Stationary entanglement between macroscopic mechanical oscillators

We show that the optomechanical coupling between an optical cavity mode and two movable cavity mirrors is able to entangle two different macroscopic oscillation modes of the mirrors. This continuous variable entanglement is maintained by the light bouncing between the mirrors and is robust against thermal noise. In fact, it could be experimentally demonstrated using present technology. Received 2 September 2002 / Received in final form 10 October 2002 Published online 7 January 2003     

Banach空间非线性混合型微分-积分方程整体解的存在性和唯一解

研究了Banach空间中非线性混合型微分-积分方程初值问题u′=f(t,u,Tu,Su),u(0)=x0的整体解,完全没有要求f的任何增性,利用Mnch不动点定理和比较结果得到了初值问题整体解的存在性和唯一解,并且给出了一致收敛于唯一解的迭代序列,改进推广和统一了已有的许多结果.     

Structure and Structural Nonrigidity of Tetrachlorodibenzo-p-Dioxin Radical Cations

Ab initio calculations showed that the tetrachlorodibenzo-para-dioxin radical cations (TCDD RCs) with a planar structure have two steady states with asymmetric dioxin cycles. The activation barriers between these states are up to 2 kcal/mole, so that the RCs may be regarded as being structurally nonrigid within the dioxin cycle. The 2,3,7,8-TCDD RC is more stable than the 1,4,6,9-TCDD RC, the energy difference being 5.2 kcal/mole. The adiabatic ionization potential of 2,3,7,8-TCDD (7.54 eV) is 0.1 eV smaller than the corresponding potential of 1,4,6,9-TCDD. These factors account for the increased hemoproteide affinity and hence increased biological activity of 2,3,7,8-TCDD.     

Dicyclopentadienyl complexes of titanium,niobium, and tungsten in the controlled synthesis of poly(methyl methacrylate)

Organometallic compounds Cp₂TiCl₂, (EtC₅H₄)₂NbCl₂, and (PrⁱC₅H₄)₂WCl₂ were assessed as additives that control polymer chain growth in the polymerization of methyl methacrylate. In the presence of compounds mentioned in amounts comparable with that of the initiator, a uniform process with no gel-effect occured and respective linear increase in the molecular weight of the polymer up to high degrees of the monomer conversion was observed.     

A thermodynamic approach with internal variables using Lagrange formalism. Part I: General framework

We present some reflections on the application of the Lagrangian formalism for continuous media locally uniform subjected to internal irreversible evolutions. The Lagrangian density, defined as the time derivative of a non-equilibrium thermodynamic potential, [Thermodynamics of Relaxation Processes using Internal variables within a Lagrange-formalism. P. Germain’s Anniversary Volume 2000. Contiuum Thermomechanics: the Art and Science of Modeling Matter’s Behaviour, 2000], contains all the symmetry properties of the system. The generalised Lagrange co-ordinates correspond to the state and internal variables of the time derivative of the generalised Gibbs potential. The latter being used within the framework of the De Donder’s method, must also account for the memory effect of the physical medium.This first part is devoted to the thermodynamic framework called the distribution of non-linear relaxations approach (DNLR) developed by C. Cunat on the basis of the generalised Gibbs’ relation.     

有限循环群的Fuzzy子群的等价类数

有限循环群G的F子群可以有无数个．但是．若当两个F子群的水平集构成的集合相等就称其等价的话，那么其等价类数是有限的。通过研究群的合成群列、商群列以及数的因数列和极大因数列找出了有限循环群的极大F子群和F子群的等价类数的求解公式．并给出二者之间的关系式．     

二次阳极氧化方法制备有序多孔氧化铝膜

通过二次阳极氧化方法制备多孔氧化铝膜与一次阳极氧化方法制备多孔氧化铝膜孔排布规律性的对比 ,结果发现 ,二次阳极氧化方法制取的多孔氧化铝膜孔排布规律性明显好于一次阳极氧化法制取的多孔膜 .在几个微米范围内 ,孔呈理想的六角排布 .去除一次阳极氧化膜后 ,二次阳极氧化得以在更良好的表面进行 ,制取的氧化铝膜孔规律性和有序度更高 .有序区域的尺寸与晶粒内的亚晶大小有一定关系     

Minimum Distance Between the Faces of Two Convex Polyhedra: A Sufficient Condition

The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large.     

Subgroup separability of graphs of abelian groups

In the present paper we give necessary and sufficient conditions for the subgroup separability of the fundamental group of a finite graph of groups with finitely generated abelian vertex groups.

     

Cauchy problems for linear thermoelastic systems of type III in one space variable

The goal of the paper is to analyse properties of solutions for linear thermoelastic systems of type III in one space variable. Our approach does not use energy methods, it bases on a special diagonalization procedure which is different in different parts of the phase space. This procedure allows to derive explicit representations of solutions. These representations help to prove results for well‐posedness of the Cauchy problem, L^P–L^q decay estimates on the conjugate line and results for propagation of singularities. Copyright © 2005 John Wiley & Sons, Ltd.