Quadratically constrained minimum cross-entropy analysis

Quadratically constrained minimum cross-entropy problem has recently been studied by Zhang and Brockett through an elaborately constructed dual. In this paper, we take a geometric programming approach to analyze this problem. Unlike Zhang and Brockett, we separate the probability constraint from general quadratic constraints and use two simple geometric inequalities to derive its dual problem. Furthermore, by using the dual perturbation method, we directly prove the strong duality theorem and derive a dual-to-primal conversion formula. As a by-product, the perturbation proof gives us insights to develop a computation procedure that avoids dual non-differentiability and allows us to use a general purpose optimizer to find an-optimal solution for the quadratically constrained minimum cross-entropy analysis.     

Solution of a class of stochastic linear-convex control problems using deterministic equivalents

In this paper, we identify a new class of stochastic linearconvex optimal control problems, whose solution can be obtained by solving appropriate equivalent deterministic optimal control problems. The term linear-convex is meant to imply that the dynamics is linear and the cost function is convex in the state variables, linear in the control variables, and separable. Moreover, some of the coefficients in the dynamics are allowed to be random and the expectations of the control variables are allowed to be constrained. For any stochastic linear-convex problem, the equivalent deterministic problem is obtained. Furthermore, it is shown that the optimal feedback policy of the stochastic problem is affine in its current state, where the affine transformation depends explicitly on the optimal solution of the equivalent deterministic problem in a simple way. The result is illustrated by its application to a simple stochastic inventory control problem.This research was supported in part by NSERC Grant A4617, by SSHRC Grant 410-83-0888, and by an INRIA Post-Doctoral Fellowship.     

直键与弯键的对称性判据

一穹键的提出人们认为,杂化轨道(HAO)角函数的最大值方向(亦即HAO的方向)指向与之键合的原子,这样形成的化学键称为“直键”。但环丙烷分子中的三个碳原子构成三元环,有60°的键角。而任意两个正交的S-P杂化轨道之间的夹角θ都不可能小于90°,因而形成C-C键的HAO,不可能指向键合原子,环上的C-C键不可能是直键,而是“弯键”(BentBond)。通常,人们认为张力分子环上的键是弯键,其他的键为直键。     

Theoretical study on the structure and property relationship of the cationic conjugated polyelectrolytes

A theoretical study using density functional theory was performed to understand the structure/property relationship of the cationic conjugated polyelectrolytes, poly[9,9-bis-(6′-N,N,N-trimethylammonium) hexyl] fluorene-alt-4,7-(2,1,3-benzothiadiazole)] (PFBT-X, where X = Br). The torsion angle between the fluorene and benzothiadiazole units in the PFBT monomer was found to substantially affect the structural and electronic properties of the cationic PFBT monomer. The changes of geometrical parameter, HOMO and LUMO energy levels, and band gap, as well as the absorption maximum are discussed in terms of the torsion in the PFBT monomer structure. For comparison, its neutral analogue, the monomer of poly(9,9-di-n-octylfluorene-alt-benzothiadiazole) (F8BT) was also studied. The length of conjugation backbone was also examined.     

Advanced kinetic tools for the evaluation of decomposition reactions

Summary An advanced kinetic study on the thermal behaviour of pyrotechnic ignition mixtures has been carried out by differential scanning calorimetry using different B/KNO3 mixtures (50:50, 30:70, 20:80) as a model reaction. The experimental conditions applied (isochoric conditions/closed crucibles and isobaric conditions/open crucibles) as well as the composition of the mixtures noticeably influences the relative thermal stabilities of the energetic materials. The kinetic study focused on the prediction of the thermal stability of the different mixtures both in extended temperature ranges and under temperature conditions at which ordinary investigation would be very difficult. Using advanced numerical tools [1], thermal ageing and influence of the complex thermal environment on the heat accumulation conditions were computed. This can be done for any surrounding temperature profile such as isothermal, non-isothermal, stepwise, modulated, shock, adiabatic conditions and additionally for temperature profiles reflecting real atmospheric temperature changes (yearly temperature profiles of different climates with daily minimal and maximal fluctuations). Applications of accurate decomposition kinetics enabled the determination of the time to maximum rate under adiabatic conditions (TMR_ad) with a precision given by the confidence interval of the predictions. This analysis can then be applied for the examination of the effects of the surrounding temperature for safe storage or transportation conditions (e.g. determination of the safe transport or storage temperatures).     

2-(8-羟基喹啉-5-磺酸-7-偶氮)-1,8-二羟基-3,6-萘二磺酸与牛血清白蛋白的相互作用

用平衡透析法和分光光度法研究了 2 (8 羟基喹啉 5 磺酸 7 偶氮 ) 1,8 二羟基 3,6 萘二磺酸与牛血清白蛋白 (BSA)在酸性溶液中的结合反应 ,认为 8Q5SAC与BSA之间的结合力是以静电引力为主的非共键作用力 ,并探讨了其结合模型。在 2 98K下 ,测得这一反应的最大结合数为 35～ 40 ,结合常数为 6 .1× 10 5L mol。还研究了溶液基本条件如酸度和离子强度等对 8Q5SAC与牛血清白蛋白分子复合物形成的影响 ,在pH =3.34条件下 ,标准工作曲线的线性范围为 0 .2 0～ 46 .90mg L。     

排序集抽样下Inverse Rayleigh分布的Fisher信息量及其在参数估计中的应用

文章分别在简单随机抽样和排序集抽样下研究了Inverse Rayleigh分布中对应样本所含刻度参数θ的Fisher信息量.数值结果表示,同等样本容量的排序集样本比简单随机样本提供更多关于θ的信息.接着分别基于简单随机样本和排序集样本构造了θ的一些优良估计,并对估计结果进行了数值比较.     

Subordination des résolvantes

Résumé Soit (V ₎₀ une résolvante définie sur un espace mesurable telle que le noyau initial est borné; on trouve une condition nécéssaire et suffisante pour qu'un noyau borné U possède une résolvante (U ₎₀ telle que U V pour tout 0. On donne plusieurs applications de ce résultat.     

Optimal life strategies in organisms exposed to recurrent critical events

The optimal partition of energy between survival and reproduction is considered for a population subject to recurrent and potentially lethal critical events. The best strategy is found by maximizing fitness, a functional derived from the Lotka equation. The dynamics is governed by a second-order, age-varying, nonlinear system. The energy storage and the probability of survival are the state variables, while the amounts of energy placed into and withdrawn from the storage are the controls. The optimal life strategy is shown to be as follows: build up the storage at the very beginning of life, and then progressively deplete it to resist the critical events.This work was partially supported by MURST Project Ricerche sui Fondamenti della Conservazione della Natura. The authors would like to thank C. Ricci for suggesting the problem and C. Matessi for helpful discussion.     

Kinetics of the surface tension of micellar solutions: Comparison of different experimental techniques

The kinetics of the surface tension of micellar solutions of nonionic surfactant Triton X-100 is measured experimentally by means of three different techniques: oscillating jet, maximum bubble pressure and inclined plate. They allow to study the micellization kinetics at various time scales (from a few milliseconds to a few seconds) in fairly large concentration region up to 50 times CMC. The experimental data are satisfactorily explained by a theoretical model accounting for the kinetics of micellization, diffusion of surfactant species and expansion of the bubble interface. By this model are computed the characteristic times of diffusion and micellization, which are of comparable magnitude (about 5 to 200 ms), and the Gibbs' elasticity. The micellization time constant corresponds to the slow relaxation process known to coincide with the disintegration of micelles. Comparing our data with other data from literature one can conclude that more realistic information for the micellization kinetics is obtained by the maximum bubble pressure and the oscillating jet method. The inclined plate seems too slow to measure the relaxation processes in micellar solutions of this surfactant.