in this paper we develop a natural generalization of schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. we prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. we prove that the operators of a dual ov-basis are continuous. we also dene the concepts of bessel, hilbert ov-basis and obt...

We explore the structure of the maximum vertex independence sets in fullerenes: plane trivalent graphs with pentagonal and hexagonal faces. At the same time, we will consider benzenoids: plane graphs with hexagonal faces and one large outer face. In the case of fullerenes, a maximum vertex independence set may constructed as follows: (i) Pair up the pentagonal faces. (ii) Delete the edges of a ...

1. Introduction. Theoretical Assumptions and Aims 1.1 In the present paper, we attempt to compare two simultaneous descriptions of natural language with a view to semiotic questions. The linguistic theories we have chosen to this end are, on the one hand, the standard theory of transformational grammar (TG), formulated in the mid-1960's by Noam Chomsky, and, on the other hand, an early version ...

Since it is well-known that the Vandermonde matrix is ill-conditioned, while the interpolation itself is not unstable in function space, this paper surveys the choices of other new bases. These bases are data-dependent and are categorized into discretely l2-orthonormal and continuously L2-orthonormal bases. The first one construct a unitary Gramian matrix in the space l2(X) while the late...

g-frames in hilbert spaces are a redundant set of operators which yield a repre-sentation for each vector in the space. in this paper we investigate the connection betweeng-frames, g-orthonormal bases and g-riesz bases. we show that a family of bounded opera-tors is a g-bessel sequences if and only if the gram matrix associated to its denes a boundedoperator.

For a positive integer n, does there exist a vertex-transitive graph r on n vertices which is not a Cayley graph, or, equivalently, a graph r on n vertices such that Aut F is transitive on vertices but none of its subgroups are regular on vertices? Previous work (by Alspach and Parsons, Frucht, Graver and Watkins, MaruSic and Scapellato, and McKay and the second author) has produced answers to ...

Let M ⊂ [n] := {0, . . . , n} and A be a family of subsets of an n element set such that |A∩B| ∈M for every A,B ∈ A. Suppose that l is the maximum number of consecutive integers contained in M and n is sufficiently large. Then |A| < min{1.62210 , 2 log 2 }. The first bound complements the previous bound of roughly (1.99)n due to Frankl and the second author [9] proved under the assumption that ...