From crystalline boryl-substituted and boryl-coupled 2,2,4,4,6,6-hexamethyl-cyclotrisilazanes to β-SiC and BN

[Me₂SiNBFN(SiMe₃)₂]₃ (1) is synthesized in the reaction of trilithiated hexamethylcyclotrisilazane with F₂BN(SiMe₃)₂. The mono- and dilithium derivatives of the six-membered ring (Me₂SiNH)₂ Me₂SiNSiFMe₂ react with the F₂B-substituted cyclotrisilazane F₂B(NSiMe₂)₃(SiFMe₂)₂ in the molar ratio 1:1 or 1:2 to give the BF-coupled rings 2 and 3. The crystal structure analysis of 1 and 3 and pyrolysis of 1 and 3 with formation of silicon boron carbonitride and its crystallisation to composite powders at very high temperatures are reported.     

From independent particle towards collective motion for two polarized electrons on a square lattice

The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L ₀ = π²(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L ₀, up to finite size corrections of order L^-2. L < L ₀ and L > L ₀ are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U ^*(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion. Received 28 March 2002 Published online 19 November 2002     

Ubiquity of relative regular sequences and proper sequences

A relative regular sequencea ₁, ...,a _r , with respect to the idealI=(a ₁, ...,a _r ) has the property thatI annihilates the Koszul homology associated to each initial subsequence. This note analyzes the concepts of relative regular and proper sequences, two notions situated in a strategic position for studying the arithmetical properties of Blow-up Algebras in the largest context of generalized Cohen-Macaulay rings.     

On the optimal control of minimum film thickness

The present paper is concerned with the study of controlling the motion of a bearing so that the thin film of lubricant separating it from its container will have the largest possible thickness. Explicit equations are derived, and the control problem is solved explicitly in some simple cases.The authors thank Dr. S. M. Rohde, Manager, Systems Analysis and Simulation Department, General Motors System Engineering Center, for many valuable discussions about this problem.     

The strength of interaction of highly retentive silanols with hydrocarbons on porasil C

Summary The paper describes how the method of gas-phase titration of the strongest adsorption sites can be utilized to calculate a relative strength of interaction of the sites with chromatographic solutes. An excellent correlation with earlier, theoretical predictions of Giddings is noted. Significant influence of the sites on the width of a chromatographic band is observed when the interactions are an order of magnitude stronger than those of normal sites. Presented at the 17th International Symposium on Chromatography, September 25–30, 1988, Vienna, Austria.     

磁场对介观耦合金属环中持续电流的影响

在考虑电荷是量子化的基础上，研究了外加磁场对介观耦合金属环中持续电流的影响.结果表明：由于存在耦合，介观金属环中总是存在附加的持续电流，附加的持续电流与电路参数及耦合系数有关.当外加磁通量按正弦规律变化时，介观耦合金属环中出现倍频与分频效应. 关键词： 介观耦合金属环 持续电流 磁场     

New algorithm to construct a stabilizing controller for linear systems over integral domains

We are concerned with the coordinate-free approach to controlsystems, which is a factorization approach but does not requirethe coprime factorizations of plants, provided only that theset of stable causal transfer functions forms an integral domain.We first present a new criterion of the feedback stabilizability.This is a generalization of the criteria in terms of reducedminors given by Sule in 1994 and in terms of quotient idealsgiven by Shankar and Sule in 1992. We then present an algorithmto construct a stabilizing controller, which is derived fromthe result given by Lin in 1998. Sule's algorithm and its derivationsneed to convert some matrices over some ring of fractions toones over the set of stable causal transfer functions, whichmay raise the unnecessarily complicated calculations. On theother hand, the algorithm of this paper does not require sucha conversion. An illustrative example to construct a stabilizingcontroller is also presented.     

用月牙形波带求圆孔夫琅禾费一级衍射环的角半径

用类似菲涅耳半波带的简单几何分析方法，近似导得了圆孔夫琅禾费衍射的中央明斑和一级明环的角半径。     

On Projective Modules with Constant Ranks

On Projective Modules with Constant RanksIn this paper,we investigate module structures of rings over which every finitely generated projective module with constant rank is stably free. As applications,we give characterizations of some related rings.     

BV solutions of a singular diffusion equation

In this paper, we study discontinuous solutions of a partial differential equation of strongly degenerate parabolic type. A notion of weak solutions of BV class is proposed, and existence and uniqueness results are obtained.