Some Regularity Criteria for Affine Semilocal Rings

The purpose of this article is to study an existence of p-bases and mainly to give some regularity criteria for semilocal rings essentially of finite type over fields.     

Some analytical results for congestion in subscriber line modules

In modern telephone exchanges, subscriber lines are usually connected to the so-called subscriber line modules. These modules serve both incoming and outgoing traffic. An important difference between these two types of calls lies in the fact that in the case of blocking due to all channels busy in the module, outgoing calls can be queued whereas incoming calls get busy signal and must be re-initiated in order to establish the required connection. The corresponding queueing model was discussed recently by Lederman, but only the model with losses has been studied analytically. In the present contribution, we study the model which takes into account subscriber retrials and investigate some of its properties such as existence of stationary regime, derive explicit formulas for the system characteristics, limit theorems for systems under high repetition intensity of blocked calls and limit theorems for systems under heavy traffic.     

Crystal Engineering: A Unique Cyclic Assembly of a 40 Membered Module Composed from Two Alternating Units Each of Benzenehexacarboxylic Acid (Mellitic Acid,MA) and 2,5-Bis-(4-pyridyl)-1,3,4-oxadiazole (4-BPO): Assembly of Modules to Macromolecules by Intermolecular Hydrogen Bonding

Abstract  Individually prepared, equivalent amounts of 2,5-bis-(4-pyridyl)-1,3,4-oxadiazole (4-BPO) and benzenehexacarboxylic acid (mellitic acid, MA) when mixed, deposited long rods, whose X-ray structure showed a unique assembly of 40 membered planar modules composed from two alternating units each of MA and 4-BPO, rather than the anticipated helical profile. Several novel features of complexes of MA with organic molecules are seen here. In almost all cases the intermolecular hydrogen bonding between MA anions is so stable that the MA anions and the complementary cations lie in separate planes. This barrier is overcome in the present case. The basic module associates to form quartets by very simple hydrogen bonding of the carboxylic groups of MA. The quartet assembly is characterized by the rotation of the left hand pair compared to the right hand pair. The mode of the macromolecular assembly is clear, that is, they are layered in alternating planes. Space group: P2₁/c with a = 9.181(1) ?, b = 9.624(1) ?, c = 29.390(2) ?, and β = 94.626(4)°. The modules are embedded in an extensively hydrogen bonded MA network. The assembly profile of MA and 4-BPO is unique and should be a harbinger for the design of novel functional assemblies. The 40-membered module mimics the self-assemblies of peptides and can be important in the design of “Haptens” from simple molecules. Index Abstract  Rod like crystals from water that are formed on mixing MA and 4-BPO are shown to consist of 4-molecule modules (MA–4-BPO–MA–4-BPO–) that contain a 40-membered ring, MA–BPO.      

(*)-serial Incidence代数(英文)

设K是一个代数闭域,A是域K上一个有限维代数.我们利用箭图方法给出了(*)-serial incidence代数的分类.     

Non-catastrophicity in multidimensional convolutional coding

The property of non-catastrophicity of multidimensional convolutional codes is studied. In particular, an algebraic and system-theoretic characterization of non-catastrophicity is offered in the multidimensional setting, and the Massey–Sain classical criterion is extended to this setting.     

Tilting modules over split-by-nilpotent extensions

Let a finite dimensional algebra R be a split extension of an algebra A by a nilpotent bimodule Q. We give necessary and sufficient conditions for a (partial) tilting module T_A to be such that T?_A R_R is a (partial) tilting module. If this is not the case, but Q_A is generated by the tilting module T_A , then there exists a quotient [Rbar] of R such that T?_A [Rbar]_[Rbar] is a tilting module.     

Graded Endomorphism Rings and Equivalences

Abstract

Let R be a G-graded ring,M a G-graded Σ-quasiprojective R- module,and E = END _R (M) its graded ring of endomorphisms. For any subgroup H of G,we prove that certain full subcategories of G/H-graded R-modules associated with M are equivalent to a quotient category of G/H-graded E-modules determined by the idempotent G-graded ideal of E consisting of endomorphisms which factor through a finitely generated submodule of M. Properties and applications of these equivalences are also examined.     

Phase transitions and overlapping modules in complex networks

Complex systems can be described in terms of networks capturing the intricate web of connections among the units they are made of. Here we review two aspects of the possible organization of such networks. First, we provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to the level of noise during the rewiring of the edges. In our studies we find a rich variety of topological phase transitions when the temperature is varied. These transitions signal singular changes in the essential features of the global structure. Next, we address a question of great current interest which is about the modular structure of networks. We describe, how to interpret the global organization as the coexistence of structural sub-units (modules or communities) associated with more highly interconnected parts. The existing deterministic methods used for large networks find separated communities, while most of the actual networks are made of highly overlapping cohesive groups of nodes. We describe a recently introduced an approach to analyze the main statistical features of the interwoven sets of overlapping communities making a step towards the uncovering of the modular structure of complex systems. Our approach is based on defining communities as clusters of percolating complete subgraphs called k-cliques. We present the basic features of the associated percolation transition of overlapping k-cliques. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique to explore overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks.     

Exact and Semisimple Differential Graded Algebras

In this paper we provide a classification theorem and a structure theorem for exact differential graded algebras, and we use the classification theorem to show that a differential graded algebra A is semisimple (as a differential graded algebra) precisely when the graded algebra Z(A) is semisimple (as a graded algebra) and A is an exact complex. We also relate exact differential graded algebras with a graded version of Hochschild cohomology.     

Representations of Finite Posets Over Discrete Valuation Rings

Given a discrete valuation ring R, a non-negative integer m, and a finite partially ordered set S, the representation type of a category rep(S*, R, m) of finite rank free R-module representations of S is characterized in terms of S and m. As an application, representation types of some categories of torsion-free abelian groups of finite rank are determined.