Generalized Brownian motion and elasticity

We introduce a family of stochastic processes which are a natural extension of Brownian motion to a tensor form. This allows us to solve a Dirichlet problem of linear elasticity obeying Lamé's equation, [1–(d– 1)]²V(x)+ [·V(x)]=0.     

Lifschitz singularities for periodic operators plus random potentials

UsingX-bounding (lower bounds by Laplacians with mixed boundary conditions and discrete analogs), we obtain the Lifschitz exponent at the bottom of the spectrum for random operators of typeH =T+V , withT a (periodic) generator of a positivity-preserving semigroup, extending results by Kirsch and Simon.     

Mechanochemical Preparation of Water-Soluble Forms of Triterpene Acids

A waste-free technology for mechanochemical processing of fir needles into a biologically active preparation that regulates plant growth was developed. A preparation exhibiting cytokinin activity due to the presence in it of water-soluble forms of triterpene acids can be prepared using the proposed method. The effectiveness of the proposed method was confirmed by instrumental methods and biological tests.     

有机硅氨基酸衍生物的研究

本文利用含氢有机硅化合物与含双键的氨基酸酯的加成反应,合成了5种新的有机硅氨基酸衍生物。介绍了一种合成N-烷基取代氨基酸酯的新方法。对新化合物进行了元素和光谱分析鉴定。     

The lion and man problem revisited

A pursuerP, whose speed is bounded by 1, wants to get closer to an evaderE, whose speed is bounded by >1.P wants to reduce his distancePE fromE below the capture radius . Both players are confined to a circular arena. This problem is equivalent to a problem discussed by Flynn, who characterized and gave numerical bounds to the least upper boundd* on the values ofPE thatE can maintain. He used direct methods and did not use Isaacs' theory.We solve our problem relying on the theory of singular surfaces in differential games. We construct and investigate barriers of the game of kind, and we replace Flynn's bounds ond* by analytical (exact) values for various speeds .The support of the TW Department of THT, Enschede, Holland, is gratefully acknowledged.     

Consistency of a linear system of inequalities

We show that a consistency check of a linear system of inequalitiesAxb reduces to check whetherQb0 for a certain matrixQ. It is a direct consequence of the Farkas-Minkowski theorem. Thus, when one has to check consistency for different values ofb, one need not run a numerical algorithm for eachb.On leave at the Electronics Research Laboratory of the University of California at Berkeley in a CNRS/NSF Exchange Program.     

Tactical problems involving uncertain actions

The purpose of this paper is to solve anm-silent versusn-silent duel with arbitrary accuracy functionsP andQ which are continuously differentiable in [0, 1] with positive derivatives in (0, 1) and such thatP(0)=Q(0)=0,P(1)(0, 1),Q(1)(0, 1). The game can be interpreted as a game in which the players know only that the numbers of their actions have binomial distribution.Part of this paper was written during the author's stay at the Institute of Statistics and Mathematical Economics, University of Karlsruhe, FRG. The author wishes to thank Prof. S. Trybua, Technical University of Wrocaw, Poland, for helpful discussion in preparing the paper and Prof. D. Pallaschke, University of Karlsruhe, FRG, for help in preparing the numerical example.     

Heat conductivity of three periodic Hard Disks via nonequilibrium molecular dynamics

We use a driving field, of the type first suggested by Evans, to generate a steady heat current in the simplest possible system, a two-dimensional periodic fluid of three hard disks. Hard-disk motion equations can be conveniently derived from repulsive constant-force or linear-force potentials by considering the infinitely repulsive limit of these potentials. We show that the isoenergetic and isokinetic forms of the nonequilibrium equations of motion generate steady-state heat conductivities differing by terms of order 1/N, whereN is the number of particles. The resulting conductivities appear to vary as the logarithm of the driving field strength. Even at low fields, the three-body periodic-system results lie well below Enskog's infinite-system prediction.     

The spherical-model limit in a random field

The spherical-model limitn of then-vector model in a random field, with either a statistically independent distribution or with long-range correlated random fields, is studied to demonstrate the correctness of the replica method in which then and replica limits limits are interchanged, provided the replica and thermodynamic limits are taken in the right order, in the case of long-range correlated random fields. A scaling form for the two-point correlation function relevant to the first-order phase transition below the lower critical dimensionality of the random system is also obtained.     

醋酸十二铵的吸附和SiO2悬浮液的稳定性

（1）测定了醋酸十二烷基铵（DAA）在CAB－O－SIL上的吸附，其等温线属双平台或LS型[1－3，5]；（2）NaCl的存在使DAA的吸附增加．但不影响其低浓度下第一平台的吸附量；HCl的存在则在全浓度范围内抑制了DAA的吸附，（3）测定了CAB－O－SIL颗粒在上述各溶液中的悬浮液的稳定性；（4）根据表面形成小胶团的吸附理论（即二步模型产）[2，3，5，]，并借助电导跟踪溶液中发生的变化，满意地解释了吸附和聚沉的实验结果．