In this paper we consider  (extended) metaplectic representation of the  semidirect product  $G_{mathbb{J}}=mathbb{R}^{2d}timesmathbb{J}$  where $mathbb{J}$ is a closed subgroup of $Sp(d,mathbb{R})$, the symplectic group. We will investigate continuous representation frame on $G_{mathbb{J}}$. We also discuss the existence of duals for such frames and give several characterization for them. Fina...

Observation of the decay of muons produced in the Earth's atmosphere by cosmic ray interactions provides a graphic illustration of the counter-intuitive space-time predictions of special relativity theory. Muons at rest in the atmosphere, decaying simultaneously, are subject to a universal time-dilatation effect when viewed from a moving frame and so are also observed to decay simultaneously in...

Given a unimodal logic Λ extending the modal logic of reflexive frames T = K⊕2p→ p (the symbol ⊕ is used in the same way as in [3]), we can define several irreflexive or non-reflexive counterparts of Λ. Our first approach will be semantical. As usual, given a set W , define ∆W := {〈x, x〉 | x ∈W}. Definition 1.1 The irreflexivization of a frame F = 〈W,R〉 is 〈W,R〉• := 〈W,R − ∆W 〉. For X a class o...

This paper presents a robust spatial spreadspectrum (SS) video watermarking scheme with adaptive detection for H.264/AVC and SVC. We introduce a fast image size change method in DCT domain to obtain a lowpass and downsized version of the video frame for embedding, which protects the watermarking signal from being damaged by downsampling during SVC encoding. And then we embed watermark bits by S...

In this paper, we propose an optimal bit allocation scheme for MPEG-4 video coding. In the proposed scheme, we assign more bits to I-frames and some selected P-frames. In order to decide optimal target bits for each intra frame, we need to calculate spatial complexity of the intra frame. We also define an absolute temporal correlation factor to measure temporal correlation between successive fr...

algebraic frames are generalizations of fourier transforms on locally compact abelian groups in the sense that the family of vectors forming the frame are replaced by a family of unbounded linear functionals. the paper studies the indexing measure space of the algebraic frames; as the investigation narrows down to the class of lower semiframes, more relations are revealed between the discret...

In Special Relativity there are infinitely many equivalence classes of frames of reference. In each such class every two frames of reference move uniformly with respect to one another. It appears that the following questions have never been asked : In which of such equivalence classes of frames of reference is Special Relativity supposed to hold ? How can we identify such a class, and do so the...

Abstract We propose a class of algebraic polynomial frames, which are computationally easier to implement than polynomial bases. We also discuss the weighted Lstability of our frames for 1 ≤ p ≤ ∞. Our analysis is based on orthogonal polynomials with respect to the weight in question, but the frame bounds are independent of the system of orthogonal polynomials used. In spite of the fact that al...