The paper discusses discrete frames as an attractive semantics for modal logic. We study questions of completeness, persistence, duality and definability. Notions of completeness, strong global completeness and complexity of dual varieties coincide for discrete frames; moreover, they are equivalent to conservativity of minimal hybrid extensions. The paper also provides some criteria of di-persi...

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...

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...

We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal Parseval wavelet frames and the additional shift invariance gain of the core subspace.

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...

This paper presents a novel scene change detection method using complexity and edge direction based on intra prediction mode in H.264/AVC compressed video. When scene change occurs, there is less temporal correlation between consecutive frames. Therefore, most of macro-blocks are encoded in intra mode. Using this property, the proposed method calculates the percentage of intra mode blocks in ea...

Video boundary detection belongs to a basis subject in computer vision. It is more important to video analysis and video understanding. The existing video boundary detection methods always are effective to certain types of video data. These methods have relatively low generalization ability. We present a novel shot boundary detection algorithm based on video dynamic texture. Firstly, the two ad...

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 ...