Minimum cost multiflows in undirected networks

LetN = (G, T, c, a) be a network, whereG is an undirected graph,T is a distinguished subset of its vertices (calledterminals), and each edgee ofG has nonnegative integer-valuedcapacity c(e) andcost a(e). Theminimum cost maximum multi(commodity)flow problem (*) studied in this paper is to find ac-admissible multiflowf inG such that: (i)f is allowed to contain partial flows connecting any pairs of terminals, (ii) the total value off is as large as possible, and (iii) the total cost off is as small as possible, subject to (ii). This generalizes, on one hand, the undirected version of the classical minimum cost maximum flow problem (when |T| = 2), and, on the other hand, the problem of finding a maximum fractional packing ofT-paths (whena 0). Lovász and Cherkassky independently proved that the latter has a half-integral optimal solution.A pseudo-polynomial algorithm for solving (*) has been developed earlier and, as its consequence, the theorem on the existence of a half-integral optimal solution for (*) was obtained. In the present paper we give a direct, shorter, proof of this theorem. Then we prove the existence of a half-integral optimal solution for the dual problem. Finally, we show that half-integral optimal primal and dual solutions can be designed by a combinatorial strongly polynomial algorithm, provided that some optimal dual solution is known (the latter can be found, in strongly polynomial time, by use of a version of the ellipsoid method).This work was partially supported by Chaire municipale, Mairie de Grenoble, France.     

Optimal error estimates of a locally one-dimensional method for the multidimensional heat equation

For the multidimensional heat equation in a parallelepiped, optimal error estimates inL ₂(Q) are derived. The error is of the order of +¦h¦² for any right-hand sidef L ₂(Q) and any initial function ; for appropriate classes of less regularf andu ₀, the error is of the order of ((+¦h¦² ), 1/2<1.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 185–197, August, 1996.     

Impossibility of a Certain Cyclotomic Equation with Applicationsto Difference Sets

Under certain conditions, we show the nonexistence ofan element in the p-th cyclotomicfield over , that satisfies . As applications, we establish the nonexistence ofsome difference sets and affine difference sets.     

CLIMATIC CHANGE SINCE LITTLE ICE AGE RECORDED BY DUNDE ICE CAP

The climatic change since the Little Ice Age recorded in the Dunde Ice Cap is presentedin this paper. There have been three cold periods and three warm periods since 1400AD.Among them, the coldest one was in the 17th century. Many evidences verified the three coldand warm variations recorded in the Dundc Ice Cap. But it was found from the comparison between the Dunde Icc Cap climatic record and thewinter temperature record in Shanghai that there was a temporal dfference in climatic changebetween East China and West China. The general trend is that the cooling and warmingprocesses in West China were earlier than that in East China. In the Dunde Ice Cap, it isnow in an anomalous warm period, while it is not as warm as in Dunde Ice Cap recordaccording to the winter temperature in Shanghai. In addition to the possible cause of temporaldifference in climatic change between West China and East China, another possible cause isthat the greenhouse effect of CO_2 may already be recognizable in the Dunde Ice Cap a     

~(13)C化学位移在达玛烷型皂甙结构研究中的应用

本文将迄今为止国内外文献报道的200余种达玛烷型皂甙类化合物的~(13)C化学位移按其结构特征分类整理,以原人参二(三)醇等为模型化合物,讨论了皂甙元结构变化引起的位移变化(Δδ_C)规律。     

On the modelling of solid state reactions.Synthesis of YAG

There is a model of yttrium aluminium garnet (YAG) synthesis presented in this article. The developed model is based on nonlinear reaction–diffusion partial differential equations. The solution was carried out numerically using finite difference techniques. We got dependability curves for diffusion and reaction rates and offered possible method to localize values of diffusion and reaction rate constants precisely enough.AMS subject classification: 35K57, 65M06     

The hole-pressure problem

There is a need to unify present hypotheses of the nature and role of the hole-pressure,p _e , and thus provide consolidation on which to base future research and understanding. This paper is intended to meet this need. Attention is directed towards the calculation ofp _e from the velocity and stress fields for viscoelastic fluids flowingacross rectangular holes. The constitutive models used are the Newtonian, Second-order and Maxwell models, for values of Reynolds number up to 10 and Weissenberg number up to 0.1.The numerical complications involved are studied through an investigation of the constituent parts ofp _e . Verification of present theory is then sought, from which justification may be derived for the estimation of elasticity fromp _e measurements. Attention is directed towards the predictions of Higashitani and Pritchard and the extension to the Tanner and Pipkin theory for Second-order fluids. The effects of variation of geometric dimensions and flow type uponp _e are also discussed.     

Variational reactive scattering calculations: computational optimization strategies

Summary We have developed efficient and accurate techniques for the calculation of quantum mechanical reaction probabilities of atom-diatom exchange reactions in the gas phase, and we have optimized a computer code employing these techniques and applied it sucessfully to several systems. In this paper we consider further strategies for improving the algorithm to allow even more demanding applications. In this context, improvement means that equivalent results can be obtained using fewer computational resources (computer time or storage) or that an equivalent expenditure of resources can yield higher accuracy. The new strategies discussed here lead to improvement in both of these areas. Two areas of special focus in the present paper are (i) the finite difference boundary value method used for calculating distorted wave Green's functions and regular solutions for scattering by the distortion potential and (ii) the choice of the distortion potential itself. Among other results included here is the first application of the outgoing wave or scattered wave variational principle to reactive scattering.     

Theoretical Study of Weakly Bound Dimers between Hydrogen Fluoride and Some Polar Molecules

Weakly bound linear and bent dimers, FH—X (where X = CO, OC, CNH, NCH, N₂O and ON₂), are investigated using the DFT B3LYP and ab initio MP2 methods with the same basis sets (6–311++G(3df,2pd)). The strengths of the H—C or H—N H‐bonds in dimers FH—CO, FH—CNH, and FH—N₂O are compared with those of the H—O or H—N H‐bonds in dimers FH—OC, FH—NCH, and FH—ON₂. The results obtained for the H‐bond distances, the elongation effect of the HF bond, the red shift of the HF stretching frequency, and the energy difference between the dimer and the charge transfer reveal that the H‐bonds of the first group of dimers are stronger than those of the second. The Gibbs energies calculated for the six dimer formations indicate that the weakly bound dimers are unstable at room temperature (T = 298 K) (FH—X's → FH + X's, ΔG < 0).     

Clathrate and inclusion compounds. Part 8 [1]. An investigation of the usefulness of the spectral substraction technique in analysing the infrared spectra of clathrates

An investigation has been carried out into the usefulness of the spectral subtraction technique in analyzing the infrared spectra of the clathrates of quinol and of Dianin's compound. Due to the flexibility of the quinol host lattice, it is not advisable to use guest-free -quinol as the reference if the host lattice in the clathrate is considerably distorted, as it is in the CH₃CN clathrate. In this case it is advisable to use another clathrate as the reference provided that the spectrum of the new reference does not contain guest bands in the region of interest. The Dianin's compound host lattice is less flexible than that of quinol, and guest-free Dianin's compound can be used as the reference irrespective of the size of the guest molecule. With both clathrates the spectral subtraction technique has revealed guest molecule bands which were previously obscured by host lattice bands.Dedicated to Professor H. M. Powell.