Invex-convexlike functions and duality

We define a class of invex-convexlike functions, which contains all convex, pseudoconvex, invex, and convexlike functions, and prove that the Kuhn-Tucker sufficient optimality condition and the Wolfe duality hold for problems involving such functions. Applications in control theory are given.The author is grateful to Professor W. Stadler and the referees for many valuable remarks and suggestions, which have enabled him to improve considerably the paper.     

光电光谱法分析钢中钙

本文研究了用光电光谱法测定钢中钙的方法 ,确定了最佳分析条件 ,分析了共存元素的干扰情况。用本方法测定钢中钙 ,具有良好的准确度和精密度 ,结果令人满意。     

Low-threshold interband cascade lasers operating above room temperature

Mid-IR type-II interband cascade lasers were demonstrated in pulsed mode at temperatures up to 325 K and in continuous mode up to 200 K. At 80 K, the threshold current density was 8.9 A/cm² and a continuous wave output power of 140 mW/facet was obtained.     

Optical investigation of cavitation erosion by laser-induced bubble collapse

By means of a new force sensor based on optical beam deflection (OBD), the mechanical effects of laser-matter interaction underwater at different incident laser energy are investigated in detail. The experimental results show that a target underwater is impacted in turn by laser-plasma ablation force and high-speed liquid-jet impulse induced by bubbles collapse in the vicinity of a solid boundary. Furthermore, the amplitudes of the two forces increase monotonously with laser energy. According to the ablation force detected by the experiment and the theoretical relationship between laser intensity and ablation pressure, the value of liquid-jet impact against a solid boundary can be easily obtained. In addition, based on the model of a collapsing bubble, some characteristic parameters, such as the liquid-jet impact velocity, the maximum bubble radius, the bubble energy can also be obtained at different laser energy, which are valuable in the corresponding research fields.     

Higher-order radiative perturbation theory

As a computationally effective tool, the first-order term of the radiative perturbation theory has been computed successfully, and has been applied in a number of areas. In this article, we develop the computational expressions for the higher-order terms of the perturbation expansion in a plane parallel atmosphere. These expressions are then implemented, and numerical results for some typical cases are presented. These results indicate that the computation is successful and that the higher-order terms are essential in cases where the first-order term alone cannot predict the perturbation with sufficient accuracy.     

Optimal control of the obstacle in a quasilinear elliptic variational inequality

In this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality and the control function is the obstacle. The state is chosen to be close to the desire profile while the H² norms of the obstacle is not too large. Existence and necessary conditions for the optimal control are established.     

Regular Approximations of Singular Sturm-Liouville Problems with Limit-Circle Endpoints

For any self-adjoint realization S of a singular Sturm-Liouville equation on an interval (a,b) with limit-circle endpoints, we construct a family of self-adjoint realizations S _r ,r ∈ (0,∞), of this equation on subintervals (a _r ,b _r ) of (a,b) such that every eigenvalue of S is the limit of a continuous eigenvalue branch of this family. Of particular interest are the cases when at least one endpoint is oscillatory or the leading coefficient function changes sign. In these cases, we show that the index determining each continuous eigenvalue branch has an infinite number of jump discontinuities and give an explicit characterization of these discontinuities.     

Isolating the most recent entry in a random recursive tree by random cuts

A recursive tree is constructed by starting with a root node and repeatedly adjoining new nodes to one node of the tree already constructed. Such a tree can represent, for example, the heirarchy of a workforce of a company that grows via recruiting. At times of economic depression, the company may decide to lay off participants, and in some cases it is a fair policy to relieve the last senior worker (most recent entry in the tree). If we remove an edge from such a tree then it falls into two subtrees one of which contains the most recent entry. If we continue to remove edges from the successively smaller subtrees that contain the most recent entry, we eventually isolate the most recent entry. We consider how many randomly selected edges must be removed in average before isolating the most recent entry by this procedure.     

Investigation of charge effects on poling and stability for corona-poled polymer films

The optimal corona-poling temperature of polymer films was accurately determined by measuring the temperature dependence of the in situ second-harmonic (SH) intensity profile under the applied poling electric field. The in situ SH intensity profile was first measured by probing both the surface voltages and the poling currents induced by surface/space charges for the corona-poled polymer films. Moreover, charge effects on the stability of the chromophore orientation were first studied by using the thermally stimulated discharge-current technique. PACS 72.20.Jv; 42.65.Ky; 73.61.Ph; 81.40.Tv