This paper explores models for arithmetics in substructural logics. In the existing literature on substructural arithmetic, frame semantics for substructural logics are absent. We will start to fill in the picture in this paper by examining frame semantics for the substructural logics C (linear logic plus distribution), R (relevant logic) and CK (C plus weakening). The eventual goal is to find ...

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...

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...

Co-expression of cytokeratin (CK) pairs has been found to be associated with specific epithelial cell types whose expressions are developmentally regulated. In the prostate, CK 8 and 18 have been identified as luminal cell-specific markers, and CK 5 and 15 have been identified as basal cell-specific markers. In this study, we report the cloning and sequencing of a full-length CK 8 cDNA (1.9 kil...

At various intervals after plating, cultures were exposed to 2-h pulses of tritium-labeled leucine. For determination of incorporated radioactivity, the creatine kinases were isolated by specific immunoprecipitation. Sodium dodecyl sulfate-gel electrophoresis was used to separate the two types of creatine kinase subunits MCK and B-CK from each other and their radioactivity was determined in the...

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...

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...

Objective(s): Infection with Pseudomonas aeruginosa has been a long-standing obstacle for clinical therapy due to the complexity of the genetics and pathogenesis, as well for widespread resistance to antibiotics, thus attaching great importance to explore effective vaccines for prevention and treatment. This paper focuses on the introduction of novel Pseudomonas aeruginosa type IV pili (T4P)-ba...

Fusion frames, and, more generally, operator-valued frame sequences are generalizations of classical frames, which are today a standard notion when redundant, yet stable sequences are required. However, the question of stability of duals with respect to perturbations has not been satisfactorily answered. In this paper, we quantitatively measure this stability by considering the associated devia...