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The chapter 3 investigates the constructive method which means that many combinatorial numbers, such as Stirling number, Bell number, harmonic number, Fibonacci number and the number of derangement, are represented to moments of some random variables. This method is used in the computation of combinatorial sums, discovery and proof of combinatorial identities.

第三章研究了构造性概率方法，即一些常见组合变量(以后统称组合数为组合变量)的概率表示，诸如Stirling数、Bell数、调和数、Fibonacci数、错排数都可以表示为一些随机变量的矩，这些概率表示可以用来研究组合和式的计算与恒等式的证明。

Key phrases are phrase that have strong text representation function, can characterize text content such as subject and kind.

关键短语是具有强文本表示功能的特征短语，在表示文本时，能将文本的内容特征鲜明地表示出来。

Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaus- sian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival prob- ability, and detection probability are all Gaussian sums.

分析的结果表明，当初始的先验强度满足高斯或者可以表示成高斯和的形式时，通过将状态噪声、观测噪声、目标的繁衍、新目标的产生、目标的存活概率和检测概率表示成高斯和的形式，之后每个时刻的后验强度均能表示成高斯和形式。

In this study, a new classification method of tolerances according to semantics and mathematical representation of basic geometric elements based on DOF is given. The representation of tolerance semantics is systematically deduced based on its mathematical definition that can characterize the semantics exactly an...

给出了基于语义的几何公差分类方法及基于自由度变动的基本几何要素数学表示方法；基于公差的数学定义，系统地推导了各种类型公差的三维语义表示方法，准确完整地表示出了其语义；最后给出实例进行应用分析

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

Rational fraction, rational base function and homogeneous coordinate.

NURBS曲线方程具有三种等价形式：有理分式表示、有理基函数表示和齐次坐标表示。

Because it is easier to implement, the calculator will use reverse Polish notation instead of infix. Reverse Polish notation is used by some pocket calculators, and in languages like Forth and Postscript.

为了更容易实现，我们在计算器中使用逆波兰表示法代替普通的中缀表示法(逆波兰表示法用在某些袖珍计算器中，Forth与Postscript等语言也使用了逆波兰表不法)。

Since representation of the subclass object starts out like the representation of a superclass object, the circle can always pretend to be a point — at the initial address of the circle's representation there really is a point's representation.

因为子类的表示开始于一个非常像其父类的结构，所以圆可以把自己伪装成一个点——圆的物理表示的地址的前面部分就是一个点的表示。

It solves the problem that the time of solving a problem is the power function of the number of rules. Usually, it is difficult to intellectualize a hydraulic component CAD softerware.

提出了与通常知识表示方法"如果-那么"不同的改进型知识表示方法，即："大前提-如果-那么"的知识表示方法，从而解决了求解问题的时间与规则数成指数型增长的问题。

L,the SCHENECTADY COUNTY CLERK ,Clerk of the County of Schenectady ,and also Clerk of the Supreme and County Courts ,being Courts of Record held therein,do hereby certify that michoc'J Love whose name is subscribed to the Certificate of acknowledgment or proof of the annexed instrument ,and thereon written ,or whose name is subscribed to the annexed instrument ,and thereon written ,or whose name is subscribed to the annexed jurat,,was at the time of taking such acknowledgment,or proof,or of administering such oath oraffirmation ,a Notary Public –commissioner of Deeds in and for said County ,residing therein ,duly commis-sioned and sword and authorized by the laws of the State of Now York to take the acknowledgments an sworn and proofs of deeds of conveyances ,for land,tenements,or heredita-ments and to administer oaths or affirmations in said County ,And further,that I am well acquainted with the handwriting of said officer and verily believe that the signature to said jurat or certificate of acknowledgement or proof is genuine

l时， schenectady县秘书，秘书的县schenectady ，也是秘书的最高人民法院和县法院，法院的纪录，因此，特此证明michoc'j爱他的名字是订阅了该证书的确认或证明对所附文书，并就此写，或他的名字是认购所附文书，并就此写，或他的名字是认购所附朱拉特，，当时的考虑，如确认，或工作证明，或管理这类宣誓oraffirmation ，公证机构-专员的事迹，并表示，县，居住的地方，适当处长sioned和剑，并授权由该州的法律制定的，现在纽约采取认知，一种宣誓和实证的事迹运输工具，为土地，物业单位，或heredita 1912年和管理宣誓或誓词中说，县，并进一步，我熟悉的笔迹的表示，官に相信签字，以表示，朱拉特或证书的确认或证明是真实的

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。