We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense we construct the leading terms of the asymptotics expansion for the resolvent of the operator described by the system. The convergence of the spectrum is est...

Let  $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $|aa_alpha-varphi(a)a_alpha|to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such  as Segal algebras and $L^1$-algebras are resp...

We analyze the problem of boundary observability of the finite-difference space semi-discretizations of the 2-d wave equation in the square. We prove the uniform (with respect to the mesh size) boundary observability for the solutions obtained by the two-grid preconditioner introduced by Glowinski [6]. Our method uses previously known uniform observability inequalities for low frequency solutio...

Constraint propagation is a general algorithmic approach for pruning the search space of a CSP. In a uniform way, K. R. Apt [1] has defined a computation as an iteration of reduction functions over a domain. In [2] he has also demonstrated the need for integrating static properties of reduction functions (commutativity and semi-commutativity) to design specialized algorithms such as AC3 and DAC...

Particle swarm optimization comes under lot of changes after James Kennedy and Russell Eberhart first proposes the idea in 1995. The changes has been done mainly on Inertia parameters in velocity updating equation so that the convergence rate will be higher. We are proposing a novel approach where particle’s movement will not be depend on its velocity rather it will be decided by constrained bi...

In this paper, a parameter-uniform convergent numerical scheme is provided for solving singularly perturbed parabolic convection-diffusion differential equations with large delay. A priori bounds on the exact solution and its derivatives derived by asymptotic analysis of problem are provided.. The discretized Crank-Nicolson method uniform mesh in time direction fitted operator upwind finite dif...

A standard approach for large scale image classification involves high dimensional features and Stochastic Gradient Descent algorithm (SGD) for the minimization of classical Hinge Loss in the primal space. Although complexity of Stochastic Gradient Descent is linear with the number of samples these method suffers from slow convergence. In order to cope with this issue, we propose here a Stochas...

The problem of characterizing learnability is the most basic question of statistical learning theory. A fundamental and long-standing answer, at least for the case of supervised classification and regression, is that learnability is equivalent to uniform convergence of the empirical risk to the population risk, and that if a problem is learnable, it is learnable via empirical risk minimization....