ANNE E HENKE, UNIVERSIT AT KASSEL Abstra t. Let k be an in nite eld of prime hara teristi and let r be a positive integer. Using admissible de ompositions, we determine expli itly the entries of the de omposition matrix of the S hur algebra S(2; r) over k and prove that any two blo ks with the same number of simple modules have the the same de omposition matrix and hen e the same Cartan matrix...

A simple axiomatic characterization of the noncommutative Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. It is proved that every quotient Itô algebra has a faithful representation in a Minkowski space and is canonically decomposed into the orthogonal sum of quantum Brownian (Wiener) algebra and quantum Lévy (Poisson) algebra. In particular,...

In this paper, we show that in each nite dimensional Hilbert space, a frame of subspaces is an ultra Bessel sequence of subspaces. We also show that every frame of subspaces in a nite dimensional Hilbert space has frameness bound.

In this paper, relations among the membership values of gener- alized fuzzy languages such as intuitionistic fuzzy language, interval-valued fuzzy language and vague language are studied. It will aid in studying the properties of one language when the properties of another are known. Further, existence of a minimized nite automaton with vague ( final) states for any vague regular language recog...

We consider rotations A; B of nite order in SO(3), about axes separated by an angle of restricted type, and attempt to classify the possible group relations between A and B. We show that the relations responsible for the symmetries of the Platonic solids have consequencies far beyond that simple geometric setting.

A measure preserving action of a countably in nite group Γ is called totally ergodic if every in nite subgroup of Γ acts ergodically. For example, all mixing and mildly mixing actions are totally ergodic. This note shows that if an action of Γ is totally ergodic then there exists a nite normal subgroup N of Γ such that the stabilizer of almost every point is equal to N. Surprisingly the proof r...

A nite set of generators for the mapping class group of a punctured nonorientable surface is given. When the surface has at least two punctures, up to conjugates there are four generators; a Dehn twist about a two-sided nonseparating simple closed curve, a crosscap slide, a boundary slide and an elementary braid.

We consider aane group schemes G over a eld k of characteristic p > 0. Equivalently , we consider nitely generated commutative k-algebras kG] (the coordinate algebra of G) endowed with the structure of a Hopf algebra. The group scheme G is said to be nite if kG] is nite dimensional (over k) and a nite group scheme is said to be innnitesimal if the ((nite dimensional) algebra kG] is local. A rat...

. We de…ne trees generated by bi-in…nite sequences, calculate their walkinvariant distribution and the speed of a biased random walk. We compare a simple random walk on a tree generated by a bi-in…nite sequence with a simple random walk on an augmented Galton-Watson tree. We …nd that comparable simple random walks require the augmented Galton-Watson tree to be larger than the corresponding tree...

The Poisson boundary for measures with a nite rst moment on polycyclic groups is shown to coincide with the corresponding contracting nilpotent Lie group. The proof is based on using a geometric \strip criterion" of boundary maximality due to the author and a simple estimate of the \neutral component" of the random walk.