In this article we introduce the notion of J-Parseval fusion frames in a Krein space K and characterize 1-uniform J-Parseval fusion frames with ζ = √ 2. We provide some results regarding construction of new J-tight fusion frame from given J-tight fusion frames. We also characterize an uniformly J-definite subspace of a Krein space K in terms of J-fusion frame. Finally we generalize the fundamen...

1 Weaving is defined as the crossing of two streams travelling in the same direction along a 2 significant section of the road without the assistance of traffic control devices. Merging and 3 diverging vehicles need to make one or more lane-changes in a limited space and time, 4 determined by the weaving section length. This situation creates intensive lane-change 5 maneuvers, combined with hea...

Controlled g-atomic subspace for a bounded linear operator is being presented and characterization has been given. We give an example of controlled K-g-fusion frame. construct new frame the Hilbert space H ? X using frames spaces X. Several useful resolutions identity on theory g-fusion have discussed. Frame pair Bessel sequences introduced.

Let {Wi}i∈I be a (redundant) sequence of subspaces each being endowed with a weight vi, and let H be the closed linear span of the Wi’s, a composite Hilbert space. Provided that {(Wi, vi)}i∈I satisfies a certain property which controls the weighted overlaps of the subspaces, it is called a fusion frame. These systems contain conventional frames as a special case, however they go far “beyond fra...

In this paper we present current state of principles and applications in static and dynamic weaving. We are concentrating on static weaving in AspectJ and dynamic weaving in PROSE PROgrammable extenSions of sErvice. The contribution of this paper is in analyses of both approaches to weaving which we aim to apply as essential mechanisms when constructing software systems by automatic evolution.

Due to the poor transfer organization in urban public transport terminal, pedestrian crowd are often forced to weaving in their transfer flow lines. Frequent weaving behaviors not only decrease passengers’ transfer comfort, but may also trigger serious crowd disaster such as trampling. In order to get accurate understanding of the weaving features of pedestrian crowd and analyze the relevant ev...

Fusion frames were recently introduced to model applications under distributed processing requirements. In this paper we study the behavior of fusion frames under erasures of subspaces and of local frame vectors. We derive results on sufficient conditions for a fusion frame to be robust to such erasures as well as results on the design of fusion frames which are optimally robust in the sense of...

This paper describes the incremental weaving implementation of Apostle, an aspect-oriented language extension to Smalltalk modelled on AspectJ. Apostle implements incremental weaving in order to make aspect-oriented programming (AOP) a natural extension of the incremental edit-run-debug cycle of Smalltalk environments. The paper analyzes build dependencies for aspect declarations, and shows tha...

Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame can be regarded as a frame-like collection of subspaces in a Hilbert Communicated by Qiyu Sun. P.G.C. and A.H. were supported by NSF DMS 0704216. G.K. would like to thank the Department of Statistics at Stanford University and the Mathematics Depar...