Let A and B be closed, convex bounded subsets of a weakly sequentially complete Banach space E which both are not compact. Then there is linear form x0⁎∈E⁎ does attain its supremum on B. In particular, given any subset A⊂E, if every x⁎∈E⁎ either attains or infimum A, then relatively The same happens for finite family but compact subsets. result only remains true in arbitrary assuming, two σ(E⁎⁎...

This paper describes Gammall og, a logic language based on multiset rewriting. The language combines the ability of describing parallel programs made of multiset transformation rules as in GAMMA with the execution model of logic programming in a strongly typed framework as in GG odel. We describe the design choices, the syntax and the semantics of the language, and a prototype implementation.

In evolutionary biology, biologists often face the problem of constructing a phylogenetic tree on a set X of species from a multiset Π of partitions corresponding to various attributes of these species. One approach that is used to solve this problem is to try instead to associate a tree (or even a network) to the multiset ΣΠ consisting of all those bipartitions {A,X − A} with A a part of some ...

It is shown that Hack’s Conjecture on Petri nets implies that for every language generated by a matrix grammar (without appearance checking), there is a non-erasing matrix grammar generating a language of the same Parikh image. Is is also shown that in this case, the classes of multiset languages generated by arbitrary and monotone multiset grammars coincide.

This paper defines multiset-valued linear index grammar and unordered vector grammar with dominance links. The former models certain uses of multiset-valued feature structures in unification-based formalisms , while the latter is motivated by word order variation and by "quasi-trees", a generalization of trees. The two formalisms are weakly equivalent, and an important subset is at most context...

A projective multiset is a collection of projective points, which are not necessarily distinct. A linear code can be represented as a projective multiset, by taking the columns of a generator matrix as projective points. Projective multisets have proved very powerful in the study of generalised Hamming weights. In this paper we study relations between a code and its dual.