A theoretical approximation scheme for Stackelberg problems

We consider the Stackelberg problem corresponding to a two-player game in which one of the two players has the leadership in playing the game. We present a general approach for approximating the considered hierarchical programming problem by a sequence of two-level optimization problems. From a practical point of view, we also give some results for asymptotically Stackelberg approximating sequences and for problems with perturbed constraints.This paper is based upon results first presented at Journées Fermat: Mathematics for Optimization, Toulouse, France, May 1985.     

Determination of the optimal initial function and the parameters for nonlinear time-delay systems

This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included.     

金属表面在反射方向产生光学二次谐波的研究(Ⅰ)

用Rudnick和Stern引入的唯象参数“a”和“b”来描述表面电流,本文推导了金属表面在反射方向产生的光学二次谐波的表达式.由此证明了:从谐波信号随入射光偏振态的变化可以直接得到关于参数“a”的信息.和过去的实验相比,这种方法能更加精确、可靠地测定“a”的数值.     

How electrons guard the space: shape optimization with probability distribution criteria

Efficient formulas for computing the probabilities of finding exactly electrons in an arbitrarily chosen volume ³ for Hartree–Fock wavefunctions are presented. These formulas allow the use of shape optimization techniques, such as level set methods, for optimizing with respect to various criteria involving such probabilities. The criterion defined as the difference between the Hartree–Fock and the independent-particle model probabilities of finding electrons in stresses the quantum effects due to the Pauli principle. We have implemented a 2D level set method for optimizing this criterion in order to study spatial separation of electron pairs in linear molecules. The method is described and the illustrative example of the BH molecule is reported.Contribution to the Jacopo Tomasi Honorary Issue     

Dynamic optimization problems with bounded terminal conditions

Bounded terminal conditions of nonlinear optimization problems are converted to equality terminal conditions via the Valentine's device. In so doing, additional unknown parameters are introduced into the problem. The transformed problems can still be easily solved using the sequential gradient-restoration algorithm (SGRA) via a simple augmentation of the unknown parameter vector . Three example problems with bounded terminal conditions are solved to verify this technique.This research was supported in part by the National Aeronautics and Space Administration under NASA Grant No. NCC 2-106.     

On the statistical mechanics of the traveling salesman problem

We consider the statistical mechanics of the traveling salesman problem (TSP) and develop some representations to study it. In one representation the mean field theory has a simple form and brings out some of the essential features of the problem. It shows that the system has spontaneous symmetry breaking at any nonzero temperature. In general the phase progressively changes as one decreases the temperature. At low temperatures the mean field theory solution is very sensitive to any small perturbations, due to the divergence of some local susceptibilities. This critical region extends down to zero temperature. We perform the quenched average for a nonmetric TSP in the second representation and the resulting problem is more complicated than the infinite-range spin-glass problem, suggesting that the free energy landscape may be more complex. The role played by frustration in this problem appears explicitly through the localization property of a random matrix, which resembles the tight binding matrix of an electron in a random lattice.     

Approximate first-order and second-order directional derivatives of a marginal function in convex optimization

Given a convex functionf: ^p × ^q (–, +], the marginal function is defined on ^p by (x)=inf{f(x, y)|y ^q }. Our purpose in this paper is to express the approximate first-order and second-order directional derivatives of atx ₀ in terms of those off at (x ₀,y ₀), wherey ₀ is any element for which (x ₀)=f(x ₀,y ₀).The author is indebted to one referee for pointing out an inaccuracy in an earlier version of Theorem 4.1.     

Optical biosensor for pharmaceuticals, antibiotics, hormones, endocrine disrupting chemicals and pesticides in water: Assay optimization process for estrone as example

Certain contaminants at trace concentrations in surface waters can have dramatic effects on the hormonal system of organisms in the aquatic environment. Therefore, immunoanalytical methods at a very low limit of detection (LOD) and a low limit of quantification (LOQ) are becoming more and more important for environmental analysis and especially for monitoring drinking water quality. Environmental monitoring of antibiotics, hormones, endocrine disrupting chemicals, and pesticides in real water samples (e.g. surface, ground or drinking water) with difficult matrices places high demands on chemical analysis. Biosensors have suitable characteristics such as efficiency in allowing very fast, sensitive, and cost-effective detection. Here we describe an assay optimization process with a fully automated immunoassay for estrone which resulted in a LOD below 0.20 ng L⁻¹ and a LOQ below 1.40 ng L⁻¹. In contrast to common analytical methods such as GC-MS or HPLC-MS, the biosensor used requires no sample pre-treatment and pre-concentration. The very low validation parameters for estrone are the result of the continuous optimization of the immunoassay. The basis of our sensitive assay is the antibody with a high affinity constant towards estrone. During the optimization process, we reduced the amount of antibody per sample and improved the chip surface modification. Finally, this proceeding led to a calibration routine with an amount of antibody of only 3.0 ng per sample (sample volume: 1.0 mL). The reduction of the amount of antibody per sample results in better validation parameters (LOD, LOQ, and IC₅₀), but this reduction leads to the current device-related limitation of the River Analyser (RIANA).For some endocrine disrupting compounds, no effect levels (NOELs) in the lower nanogram per liter range are reported. This defines the challenge, which analytical methods have to compete with and our RIANA instrument with its improved sensitivity for the detection of a single hormone in the lower nanogram per liter range is a powerful tool in aquatic analytics in addition to the common analytical methods.     

A conformational analysis method for understanding the energy landscapes of clusters.

A newly developed unbiased structural optimization method, named dynamic lattice searching (DLS), is proposed as an approach for conformational analysis of atomic/molecular clusters and used in understanding the energy landscape of large clusters. The structures of clusters are described in terms of the number of basic tetrahedron (BT) units they contain. We found that the hit numbers of different structural motifs in DLS runs is proportional to the number of BTs. A parameter T(max) is defined to limit the maximal number of atoms moved in a structural transition. Results show that T(max) is a key parameter for modulating the efficiency of the DLS method and has a great influence on the hit number of different motifs in DLS runs. Finally, the effect of potential range on the conformational distribution of the (Morse)(98) cluster is also discussed with different potential-range parameters.     

聚醚醚酮微结构及反应特性的量子化学研究

利用AM1对聚醚醚酮重复单元进行条件优化,得出了此分子的最优构型,明确了聚醚醚酮分子链的微观构象,并在此构象基础上进行量子化学计算,给出了健序、净电荷、前线轨道等信息,从理论上研究了聚醚醚酮的磺化反应及热分解反应的一些特性.