support rendered by INTAS Grant 97 31961 is gratefully acknowledged.     

Jagged Partitions

By jagged partitions we refer to an ordered collection of non-negative integers (n₁, n₂,..., n_m) with n_m≥ p for some positive integer p, further subject to some weakly decreasing conditions that prevent them for being genuine partitions. The case analyzed in greater detail here corresponds to p = 1 and the following conditions n_i≥ n_i+1−1 and n_i≥ n_i+2. A number of properties for the corresponding partition function are derived, including rather remarkable congruence relations. An interesting application of jagged partitions concerns the derivation of generating functions for enumerating partitions with special restrictions, a point that is illustrated with various examples. 2000 Mathematics Subject Classification: Primary—05A15, 05A17, 05A19     

Groups associated with minimal flows

Let S be topological semigroup, we consider an appropriate semigroup compactification of S. In this paper we study the connection between subgroups of a maximal group in a minimal left ideal of , which arise as equivalence classes of some closed left congruence, and the minimal ow characterized by the left congruence. A particular topology is defined on a maximal group and it is shown that a closed subgroup under this topology is precisely the intersection of an equivalence class with the maximal group for some left congruence on .     

Towards an Effectivisation of the Riemann Theorem

Let Q be a connected and simply connected domain on the Riemann sphere, not coinciding with the Riemann sphere and with the whole complex plane ℂ. Then, according to the Riemann Theorem, there exists a conformal bijection between Q and the exterior of the unit disk. In this paper, we find an explicit form of this map for a broad class of domains with analytic boundaries. Communicated by M. A. Shubin (Moscow) Mathematics Subject Classifications (2000): 30Cxx, 37Kxx.     

Supersymmetric solution of gauge hierarchy problem

Some recent developments with respect to the resolution of the gauge hierarchy problem in grand unified theories by supersymmetry are presented. A general argument is developed to show how global supersymmetry maintains the stability of the different mass-scales under perturbative effects.