We give a characterization of the simple, and of the subdirectly irreducible boolean algebras with operators (including modal algebras), in terms of the dual descriptive frame. These characterizations involve a special binary quasi-reachability relation on the dual structure; we call a point u a quasi-root of the dual structure if every ultrafilter is quasireachable from u. We prove that a bool...

Estimation from multiframe survey data is essentially a problem of combining domain estimates such that the new auxiliary information (for key study variables, z) obtained from several estimates for overlapping domains is used in addition to the usual auxiliary information for sociodemographic and geographic variables (x) used in poststratification. A natural approach is to use optimal regressi...

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this paper is a continuation of [uniformities and covering properties for partial frames (i)], in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. after presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in th...

This paper presents a novel algorithm for obtaining a high spatio-temporal resolution video from two video sequences. These sequences are high resolution with low frame rate and low resolution with high frame rate. To this end, we introduce a dual sensor camera that can capture these sequences with the same field of view simultaneously. The proposed method observes motion information through th...

A generalized continuous frame is a family of operators on a Hilbert space H which allows reproductions of arbitrary elements of H by continuous superpositions. Generalized continuous frames are natural generalization of continuous and discrete frames in Hilbert spaces which include many recent generalization of frames. In this article,we associate to a generalized continuous frame suitable Ban...

In this article, we discuss some recent developments on pairs of dual wavelet frames in Sobolev spaces constructed by the Oblique Extension Principle (OEP) from refinable function vectors. Our investigation sheds a new light on understanding the OEP method for constructing MRA dual wavelet frames.

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...

We demonstrate that for all linear devices and/or sensors, signal requisition and reconstruction is naturally a mathematical frame expansion and reconstruction issue, whereas the measurement is carried out via a sequence generated by the exact physical response function (PRF) h of the device, termed sensory frame {hn}. The signal reconstruction, on the other hand, will be carried out using the ...

Video super-resolution for dual-mode cameras in single-view and mono-view scenarios is studied in this thesis. Dual-mode cameras are capable of generating high-resolution still images while shooting video sequences at low-resolution. High-resolution still images are used to form a regularization function for solving the inverse problem of super-resolution. Exploiting proposed regularization fun...