partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

In this paper, we present a new semantics for the well-known normal system of modal logic K based on the notion of convergence spaces. The purpose is to use convergence spaces to model and reason about systems with both discrete and continuous states, so-called hybrid state spaces. K is sound and complete with respect to the class of convergence space models, and we show that Kripke frames and ...

the generalization of p-frame in banach spaces is considered in this paper. the concepts of an $tilde{x}$-frame and a system conjugate to $tilde{x}$-frame were introduced. analogues of the results on the existence of conjugate system were obtained. the stability of $tilde{x}$-frame having a conjugate system is studied.

Abstract Recently, frame multipliers, pair frames, and controlled frames have been investigated to improve the numerical efficiency of iterative algorithms for inverting operator other applications frames. In this paper, concept biframe is introduced a Hilbert space. A sequences in space that applies an inequality similar inequality. Also, it can be regarded as generalization special kind The b...

Title of dissertation: GABOR FRAMES FOR QUASICRYSTALS AND K-THEORY Michael Kreisel, Doctor of Philosophy, 2015 Dissertation directed by: Professor Jonathan Rosenberg Department of Mathematics We study the connection between Gabor frames for quasicrystals, the topology of the hull ΩΛ of a quasicrystal Λ and the K-theory of an associated twisted groupoid algebra. In particular, we construct a fin...

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We develop a novel and unifying setting for phase retrieval problems that works in Banach spaces and for continuous frames and consider the questions of uniqueness and stability of the reconstruction from phaseless measurements. Our main result states that also in this framework, the problem of phase retrieval is never uniformly stable in infinite dimensions. On the other hand, we show weak sta...