Progressive collapse is a condition where local failure of a primary structural component leads to the collapse of neighboring members and the whole structure, consequently. In this paper, the progressive collapse potential of seismically designed steel dual systems with buckling restrained braces is investigated using the alternate path method, and their performances are compared with those of...

It is well known that the category KHaus of compact Hausdorff spaces is dually equivalent to the category KRFrm of compact regular frames. By de Vries duality, KHaus is also dually equivalent to the category DeV of de Vries algebras, and so DeV is equivalent to KRFrm, where the latter equivalence can be described constructively through Booleanization. Our purpose here is to lift this circle of ...

Abstract. Dual Gramian analysis is one of the fundamental tools developed in a series of papers [37, 40, 38, 39, 42] for studying frames. Using dual Gramian analysis, the frame operator can be represented as a family of matrices composed of the Fourier transforms of the generators of (generalized) shiftinvariant systems, which allows us to characterize most properties of frames and tight frames...

This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in terms of the elements of E via a map a : I → G. A fundamental set of equalities are shown betwee...

This paper deals with structural issues concerning wavelet frames and their dual frames. It is known that there exist { a j / 2 ? ( ? ? k b ) } , ? Z in L R for which no frame has structure. We first generalize this result by proving approximately Motivated we show imposing very mild decay condition on the Fourier transform of generator certain oversampling N indeed an frame; most importantly, ...

The main purpose of this paper is to find other measurements for constructing optimal duals that minimize the reconstruction errors, when erasures occur. Some known results are investigated with some measurements. Moreover, we investigate extreme points set all 1-erasure by seminorms. Furthermore, examples provided clarification.

This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis are made by two frames, respectively. The goal is to give some results about localization spectra identify regions complex plane containing using information symbols.