In our previous work [4] we showed that the extension property holds for linear codes over a finite module alphabet with respect to the symmetrized weight composition if and only if the socle of the alphabet is cyclic. For alphabets with a noncyclic socle we proved the existence of an unextendable isometry. However, our construction was implicit. This paper deals with a particular case of an al...

Let $H$ be a complex Hilbert space and let ${\mathcal F}_{s}(H)$ the real vector formed by all self-adjoint finite rank operators on $H$. We prove following non-injective version of Wigner's theorem: every linear operator sending one projections to (without any additional assumption) is induced or conjugate-linear isometry it constant set projections.

by using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2vbp) withdirichlet, neumann and cauchy types boundary conditions. the moment at the knots isapproximated by central finite-difference method. the order of convergence of the methodand the theory is illustrated by solving tes...

A pseudo-Euclidean space (R, μ) is such a Euclidean space R associated with a mapping μ : − → V x → x − → V for x ∈ R, and a linear isometry T : (R, μ) → (R, μ) is such a linear isometry T : R → R that Tμ = μT . In this paper, we characterize curvature of s-line, particularly, Smarandachely embedded graphs and determine linear isometries on (R, μ).

The purpose of this paper is twofold. The first is to point out that the Restricted Isometry Property (RIP) does not hold in many applications where compressed sensing is successfully used. This includes fields like Magnetic Resonance Imaging (MRI), Computerized Tomography, Electron Microscopy, Radio Interferometry and Fluorescence Microscopy. We demonstrate that for natural compressed sensing ...

In this paper, we address the question of information preservation in ill-posed, non-linear inverse problems, assuming that the measured data is close to a low-dimensional model set. We provide necessary and sufficient conditions for the existence of a so-called instance optimal decoder, i.e., that is robust to noise and modelling error. Inspired by existing results in compressive sensing, our ...

Isometry classes of linear codes can be expressed as orbits under the group action of a wreath product. Some combinatorial and algebraic methods are discussed which can be applied for generating linear codes distributed uniformly at random over all isometry classes.

We show that as long as the restricted isometry constant δ2k < 1/2, there exist a value q0 ∈ (0, 1] such that for any q < q0, each minimizer of the nonconvex `q minimization for the sparse solution of any underdetermined linear system is the sparse solution.

We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived.