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关键词： real-part BEM   plate vibration   spurious eigenvalue   circulant   degenerate kernel   Fourier series   SVD updating technique  

摘要： In this paper, a real-part BEM for solving the eigenfrequencies of plates is proposed for saving half effort in computation instead of using the complex-valued BEM. By employing the real-part fundamental solution, the spurious eigenequations in conjunction with the true eigenequation are obtained for free vibration of plate. To verify this finding, the circulant is adopted to analytically derive the true and spurious eigenequations in the discrete system of a circular plate. In order to obtain the eigenvalues and boundary modes at the same time, the singular value decomposition (SVD) technique is utilized. For the continuous system, mathematical analysis for the spurious eigenequation was done by using the degenerate kernel and Fourier series. Good agreement of the analytical solutions (continuous and discrete systems) is made. Three cases, clamped, simply-supported and free circular plates, are demonstrated analytically and numerically to see the validity of the present method. SVD updating technique is adopted to suppress the ocurrence of the spurious eigenvalues, and a clamped plate is demonstrated analytically for the discrete system in this paper.

ISBN: (纸本)7308037657

关键词： 数学分析  

ISBN: (数字)7560920276 ISBN: (纸本)7560920276

摘要： 21世纪数学系列教材:本册书内容为一元函数微积分和微分方程。分为讲述了集合与函数、极限与连续、一元函数微分学、一元函数积分学、微分方程等内容。

关键词： limestone   stochastic simulation   trace length   fracture spacing  

摘要： A statistical, rule-based algorithm for generating fracture patterns similar to those observed in Limestone is presented. For each fracture set, initial seed points are randomly positioned within the modelled domain with the same density as the fractures observed in the field. An orientation is associated with each point by sampling from the distribution of orientations for the corresponding fracture set. Fractures are then allowed to grow from the seed points in both directions with this orientation until they meet other fractures whereupon they continue or terminate according to a fixed probability. A mathematical analysis of this method is presented for the case in which fractures within a set are assumed to be parallel. Approximations to the distribution of semi-trace lengths are derived which are shown to be in good agreement with simulation results. Fracture spacing distributions are also derived for this case.

ISBN: (纸本)7560728014

ISBN: (纸本)7111146891

关键词： arteriole   chemical reaction   diffusion   mass transport   mathematical model   oxygen   oxygen consumption   nitric oxide   nitric oxide synthase  

摘要： Biotransport of nitric oxide (NO) and of oxygen (O-2) in the microcirculation are inherently interdependent, since all nitric oxide synthase (NOS) isoforms (eNOS, nNOS, and iNOS) require O-2 to produce NO. Furthermore, tissue O-2 consumption is reversibly inhibited by NO. To investigate these complex interactions, a mathematical model was developed for coupled mass transport of NO and O-2 around a cylindrical arteriole using finite element computational methods. Steady-state radial NO and O-2 gradients in the bloodstream, plasma layer, endothelium, vascular wall, and surrounding tissue were simulated for different conditions. Special cases of the model were solved, including O-2-dependent NO production from eNOS alone, and with additional NO production from either nNOS or iNOS at specified locations. The model predicts that (a) concentration changes in one species can have significant effects on transport of the other species with the degree of interaction dependent on spatial gradients;(b) eNOS NO production rates required to maintain the concentration of NO in the vascular wall are more dependent on NO scavenging in blood than in tissue;(c) relatively low rates of NO production in tissue from either nNOS or iNOS can elevate vascular wall NO, compensating for possible reductions in NO production from eNOS;(d) depending on their physical location, nNOS and iNOS can be very sensitive to O-2;and (e) increased tissue NO can increase O-2 delivery to more distal regions by inhibiting O-2 consumption in other regions. (C) 2004 Elsevier Inc. All rights reserved.

关键词： 单室模型   微分方程   牛顿迭代法   一元线性回归  

摘要： 本文针对血液中酒精含量随时间变化的特征,通过VB语言程序对一元线性回归求解模型进行了计算。利用单室血管外给药原理建立模型(1)(2)(3),并对题中大李所遭遇到的情况做出了合理的解释。

关键词： 函数极值   初等解法   高等解法   数学分析   学习兴趣  

摘要： 讨论函数极值的初等解法和高等解法的各自特点并对两种方法进行了比较,通过两种解法的比较,在教学中可以更好的培养学生的学习兴趣,对培养学生的能力有一定的作用.

关键词： 超高相对分子质量聚乙烯   冻胶纤维   萃取   扩散系数  

摘要： 对超高相对分子质量聚乙烯(UHMWPE)冻胶纤维萃取体系中溶剂与萃取剂的双扩散过程进行了数学分析,推导出纤维溶剂扩散系数的计算公式。纤维溶剂的萃取扩散系数可用于表征萃取剂的萃取能力。通过纤维溶剂萃取扩散系数的大小,结合冻胶纤维萃取的本质和目的,选定二氯甲烷为最佳萃取剂。讨论了影响纤维溶剂扩散系数的因素,结果表明:超声萃取时纤维溶剂扩散系数要比静置萃取时大,并随萃取浴温度的升高而增加,随冻胶纤维半径的增加而减小。