Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical numerical perspectives. Namely, we show convergence the method establish properties couple majorization approaches for associated problems. also test monotone al...

Euclidean distance matrices (EDM) are symmetric nonnegative with several interesting properties. In this article, we introduce a wider class of called generalized (GEDMs) that include EDMs. Each GEDM is an entry-wise matrix. A not unless it EDM. By some new techniques, show many significant results on can be extended to matrices. These contain about eigenvalues, inverse, determinant, spectral r...

The Rayleigh–Ritz method is widely used for eigenvalue approximation. Given a matrix X with columns that form an orthonormal basis for a subspace X , and a Hermitian matrix A, the eigenvalues of XHAX are called Ritz values of A with respect to X . If the subspace X is A-invariant, then the Ritz values are some of the eigenvalues of A. If the A-invariant subspace X is perturbed to give rise to a...

In this paper, we consider the joint design of source precoding matrix and the relay precoding matrix in a two-hop multiple-input multiple-output relay network. The goal is to find a pair of matrices in order to minimize the power consumption and at the same time meet pre-selected quality of service constraints that are defined as the mean square error of each data stream. Using majorization th...

The kaon bag parameter BK , which is required for constraining the CP violation parameter in the Cabibbo-Kobayashi-Maskawa matrix from experiment, has been successfully calculated with the Kogut-Susskind(KS) quark action, taking advantage of its UA(1) chiral symmetry[1]. A recent systematic calculation of BK with high statistics[2], however, reveals that the systematic uncertainties in the pert...

Weak processes involving light hadrons in general, and kaons in particular, have contributed significantly to our understanding of fundamental interactions over the years. Most recently, the measurement of a non-vanishing Re ǫ/ǫ in K → ππ decays by KTeV [1] and NA48 [2] has provided unambiguous evidence for direct CP violation. In constraining the Standard Model (SM), the physics of kaons is co...

It is convenient to define H(X) = Hα(X) = −∞ when X is discrete, e.g., degenerate. (Our notation differs from that of Karlin and Rinott 1981 here.) We study the entropy of a weighted sum, S = ∑n i=1 aiXi, of i.i.d. random variables Xi, assuming that the density f of Xi is log-concave, i.e., supp(f) = {x : f(x) > 0} is an interval and log f is a concave function on supp(f). The main result is th...