Schrodinger方程组的最小能量驻波解

Schrodinger方程组出现在许多数学物理模型中.文章主要研究这种方程组基态解的存在性,独特之处在于使用新的方法证明了:当给定方程组中作用参数的适当范围后,"相应函数"的下确界比单个方程时该函数的下确界要小,从而可以找到方程组的基态解而有别于单个方程时的基态解.     

巧用消元法 妙解方程组

解一次方程组的基本方法是代入消元法与加减消元法.在解方程组时,若能根据方程组的结构特征,巧妙应用这两种方法,则能化难为易,迅速求解,达到事半功倍的效果.下面以九     

解Maxwell--Dirac方程组的守恒差分格式

提出了一种解Maxwell—Dirac（MD）方程组的守恒数值格式．第一部分将Minkowski空间中一维MD方程组转化为只包含两个无量纲变量的模型．然后介绍时间分裂法的思想,并且将其应用到转化后的模型．第三部分对MD方程组分裂后的两部分分别应用有限差分方法求解．此数值格式在时间方向是一阶精度,在空间方向是二阶精度的,并且得到守恒性等性质．最后应用实例验证数值格式的精度及守恒性等性质．     

Schrdinger方程组的最小能量驻波解

Schrdinger方程组出现在许多数学物理模型中。文章主要研究这种方程组基态解的存在性,独特之处在于使用新的方法证明了:当给定方程组中作用参数的适当范围后,"相应函数"的下确界比单个方程时该函数的下确界要小,从而可以找到方程组的基态解而有别于单个方程时的基态解。     

轮换方程组解法例谈

所谓轮换方程组是指如果一个方程组中的所有字母按某种次序轮换后,得到的方程组与原方程组相同.这类方程组解法灵活多样,技巧性强,学生难于掌握,现择几例介绍几种常用解法供同学们学习借鉴.     

辅助方程构造耦合KdV方程组的精确解

通过辅助方程和函数相结合的一种方法,并借助符号计算系统Mathematica求解了耦合KdV方程组的类Jacobi椭圆函数精确解以及退化后的类孤波解.     

特殊方程组的特殊解法

有些二元一次方程组有特殊的结构,若选择适当的方法,可以使这些方程组的求解变得简单易行.一、可整体换元的方程组的解法例1解方程组3(x+y)-4(x-y)=1,x+y2+x-6y=1.分析从形式上看,这个方程组比较复杂,应先将每一个方程都进行化简,化成二元一次方程组的一般形式,然后再选择代入法或加减法来求解.但是,通过观察可以发现,方程组中两个未知数出现的形式只有(x+y)     

简析麦克斯韦方程组在物理学中的地位

麦克斯韦方程组的产生和对电磁波的预言推动了物理学的发展,完善了电磁学理论,确立了电荷、电流与电场、磁场之间的普遍联系,揭示了电磁现象的基本属性.本文利用麦克斯韦方程组推证了库仑定律、法拉第电磁感应定律等十个电磁学理论的基本原理和基本规律,说明了麦克斯韦方程组是物理学的基础,是电磁学理论的高度浓缩,论证了它在物理学中的核心地位,全面说明了麦克斯韦方程组的意义.     

方程组的整体解法

灵活运用整体思维方法来解方程组，能够化繁为简，快速准确地求出方程组的解。本现主要以义务教育教材《代数》第一册(下)中的习题和竞赛题为例，介绍几种方程组的整体解法，供同学们学习时参考。     

二阶方程组特征值边值问题的正解

利用锥上的不动点指数定理研究了一类二阶方程组特征值边值问题正解的存在性,在λ充分小,f与g满足更广泛的条件下得到了两个正解,推广和改进了原有的结果.     

李雅普诺夫方程的推广

定义了能控性矩阵及能观性矩阵,利用矩阵方程讨论了推广的李雅普诺夫方程的解的存在及唯一性.     

Fun with differential equations

You are familiar, from high school, with the trigonometric functions sin x and cos x. We shall discuss these functions starting from the differential equations that describe these functions.     

Simple equations in physics

Experience shows that many pupils find difficulty with quantitative aspects of physics. While the truth of this statement appears self evident, it nevertheless fails to indicate anything other than a most diffuse approach to improving the situation, e.g., to be more successful in developing pupils’ mathematical ability.

The role of mathematics in enhancing, supporting or limiting progress in learning physics is a complex one. However, some specificity is required if epistemological and pedagogical changes are sought to reduce learning difficulties. This is not easy to achieve.

In the present paper performance on a number of assessment items used by the Assessment of Performance Unit (APU) is presented to explore one aspect of the relationship between ability in mathematics and learning in physics. The evidence presented suggests that this aspect, namely using expressions of the type a = b/c, need not in itself be a limiting factor.     

麦克斯韦方程组形式的讨论

提出了麦克斯韦方程组的一种新的构建形式,突出了电荷守恒定律.     

破产分布及其方程

In this paper, the ruin distributions were analyzed, Including the distribution of surplus immediately before ruin, the distribution of claim at the time of ruin, the distribution of deficit, and the distribution of surplus at the beginning of the claim period before ruin. Several Integral equations for the ruin distributions were derived and some solutions under special conditions were obtained.     

麦克斯韦方程组形式的讨论

提出了麦克斯韦方程组的一种新的构建形式，突出了电荷守恒定律。     

逻辑方程求解初步

本文通过研究逻辑变量之间的函数关系,利用分解定理和函数最小项展开式理论,总结出求解逻辑方程的一般方法。     

Learning from equations or words

A series of four experiments was designed to study the cognitive load consequences of learning from equations, as compared to words. Cognitive load theory suggests that some instructional procedures require learners to engage in cognitive activities solely because of the manner in which information is presented rather than because of intrinsic characteristics of the material. As a consequence, a heavy extraneous cognitive load that interferes with learning may be imposed. It is suggested that in studying equations with unfamiliar notations, a heavy extraneous cognitive load is generated because mental integration of notations and meanings is required. The results of Experiment 1 supported this suggestion. Experiment 2 found that when an equation format involves simple equations and familiar notations, it is more effective than an equivalent verbal format which requires substantial reading. Experiment 3 showed that when the use of notations becomes automated after extended practice and thus reduces the extraneous cognitive load required to mentally integrate notations and meanings, an equation format can be more effective than a verbal format. Experiment 4 indicated that supplementing a concise equation format with extensive verbal information does not assist learning, because processing the extensive verbal information induces a heavy cognitive load which creates redundancy effects. It was concluded that the efficacy of equations or words may depend, in part, on their cognitive load consequences.     

The Embedding Method for Nonsmooth Equations

1IntroductionTherehavebeenmailystudiesonnonsllloothequatiollsl"'"]F(x)=0,FiD=R"-R",((l.l)butfewauthorsusedembedding1lletllodtosolve'theequations(1.l).In1990,S.M.RobinsonstudiedthenonsnlootllembeddingmethodforaclassofBdifferentiableequationsill[51.WhenFiss…     

Helmhoz方程的Legendre展开方法

A spectral method based on the Legendre polynomials for solving Helmholz equations was proposed. With an explicit formula for the Legendre polynomials in terms of arbitrary order of their derivatives, the successive integration of the Legendre polynomials was represented by the Legendre polynomials. Then the method was formulized for secondorder differential equations in one dimension and two dimensions. Numerical results indicate that the suggested method is significantly accurate and in satisfactory agreement with the exact solution.