Let Y denote a D-class symmetric association scheme with D ≥ 3, and suppose Y is almostbipartite Pand Q-polynomial. Let x denote a vertex of Y and let T = T (x) denote the corresponding Terwilliger algebra. We prove that any irreducible T -module W is both thin and dual thin in the sense of Terwilliger. We produce two bases for W and describe the action of T on these bases. We prove that the is...

In this paper, the physical-layer redundancy method is proposed for the fault-tolerant industrial network. The proposed method consists of the fault detection method and the correction method. The fault detection method uses events created by the state transition in the IEEE 802.4 MAC sublayer and the periodic status frame check for the detection of the fault. The fault correction method correc...

We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of properly stratified algebras for which the characteristic tilting and cotilting modules coincide is closed under taking the Ringel dual. Studying stratified...

Abstract. This is a continuation of an article from the previous issue. In this section, we determine the structure of a thin, irreducible module for the Subconstituent algebra of a Pand Qpolynomial association scheme. Such a module is naturally associated with a Leonard system. The isomorphism class of the module is determined by this Leonard system, which in turn is determined by four paramet...

We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of properly stratified algebras for which the characteristic tilting and cotilting modules coincide is closed under taking the Ringel dual. Studying stratified...

This is the second part of the article [3]. In the first paper we developed a cyclic homology theory for B–module coalgebras with coefficients in stable B–module/comodules where B was just a bialgebra. The construction we gave for the cyclic homology theory for B–module coalgebras used mainly the coalgebra structure on B. In the first part of this paper, we present the dual picture. Namely, a c...

In this paper, we present a new dual-level matching algorithm for 3-stage Clos-network packet switches, called d-MAC. Using a two-level matching algorithm, namely module-level matching and port-level matching, d-MAC is highly scalable and maintains high system performance. The module-level matching is responsible for finding the module-to-module matching according to the queue status of the swi...

The faithful quasi-dual H and strict quasi-dual H ′ of an infinite braided Hopf algebra H are introduced and it is proved that every strict quasi-dual H ′ is an HHopf module. The connection between the integrals and the maximal rational Hsubmodule H of H is found. That is, H ∼= ∫ l H ⊗H is proved. The existence and uniqueness of integrals for braided Hopf algebras in the Yetter-Drinfeld categor...

The automorphism group of a binary doubly-even self-dual code is always contained in the alternating group. On the other hand, given a permutation group G of degree n there exists a doubly-even self-dual G-invariant code if and only if n is a multiple of 8, every simple self-dual F2G-module occurs with even multiplicity in F n 2 , and G is contained in the alternating group.

Graphs composed of node and link are the most common way of representing street networks for any analysis beyond pure visual representation. The intuitive primal approach to convert a physical street network into an abstract mathematical graph is mapping street intersections as nodes while mapping street segments between intersections as links connecting nodes in the graph. Correspondingly, a d...