Solution of the hyperbolic mild‐slope equation using the finite volume method

A finite volume solver for the 2D depth‐integrated harmonic hyperbolic formulation of the mild‐slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov‐type second‐order finite volume scheme, whereby the numerical fluxes are computed using Roe's flux function. The eigensystem of the mild‐slope equations is derived and used for the construction of Roe's matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality‐free. Copyright © 2003 John Wiley & Sons, Ltd.     

On disjoint configurations in infinite graphs

For a graph A and a positive integer n, let nA denote the union of n disjoint copies of A; similarly, the union of ?₀ disjoint copies of A is referred to as ?₀A. It is shown that there exist (connected) graphs A and G such that nA is a minor of G for all n??, but ?₀A is not a minor of G. This supplements previous examples showing that analogous statements are true if, instead of minors, isomorphic embeddings or topological minors are considered. The construction of A and G is based on the fact that there exist (infinite) graphs G₁, G₂,… such that G_i is not a minor of G_j for all i ≠ j. In contrast to previous examples concerning isomorphic embeddings and topological minors, the graphs A and G presented here are not locally finite. The following conjecture is suggested: for each locally finite connected graph A and each graph G, if nA is a minor of G for all n ? ?, then ?₀A is a minor of G, too. If true, this would be a far‐reaching generalization of a classical result of R. Halin on families of disjoint one‐way infinite paths in graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 222–229, 2002; DOI 10.1002/jgt.10016     

雍正皇帝与永明延寿禅师

从雍正视永明延寿为历代禅德之最,视永明延寿为心心相印者,极为重视永明延寿著作之刊刻流布及以永明延寿思想为其评判的标准与依据等方面,可以见出雍正皇帝与延寿禅师在禅学思想上的密切联系。进而根据清初社会状况及佛教尤其是禅宗演变的大背景,就雍正对永明延寿禅师的极力推崇与高度评价的原因及影响作出系统分析。     

易中天《品三国》补正

易中天教授在《品三国》中，把历史唯物主义具体化，提出了评论历史人物和历史事件的三项准则，即：“还原”、“比较”、“分析”。易教授在贯彻这三项原则时也难免有疏漏之处：一、把襄阳、赤壁之战说成曹刘之战不能成立；二、曹操一封信促成孙刘联盟的提法不妥；三、《白衣渡江》引用了《吕蒙传》上有两条错误的史料。     

Symmetry specified enumeration of substituted derivatives: an easy solution to the complex problem

Several sophisticated methods to solution of symmetry specified enumeration problems are available in the modern literature. In this paper we propose a simple technique that allows one to manually compute the exact numbers of fixed-symmetry derivatives for a given structure either with inclusion or ignoring the substitution patterns. The basic idea of the method suggested consists in the derivation of Pólya-like cycle indices for the automorphism groups of specially constructed orbit partition graphs; the expansion of these indices and subsequent simple calculations result in the desired numbers of substituted derivatives with achiral substituents. Limitations of the new technique (and a method suggested earlier) depend on the relevance of the orbit partitions for particular subgroups of the point symmetry group. For illustration purposes, the results obtained for the prismane (D _3h ) and adamantane (T _d ) structures are discussed. In the former case the numbers of substituted derivatives can be found for all subgroups of the D _3h group, whereas in the latter case these numbers can be determined for eight out of eleven subgroups of the T _d point symmetry group. This work is based on the text of the lecture presented by the authors at the 5th All-Russia Conference on Molecular Modeling (Moscow, April 2007). The paper deals with the methodology and detailed treatment of applied aspects related to solution of enumeration problems for substituted derivatives with prescribed symmetry groups. Unlike the known methods of symmetry specified enumeration, the technique suggested is simple enough and may be regarded as generalization of the Pólya methodology, which is widely used by chemists. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 227–245, February, 2008.     

Rheological properties of polyacrylates used as synthetic road binders

Most adhesives and binders, including bitumen for asphalt mixture production, are presently produced from petrochemicals after the refining of crude oil. The fact that crude oil reserves are a finite resource means that in the future, it may become necessary to produce these materials from alternative and probably renewable sources. Suitable resources of this kind may include polysaccharides, plant oils and proteins. This paper deals with the synthesis of polymer binders from monomers that could, in future, be derived from renewable resources. These binders consist of polyethyl acrylate (PEA) of different molecular weight, polymethyl acrylate (PMA) and polybutyl acrylate (PBA), which were synthesised from ethyl acrylate, methyl acrylate and butyl acrylate, respectively, by atom transfer radical polymerisation. The rheological properties of these binders were determined by means of oscillatory testing using a dynamic shear rheometer and combinations of stress/strain, temperature and frequency sweeps. The results indicate that PEA can be produced to have rheological properties similar to that of ‘soft’ 100/150 penetration grade bitumen, PMA with similar rheological properties to that of ‘hard’ 10/20 penetration grade bitumen, while PBA, due to its highly viscous nature and low dynamic moduli, cannot be used on its own as a binder. The synthetic polymers were found to be thermo-rheologically simple, and the shift factors, used to produce the dynamic moduli master curves, were found to fit an Arrhenius function.     

水电站钢蜗壳与外围混凝土结构的受力特性研究

应用三维有限元法，结合我国龙羊峡，岩滩，宝珠寺水电站的厂房蜗壳结构，研究了钢蜗壳与外围混凝土之间设置软垫层情况下的蜗壳与外围混凝土结构的位移及应力分布规律，给出了钢蜗壳及外围混凝土结构的几个主要受力特性。     

日式经营管理在邃变

８０年代引人注目的日式经营管理，９０年代来其许多本质性特征却发生了意味深长的变化。注视并研究这些变化意义甚大。本文重在概括日式经营管理现正经历的变化。