算子的拟酉等价性

本文在复的，可析的、无限维Ｈｉｂｅｒｔ空间Ｈ中引进了算子拟酉等价性的概念；获得了几个重要结果。     

A complementary thermodynamic limit for classical Coulomb matter

The canonical equilibrium measure of classical two-component Coulomb matter with regularized interactions is analyzed in a finite volume. It is shown that, in the mean-field regime, the one-particle density is inhomogeneous on a new characteristic length scale _inh. For a system ofN positive andN negative particles, _inh and the characteristic length scale of correlations _corr (=Debye screening length) are related via _inh=(2N)^1/2 _corr. The major conceptual conclusion that is drawn from this is that one needs two nontrivial complementary thermodynamic limits to define the equilibrium thermodynamics of two-component Coulomb systems. One of them is the standard thermodynamic limit (infinite volume), where one takesN, _corr fixed. Its complementary limit is characterized byN, _inh fixed, and is a finite-volume inhomogeneous mean-field limit. The most prominent new feature in the mean-field thermodynamic limit, which is absent in the standard thermodynamic limit, is an anomalous first-order phase transition where the Coulomb system explodes or implodes, respectively. The phase transition is connected with the existence of a metastable plasma phase far below the ionization temperature.     

Solution of a class of stochastic linear-convex control problems using deterministic equivalents

In this paper, we identify a new class of stochastic linearconvex optimal control problems, whose solution can be obtained by solving appropriate equivalent deterministic optimal control problems. The term linear-convex is meant to imply that the dynamics is linear and the cost function is convex in the state variables, linear in the control variables, and separable. Moreover, some of the coefficients in the dynamics are allowed to be random and the expectations of the control variables are allowed to be constrained. For any stochastic linear-convex problem, the equivalent deterministic problem is obtained. Furthermore, it is shown that the optimal feedback policy of the stochastic problem is affine in its current state, where the affine transformation depends explicitly on the optimal solution of the equivalent deterministic problem in a simple way. The result is illustrated by its application to a simple stochastic inventory control problem.This research was supported in part by NSERC Grant A4617, by SSHRC Grant 410-83-0888, and by an INRIA Post-Doctoral Fellowship.     

Surface properties of finite classical Coulomb systems: Debye-Hückel approximation and computer simulations

We report analytical and numerical studies of surface correlations in finite, homogeneously polarizable, classical Coulomb systems placed in an insulating or conducting environment. Their purpose is to understand the phenomenological, shape-dependent laws of electrostatics, from the point of view of statistical mechanics; we focus on the knowledge of the dielectric susceptibility of the system, a quantity proportional to the equilibrium fluctuation of the system's instantaneous polarization per unit volume. This goal has been achieved for a system in a conducting state. The picture is that the shape-dependent part of the susceptibilities results from the action of unbounded observables (the second moments of the instantaneous polarization of the system) on long-range surface correlations and that the relations of electrostatics are verified by means of shape-dependent thermodynamic limits. This picture is supported (i) by exact solutions and asymptotic analysis of the Debye-Hückel approximation of multicomponent plasmas in disks and spheres with insulating and conducting environment and also in ellipses in a vacuum, and (ii) by computer simulations of a one-component plasma in a disk with different environments, notably a conducting environment with permeable and impermeable wall. These observations have revealed for the first time the reason why the susceptibility of a conducting disk in a conductor with impermeable walls diverges linearly with the radius of the disk: this is due to the occurrence of long-range radial correlations in the conductor. These findings are quantitatively interpreted in terms of a novel canonical Debye-Huckel approximation as contrasted to the ordinary grand canonical version. Lastly a fresh look at the problem of the surface correlations of a conductor in a vacuum, which places the observer close to the surface of the conductor but in the vacuum, is presented and applied to the disk, the ellipse, the cylinder, the sphere, and the wedge.     

A class of interaction-round-a-face models and its equivalence with an ice-type model

A new model (called the Temperley-Lieb interactions model) is introduced, in two-dimensional lattice statistics, on a square lattice . The Temperley-Lieb equivalence of this model to the six-vertex, self-dual Potts, critical hard-hexagons and critical nonintersecting string models is established. A graphical equivalence of this model to the six-vertex model generalizes this equivalence to noncritical cases of the above models. The order parameters of a specialization of this model are studied.     

Computation of density of perfluoroalkyl methacrylates: a molecular modeling approach

Molecular dynamics simulations have been carried out on different perfluoroalkyl methacrylates to predict their densities. Density calculations on selected perfluoroalkyl methacrylates have been performed using molecular dynamics in the NPT ensemble by employing COMPASS force field. The calculated density values compared quite well with the experimental data reported in the literature.     

Simple algorithm for isothermal-isobaric molecular dynamics

We review principles of non-Hamiltonian statistical mechanics and present a new set of equations and integration algorithm for isothermal-isobaric dynamics. The chief advantage of the present scheme is that it is somewhat simpler than previous methods. We perform numerical simulations to test the accuracy of the algorithm and compare its stability to that of a "gold standard," a symplectic integrator for Hamiltonian dynamics of the same system. The stability of the isothermal-isobaric algorithm is comparable to the stability of the symplectic integrator.     

?*-extensions of tori, higher chow groups and applications to incidence equivalence relations for algebraic cycles

LetX be a smooth projective variety over an algebraically closed fieldk. We repeat Bloch's construction of aG _m -biextension (torseur)E over CH _hom ^p (X)×CH _hom ^q (X) forp+q=dim(X)+1. First we show that in characteristic zeroE comes via pullback from the Poincaré biextension over the corresponding product of intermediate Jacobians which has been conjectured by Bloch and Murre. Then the relations betweenE and various equivalence relations for algebraic cycles are studied. In particular we reprove Murre's theorem stating that Griffiths' conjecture holds for codimension 2 cycles, i.e. every 2-codimensional cycle which is algebraically and incidence equivalent to zero has torsion Abel-Jacobi invariant.     

On quadratic forms of height two and a theorem of Wadsworth

Let and be anisotropic quadratic forms over a field of characteristic not . Their function fields and are said to be equivalent (over ) if and are isotropic. We consider the case where and is divisible by an -fold Pfister form. We determine those forms for which becomes isotropic over if , and provide partial results for . These results imply that if and are equivalent and , then is similar to over . This together with already known results yields that if is of height and degree or , and if , then and are equivalent iff and are isomorphic over .