Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing

We study the large-time behavior and rate of convergence to the invariant measures of the processes dX (t)=b(X) (t)) dt + (X (t)) dB(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/² , the transition density has a good lower bound and when the process has run for about exp( – )/², it is very close to the invariant measure. LetL =(²/2) – U · be a second-order differential operator on ^d. Under suitable conditions,L ^z has the discrete spectrum

Heat “polynomials” for a singular differential operator on (0, ∞)

We generalize the theory of the heat polynomials introduced by P. V. Rosenbloom and D. V. Widder for a more general class of singular differential operator on (0, ). The heat polynomials associated with the Bessel operator and studied by D. T. Haimo appear as a particular case in this paper. In the special cases of second derivative and Bessel operators the heat polynomials are in fact polynomials inx andt, however, this property does not hold in general.Communicated by Tom. H. Koornwinder.     

Circuit-switching networks with FIFO plus justifying blockout service on infinite graphs

A class of circuit-switching open queueing networks is discussed. The main result of the paper is that if extra message flows are not too intensive and the path distribution is mainly concentrated on the paths of (graph) distance 1 (nearest neighbour connections), then the network has a unique stationary working regime, no matter how large the configuration graph of the network is. Standard properties of this regime are established such as decay of correlation and continuity.     

Markovian network processes: Congestion-dependent routing and processing

A Markovian network process describes the movement of discrete units among a set of nodes that process the units. There is considerable knowledge of such networks, often called queueing networks, in which the nodes operate independently and the routes of the units are independent. The focus of this study, in contrast, is on networks with dependent nodes and routings. Examples of dependencies are parallel processing across several nodes, blocking of transitions because of capacity constraints on nodes, alternate routing of units to avoid congestion, and accelerating or decelerating the processing rate at a node depending on downstream congestion. We introduce a general network process representing the numbers of units at the nodes and derive its equilibrium distribution. This distribution takes the form of a product of functions of vectors in which the arguments of the functions satisfy an interchangeability property. This new type of distribution may apply to other multi-variate processes as well. A basic idea in our approach is a linking of certain micro-level balance properties of the network routing to the processing rates at the nodes. The link is via routing-balance partitions of nodes that are inherent in any network. A byproduct of this approach is a general characterization of blocking of transitions without the restriction that the process is reversible, which had been a standard assumption. We also give necessary and sufficient conditions under which a unit moving in the network sees a time average for the unmoved units (called the MUSTA property). Finally, we discuss when certain flows between nodes in an open network are Poisson processes.This research was sponsored in part by Air Force Office of Scientific Research contract 84-0367.     

Minimum concave cost production system: A further generalization of multi-echelon model

We will consider a concave minimization problem associated with a series production system in which raw material is processed inm consecutive facilities. The products at some facility are either sent to the next facility or stocked in the warehouse. The amount of demand for the final products during periodi, i = 1,,n, are known in advance. Our problem is to minimize the sum of processing, holding and backlogging cost, all of which are assumed to be concave.The origin of this model is the classical economic lot size problem of Wagner and Whitin and was extensively studied by Zangwill. This model is very important from the theoretical as well as practical point of view and this is one of the very rare instances in which polynomial time algorithm has been constructed for concave minimization problems.The purpose of this paper is to extend the model further to the situation in which time lag is associated with processing at each facility. We will propose an efficient O(n ⁴ m) algorithm for this class of problems.     

Hydrogel nanonetworks with functional core-shell structure

Nanohydrogel particles of poly(acrylonitrile-co-N-isopropylacrylamide (p(AN-c-NIPAM)) were synthesized using a microemulsion polymerization technique. Highly monodisperse nanohydrogel particles e.g. 50-150 nm, and various morphology such as core-shell and connected beads were obtained. It was shown that the shell thickness and the size of particles can be tuned by the monomer concentrations and their ratios as well as by the utilization of different crosslinkers. The hydrophobic core monomer, AN was converted to amidoxime groups to increase the hydrophilicity of the nanogels which provide more hydrophilic character and impart new functionality to the nanonetwork. Transmission electron microscopy (TEM), and dynamic light scattering (DLS) techniques were employed for the particle size characterizations. The amidoximation reaction was confirmed by FT-IR spectroscopy.     

人工神经网络方法预测气相色谱保留值

本文运用一典型的人工神经网络模型－“反向传播“模型的改进形式，研究了诱导效应指数Ｉ，摩尔折射度Ｒｏ，疏水亲脂参数ＩｇＰ，以及分子联通性指数与气象色谱保留行为的关系，实现了对色谱保留植的预测。神经网络预测模型的最大相对误差不超过８．７％。结果表明，该方法性能良好，可望成为色谱保留值预测的有效手段。     

二价稀土金属有机配合物的合成及反应

本文将试图对二价的铕、镱、和钐的有机配合物的合成,结构及反应性能作了较为全面的综述。     

芳烃金属配合物在有机合成中的应用

本文讨论了芳烃金属配合物中的芳香部份在与金属配合后性质上的变化,以及这些变化后的性质在有机合成中的应用。     

碱土金属邻苯二甲酸盐的振动光谱

测定了CaPHT·H2O和两种CaPHT的晶体结构, 其空间群分别属于P21/c(C2h^5,Z=4), P21/m(C2h^2, Z=8)和P2/m(C2h^1, Z=6), 研究CaPHT·H2O、CaPHT(A)、CaPHT(B)、MgPHT、SrPHT和BaPHT的IR及CaPHT·H2O的拉曼光谱, 讨论了固体样品中PHT与碱土金属离子的配位结构及其对光谱的影响。