A short note on the entrainment and exit boundary conditions

An attempt is made to find out the suitable entrainment and exit boundary conditions in laminar flow situations. Streamfunction vorticity formulation of the Navier–Stokes equations are solved by ADI method. Two‐dimensional laminar plane wall jet flow is used to test different forms of the boundary conditions. Results are compared with the experimental and similarity solution and the proper boundary condition is suggested. The Kind 1 boundary condition is recommended. It consists of zero first derivative condition for velocity variable and for streamfunction equation, mixed derivative at the entrainment and exit boundaries. Copyright © 2005 John Wiley & Sons, Ltd.     

Desargues定理的推广

本文将射影几何著名的Desargues透视三点形定理推广到四面体和三维射影空间的完全n(n≥4)点形(体)中。     

Discontinuous travelling wave solutions for certain hyperbolic systems

In an earlier paper on a malignant cell invasion model (Marchantet al., SIAM J. Appl. Math, 60, 2000) we introduced a novelform of discontinuous travelling wave solution. These solutionscould be studied easily by combining behaviour within a phaseplane with the Rankine–Hugoniot shock conditions, whichdescribe properties (such as the ratio of the jump discontinuitiesto the speed of propagation) that solutions may possess. Theseresults were new for several reasons. The shock conditions relateto hyperbolic equations (which the model is) but were appliedin a travelling wave ordinary differential equation phase planeusing techniques that usually apply to parabolic reaction–diffusionsystems. In addition the solutions possess singular behaviournear several points in the phase plane but in spite of thisthere exists a robust and stable family of physically interestingsolutions. In this paper we discuss two previously studied models, oneof detonation theory and one of angiogenesis. We show that eachof these models also possesses a family of discontinuous travellingwave solutions which was not previously discovered. Of particularinterest is the solution which has a blunt interface at thefront of the invading profile. In all three models it is thissolution that is seen to stably evolve from physically relevantinitial data, and for physically relevant parameter values. This work confirms the robustness of these novel travellingwave solutions and their applicability to a wider range of mathematicalmodelling situations.     

On covering bridged plane triangulations with balls

We show that every plane graph of diameter 2r in which all inner faces are triangles and all inner vertices have degree larger than 5 can be covered with two balls of radius r. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 65–80, 2003     

否定毛细永动机的唯象理论

本文从毛细现象自身所满足的规律、弯曲液面所具有的性质着手，给出了一种否定毛细永动机的唯象理论。     

非惯性系中变质量力学系统的变分原理及应用

利用附加惯性力的方法建立了非惯性系中变质量力学系统的Gauss变分原理,由此得到了非惯性系中变质量非完整系统运动方程的各种形式,最后提出了广义惯性力的广义非惯性势的概念并进一步给出上述方程的简化形式。     

QSTEM技术中晶面指数的模糊逼近

本文阐述了 QSTEM 技术中获得的晶面夹角值与晶面指数之间的位相关系,提出了测量值与理论值的隶属度,建立了测量值与晶面指数之间的模糊关系——矩阵 A,通过两个例子,说明了模糊逼近的具体方法以及参数 T、m 和算子 H 等的具体意义。     

平面机构运动数字化控制系统的设计

介绍了平面机构运动数字化控制系统的设计，其设计主要是对机械原理实验室中平面机构运动演示板进行改进，从原来的以单片机为控制核心到以微机系统为核心，系统控制本质是通过对解说语音文件的操作来达到对126个机构进行任意的操作，并且在性能上实现了易调试、可视化、多媒体等特点和功能，使教学效果得到显著提高，同时对于工业网络控制也具有一定的借鉴作用。     

周期摄动保守系统的存在性定理

本文利用全局反函数定理讨论了一类非线性边值问题解的存在性与唯一性.     

TERNARY OPERATIONS AS PRIMITIVE NOTIONS FOR PLANE GEOMETRY II

We proved in the first part [1] that plane geometry over Pythagorean fields is axiomatizable by quantifier-free axioms in a language with three individual constants, one binary and three ternary operation symbols. In this paper we prove that two of these operation symbols are superfluous.