We study homological and geometric properties of differential algebras of finite type over a base field. The main results concern rigid dualizing complexes over such algebras.

In this paper we consider generalized metric spaces in the sense of Lawvere and the categorical Isbell completion construction. We show that this is an analogue of the tight span construction of classical metric spaces, and that the Isbell completion coincides with the directed tight span of Hirai and Koichi. The notions of categorical completion and cocompletion are related to the existence of...

In this paper, we present a novel hybrid keyword spotting system that combines supervised and semi-supervised competitive learning algorithms. The rst stage is a S-SOM (Semi-supervised SelfOrganizing Map) module which is speci cally designed for discrimination between keywords (KWs) and non-keywords (NKWs). The second stage is an FDVQ (Fuzzy Dynamic Vector Quantization) module which consists of...

An action of the Yangian of the general linear Lie algebra glN is defined on every irreducible integrable highest weight module of ĝlN with level > 2. This action is derived, by means of the Drinfeld duality and a subsequent semi-infinite limit, from a certain induced representation of the degenerate double affine Hecke algebra H. Each vacuum module of ĝlN is decomposed into irreducible Yangian...

An action of the Yangian of the general linear Lie algebra glN is defined on every irreducible highest weight module of ĝlN with integer level > 2. This action is derived, by means of the Drinfeld duality and a subsequent semi-infinite limit, from a certain induced representation of the degenerate double affine Hecke algebra H. Each vacuum module of ĝlN is decomposed into irreducible Yangian re...

The trellis of a finite Abelian group code is locally (i.e., trellis section by trellis section) related to the trellis of the corresponding dual group code which allows to express the basic operations of the a posteriori probability (APP) decoding algorithm (defined on a single trellis section of the primal trellis) in terms of the corresponding dual trellis section. Using this local approach,...

In this paper, we present a new decomposition algorithm for solving large-scale multistage stochastic programs (MSSP) with endogenous uncertainties. Instead of dualizing all the initial non-anticipativity constraints (NACs) and removing all the conditional non-anticipativity constraints to decompose the problem into scenario subproblems, the basic idea relies on keeping a subset of NACs as expl...

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

The source of a simple kG-module, for a finite p-solvable group G and an algebraically closed field k of prime characteristic p, is an endo-permutation module (see [Pu1] or [Th]). L. Puig has proved, more precisely, that this source must be isomorphic to the cap of an endo-permutation module of the form ⊗ Q/R∈S Ten P Q Inf Q Q/R(MQ/R), where MQ/R is an indecomposable torsion endo-trivial module...