One of the first remarkable results in representation theory artin algebras, due to Auslander and Ringel-Tachikawa, is characterisation when an algebra representation-finite. In this paper, we investigate aspects representation-finiteness general context exact categories sense Quillen. framework, introduce “big objects” prove Auslander-type “splitting-big-objects” theorem. Our approach generali...

In this paper we show how the two well-known integer representation theorems which are associated with the name of Zeckendorf may be generalized as dual systems by constructing colored tree sequences whose shade sets partition Z = {1, 2, . . . } . Many interesting properties of the representations can be observed directly from the tree diagrams, and the proofs of the properties can truly be sai...

In this paper the definition of semiseparable matrices is investigated. Properties of the frequently used definition and the corresponding representation by generators are deduced. Corresponding to the class of tridiagonal matrices another definition of semisepar-able matrices is introduced preserving the nice properties dual to the class of tridiagonal matrices. Several theorems and properties...

Some aspects of the theory of Boolean algebras and distributive lattices -in particular, the Stone Representation Theorems and the properties of filters and ideals -are analyzed in a constructive setting.

In this paper we discuss some fundamental results in real and functional analysis including the Riesz representation theorem, the Hahn-Banach theorem, and the Baire category theorem. We also discuss applications of these theorems to other topics in analysis.

Considering a binary operation as a ternary relation permits certain sections of the latter (which are functions) to be used in representing an abstract semigroup as a family of the self-maps of its underlying set under function composition. The idea is thus seen to be entirely similar to the way that the sections of a partial ordering under set inclusion represent the (abstract) partially orde...

In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real ...

We consider the Teichmüller flow on the unit cotangent bundle of the moduli space of compact Riemann surfaces with punctures. We show that it is exponentially mixing for the Ratner class of observables. More generally, this result holds for the restriction of the Teichmüller flow to an arbitrary connected component of stratum. This result generalizes [AGY] which considered the case of strata of...

Version of 8/13/05 By Jason Fulman University of Pittsburgh Department of Mathematics, 301 Thackeray Hall, Pittsburgh PA 15260 email: [email protected] Abstract: Stein’s method is used to prove limit theorems for random character ratios. Tools are developed for four types of structures: finite groups, Gelfand pairs, twisted Gelfand pairs, and association schemes. As one example an error term...

This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premisses. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, and Magidor (1990) and Makinson (1989), (1993). A selection function picks out from a given set o...