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关键词： Eutrophication   Existence   Uniqueness   Weak solution   Very weak solution  

摘要： In this paper we present and analyze a nutrient-phytoplankton-zooplankton-organic detritus-dissolved oxygen mathematical model simulating eutrophication processes into aquatic media. As a main result, we obtain existence and uniqueness results for the solution of the system. under realistic hypotheses of non-smooth coefficients (in particular, a non-regular water velocity). This lack or regularity prevent us from using the standard semigroup approach, forcing us towards the utilization of more refined techniques. (C) 2008 Elsevier Inc. All rights reserved.

关键词： Casagrande法   3次多项式   回归分析   先期固结压力   程序  

摘要： Casagrande经验作图法是国际上通用的确定先期固结压力的方法,但其存在以下缺点:曲线绘制繁琐、若绘图比例不合适,则最小曲率半径点不易确定、人为判断误差较大。而工程中所采用的土工试验数据处理商用软件计算先期固结压力,其算法、精度分析是黑匣子,结果精度值得商榷。在总结以往研究成果基础上,结合理论研究和工程实践要求,依据《土工试验方法标准》[1],采用3次多项式和最小二乘法回归拟合压缩曲线,并考虑绘图比例影响,编写程序确定先期固结压力,最后通过具体工程土工试验数据验证了程序求解不仅能避免经验作图法的缺陷,而且结果直观清晰。

关键词： 非线性偏微分方程组   非线性方程组   柯西问题   应用   非线性薛定谔方程   演算   数学分析   量子物理学  

摘要： G．梅梯维埃 著 非线性偏微分方程组是当前数学分析研究的核心，它有着许多重要的实际应用，例如量子物理学中的非线性薛定谔方程。众所周知，非线性数学比线性数学难度要大的多，因此，从20世纪后半叶，数学家通过各种方法企图对非线性问题取得突破。

关键词： 一阶线性数列通项   求解策略   高中   数学分析  

摘要： 例题 已知al=1，an=2an-1＋3（n=2，3，…），求数列{an}的通项公式。

关键词： 小学   数学题   数学分析   解题方法  

摘要： 一天：小白兔、小公鸡、小狐狸玩捉迷藏游戏。突然，小白兔发现了一大片草莓；三人一拥而上，很快就把这些草莓采到了一个篮子里，数数共有168个。

关键词： Muscle model   Muscle architecture   Motor unit   EMG simulation  

摘要： Modeling of muscle architecture, which aims to recreate mathematically the physiological structure of the muscle fibers and motor units, is a powerful tool for understanding and modeling the mechanical and electrical behavior of the muscle. Most of the published models are presented in the form of algorithms, without mathematical analysis of mechanisms or outcomes of the model. Through the study of the muscle architecture model proposed by Stashuk, we present the analytical tools needed to better understand these models. We provide a statistical description for the spatial relations between motor units and muscle fibers. We are particularly concerned with two physiological quantities: the motor unit fiber number, which we expect to be proportional to the motor unit territory area: and the motor unit fiber density, which we expect to be constant for all motor units. Our results indicate that the Stashuk model is in good agreement with the physiological evidence in terms of the expectations outlined above. However, the resulting variance is very high. In addition. a considerable 'edge effect' is present in the outer zone of the muscle cross-section. making the properties of the motor units dependent on their location. This effect is relevant when motor unit territories and muscle cross-section are of similar size. (C) 2008 Elsevier Inc. All rights reserved.

关键词： 数学分析   高等学校   教学参考资料  

ISBN: (纸本)9787560929538

摘要： 本书主要介绍了实数与数列极限、函数、极限与连续性、导数与微分、微分中值定理与利用导数研究函数等。

关键词： Bingham fluids   variational inequalities of second kind   path-following methods   semi-smooth Newton methods  

摘要： This paper is devoted to the numerical solution of stationary laminar Bingham fluids by path-following methods. By using duality theory, a system that characterizes the solution of the original problem is derived. Since this system is ill-posed, a family of regularized problems is obtained and the convergence of the regularized solutions to the original one is proved. For the update of the regularization parameter, a path-following method is investigated. Based on the differentiability properties of the path, a model of the value functional and a correspondent algorithm are constructed. For the solution of the systems obtained in each path-following iteration a semismooth Newton method is proposed. Numerical experiments are performed in order to investigate the behavior and efficiency of the method, and a comparison with a penalty-Newton-Uzawa-conjugate gradient method, proposed in [Dean et al., J. Non-Newtonian Fluid Mech. 142 (2007) 36-62], is carried out.

关键词： decision analysis   probability   simulation   sports   statistics  

摘要： The International Badminton Federation recently introduced rule changes to make the game faster and more entertaining, by influencing how players score points and win games. We assess the fairness of both systems by applying combinatorics, probability theory and simulation to extrapolate known probabilities of winning individual rallies into probabilities of winning games and matches. We also measure how effective the rule changes are by comparing the numbers of rallies per game and the scoring patterns within each game, using data from the 2006 Commonwealth Games to demonstrate our results. We then develop subjective Bayesian methods for specifying the probabilities of winning. Finally, we describe how to propagate this information with observed data to determine posterior predictive distributions that enable us to predict match outcomes before and during play.

关键词： Elbow   Static   Analysis of substances   Contracture of elbow joint  

摘要： Elbow joint contractures are often treated by using static progressive, dynamic, turnbuckle, or serial static splinting. These splint designs are effective in regaining functional elbow range of motion due to the high forces applied to the contracted tissues;however, regaining terminal elbow extension remains a challenge. Static progressive splints are commonly used to initiate treatment, however, are considered less effective in regaining terminal extension. Recently, the concept of converting a static progressive splint into a three-point static progressive splint (TPSPS) to regain terminal extension has been introduced. This paper mathematically analyzes the compressive and rotational forces in static progressive and TPSPSs. Our hypothesis was that three-point static progressive splinting was superior to the standard static progressive elbow extension splint in applying rotational forces to the elbow at terminal extension.