查询词典 mathematical analysis

Composite function is one of the important objects of mathematical analysis research,and some of it's analysis natures such as monotony, boundedness, limit,continuity, derivability,integrability are important content in the mathematical analysis,they are also important tool to study other objects in mathematics.

复合函数是数学分析研究的重要对象之一，它的一些分析性质（如单调性，有界性，极限，连续性，可导，可积性）是数学分析中的重要内容，也是研究数学中其它对象的重要工具。

In the light of the complex, high-level and non-linear feature of the mathematical model which describe the transport of the coalbed methane, this paper study the fully-implicit solving method of the mathematical model in detail. Based on the complexity of the algebraic equations which are formed eventually, according to the alternating direction implicit difference pattern, this paper use the iterative method and the fully main element Gauss-Jordan eliminating method to solve equations, which is to use the iterative method to determine coefficient matrix and use the fully main element Gauss-Jordan method to solve th linear algebraic equation group, at the same time of studying the solving method of the mathematical model, according to the devising requirement of FORTRAN77 program structure, this paper draw up computer program and form the corresponding computer model, and verify the validity and reliability of the model in theory by operating the model.

重点研究了模型内、外边界及有关参数的处理，针对描述煤层甲烷运移的数学模型是一个复杂、高阶非线性数学模型的特点，详细研究了模型的全隐式求解方法，根据最后形成的代数方程组的复杂性，按交替方向隐式差分格式，采用迭代与全选主元高斯约当消去法相结合的方法求解方程：即确定系数矩阵采用迭代法，求解线性方程组时采用全选主元高斯约当消去法，在研究模型解法的同时按FORTRAN结构化程序设计的要求，编制计算机程序，形成相应的CBMRS计算机模型，并通过模型的运行从理论上证明了模型的正确性与可靠性。

Mathematics: Understands and applies basic and advanced properties of the concepts of geometry; Use the Pythagorean theorem and its converse and properties of special right triangles to solve mathematical and real-world problems; Understands the basic concepts of right triangle trigonometry (e.g., basic trigonometric ratios such as sine, cosine, and tangent); Uses trigonometric ratio methods to solve mathematical and real-world problems (e.g., determination of the angle of depression between two markers on a contour map with different elevations); Uses properties of and relationships among figures to solve mathematical and real-world problems e.g., uses the property that the sum of the angles in a quadrilateral is equal to 360 degrees to square up the frame for a building; uses understanding of arc, chord, tangents, and properties of circles to determine the radius given a circular edge of a circle without the center

数学：理解和应用几何概念的初级和高级特性；用毕德哥拉斯定理、逆定理以及特殊直角三角形性质解决数学的和现实世界的问题；理解基本的直角三角形三角比；运用三角比方法解决数学的或现实的问题。（等高线图上的两个标记之间的俯角确定）运用形体之间的关系及其属性解决数学的或现实的问题（利用四边形内角和等于360度来为建筑物框架取正，运用弧，弦，切线和圆的性质确定缺少中心的一段圆弧的圆心

IGMs are a kind of experimentally new-identified optical mode, standing with apparent potential in design and application. However, the mathematical expression of IGMs under Elliptic Cylindrical coordinates, preventing us from understanding IGMs instinctively, stands a formidable challenge in application. The pure mathematical expressions of IGMs are composed by a great deal of calculation, which also bids us no help in common use. I am, therefore, prompted to build an easier mathematical approach in this study.

Ince- Gaussian modes为在实验中可见的一种崭新型态的光学模态，对於我们在应用和设计上的实现，拥有许多潜力；然而，由於IGMs是在椭圆圆柱座标系下的数学来表示，造成了我们无法直觉的去了解，也成了我们在使用上的一大考验； IGMs的不易亲近，也让我们无从进一步去了解其物理特性，若纯粹以数学出发，又包含了庞大的运算，无法达到普遍的运用，是故我希望能在这篇论文使用简单的数学描述来达成对IGMs较平易近人的理解。

According to the problems that are encountered in designing the mathematical knowledge representation language in NKI (national knowledge infrastructure) and after the discussion of ontological assumptions for mathematical objects, two kinds of formalisms for the representation of mathematical knowledge are provided. One is a description logic in which the range of an attribute can be a formula in some logical language; and another is a first order logic in which an ontology represented by the description logic is a part of the logical language.

根据在设计NKI(national knowledge infrastructure)的数学知识表示语言中遇到的问题，并在讨论了数学对象的本体论假设的基础上提出了两种数学知识的表示方法：一种是以一个逻辑语言上的公式为属性值域的描述逻辑；另一种是以描述逻辑描述的本体为逻辑语言的一部分的一阶逻辑。

The basic spirit of Pythagoreanism is the pursuit of the mathematical harmoniousness of the universe, and it can guide scientists to characterize the internal mystery of the physical world in terms of mathematical language and mathematical formula successfully and it fit to the current computationalism.

毕达哥拉斯主义的基本精神，正是追求宇宙的数学和谐性的思想，它能成功地引导科学家使用数学语言、公式来刻画物理世界的内在奥秘，这是与当今流行的"计算主义"相互呼应的。

For single-layer fabric, weaves are re-grouped for the purpose of mathematical description, and they fall into three groups: regular weaves, pre-regular weaves and irregular weaves. And then the mathematical models of every group are established, the parameters and the qualifications of weaves automatic generation are offered too. For multi-layer fabric, Kronecker product and yarn grouping of different layers according to the arrangement ratio are combined together to explore the mathematical model of weaves automatic generation. The qualifications of forming the multi-layer weaves are also discussed.

对单系统织物组织类别，首先根据数学描绘的需要进行了重新划分，分为规则组织、准规则组织和非规则组织，接着分别建立了各种类别组织的数学模型，并对组织自动生成的参数和组织构成条件进行了归纳和总结；对于多系统组织的重组织和层组织，结合不同系统纱线按排列比的分组法和矩阵的Kronecker叉积运算建立了组织结构矩阵自动生成的数学模型，并对多系统组织构成条件的数学模型进行了分析。

The paper analyses material transportation problem and give the solvable methods; analyses delivery vehicle route problem, and then construct its corresponding mathematical model and present a heuristic algorithm based on C—W algorithm; analyses the optimum scheduling problem of trucks, and then construct its corresponding mathematical model and put forward a new algorithm; analyses the Postal Transportation Problem which will perhaps be used in supply chain of manufacturing system, and then construct its corresponding mathematical model and present an approximation algorithm.

分析了制造系统供应链中供需平衡、供需不平衡、有转运等各种情况下的物资调运问题，给出了求解方法；分析了制造系统供应链配送作业中的配送车辆路线问题，建立了相应的数学模型，提出了一种基于C-W算法的启发式算法，该算法较好地解决了有时间约束的配送问题；分析了制造系统供应链中的货运卡车优化调度问题，建立了相应的数学模型，提出了一种基于表上作业法的求解算法；分析了制造系统供应链中有潜在利用价值的邮政运输方式问题，在详细描述了该问题的基础上，建立了相应的数学模型，提出了一种近似求解算法，该算法较好地解决了邮政运输方式这样的多种物流、多种运输方式，有严格时限和众多外部约束的特大型、复杂、并行的交连系统的计划调度问题。

Mathematical model 3.7, 3.16 and 3.30 are the mathematical model of a equilibrium population, and they can be converted into mathematical models of panmixia population and nonequilibrium selfing population.

它可以转换为随机交配群体的数学模型和非平衡自交群体的数学模型。

First introduced highway alignment's definition, the significance, the developing process and the CASIO series calculator in the highway surveying computation application; Using the traverse survey computation's two basic mathematical model (azimuth calculation, coordinate calculation), compile the corresponding procedure to solve echo the wire coordinate computation; With the aid in the mathematical model which three, four and so on leveling's field operations calculate, compiles the corresponding procedure to solve the road elevation survey computation; According to relaxes the circular curve principal point and the detail coordinate computation mathematical model, based on this programs the solution to relax the circular curve coordinate principal point and the detail coordinate computation, then further develops this procedure to use to calculate the circular curve principal point and the detail coordinate computation.

首先介绍了公路线路的定义、意义、发展过程和CASIO 系列计算器在公路测量计算的应用；利用导线测量计算的两种基本数学模型，编写相应的程序以解决附和导线坐标计算；借助于三、四等水准测量的外业计算的数学模型，编写相应的程序以解决公路高程测量的计算；根据缓和圆曲线主点及细部点的坐标计算的数学模型，在此基础上编程解决缓和圆曲线坐标主点及细部点坐标的计算，然后进一步开发此程序用以计算圆曲线主点及细部点的坐标计算。

Salt is good, but if the salt becomes flat and tasteless, with what do you season it?

14：33 盐本是好的，盐若失了味，可用什么叫它再咸呢？

He reiterated that the PLA is an army of the people under the leadership of the Communist Party of China.

他重申，人民解放军是在中国共产党领导下的人民军队。