On consistency of bounding operations in deterministic global optimization

This technical comment refers to the discussion of strong consistency of several bounding procedures in Lemma 2.1 and Proposition 2.1 of Ref. 1. A necessary clarification is given of the notion of convergence _q in Lemma 2.1, and a derivation of Proposition 2.1 is presented that includes a new and simple consistency proof of the classical bounding by convex envelopes used in many branch-and-bound procedures.     

Random tunneling by means of acceptance-rejection sampling for global optimization

Any global minimization algorithm is made by several local searches performed sequentially. In the classical multistart algorithm, the starting point for each new local search is selected at random uniformly in the region of interest. In the tunneling algorithm, such a starting point is required to have the same function value obtained by the last local minimization. We introduce the class of acceptance-rejection based algorithms in order to investigate intermediate procedures. A particular instance is to choose at random the new point approximately according to a Boltzmann distribution, whose temperatureT is updated during the algorithm. AsT 0, such distribution peaks around the global minima of the cost function, producing a kind of random tunneling effect. The motivation for such an approach comes from recent works on the simulated annealing approach in global optimization. The resulting algorithm has been tested on several examples proposed in the literature.     

6AZO-CONTAINING SELF-ASSEMBLY ULTRA-THIN FILMS AND THEIR PHOTOVOLTAIC PROPERTIES

A kind of azo-containing resin (Azo-R) was synthesized by a simple way through the coupling reaction of 2-nitro-N-methyldiphenylamine-4-diazoresin (NDR) with phenol, and a new covalentely attached multilayer film from Azo-R as H-donor and photosensitive diazoresin, diphenylamine-4-diazoresin (DR) as H-acceptor via H-bonding attraction by selfassembly technique has been fabricated. Following the decomposition of diazonium group of DR under exposure to UV light, the H-bonds between the layers of the film convert to covalent bonds and the film becomes very stable toward polar solvents or electrolyte aqueous solutions. Thus the UV-irradiated azo-containing films can be used to measure photocurrent in a conventional three-electrode photoelectrochemical cell using KCl as supporting electrolyte. It was confirmed that the azo-containing multilayer film is responsible for the photocurrent generation.     

5-氟尿嘧啶-1-乙酸合铜(Ⅱ)的合成及其与DNA的作用

The 5-fluorouracil-1-acetic acid (5FuAA) and its Cu(Ⅱ) complex (5FuAACu) were synthesized and the date for the crystal complex was obtained. The interaction of 5-fluorouracil-1-acetic acid (5FuAA) and its Cu(Ⅱ) complex (5FuAACu) with DNA was also investigated by using spectral, viscometric, electrochemical and agarose gel electrophoresis methods. The results of interaction with DNA suggest that both 5FuAA and 5FuAACu can bind to DNA in a static electricity attraction mode. But the attraction of 5FuAACu is greater than that of 5FuAA.     

Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms

In this paper, we investigate the Novikov equation with weak dissipation terms. First, we give the local well-posedness and the blow-up scenario. Then, we discuss the global existence of the solutions under certain conditions. After that, on condition that the compactly supported initial data keeps its sign, we prove the infinite propagation speed of our solutions, and establish the large time behavior. Finally, we also elaborate the persistence property of our solutions in weighted Sobolev space.     

Computing global minima to polynomial optimization problems using Gröbner bases

The local optimality conditions to polynomial optimization problems are a set of polynomial equations (plus some inequality conditions). With the recent techniques of Gröbner bases one can find all solutions to such systems, and hence also find global optima. We give a short survey of these methods. We also apply them to a set of problems termed with exact solutions unknown in the problem sets of Hock and Schittkowski. To these problems we give exact solutions.     

有阻尼Sine－Gordon方程的全局吸引子的维数

本文通过引入新范数,得到有阻尼Ｓｉｎｅ－Ｇｏｒｄｏｎ方程的Ｄｉｒｉｃｈｌｅｔ问题的全局吸引子的维数的一个估计．结果表明：当“阻尼”与“扩散”同时增大或正弦项系数减小时,吸引子的维数减小．特别地,得到了零维吸引子存在的参数条件．     

Series representation for semistable laws and their domains of semistable attraction

If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk _n wherek _n+1 ck _n then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG).     

A global pinching theorem for compact surfaces inS 3 with constant mean curvature

LetM be a compact minimal surface inS ³. Y. J. Hsu^[5] proved that if S₂22, thenM is either the equatorial sphere or the Clifford torus, whereS is the square of the length of the second fundamental form ofM, ·₂ denotes theL ²-norm onM. In this paper, we generalize Hsu's result to any compact surfaces inS ³ with constant mean curvature.Supported by NSFH.     

A global Newton method II: Analytic centers

This paper modifies the convergence conditions of a back-tracking global Newton method announced in Goldstein (1991), making them sharper and easier to apply. A new version of the Kantorovich inequalities is presented that is simple to state and prove. An application is made to the centering problem for polytopes. Based on an idea of Ye (1989), an algorithm is given for the feasibility problem of linear inequalities.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.