乙二醇／水与丙三醇／水体系的焓浓图与浓图

本文基于乙二醇／水与丙三醇／水两组二元体系在不同温度下的实验数据,对超额焓数据应用局部作用模型拟合,并分析拟合效果与拟合参数变化情况,发现Wilson模型拟合效果较好。通过Wilson方程的活度系数表达形式,推算了两组体系的气液平衡,并进而计算了两组体系的焓浓图与(火用)浓图。     

The one-dimensional 1/4-filled Hubbard model with alternating interactions

The one-dimensional Hubbard model with different on-site interaction on the even (U_a) and odd (U_b) sites is considered within the framework of the weak coupling approach. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system and to the dynamical generation of a commensurability gap in the charge excitation spectrum for U_a ≠ U_b and U_a>0 or U_b>0. Depending on the relation between the bare coupling constants the system shows four different regimes of behaviour in the infrared limit corresponding to normal metal, nonmagnetic insulator, antiferromagnetic insulator and superconducting states. The extended model including interaction between particles on nearest and next-nearest neighbour sites is also considered.     

Phase Diagram of the Two-dimensional t–t′ Falicov-Kimball Model

The ground-state phase diagram of the two-dimensional Falicov-Kimball model with nearest-neighbour and next-nearest-neighbour hoppings has been studied in the perturbative regime where hoppings are small compared with the on-site Coulomb interaction. The phase diagram at fourth-order exhibits a richer structure than the one of the ordinary Falicov-Kimball model. PACS numbers: 71.10.Fd, 71.21.+a, 75.10.Hk, 75.30.Kz     

The Phonon Boltzmann Equation, Properties and Link to Weakly Anharmonic Lattice Dynamics

For low density gases the validity of the Boltzmann transport equation is well established. The central object is the one-particle distribution function, f, which in the Boltzmann-Grad limit satisfies the Boltzmann equation. Grad and, much refined, Cercignani argue for the existence of this limit on the basis of the BBGKY hierarchy for hard spheres. At least for a short kinetic time span, the argument can be made mathematically precise following the seminal work of Lanford. In this article a corresponding program is undertaken for weakly nonlinear, both discrete and continuum, wave equations. Our working example is the harmonic lattice with a weakly nonquadratic on-site potential. We argue that the role of the Boltzmann f-function is taken over by the Wigner function, which is a very convenient device to filter the slow degrees of freedom. The Wigner function, so to speak, labels locally the covariances of dynamically almost stationary measures. One route to the phonon Boltzmann equation is a Gaussian decoupling, which is based on the fact that the purely harmonic dynamics has very good mixing properties. As a further approach the expansion in terms of Feynman diagrams is outlined. Both methods are extended to the quantized version of the weakly nonlinear wave equation.The resulting phonon Boltzmann equation has been hardly studied on a rigorous level. As one novel contribution we establish that the spatially homogeneous stationary solutions are precisely the thermal Wigner functions. For three phonon processes such a result requires extra conditions on the dispersion law. We also outline the reasoning leading to Fourier’s law for heat conduction.     

Periodic Duffing delay equations with state dependent impulses

Conditions are obtained for the Duffing equation with delay and state dependent impulses to admit a periodic solution.     

Thermodynamic Study of the Solid-Liquid Equilibria in the Systems MIPO3-Pr(PO3)3 (MI=Na,Rb, Cs OR Ag)

A previously established equation of a stoichiometric phase liquidus curve was applied to determination of the phase diagrams of the systems M^IPO₃-Pr(PO₃)₃ (with M^I=Na, Rb, Cs or Ag). The temperature, enthalpy and entropy of fusion were calculated for each solid phase with the exception of silver polyphosphate, the crystallization field of which was very limited. The enthalpy of fusion of the polyphosphate Pr(PO₃)₃ was determined from the DTA curve. The melting enthalpy of Pr(PO₃)₃ calculated from the different binary systems was approximately equal to the measured value. The calculated temperatures and compositions were in good agreement with those determined experimentally. This revised version was published online in July 2006 with corrections to the Cover Date.     

State space calculations for discrete probability densities

State space methods have proved to be powerful theoretical and computational tools in a number of areas of applications, in particular filtering and control theory. In this paper we advocate the use of state space methods for the study of discrete probability densities on the set {0,1,2,…}. The fundamental approach is to consider the class of all discrete probability densities that can be represented as the impulse response/convolution kernel of a finite dimensional discrete time state space system. We show that all standard operations such as the calculation of moments, convolution, scaling, translation, product, etc. can be carried out using system representations.     

Crystallization of chiral compounds 3. 3-phenoxypropane-1,2-diol and 3-(2-halophenoxy)propane-1,2-diols

Specific features of melting of crystalline samples of 3-(2-R-phenoxy)propane-1,2-diols with different enantiomeric compositions were studied by differential scanning calorimetry. The melting points and enthalpies of melting for the racemate and individual stereoisomers were determined. Binary phase diagrams were constructed. The entropy of mixing of individual enantiomers in the liquid phase and the free energy of formation of the racemic compound were calculated. The thermochemical data indicate that the racemates are formed upon the crystallization of phenoxy-and 2-fluorophenoxy-containing compounds, while crystallization of the chloro-, bromo-, and iodo-substituted analogs would form racemic conglomerates. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 225—232, February, 2006.     

Semiconcavity results for constrained optimal control problems in a half-space

In this paper we give semiconcavity results for the value function of some constrained optimal control problems with infinite horizon in a half-space. In particular, we assume that the control space is the l¹-ball or the l^∞-ball in Rn.     

一种故障树分析的新算法

本论文中，首先引入了ＢＤＤ（ＢｒｉｎａｒｙＤｅｃｉｓｉｏｎＤｉａｇｒａｍｓ－ＢＤＤ）的概念，介绍由故障树到ＢＤＤ转化算法一递归法，及ＢＤＤ进行故障树分析的方法。