We address the question of exact controllability of the wave and Schrödinger equations perturbed by a singular inverse-square potential. Exact boundary controllability is proved in the range of subcritical coefficients of the singular potential and under suitable geometric conditions. The proof relies on the method of multipliers. The key point in the proof of the observability inequality is a ...

A popular methodology of studying spatial income inequality is analysis of beta-convergence (i.e. an inverse relationship between current income per capita and its initial level). Its widespread use is based on a belief that the economic growth theory predicts income convergence among economies (countries or regions within a country), and that beta-convergence suggests decreasing income inequal...

In this paper, which is the sequel to [GN04a], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually incoherent bases introduced by Donoho and Huo. The Bernstein inequality obta...

The theory of evolutionary variational inequalities fits very well in a lot of optimization problems, like for example the dynamic oligopolistic market equilibrium problem that we describe in this paper. But here, the authors analyze the behavior of control policies whose aim is to regulate the exportation through the adjustments of supply taxes or incentives on the firms. This is considered as...

Gwinner (1981) proved an existence theorem for a variational inequality problem involving an upper semicontinuous multifunction with compact convex values. The aim of this paper is to solve this problem for a multifunction with open inverse values.

In this study, generalized multivalued vector inverse quasi-variational inequality problems are developed, and error bounds obtained in terms of the residual gap function, regularized D-gap function. With help these constraints, one can effectively estimate distances between any feasible point solution set involving inequality.

In this paper, we give some sharper refinements and generalizations of inequalities related to Shafer-Fink's inequality for the inverse sine function stated in Theorems 1, 2, and 3 of Bercu (Math. Probl. Eng. 2017: Article ID 9237932, 2017).

Based on minimizing a piecewise diierentiable lp function subject to a single inequality constraint, this paper discusses algorithms for a discretized regularization problem for ill-posed inverse problems. We examine computational challenges of solving this regularization problem. Possible minimization algorithms such as the steepest descent method, iteratively weighted least squares (IRLS) met...

BACKGROUND WHO estimates that 8.4 million deaths will be counted a year due to tobacco by 2020, and 70% of those deaths will occur in developing countries. Examination of the magnitude of socioeconomic differences in smoking between different age groups reveals specific groups anti-smoking programs should target on. This study aimed to measure socioeconomic gradients related inequality in smoki...