The strong approximation property and the weak bounded approximation property

We show that the strong approximation property (strong AP) (respectively, strong CAP) and the weak bounded approximation property (respectively, weak BCAP) are equivalent for every Banach space. This gives a negative answer to Oja's conjecture. As a consequence, we show that each of the spaces _c0$c_0$ and _?1${?}_1$ has a subspace which has the AP but fails to have the strong AP.     

Constraint Qualifications for Mathematical Programs with Equilibrium Constraints and their Local Preservation Property

This paper studies the system of constraint qualifications tailored for mathematical programs with equilibrium constraints. The main focuses are on the relations among them and their local preservation property. After giving a relaxed version of the constant positive linear dependence constraint qualification for mathematical programs with equilibrium constraints, we establish some new relations among the tailored constraint qualifications. Then, we investigate their local preservation property. Finally, we present several results on the isolatedness of local minimizers. The paper contains some proof techniques that seem to be new in the literature of mathematical programs with equilibrium constraints. The obtained results complement and improve some recent ones in this direction.     

On $$epsilon $$ ϵ -solutions for robust semi-infinite optimization problems

Positivity - In this paper, we consider semi-infinite optimization problems involving a convex objective function and infinitely many convex constraint functions with data uncertainty, and give its...     

Highly Efficient Visible‐Light Plasmonic Photocatalyst Ag@AgBr

Visible improvements : Owing to the plasmon resonance of silver nanoparticles deposited on the surface of AgBr, the newly‐prepared plasmonic photocatalyst Ag§AgBr has a strong absorption in the visible region (see picture) and shows high efficiency in the photodegradation of organic pollutants under visible light.

     

Continuity of the Solution Map in Parametric Affine Variational Inequalities

A systematic study of the upper semicontinuity and the lower semicontinuity of the solution map in parametric affine variational inequalities is given in this paper. Several examples are constructed to analyze the results. This work was supported by Korea Research Foundation Grant (KRF 2001-015-DP0049), the APEC Postdoctoral Fellowships Program, and the KOSEF Brain Pool Program.