in this paper, we establish an existence result of the solution for an generalized strong vector variational inequality already considered in the literature and as applications we obtain a new coincidence point theorem in hilbert spaces.

In this article, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion B∗-algebras are equivalent to the category of real vector spaces, the category of real Hilbert spaces and the category of real C∗-algebras respectively. We will also give a Riesz representation theorem for quaternion...

Fusion frames are an extension to frames that provide a framework for applications and providing efficient and robust information processing algorithms. In this article we study the erasure of subspaces of a fusion frame.  

A fundamental question in operator theory is: how rich is the collection of oprrators on a given Banach space? For classical spaces, especially Hilbert space, a well developed theory of operators exists. However a Banach space may have far fewer operators than one might expect. Shelah [S] has constructed a nonseparable Ba~lach space X , for which the space of operators with separable range has ...

A common approach to innovation, parallel search, is to identify a large number of opportunities and then to select a subset for further development, with just a few coming to fruition. One potential weakness with parallel search is that it permits repetition. The same, or a similar, idea might be generated multiple times, because parallel exploration processes typically operate without informa...

Abstract In a typical innovation process, the innovator identifies or generates a set of raw opportunities or “ideas” before selecting one or more for further investment. This mode of innovation can be thought of as search within the opportunity space. In this paper we characterize some properties of innovation opportunity spaces as reflected by the set of ideas collected, and address three mai...

We introduce observation frames as an extension of ordinary frames. The aim is to give an abstract representation of a mapping from observable predicates to all predicates of a specific system. A full subcategory of the category of observation frames is shown to be dual to the category of F! topological spaces. The notions we use generalize those in the adjunction between frames and topological...

This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space $H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$

We develop a version of Herbrand’s theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable functions in Hilbert spaces expanded by a group of generic unitary operators and Hilbert spaces expanded by a generic subspace. We also show how Herbrand’s theor...

Future mixed reality systems will need to support large numbers of simultaneous, non-expert users at reasonable per-user costs if they are to be widely deployed within society in the short to medium term. We have constructed a prototype of such a system, an interactive entertainment space called Ada that was designed to behave like a simple organism. Using Ada we conducted two studies: the firs...