This is an introduction to the problems connecting frame theory and the Kadison-Singer Problem. 1. Overview For an extensive introduction to the aspects of frame theory needed for an understanding of the Kadison-Singer Problem we refer to the survey paper [3], which is posted in this section of the web page “The Kadison-Singer Problem”. In the following section we will just give the basic defin...

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We show that the rest mass of a system consisting of two photons is a relativistic invariant having the same magnitude in all inertial reference frames in relative motion. A scenario which starts with two photons where their frequencies are equal to each other the magnitude of the rest mass of the system depends on the angle θ’, made by the momentums of the two photons being equal to zero for θ...

Frame representations (e.g. wavelets) and subspace projections are important tools in many image processing applications. A unified framework for frames and subspace bases, as well as bases and subspace frames, is developed for finite dimensional vector spaces. Dual (subspace) bases and frames are constructed and the theory is generalized to weighted norms and seminorms. It is demonstrated how ...

in recent years, the trend in solving optimization problems has been directed toward using heuristic algorithms such as neural networks, genetic and ant colony algorithms. the main reason for this trend can be attributed to the fact that these algorithms can be efficiently adjusted to the specific search space to which they are applied and consequently they can be used for many optimization pro...

BACKGROUND AND PURPOSE Computerized 3-dimensional (3-D) motion measurement systems are used by those interested in human motion. The purposes of this study were (1) to determine the limits of accuracy in determining intersegmental angles during pendular motion at varying speeds and (2) to determine changes in accuracy introduced by autodigitization and digitization by experienced manual raters....

The self-complementary subset T0 = X0 [symbol: see text] ¿AAA, TTT¿ with X0 = ¿AAC, AAT, ACC, ATC, ATT, CAG, CTC, CTG, GAA, GAC, GAG, GAT, GCC, GGC, GGT, GTA, GTC, GTT, TAC, TTC¿ of 22 trinucleotides has a preferential occurrence in the frame 0 (reading frame established by the ATG start trinucleotide) of protein (coding) genes of both prokaryotes and eukaryotes. The subsets T1 = X1 [symbol: se...