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...

 Let $R=oplus_{nin Bbb N_0}R_n$ be a Noetherian homogeneous ring with local base ring $(R_0,frak{m}_0)$, $M$ and $N$ two finitely generated graded $R$-modules. Let $t$ be the least integer such that $H^t_{R_+}(M,N)$ is not minimax. We prove that $H^j_{frak{m}_0R}(H^t_{R_+}(M,N))$ is Artinian for $j=0,1$. Also, we show that if ${rm cd}(R_{+},M,N)=2$ and $tin Bbb N_0$, then $H^t_{frak{m}_0R}(H^2_...

We find a sufficient condition that H is not level based on a reduction number. In particular, we prove that a graded Artinian algebra of codimension 3 with Hilbert function H = (h0, h1, . . . , hd−1 > hd = hd+1) cannot be level if hd ≤ 2d + 3, and that there exists a level Osequence of codimension 3 of type H for hd ≥ 2d+k for k ≥ 4. Furthermore, we show that H is not level if β1,d+2(I ) = β2,...

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...