Minimal linear codes are linear codes such that the support of every codeword does not contain the support of another linearly independent codeword. Such codes have applications in cryptography, e.g. to secret sharing. We pursue here their study and construct asymptotically good families of minimal linear codes. We also push further the study of quasi-minimal and almost-minimal linear codes, re...

The purpose of this paper is to establish some weak convergence theorems of modified two-step iteration process with errors for two asymptotically quasi-nonexpansive non-self mappings in the setting of real uniformly convex Banach spaces if E satisfies Opial’s condition or the dual E∗ of E has the Kedec-Klee property. Our results extend and improve some known corresponding results from the exis...

We provide a feasible generalized least squares estimator for (unrestricted) multivariate GARCH(1,1) models. We show that the estimator is consistent and asymptotically normally distributed under mild assumptions. Unlike the (quasi) maximum likelihood method, the feasible GLS is considerably fast to implement and does not require any complex optimization routine. We present numerical experiment...

In this paper we propose two strongly convergent parallel hybrid iterative methods for finding a common element of the set of fixed points of a family of asymptotically quasi φ-nonexpansive mappings, the set of solutions of variational inequalities and the set of solutions of equilibrium problems in uniformly smooth and 2-uniformly convex Banach spaces. A numerical experiment is given to verify...

We introduce an iterative algorithm for finding a common element of the set of common fixed points of a finite family of closed quasi-φ-asymptotically nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the variational inequality problem for a γ-inverse strongly monotone mapping in Banach spaces. Then we study the strong convergence of the algorith...

We have frequency doubled a 1319-nm Nd:YAG laser in a quasi-phase-matched LiNbO(3) waveguide and used the asymptotically equal to1-mW second-harmonic output to investigate the (127)I(2) transitions near 660 nm. We reached submegahertz laser-frequency stability at a (vacuum) wavelength of 1319.098 nm by locking the second harmonic to the center of the P(48)6-6 transition.

In this paper, a recently suggested general procedure which leads to an eigenvahre eqnation for apertnre problems is specialized to the range of frequencies for which the maximnm linear dimension of the aperture [ is much smaller than the wavelengths, known as the Rayleigh region. As kl asymptotically approaches zero, we arrive at a set of two eigenvahre equations which aided by the edge condit...

A thermodynamical description for the quasi-static collapse of radiating, self-gravitating spherical shells of matter in anti-de Sitter space-time is obtained. It is shown that the specific heat at constant area and other thermodynamical quantities may diverge before a black hole has eventually formed. This suggests the possibility of a phase transition occurring along the collapse process. The...

We prove that an implicit iterative process with errors converges weakly and strongly to a common fixed point of a finite family of asymptotically quasi-nonexpansive mappings on unbounded sets in a uniformly convex Banach space. Our results generalize and improve upon, among others, the corresponding recent results of Sun (2003) in the following two different directions: (i) domain of the mappi...

The purpose of this paper is to introduce a class of total quasi-φ-asymptotically nonexpansivenonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the co...