On the Continuity of Julia Sets and Hausdorff Dimension of N CP and Parabolic Maps

Denote by HD(J(f))the Hansdorff dimension of the Julia set J(f)of a rational function f.Our first result asserts that if f is an NCP map,and f_n→f horocyclically, preserving sub-critical relations,then f_n is an NCP map for all n(?)0 and J(f_n)→J(f)in the Hausdorff topology.We also prove that if f is a parabolic map and f_n is an NCP map for all n(?)0 such that f_n→f horocyclically,then J(f_n)→J(f)in the Hansdorff topology, and HD(J(f_n))→HD(J(f)).     

Lower bounds and modified LPT algorithm for k-partitioning problems with partition matroid constraint

In this paper,the k-partitioning problem with partition matroid constraint is consid- ered.LPT algorithm is modified to fit the problem and its worst-case performance is analyzed. The lower bounds of optimal solution for the min-max problem are given.     

Completely Regular Designs of Strength One

We study a class of highly regular t-designs. These are the subsets of vertices of the Johnson graph which are completely regular in the sense of Delsarte [2]. In [9], Meyerowitz classified the completely regular designs having strength zero. In this paper, we determine the completely regular designs having strength one and minimum distance at least two. The approach taken here utilizes the incidence matrix of (t+1)-sets versus k-sets and is related to the representation theory of distance-regular graphs [1, 5].     

粗糙集理论在属性约简及知识分类中的应用

本针对不完备信息系统属性约简的两种定义，证明了两的等价性。在此基础上结合粗糙集理论提出了相似矩阵、相似区间的概念，并将其应用于不完备信息系统知识分类的问题中。     

Statistical Ensemble and Quantization of Thermodynamics

We derive the equations of quantized thermodynamics from the Gibbs ensemble and obtain a representation of the new equations which permits a formal passage to the Bardeen--Cooper--Schrieffer equations.     

Role of electronic partition function in quantitative SIMS using the Saha-Eggert equation

Methods of obtaining the electronic partition functionsZ were discussed with an intention to use them for the Saha-Eggert quantification in SIMS. The Lagrange's interpolation formula and the least-squares method were applied to the published values ofZ to obtain the expression for calculatingZ at arbitrary temperatures. With the aid of the Saha-Eggert equation, the secondary-ion currents from Ni-Cr and Fe-Ni-Cr alloys were converted into the elemental concentrations for the two types ofZ: those obtained with the above methods and those with the approximate fifthorder polynomials presented by de Galan and others. It was proved, from the comparison of the calculated concentrations, that the latter are valid for the quantification in SIMS using the Saha-Eggert equation. The largest error in the elemental concentrations was 22% for the Ni-Cr alloy and 7% for the Fe-Ni-Cr alloy.     

Carbon layer open tubular capillary columns

Capillary columns coated with Carbopack materials, which provide separation by a mixed partition/adsorption mechanism or by adsorption alone, have recently been developed. The reproducibility of the columns is demonstrated and applications shown in which they provide separations which are either unique or are faster than can be achieved with the wall coated open tubular capillary columns currently available.     

The partition‐of‐unity method for linear diffusion and convection problems: accuracy,stabilization and multiscale interpretation

We investigate the effectiveness of the partition‐of‐unity method (PUM) for convection–diffusion problems. We show that for the linear diffusion equation, an exponential enrichment function based on an approximation of the analytic solution leads to improved accuracy compared to the standard finite‐element method. It is illustrated that this approach can be more efficient than using polynomial enrichment to increase the order of the scheme. We argue that the PUM enrichment, can be interpreted as a subgrid‐scale model in a multiscale framework, and that the choice of enrichment function has consequences for the stabilization properties of the method. The exponential enrichment is shown to function as a near optimal subgrid‐scale model for linear convection. Copyright © 2003 John Wiley & Sons, Ltd.     

Lattice models for hydrogen-bonded solvents

A class of lattice models for a binary mixture is defined by assuming that one of the components may form bonds to neighboring molecules of the same species. It is assumed that the fugacity of a molecule depends on the number of bonds which connect the molecule to other molecules. If no molecule is allowed to be connected by more than two bonds to other molecules, then no phase transition occurs, while phase transition can occur if more than two bonds are allowed. If only two or no bonds are allowed, then the model can be solved rigorously for certain planar lattices by transforming it to a dimer covering problem; this model shows behavior similar to the Ising model in zero magnetic field.Work supported by National Science Foundation grant GP-26526.On leave of absence from Corpus Christi College, Cambridge, England.On leave from the University of Copenhagen.