The variety of Heyting algebras has a nice property that HS = SH. Heyting algebras are the algebraic dual of intuitionistic descriptive frames. The goal of this paper is to define proper dual notions so as to formulate this algebraic properties in the frame language, and to give a frame-based proof of this property and some other duality theorems.

Frames are the foundation of the linear operators used in the decomposition and reconstruction of signals, such as the discrete Fourier transform, Gabor, wavelets, and curvelet transforms. The emergence of sparse representation models has shifted of the emphasis in frame theory toward sparse l1-minimization problems. In this paper, we apply frame theory to the sparse representation of signals i...

OBJECTIVES We assessed the comparability of self-reported smoking prevalence estimates from a dual-frame survey with those from two large-scale, national surveys. METHODS The Social Climate Survey of Tobacco Control (SCS-TC) obtained self-reported current smoking status via a dual-frame methodology in the fall of 2010. One frame used random digit dialling procedures and consisted of household...

In this paper, we introduce the concept of family of local atoms in a 2-inner product space and then this concept is generalized to an atomic system. Besides, a characterization of an atomic system lead to obtain a new frame. Actually this frame is a generalization of previous works.

a heyting algebra is a distributive lattice with implication and a dual $bck$-algebra is an algebraic system having as models logical systems equipped with implication. the aim of this paper is to investigate the relation of heyting algebras between dual $bck$-algebras. we define notions of $i$-invariant and $m$-invariant on dual $bck$-semilattices and prove that a heyting semilattice is equiva...

We design alternative dual frames for linearly reconstructing signals from Sigma-Delta (Σ∆) quantized finite frame coefficients. In the setting of sampling expansions for bandlimited functions, it is known that a stable rth order Sigma-Delta quantizer produces approximations where the approximation error is at most of order 1/λ , and λ > 1 is the oversampling ratio. We show that the counterpart...

Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual relationship. We will show that controlled frames are equivalent to standard frames and so this concept gives a generalized way to check the frame condition, while ...

This paper introduces an optical 2-axis Micro Electro-Mechanical System (MEMS) micromirror actuated by a pair of electrothermal actuators and a set of passive torsion bars. The actuated element is a dual-reflective circular mirror plate of 1 mm in diameter. This inner mirror plate is connected to a rigid frame via a pair of torsion bars in two diametrically opposite ends located on the rotation...

With the proliferation of digital video and the popularity of video streaming applications, it is highly desirable to find and access video segments of interest by searching through the content of video at a speed that is faster than a normal playback. The key functions that enable quick browsing of video are fast-forward and fastreverse playbacks. However, motion-compensated prediction adopted...