Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and u...

Let Ω be a bounded C∞-smoothly bounded domain in C. For such a domain we define a new notion between strict pseudo-convexity and pseudo-convexity: the size of the set W of weakly pseudo-convex points on ∂Ω is small with respect to Minkowski dimension: near each point in the boundary ∂Ω, there is at least one complex tangent direction in which the slices of W has a upper Minkowski dimension stri...

the most conventional method for lateral bracing of steel frames is using diagonal and x steel braces. in conventional method, braces of frame emplace in one bay or more, relative to structural requirement, from first to last story without displace the braces emplacement on height as columnar form. this pattern is a preliminary and simplest bracing template that the generally codes present base...

The subject of this article is the duality principle, which, well beyond its stand at the heart of Gabor analysis, is a universal principle in frame theory that gives insight into many phenomena. Its fiber matrix formulation for Gabor systems is the driving principle behind seemingly different results. We show how the classical duality identities, operator representations and constructions for ...

Members of newly formed design teams have different frames – implicit values, goals and assumptions – each of them hold about what problems are important and how they are best addressed. In the early, informal phases of design projects, these frames, and the degree to which they are shared within the team, have substantial consequences. However, little is known about the interactions and activi...

We introduce a new class of frames with strong symmetry properties called geometrically uniform frames (GU), that are defined over an abelian group of unitary matrices and are generated by a single generating vector. The notion of GU frames is then extended to compound GU (CGU) frames which are generated by an abelian group of unitary matrices using multiple generating vectors. The dual frame v...

Abstract. The time-frequency analysis of a signal is often performed via a series expansion arising from well-localized building blocks. Typically, the building blocks are based on frames having either Gabor or wavelet structure. In order to calculate the coefficients in the series expansion, a dual frame is needed. The purpose of the present paper is to provide constructions of dual pairs of f...

Abstract. In this paper, we mainly parameterize g-frames in Hilbert space in terms of operators. Firstly, under the condition that there exists a g-orthonormal basis we establish the one to one correspondence between different kinds of g-frames with certain kinds of operators. Then we parameterize g-frames without the above restriction. Finally, we consider some special g-frames, and their oper...

Construction of wavelet frames with matrix dilation is studied. We found a necessary condition and a sufficient condition under which a given pair of refinable functions generates dual wavelet systems with a given number of vanishing moments. For image compression and some other applications, it is very desirable to have wavelets with vanishing moment property. In particular, vanishing moments ...

Weaving frames have potential applications in wireless sensor networks that require distributed processing of signals under different frames. In this paper, we study some new properties weaving generalized (or g-frames) and orthonormal bases g-orthonormal bases). It is shown a g-frame its dual are woven. The inter-relation optimal bounds universal studied. Further, present characterization g-fr...