函数

Liouville"s Theorem on entire functions is proposed as a proving method for theta function identities. Several identities are exemplified, such as the quintuple and septuple product identities; four symmetric difference identities related to the Ramanujan"s congruence modulo 11 on the partition function; as well as two theta function identities on the Rogers-Ramanujan functions G and H.

作者提出利用Liouville定理作为证明theta函数恒等式的基本方法，并以Watson五重积，Hirschhorn七重积恒等式，四个与分拆函数中Ramanujan的模11同余有关的对称差恒等式，以及两个与Rogers-Ramanujan函数G，H有关的theta函数恒等式为范例，论证这种方法的有效性。

In Chapter 4, we give a new proof of the local Lipschitz continuity of H-convex functions on the Heisenberg group. For a Carnot group of step two, we obtain a characterization of H-convex functions and prove that H-convex functions are locally Lipschitz continuous.

第四章，我们导出了Heisenberg群上H-凸函数的Lipschitz连续性的一个新证明，对于二阶Carnot群，我们给出了H-凸函数的一个特征并证明了Carnot群上H-凸函数是局部Lipschitz连续函数。

Field data of pedestrian flow was collected in Chinese comprehensive passenger transport terminal—Xizhimen underground station using video recording, and then selected and analyzed by statistic analysis software SPSS. Parameters relation models for pedestrian flow on different terminal facilities were established based on data statistics. The results show that the pedestrian flow-density relation model is quadratic equation in corridor; the flow-space relation model is quadratic equation when space is below a certain value and is logarithmic equation when space is above the value; the speed-density relation model is linear equation. The models on stairs show the similar characteristics, but the eigenvalue is different.

对国内综合交通客运枢纽——北京西直门地铁站行人流数据进行视频采集，采用统计分析软件SPSS对行人流参数数据进行筛选及拟合分析，建立了不同设施的行人流参数关系曲线及函数模型，研究结果表明，水平通道处行人流量与密度呈二次函数关系、流量与空间在某一临界点两侧分别呈二次函数及对数函数关系、速度与密度呈线性关系，楼梯处与之相似但特征点数值存在差异。

In this paper employing periodic function of complex function, a power function and a logarithmic function were constructed to obtain Principle Quantum Number , Angular Quantum Number , Magnetic Quantum Number , Spin Quantum Number and the relations between them.

利用复变函数中周期函数结构，构造了一个幂函数和一个对数函数。给出了电子的主量子数、角量子数、磁量子数和自旋量子数，以及它们之间的关系。

To generalize convex functions, Zalinescu introduced the concepts of uniformly convex functions in 1983, and discussed some properties for them;under the conditions of upper semicontinuity and lower semicontinuity, some equivalent conditions were given by Yang in 1998, so that criteria for uniformly convex functions are simplified.

作为对凸函数的推广，1983年Zalinescu提出了一致凸函数的概念，并讨论了它们的一些性质特点；1998年Yang在上半连续和下半连续条件下给出了一致凸函数的一些等价条件，简化了一致凸性函数类的判别条件。

For the joint density function of 2-D continuous random variables, a new function can be obtained by upper limit-variable integral, and then, by normalization of the new function according to the property of density functions, a general marginal density function was constructed.

对二维连续型随机变量的联合密度函数，在一定要求下变上限积分得到新函数，依据密度函数性质进行规范化，从而构造出一个广义的边缘密度函数。

This paper describes the application of a quadratic function, namely : the use of quadratic function for Inequality, discuss other monotone function with the most value, the real roots distribution, series of comprehensive, quadratic function embodied in the high school math widely used.

本文主要介绍二次函数的应用，即：利用二次函数解不等式，讨论其他函数的单调性与最值、实根分布，数列中的应用等综合问题，体现了二次函数在高中数学中的广泛应用。

Using the quartic rational spline function, we can construct a net of feature curves passing through the four corner points P_ which situate at the rows (U-direction) and columns (V-direction) of a m×n rectangular control mesh.

本文构造了3／1型插值有理样条即分子、分母分别为三次、一次多项式的插值函数，该样条函数不仅可通过导数参数的选取，使得插值函数保单调，还可使得插值函数保凸。

The function δ is introduced according to the property of the large forward scattering coefficient of the scattering particles in bad weather and the decomposition for phase function is normalized.

根据恶劣天气中散射粒子的前向散射系数大的特点，引入δ函数，将相函数进行归一化分解；把得到的简化点扩散函数作为大气的退化函数，与退化图像一起进行频域复原滤波。

Productive expansion curve is the orbit of equilibrium point's variation in optimum factor combination caused by expanding firm's produce scale when not changing the price of produce factors.

文章在Cobb-Dauglas生产函数的基础上，推导出扩展线的参数方程，并得到成本支出与产量之间的一个函数关系，用以分析规模报酬的情况。1 Cobb-Dauglas生产函数Cobb-Dauglas生产函数是由数学家柯布和经济学家道格拉斯于上世纪30年代初一起提出来的。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。