An Algorithm for the Global Optimization of a Class of Continuous Minimax Problems

We propose an algorithm for the global optimization of continuous minimax problems involving polynomials. The method can be described as a discretization approach to the well known semi-infinite formulation of the problem. We proceed by approximating the infinite number of constraints using tools and techniques from semidefinite programming. We then show that, under appropriate conditions, the SDP approximation converges to the globally optimal solution of the problem. We also discuss the numerical performance of the method on some test problems. Financial support of EPSRC Grant GR/T02560/01 gratefully acknowledged.     

The Isoenergetic KAM-Type Theorem at Resonant Case for Nearly Integrable Hamiltonian Systems

In this paper, we study the persistence of resonant invariant tori on energy surfaces for nearly integrable Hamiltonian systems under the usual R$\ddot{u}$ssmann nondegenerate condition. By a quasilinear iterative scheme, we prove the following things: (1) The majority of resonant tori on a given energy surface will be persisted under R$\ddot{u}$ssmann nondegenerate condition. (2) The maximal number about the preserved frequency components on a perturbed torus is characterized by the smaller of the maximal rank of the Hessian matrices of the unperturbed system and the nondegeneracy of resonance. (3) If unperturbed systems admit subisoenergetic nondegeneracy on an energy surface, then the majority of the unperturbed resonant tori on the energy surface will be persisted and give rise to a family of perturbed tori with the same energy, whose frequency ratios among respective ''nondegenerate'' components are preserved.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

基于Bayes方法的诊断模型分析

文中证明了在Bayes框架下,当漂移参数7服从有信息先验时,在相当广泛的统计模型中,数据删除模型(CDM)和均值漂移模型(MSOM)的参数估计不相等,几个数值例子验证了相应的结论.     

SYNTHESIS, CHARACTERIZATION, METAL-UPTAKE BEHAVIOR OF BIS（BENZIMIDAZOLE） RESIN SUPPORTED ON EPOXIDE POLYMER

The new chelate resins, abbreviated as PNBMZs and PBBMZs based on epoxide polymer, were synthesized by polycondensation of N,N-diglycidyl-4-glycidyloxyaniline or 1,4-bis（2,3-epoxypropyl）benzene with the primary amine group of 1,3-bis（benzimidazol-2yl）propylamine （BBPAH）. The ion exchangers contain 2.71-3.23 mmol of the ligand contents per gram of the resin. Batch extraction capacities were determined for the metal chloride salts in buffer solutions in the pH range from -1 to 6.0. The chelate resins were very selective for Cu^2＋, Zn^2＋, Cd^2＋ in the presence of other divalent transition metal ions. The maximum uptake capacities of PNBMZ （synthetic molar ratio = 1：1.5） under non-competitive condition were found to be 0.94 mmol/g for Cu^2＋ at pH = 2, 1.3 mmol/g for Cd^2＋ at pH = 1 and 1.75 mmol/g for Zn^2＋ at pH = -1 respectively. While in the case of PBBMZ, it was 1.39 mmol/g for Cd〉 at pH = 1. The metal-uptake behaviors for both of them showed strong pH dependence, and their extraction capacities increase with decreasing pH. The uptake of Cu^2＋ by the resin PNBMZs at pH = 1 was found to be rather fast with t1/2 = 18 min. Metal-uptake experiments under competitive conditions also confirm that the chelate resins have a high selectivity for Cu^2＋, Zn^2＋, Cd^2＋ and the contrary pH dependence.     

教育实证研究中样本选择的原则及品质要求

我国教育研究领域大力倡导实证研究,却面临操作指南缺乏和品质标准不够明晰的问题,导致高质量的实证研究案例不多。研究样本的数量及其代表性或立意是保证实证研究品质的重要因素,讨论了定量研究和质性研究中选择研究样本的原则,明确了实证研究论文写作中研究样本部分的品质指标及内容要求,利用构建的品质指标及内容要求分析了4个教育实证研究论文案例。研究发现,提升我国教育实证研究质量的任务还是比较艰巨的。     

化学与刑侦

化学原理在侦破工作中应用的重要性日益突出,以化学为基础的侦破技术在近年来得到了迅速发展,成为打击犯罪、维护治安的重要手段。本文介绍了几种重要的分析方法在刑侦工作中的重要应用。     

Resource augmentation for online bounded space bin packing

We study online bounded space bin packing in the resource augmentation model of competitive analysis. In this model, the online bounded space packing algorithm has to pack a list L of items in (0,1] into a small number of bins of size b1. Its performance is measured by comparing the produced packing against the optimal offline packing of the list L into bins of size 1.We present a complete solution to this problem: For every bin size b1, we design online bounded space bin packing algorithms whose worst case ratio in this model comes arbitrarily close to a certain bound ρ(b). Moreover, we prove that no online bounded space algorithm can perform better than ρ(b) in the worst case.     

Periodic solutions to a kind of neutral functional differential equation in the critical case

In this paper, we consider a kind of neutral functional differential equation as follows: