The purpose of this article is to derive the generalized formula of relativistic phase velocity transformation, by utilizing the Lorentz transforms on the wavevector k and frequency w for the moving inertial frame relative to the static system moving uniformly in an arbitrary direction. Furthermore, some significant cases are discussed. R 6 w & Cet essai est pour dCriver le gCniralisateur formu...

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...

This paper presents a POCS-based algorithm for consistent reconstruction of a signal x 2 R from any subset of quantized coe cients y 2 R in an N K overcomplete frame expansion y = Fx, N = 2K. By choosing the frame operator F to be the concatenation of two K K invertible transforms, the projections may be computed in R using only the transforms and their inverses, rather than in the larger space...

The excess of a sequence in a Hilbert space H is the greatest number of elements that can be removed yet leave a set with the same closed span. This paper proves that if F is a frame for H and there exist infinitely many elements gn ∈ F such that F \ {gn} is complete for each individual n and if there is a uniform lower frame bound L for each frame F \ {gn}, then for each ε > 0 there exists an ...

A circle C holds a convex body K ⊂ R3 if K can’t be moved far away from its position without intersecting C . One of our results says that there is a convex body K ⊂ R3 such that the set of radii of all circles holding K has infinitely many components. Another result says that the circle is unique in the sense that every frame different from the circle holds a convex body K (actually a tetrahed...

The goal of voice conversion systems is to modify the voice of a source speaker to be perceived as if it had been uttered by another specific speaker. Many approaches found in the literature work based on statistical models and introduce an oversmoothing in the target features. Our proposal is a new model that combines several techniques used in unit selection for text-tospeech and a non-gaussi...

An independent set S of a connected graph G is called a frame if G − S is connected. If |S| = k, then S is called a k-frame. We prove the following theorem. Let k ≥ 2 be an integer, G be a connected graph with V (G) = {v1, v2, . . . , vn}, and degG(u) denote the degree of a vertex u. Suppose that for every 3-frame S = {va, vb, vc} such that 1 ≤ a < b < c ≤ n, degG(va) ≤ a, degG(vb) ≤ b − 1 and ...

We consider the set of all linear combinations with integer coefficients of the vectors of a unit tight equiangular (k, n) frame and are interested in the question whether this set is a lattice, that is, a discrete additive subgroup of the k-dimensional Euclidean space. We show that this is not the case if the cosine of the angle of the frame is irrational. We also prove that the set is a latti...

For a separated sequence Λ = {λk}k∈Z of real numbers there is a close link between the lower and upper densities D−(Λ), D(Λ) and the frame properties of the exponentials {ek}k∈Z: in fact, {ek}k∈Z is a frame for its closed linear span in L(−γ, γ) for any γ ∈]0, πD−(Λ)[∪]πD+(Λ),∞[. We consider a classical example presented already by Levinson [10] with D−(Λ) = D(Λ) = 1; in this case, the frame pr...

A proper treatment of K-mixing is the key to understanding K-isomers. Here, we present a method based on the projected shell model. This method differs from the usual description of multi-quasiparticle states by introducing a transformation to the laboratory frame and a subsequent configuration mixing in that frame. It allows a quantitative study on the degree of K-violation through direct calc...