An Algorithm Based on Active Sets and Smoothing for Discretized Semi-Infinite Minimax Problems

We present a new active-set strategy which can be used in conjunction with exponential (entropic) smoothing for solving large-scale minimax problems arising from the discretization of semi-infinite minimax problems. The main effect of the active-set strategy is to dramatically reduce the number of gradient calculations needed in the optimization. Discretization of multidimensional domains gives rise to minimax problems with thousands of component functions. We present an application to minimizing the sum of squares of the Lagrange polynomials to find good points for polynomial interpolation on the unit sphere in ℝ³. Our numerical results show that the active-set strategy results in a modified Armijo gradient or Gauss-Newton like methods requiring less than a quarter of the gradients, as compared to the use of these methods without our active-set strategy. Finally, we show how this strategy can be incorporated in an algorithm for solving semi-infinite minimax problems.     

Tadpole‐shaped amphiphilic copolymers prepared via RAFT polymerization and click reaction

The tadpole‐shaped amphiphilic copolymers with cyclic polystyrene as the head and a linear poly(N‐isopropylacrylamide) as the tail have been successfully synthesized by combination of reversible addition‐fragmentation chain transfer (RAFT) polymerization and “click” reaction. The synthesis involves two main steps: (1) preparation of a linear acetylene‐terminated PNIPAAM‐b‐PS with a side azido group anchored at the junction between two blocks; (2) intramolecular cyclization reaction to produce the cyclic PS block using “click” chemistry under high dilution. The structures, molecular weights, and molecular weight distributions of the resulted intermediates and the target polymers were characterized by their ¹H NMR, FTIR, and gel permeation chromatography. The difference of surface property between tadpole‐shaped polymer and its linear precursor was observed, and the water contact angles on the former surface are larger than that of the latter surface. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2390–2401, 2008     

Asymptotics for solutions of a defective renewal equation with applications

In this paper, we derive non-exponential asymptotic forms for solutions of defective renewal equations. These include as special cases asymptotics for compound geometric distribution and the convolution of a compound geometric distribution with a distribution function. As applications of these results, we study the Gerber-Shiu discounted penalty function in the classical risk model and the reliability of a two-unit cold standby system in reliability theory.      

Operation of a resistive-gate MESFET oscillator in thesingle-domain transit-time mode

Resistive-gate (RG) MESFET oscillators having gate sheet resistance of 30 kΩ/sq are operated in the single-domain transit-time mode. Frequencies from 6 to 28 GHz are observed, inversely proportional to channel length. Unlike a lateral Gunn diode, operation is essentially independent of drain-to-source voltage, indicating that channel conditions are controlled by the potential drop along the resistive gate. The authors conclude that contiguous domains cannot form in the channel unless the gate sheet resistance is reduced to about 3 kΩ/sq     

Critical exponents for nonlinear diffusion equations with nonlinear boundary sources

This paper is concerned with the large time behavior of solutions to two types of nonlinear diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent q₀ and the critical Fujita exponent qc for the problems considered, and show that q₀=qc for the multi-dimensional porous medium equation and non-Newtonian filtration equation with nonlinear boundary sources. This is quite different from the known results that q₀<qc for the one-dimensional case.     

Microscopic explosive boiling induced by a pulsed-laser irradiation

This paper presents an experimental study of microscopic explosive boiling introduced by a pulsed laser. The violent explosive boiling was observed in the liquid film, and the vapor bubbles together with liquid droplets were expelled from the platinum film. It is found that the apparent bubble nucleation temperature is a strong function of the heating rate. The pressure signal appears as continuous oscillation and is intensified as laser power density increases.     

彩色滤光膜色度测试系统的研究

彩色滤光膜(CF)色度指标对彩色液晶显示器的显示性能有着重要的影响,采用传统的分光光度计测量CF光谱透过率存在着严重的混光现象,研究分析了CF色度参数的表征与测试原理,设计了高精度的显微光谱测试系统。系统能够精密测试50μm尺寸样品的光谱特性,并且得到±0.005的色度座标测试精度。系统已应用在彩色滤光膜与彩色液晶显示器生产企业,取得了良好的效果。     

自映射的过滤子、Ω-稳定性及R-稳定性

在文献[1]中我们得到了关于自映射的一系列结果,这些结果或多或少都与微分同胚情形的结论相似。本文以过滤子为过渡,得到Q-稳定性及R-稳定性。我们遵循微分同胚情形的线索,本文与文献[1]中的论述密切相关。为了节省篇幅,除非特殊申明,我们不再重复文献[1]中的结论。