Optimization technique based on learning automata

Optimization techniques are finding increasingly numerous applications in process design, in parallel to the increase of computer sophistication. The process synthesis problem can be stated as a largescale constrained optimization problem involving numerous local optima and presenting a nonlinear and nonconvex character. To solve this kind of problem, the classical optimization methods can lead to analytical and numerical difficulties. This paper describes the feasibility of an optimization technique based on learning systems which can take into consideration all the prior information concerning the process to be optimized and improve their behavior with time. This information generally occurs in a very complex analytical, empirical, or know-how form. Computer simulations related to chemical engineering problems (benzene chlorination, distillation sequence) and numerical examples are presented. The results illustrate both the performance and the implementation simplicity of this method.Nomenclature c _i penalty probability - cp precision parameter on constraints - D variation domain of the variablex - f(·) objective function - g(·) constraints - i,j indexes - k iteration number - N number of actions - P probability distribution vector - p _i ith component of the vectorP as iterationk - r number of reactors in the flowsheet - u(k) discrete value or action chosen by the algorithm at iterationk - u _i discrete value of the optimization variable in [u _min,u _max] - u _min lowest value of the optimization variable - u _max largest value of the optimization variable - Z random number - x variable for the criterion function - xp precision parameter on criterion function - W(k) performance index unit output at iterationk - ₀, ₁ reinforcement scheme parameters - _p sum of the probability distribution vector components     

Extension to R + n+1 of singular integrals and fractional integrals

In this paper, a natural R ₊ ⁿ⁺¹ extension of singular integrals, i.e.,T _κ:f→K*φ _t *t with K a standard C-Z kernel and ϕ usual one, is investigated. One of the main results is: Let (dμ, udx) ∈C₁ and u-Mw, w∈A_∞, then T_k is of type (L^p(udx), L^p(dμ)). As a related topic, a maximal operator is proved to be of type , where , provided (dμ, udx) ∈C₁ and u∈ A_∞. Supported by National Science Foundation of China     

Sur une conjecture de M. Kac

Summary We consider the following heat conduction problem. Let K be a compact set in Euclidean space ³. Suppose that K is held at the temperature 1, while the surrounding medium is at the temperature 0 at time 0. Following Spitzer we investigate the asymptotic behaviour of the integral E _K (t) which represents the total energy flow in time t from the set K to the surrounding medium ³–K. An asymptotic expansion is given for E _K (t) which refines a theorem due to Spitzer. This expansion also verifies and improves a formal calculation of Kac. Similar results are proved in higher dimensions. Up to the constant m(K), the quantity E _K (t) can be interpreted as the expected value of the volume of the Wiener sausage associated with K and a d-dimensional Brownian motion. This point of view both plays a major role in the proofs and leads to a probabilistic interpretation of the different terms of the expansion.     

血卟啉衍生物的色谱分离

本文拟定的纸色谱法是以苯-乙酸乙酯-甲醇-乙酸(9:2:1:1)作展开剂,将血卟啉衍生物(HPD)分离为五部份,分别测定各部份浸取液的荧光发射光谱,作为一种对血卟啉衍生物组份作对比鉴定的参考方法。采用Ward的高效液相色谱程序对比研究结果表明,国产与美国产HPD的组份近似,均以血卟啉为主要组份,而前者血卟啉的含量较高;二者还均含有羟乙基乙烯基衍生物和羟基乙酸酯,初步研究了血卟啉衍生物在甲醇-水溶剂系统中的高效液相色谱行为,进一步将血卟啉衍生物分离为九部份,有利于单一组份研究。     

软珊瑚Sinularia sp.中次生代谢产物的结构鉴定

细胞毒性;软珊瑚Sinularia sp.中次生代谢产物的结构鉴定