Approximate minimum-cost multicommodity flows in\tilde O(ɛ −2 KNM) timetime

We show that an ε-approximate solution of the cost-constrainedK-commodity flow problem on anN-nodeM-arc network,G can be computed by sequentially solving O(K(? ^?2+logGK) logGM log (G? ^?1 GK)) single-commodity minimum-cost flow problems on the same network. In particular, an approximate minimum-cost multicommodity flow can be computed in $\tilde O$ (G? ^?2 GKNM) running time, where the notation Õ(·) means “up to logarithmic factors”. This result improves the time bound mentioned by Grigoriadis and Khachiyan [4] by a factor ofM/N and that developed more recently by Karger and Plotkin [8] by a factor of? ^?1. We also provide a simple $\tilde O$ (NM)-time algorithm for single-commodity budget-constrained minimum-cost flows which is $\tilde O$ (? ^?3) times faster than the algorithm developed in the latter paper.     

The matched queueing network PH/M/c→oPH/PH/1

We consider a matched queueing network PH/M/coPH/PH/1, where the output of the first subsystem PH/M/c is regarded as one of the inputs of the second subsystem and matched with another input of PH-renewal process, and they are served by a single server with PH-service-distribution. The stationary state probabilities, the distribution of the virtual waiting times in the two subsystems, and the distribution of the total virtual waiting time are derived.The work was supported by the Max-Planck-Gesellschaft, Germany, and the Chinese Academy ofSciences.     

Rigorous results on the thermodynamics of the dilute Hopfield model

We study the Hopfield model of an autoassociative memory on a random graph onN vertices where the probability of two vertices being joined by a link isp(N). Assuming thatp(N) goes to zero more slowly thanO(1/N), we prove the following results: (1) If the number of stored patternsm(N) is small enough such thatm(N)/Np(N) 0, asN, then the free energy of this model converges, upon proper rescaling, to that of the standard Curie-Weiss model, for almost all choices of the random graph and the random patterns. (2) If in additionm(N) < ln N/ln 2, we prove that there exists, forT< 1, a Gibbs measure associated to each original pattern, whereas for higher temperatures the Gibbs measure is unique. The basic technical result in the proofs is a uniform bound on the difference between the Hamiltonian on a random graph and its mean value.     

Repeat Space Theory Applied to Carbon Nanotubes and Related Molecular Networks. I

The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons. The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube (a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply. Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem (ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series. The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via resolution of singularities and related methods’ published in the JOMC.     

Simultaneous kinetic determination of thiocyanate and sulfide using eigenvalue ranking and correlation ranking in principal component-wavelet neural network

In this work, two toxic compound, sulfide and thiocyanate were determined simultaneously using kinetic spectrophotometry. These anions have shown the catalytic effects on the reaction between iodine and azide. Since the system was nonlinear, a nonlinear model, principal component-wavelet neural network (PC-WNN) was used as the multivariate calibration method. The principal component analysis was used to decrease the dimension of the original matrix. In other words, the scores of the PCs, 5, instead of the original variables, 301, were used as the input for the model. Two methods were used to select the most relevant principal components: eigenvalue ranking and correlation ranking. In this work, eigenvalue and correlation ranking methods have shown better results for thiocyanate and sulfide, respectively, and it can be concluded that these methods are complementary. The WNN has several advantages relative to other types of neural network such as better convergence ability. The data set was divided to calibration, prediction and validation sets. Each set was selected so that the concentrations of the analytes were approximately covered the entire ranges of the analytes. Mean relative error for thiocyanate and sulfide in validation set were 8.5 and 10.6, respectively. Thiocyanate and sulfide can be determined in the range of 60–700 ng ml⁻¹ and 20–400 ng ml⁻¹, respectively. The proposed method was applied for the determination of sulfide and thiocyanate in real samples such as tap, waste and river waters with satisfactory results.     

Aa1Dd1-Aa2Dd2型氢键体系的网络结构参数

利用溶胶-凝胶分配理论对氢键溶液的模型体系进行研究, 给出了体系的凝胶化条件以及凝胶点后氢键网络中各类结构参数的计算方案, 并进行了相应的数值计算. 结果表明, 当两类质子受体基团的活性不同时, 质子受体基团的竞争作用对网络结构有一定影响. 这为控制氢键网络结构特征提供了可能的理论线索.     

Synthesis, crystal structure and characterization of a 2-D network organic-inorganic hybrid polymer with [α-BW12O40]5- as building blocks

A two-dimensional network compound [Ce(DMF)4(H2O)][α-BW12O40]·H2O·(HDMA)2 (HDMA = protoned dimethylamine, DMF = N,N-dimethylformamide) was synthesized from α-H5BW12O40·nH2O, Ce(NO3)3·6H2O and DMF and characterized by IR, UV spectra and TG-DTA. The result of the X-ray single crystal diffraction indicates that the crystal is monoclinic, space group P21/n, with unit cell dimensional: a = 1.1983(3), b = 2.4216(5), c = 1.9517(4) nm, β = 92.91(3)°, Z = 4, R1 = 0.07710, wR2 = 0.1416. Structural analysis indicates that every [Ce(DMF)4(H2O)]3-building block is surrounded by three adjacent [α-BW12O40]5-polyanions, meanwhile, every [α-BW12O40]5-polyanion interconnects with three neighboring [Ce(DMF)4(H2O)]3+ subunits, by making use of which two-dimensional network structure can be constructed. The result of thermogravimetric analysis manifests that the title compound has two-stage weight loss and the decomposition temperature of the title polyanionic framework is 560℃. The electrochemical analysis shows the title polyanion has three-step redox processes in the pH = 4-7 media.     

Equilibrium conformations of polymer chains Part II. Conformons in networks

With regard to the ideal network it is shown that the concept ofN non-interacting polymer chains can be transformed in a problem of non interacting excitations (called conformons) for rubber elasticity. Modelling the interaction on permanent crosslinks as a scattering problem and taking the finite chain length into account, an interpretation of the second Mooney coefficient can be given. There is some evidence that the junctions move by constrained self diffusion.Dedicated to Prof. Dr. W. Ruland on the occasion of his 60th birthday.     

Room Temperature Solid State Reaction Involving Structural Transformation of Covalent Oxide Network

An interesting structural transformation from a two dimensional (2d) covalent oxide network with a layered structure to a three-dimensional (3d) network with a tunnel structure was found at room temperature in the mixture of hydrated alkali-metal molybdenum bronze and amorphous alkali-metal molybdate. From various experimental results it was concluded that the transformation was due to a room temperature solid state reaction.     

阴离子嵌段共聚的交联聚苯乙烯的网络链长多分散性与网络结构非均一性

用链长分布不同的活性聚苯乙烯子聚物与二乙烯基苯进行阴离子嵌段共聚,合成了一系列两相模型交联网络。以作者等提出的方法测定了所合成网络的结构非均一因子Z。实验测定的网络结构非均一因子Z与交联前聚苯乙烯活性链的分子量分布宽度指数d之间有平行的相应变化规律,表明所给予的非均一因子Z的物理意义是合理的。同时说明,子聚物链长分布较宽时,在网络的高交联区中除了二乙烯基苯外,还有一些对溶胀无贡献的子聚物以悬挂链的形式存在。