关于Erdoes猜想的证明

文章对Erdoes猜想中正整数n的值进行分类．除了n为4m-3（m=6R＋1）形的奇数外，逐类直接给出了具体表示。对于n为4m-3形的奇数，文章采用命题转化法及反证法．并用自变量与函数值的一一对应关系证明了Erdoes猜想成立。     

Chemical Reactivity of Tetrasulfur Tetranitride: Synthesis,Physical Properties,and Structural Characterization of the Amorphous Phase Cu7S4N4

Tetrasulfur tetranitride, S₄N₄, reacts with elemental Cu within inert solvents to a black‐blue material of approximate composition Cu₇S₄N₄ which is totally amorphous to X‐rays and which cannot be made crystalline by either thermal treatment or electron radiation. Cu₇S₄N₄ explodes if heated above 234 °C or when subjected to mechanical shock to eventually yield copper(I) sulfide; this together with the characteristic infrared spectrum of Cu₇S₄N₄ indicates the presence of molecular S₄N₄ units inside the amorphous phase. The metastable nature of Cu₇S₄N₄ is also mirrored by electron microscopy which furthermore allows the structural characterization of its degradation products. Based on experimental EXAFS data offering characteristic Cu—N and Cu—S distances, a theoretical crystalline approximant of Cu₇S₄N₄ was suggested and structurally optimized by density‐functional total‐energy calculations including periodic boundary conditions. This model incorporates a central S₄N₄ unit bonded to three shells of Cu atoms of different functionalities; in addition, a partial rupture of the S₄N₄ unit is likely to allow for a lowering of the total energy of the metastable phase. The latter observation supports the impossibility to make Cu₇S₄N₄ crystallize using ₄N₄ crystallize using whatever kind of measures.     

A simple four-node quadrilateral finite element for plates

A simple and accurate four-node quadrilateral finite element based on the Mindlin plate theory and Kirchhoff constraints is presented for general thin plate bending applications. The derivation of the element stiffness properties is straightforward, starting with a specified eight-node interpolation; usual discrete Kirchhoff (DK) constraints are employed to constrain out the four midside nodes of the element. The present resulting DK element passes patch tests with elements of arbitrary and even highly distorted mesh types. Numerical studies of the element convergence behaviours are undertaken for various plate bending problems so far investigated. It is indicated from comparative examples that fairly good convergence characteristics have been achieved.     

Server-Agents-Users通信系统的Stackelberg模型

在多媒体通信系统中引入代理服务器，使其成为Server—Agents—Users系统，并用对策论的Stackelberg理论研究该系统．针对Server、Agents和Users地位不平等的情况，建立了该系统的Stackelberg策略模型，得到一个三层规划模型．     

TiO2∶Mo体系的光子雪崩上转换

在 978nm激光二极管的激发下 ,Mo掺杂的TiO2 材料表现出很强的宽带上转换发光 ,该发光来源于 [MoO4]2 - 基团的激发态3T1 ,3T2 能级到基态1 A1 能级的电子跃迁 .通过研究发光强度与抽运功率的关系及上转换发光的上升时间曲线 ,发现TiO2 ∶Mo体系的上转换发光中存在着雪崩机制 ,应用转换函数理论分析了光子雪崩的产生条件和主要特征 ,理论结果和实验数据很好地符合     

Coupled lubrication and Stokes flow finite elements

A method is developed for performing a local reduction of the governing physics for fluid problems with domains that contain a combination of narrow and non‐narrow regions, and the computational accuracy and performance of the method are measured. In the narrow regions of the domain, where the fluid is assumed to have no inertia and the domain height and curvature are assumed small, lubrication, or Reynolds, theory is used locally to reduce the two‐dimensional Navier–Stokes equations to the one‐dimensional Reynolds equation while retaining a high degree of accuracy in the overall solution. The Reynolds equation is coupled to the governing momentum and mass equations of the non‐narrow region with boundary conditions on the mass and momentum flux. The localized reduction technique, termed ‘stitching,’ is demonstrated on Stokes flow for various geometries of the hydrodynamic journal bearing—a non‐trivial test problem for which a known analytical solution is available. The computational advantage of the coupled Stokes–Reynolds method is illustrated on an industrially applicable fully‐flooded deformable‐roll coating example. The examples in this paper are limited to two‐dimensional Stokes flow, but extension to three‐dimensional and Navier–Stokes flow is possible. Copyright © 2003 John Wiley & Sons, Ltd.     

The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands

By showing that there is an upper bound for the price of anarchyρ(Γ) for a non-atomic congestion game Γ with only separable cost maps and fixed demands, Roughgarden and Tardos show that the cost of forgoing centralized control is mild. This letter shows that there is an upper bound for ρ(Γ) in Γ for fixed demands with symmetric cost maps. It also shows that there is a weaker bound for ρ(Γ) in Γ with elastic demands.     

架起传统与现代的桥梁--建筑历史与理论课程体系教学改革的思考

重新审视建筑历史理论教学的目标、内容、教学方式和手段，通过对国内几座有影响的建筑院校的调研，比较各个院校在这些问题及途径上的异同，分析其利弊，以期促进建筑历史与理论课程体系教学的建设和改革．     

A complete set of numerical invariants for a subfactor

We show that certain numerical invariants associated naturally to a subfactor planar algebra constitute a complete family in the sense of determining the isomorphism class of the subfactor planar algebra.In the course of the proof, we show also that planar algebra isomorphisms of subfactor planar algebras can always be chosen to be ∗-preserving. This latter statement generalises the fact that ‘Hopf algebra isomorphisms of finite-dimensional Kac algebras can be chosen to be ∗-preserving’.