On Properties of Spaces Defined in Terms of Semi-Regular Sets

A set A of a topological space (X,) is semi--open if A is the union of semi-regular sets, i.e. sets which are both semi-open and semi-closed. Recently, several covering properties in terms of semi--open sets have been introduced. The aim of this paper is to study the relativity of those properties with respect to arbitrary subsets. We give new characterizations of s-regular, s-normal, semi-Hausdorff and -spaces.     

On Quantitative Stability in Optimization and Optimal Control

We study two continuity concepts for set-valued maps that play central roles in quantitative stability analysis of optimization problems: Aubin continuity and Lipschitzian localization. We show that various inverse function theorems involving these concepts can be deduced from a single general result on existence of solutions to an inclusion in metric spaces. As applications, we analyze the stability with respect to canonical perturbations of a mathematical program in a Hilbert space and an optimal control problem with inequality control constraints. For stationary points of these problems, Aubin continuity and Lipschitzian localization coincide; moreover, both properties are equivalent to surjectivity of the map of the gradients of the active constraints combined with a strong second-order sufficient optimality condition.     

Idealization of Some Weak Separation Axioms

An ideal is a nonempty collection of subsets closed under heredity and finite additivity. The aim of this paper is to unify some weak separation properties via topological ideals. We concentrate our attention on the separation axioms between T ₀ and T _1/2. We prove that if (X,,I) is a semi-Alexandroff T _I -space and I is a -boundary, then I is completely codense.     

Quasi-Normal Spaces and πg-Closed Sets

We introduce the notion of g-closed sets and use it to obtain a characterization and preservation theorems of quasi-normal spaces.     

Influence of the particle size distribution on the thermal conductivity of nanofluids

In a previous study, we have obtained an equation to predict the thermal conductivity of nanofluids containing nanoparticles with conductive interface. The model is maximal particle packing dependent. In this study, the maximal packing is obtained as a function of the particle size distribution, which is the Gamma distribution. The thermal conductivity enhancement depends on the averaged particle size. Discussion concerning the influence of the suspension pH on the particle packing is made. The proposed model is evaluated using number of sets from the published experimental data to the thermal conductivity enhancement for different nanofluids.     

A Proof of the Necessity of Linear Independence Condition and Strong Second-Order Sufficient Optimality Condition for Lipschitzian Stability in Nonlinear Programming

For a nonlinear programming problem with a canonical perturbations, we give an elementary proof of the following result: If the Karush–Kuhn–Tucker map is locally single-valued and Lipschitz continuous, then the linear independence condition for the gradients of the active constraints and the strong second-order sufficient optimality condition hold.     

Isolated calmness of solution mappings in convex semi-infinite optimization

This paper is concerned with isolated calmness of the solution mapping of a parameterized convex semi-infinite optimization problem subject to canonical perturbations. We provide a sufficient condition for isolated calmness of this mapping. This sufficient condition characterizes the strong uniqueness of minimizers, under the Slater constraint qualification. Moreover, on the assumption that the objective function and the constraints are linear, we show that this condition is also necessary for isolated calmness.     

The Euler approximation in state constrained optimal control

We analyze the Euler approximation to a state constrained control problem. We show that if the active constraints satisfy an independence condition and the Lagrangian satisfies a coercivity condition, then locally there exists a solution to the Euler discretization, and the error is bounded by a constant times the mesh size. The proof couples recent stability results for state constrained control problems with results established here on discrete-time regularity. The analysis utilizes mappings of the discrete variables into continuous spaces where classical finite element estimates can be invoked.