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.     

Recursive solution of linear-quadratic Nash games for weakly interconnected systems

A recursive method is developed for the solution of coupled algebraic Riccati equations and corresponding linear Nash strategies of weakly interconnected systems. It is shown that the given algorithm converges to the exact solution with the rate of convergence ofO(²), where is a small coupling parameter. In addition, only low-order systems are involved in algebrdic computations; the amount of computations required does not grow per iteration and no analyticity assumption is imposed on the system coefficients.This work was supported by Rutgers University Research Council under Grant No. 2-02188.     

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.     

卤代化合物的碳—13化学位移模拟

用人工神经网络和多元回归方法对含２个碳的２１个卤代化合物的３５个化学位移进行计算机图像模拟，结果表明，人工神经网络方法优于多元回归方法，同时此种方法处理这类问题有明显的优势，波谱模拟技术在有机化合物结构解析中是非常有用的方法。     

电感耦合等离子体原子发射光谱分析中不同电离电位元素基体效应的比较研究

选择不同电离电位的基体元素K、Na、La、Y和Mg,比较研究了它们对分析元素谱线强度的影响,其影响程度与谱线激发电位及基体元素电离电位有定量的相关关系。碱金属基体(K、Na)和非碱金属基体(La、Y和Mg)对分析元素检出限、背景强度及其相对标准偏差的影响显著不同,后者的记忆效应也大于前者。La的电离电位与Na相差不大。但其基体效应与Y相似,表明墓体效应与基体元素的化学性质有关。     

Accuracy and long-term reproducibility of lead isotopic measurements by multiple-collector inductively coupled plasma mass spectrometry using an external method for correction of mass discrimination

The precision of isotopic measurements of Pb by thermal ionization mass spectrometry (TIMS) is limited by the fact that this element does not possess an invariant isotope ratio that can be used for the correction of mass fractionation by internal normalization. Multiple-collector inductively coupled plasma mass spectrometry (MC-ICPMS) can overcome this limitation, because with plasma ionization, elements with overlapping mass ranges are thought to display identical mass discrimination. With respect to Pb, this can be exploited by the addition of Tl to the sample solutions; the mass discrimination factor obtained for Tl can then be used for the correction of the measured Pb isotope ratios. In this article we present the results of a detailed study that investigates the accuracy and precision of such an external correction technique for mass discrimination based upon the results of multiple analyses of a mixed standard solution of NIST SRM-981 Pb and SRM-997 Tl. Our data indicate that normalization of the Pb isotope ratios to the certified isotopic composition of SRM-997 Tl produces Pb isotopic results that are significantly lower than recently published reference values by TIMS. This systematic offset can be eliminated by renormalization of the Pb data to a different Tl isotopic composition to obtain an empirically determined mass discrimination factor for Pb that generates accurate results. It is furthermore shown that a linear law is least suited for the correction of mass discrimination, whereas a power or exponential law function provide significantly more accurate and precise results. In detail, it appears that a power law may provide the most appropriate correction procedure, because the corrected Pb isotope ratios display less residual correlations with mass discrimination compared to the exponentially corrected data. Using an exponential or power law correction our results, obtained over a period of over seven months, display a precision (2σ) of better than 60 parts per million (ppm) for ²⁰⁸Pb/²⁰⁶Pb and ²⁰⁷Pb/²⁰⁶Pb and of better than 350 ppm for ²⁰⁶Pb/²⁰⁴Pb, ²⁰⁷Pb/²⁰⁴Pb/²⁰⁴Pb, and ²⁰⁸Pb/²⁰⁴Pb. This represents a significant improvement compared to conventional TIMS techniques and demonstrates the potential of MC-ICPMS for routine, high-precision measurements of Pb isotopic compositions.     

氨基羧酸纤维分离富集-电感耦合等离子体原子发射光谱法测定多种痕量稀土元素

本文制备了氨基羧酸纤维滤纸片作为柱填充物，成功地分离和富集了地化样品中的多种稀土元素。富集后的稀土元素采用电感耦合等离子体原子发射光谱法测定，回收率为90％～109％。本文还对基体干扰及其消除进行了研究。     

人工神经网络及其在分析化学中的应用

人工神经网络是一种新兴的计算方法，有着广阔的发展前途，目前在分析化学领域已经有了多方面的应用。本文简要介绍了人工神经网络的原理及其在分析化学中的应用。     

Networks and chain coverings in partial orders and their products

For an arbitrary poset P, subposets {P _i : 1ik} form a transitive basis of P if P is the transitive closure of their union. Let u be the minimum size of a covering of P by chains within posets of the basis, s the maximum size of a family of elements with no pair comparable in any basis poset, and a the maximum size of an antichain in P. Define a dense covering to be a collection D of chains within basis posets such that each element belongs to a chain in D within each basis poset and is the top of at least k-1 chains and the bottom of at least k-1 chains in D. Dense coverings generalize ordinary chain coverings of poset. Let d=min {|D|–(k–1)|P|}. For an arbitrary poset and transitive basis, a convenient network model for dense coverings yields the following: Theorem 1: da, with equality iff P has a minimum chain decomposition in which every pair of consecutive elements on each chain are comparable in some basis poset. Theorem 2: usda. Theorem 3: s=d iff s=a. The most interesting special case is where the transitive basis expresses P as the product of two posets, in which case u and s measure the minimum and maximum sizes of unichain coverings and semiantichains.