A Vector Lattice Topology and Function Space Representation

On the character space of Banach vector-valued function algebras

‎Given a compact space $X$ and a commutative Banach algebra‎ ‎$A$‎, ‎the character spaces of $A$-valued function algebras on $X$ are‎ ‎investigated‎. ‎The class of natural $A$-valued function algebras‎, ‎those whose characters can be described by means of characters of $A$ and‎ ‎point evaluation homomorphisms‎, ‎is introduced and studied‎. ‎For an‎ ‎admissible Banach $A$-valued function algebra...

Menger probabilistic normed space is a category topological vector space

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

Vector partition function and representation theory

We apply some recent developments of Baldoni-Beck-CochetVergne [BBCV05] on vector partition function, to Kostant’s and Steinberg’s formulae, for classical Lie algebras Ar, Br , Cr , Dr . We therefore get efficient Maple programs that compute for these Lie algebras: the multiplicity of a weight in an irreducible finite-dimensional representation; the decomposition coefficients of the tensor prod...

Sentence Clustering Using Continuous Vector Space Representation

In this paper, we present a clustering approach based on the combined use of a continuous vector space representation of sentences and the k-means algorithm. The principal motivation of this proposal is to split a big heterogeneous corpus into clusters of similar sentences. We use the word2vec toolkit for obtaining the representation of a given word as a continuous vector space. We provide empi...

Vector Calculus and the Topology of Domains in 3-Space