A reformulation-convexification approach for solving nonconvex quadratic programming problems

In this paper, we consider the class of linearly constrained nonconvex quadratic programming problems, and present a new approach based on a novel Reformulation-Linearization/Convexification Technique. In this approach, a tight linear (or convex) programming relaxation, or outer-approximation to the convex envelope of the objective function over the constrained region, is constructed for the problem by generating new constraints through the process of employing suitable products of constraints and using variable redefinitions. Various such relaxations are considered and analyzed, including ones that retain some useful nonlinear relationships. Efficient solution techniques are then explored for solving these relaxations in order to derive lower and upper bounds on the problem, and appropriate branching/partitioning strategies are used in concert with these bounding techniques to derive a convergent algorithm. Computational results are presented on a set of test problems from the literature to demonstrate the efficiency of the approach. (One of these test problems had not previously been solved to optimality). It is shown that for many problems, the initial relaxation itself produces an optimal solution.     

利用共振辐射压力获得准单一速度原子束

报道了利用行波场的共振辐射压力获得准单一速度原子束的实验研究结果，并进行了理论分析。实验上利用斜入射失谐为－１００ＭＨｚ行波光场共振作用原子束可使准单一速度原子束偏转１．７ｍｍ，速度宽度小于５８ｍ／ｓ。     

QSPR approach to the calculation of rate constants of homolysis of nitro compounds in different states of aggregation

A method for the theoretical estimation and prediction of rate constants of homolysis of nitro compounds of different chemical classes in the gas phase is proposed on the basis of the QSPR approach.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1653–1656, September, 1995.The authors express gratitude to B. A. Lur'e (D. I. Mendelev Moscow Academy of Chemical Technology) for fruitful advice during discussion of the results.     

On inference concerning time-dependent queue performance: The M/G/1 example

This paper proposes easily-computed approximations to the finite-time expected waiting time for anM/G/1 system starting from an empty state. Both unsaturated (ρ<1) and saturated (ρ>1) conditions are considered. Numerical evidence is presented to indicate that the quality of the approximations is usefully good, especially when ease of computation is an issue. Further, the methodology is adapted to assess expected waiting time when inference must be made from a random sample of service times, and the decision is made to do so nonparametrically, i.e., without fitting a specific function. The results appear reasonable and potentially useful, and are not burdensome to obtain. The methodology investigated can also be applied to the variety of queueing models that are close siblings ofM/G/1: priority and breakdowns and “vacations” being examples. Of course other approximating and inferential options remain to be investigated.     

复合结构界面粘接强度的声-超声评价研究

基于Ritec-SNAP测量系统建立了声-超声技术实验系统,分析了在声-超声技术评价过程中用声信号的幅频特性及应力波因子表征复合结构界面粘接强度的可行性。用粘接层的固化过程模拟复合粘接板粘接强度的变化过程,以粘接层的固化时间作为粘接强度的间接表征参量,借助于已建立的实验系统对复合结构粘接强度的评价问题进行了实验研究。实验结果表明,应力波因子与反映界面粘接强度的粘接层固化时间呈单调对应关系,且不同固化时期的应力波因子存在明显的不同特性,表明用应力波因子评价复合结构的界面粘接强度具有可行性。     

Rotation of magnetization in unison and langevin equations for a large spin

A single-domain ferromagnetic particle is represented as a large spin (model of rotation in unison) whose stochastic dynamics is derived from a spin-boson Hamiltonian. It is shown in the Markovian limit that thermal equilibrium exists provided that the fluctuation-dissipation theorem is supplemented by a symmetry constraint which for bilinear anisotropic and nonlinear (magnetoelastic) spin-bath coupling can only be satisfied in the underdamped limit. Only for bilinear isotropic coupling (Gilbert's theory) is it satisfied identically for arbitrary damping strength. Uniaxial and cubic symmetries are considered. For a model uniaxial crystal the thermal decay rate of M and the thermal enhancement of the macroscopic quantum tunneling rate are calculated for Gilbert and magnetoelastic dissipative couplings and compared. The effects of memory are discussed.     

Exact Excitation and Abundant Localized Coherent Soliton Structures of (2+1)-Dimensional Perturbed AKNS System

A simple and direct method is applied to solving the (2+1)-dimensional perturbed Ablowitz-Kaup-Newell-Segur system (PAKNS). Starting from a special Backlund transformation and the variable separation approach, we convert the PAKNS system into the simple forms, which are four variable separation equations, then obtain a quite generalsolution. Some special localized coherent structures like fractal dromions and fractal lumps of this model are constructed by selecting some types of lower-dimensional fractal patterns.     

非线性规划的不使用导数的解析方法—统一探讨

本文从统一的角度给出了解约束优化问题的修正的解析方法,即用梯度的近似值代替梯度的解析方法,并在较弱的条件下证明了其全局收敛性。本文结果扩大了解析方法的应用范围,为优化算法的实现提供了理论依据.     

General Solution and Localized Coherent Soliton Structures of the (2+1)-Dimensional Generalized Davey-Stewarson Equations

In this paper, the variable separation approach is used to obtain localized coherent structures of the (2 1)-dimensional generalized Davey-Stewarson equations: iqt 1/2(qxx qyy) (R S)q = O, Rx=-σ/2|q|2y Sy = -σ/2|q|2/x.Applying a special Backlund transformation and introducing arbitrary functions of the seed solutions, an abundance of the localized structures of this model is derived. By selecting the arbitrary functions appropriately, some special typesof localized excitations such as dromions, dromion lattice, breathers, and instantons are constructed.     

Application of the model‐free approach to low molecular weight systems with hindered internal rotation: cinnamoylmesitylene

We investigated the molecular dynamics of the molecule of cinnamoylmesitylene, a substituted chalcone. Known rotation barriers for the O?C‐4—C‐3?C‐2 bond of substituted chalcones are in the range of values accessible to modern NMR techniques. The internal rotation about the C‐3—C‐4 bond is found to be fast relative to the complete lineshape analysis (CLSA) time‐scale. To determine the activation parameters of overall and internal motions of the molecule, the Lipari–Szabo model‐free analysis of the relaxation times and heteronuclear NOE data was used instead. Simultaneous analysis of both heteronuclear spin–lattice relaxation times and NOE data for the two carbon atoms C‐2 and C‐7 in the O?C‐4—C‐3?C‐2 and mesitylene fragments at different temperatures was performed. The correlation times and activation energies of overall and internal motions and the generalized order parameter, which are measures of the molecular mobility, were thus determined. The standard enthalpies of activation, ΔH^≠, calculated from the experimental data for C‐2 and C‐7, are 5.6 and 6.6 kcal mol^?1, respectively. Theoretical estimates of the barriers to internal rotations by ab initio MO calculations were made to verify the experimental results. The agreement between the NMR and theoretical results was good. Copyright © 2003 John Wiley & Sons, Ltd.