函数常数

In this Paper, the author proved the theorem: Let fbe an nonconstant periodic function of exponential type and positive lower order , and g be an entire function of finite order If g is permutable with f, then g≡for gz

本文证明了如下定理：设 f为非常数指数型周期函数，且具有正下级，g为有穷级整函数。若 f与g可交换，则 g≡ f或 g≡ z

To overcome the false result with piecewise constant regions produced by the binary zero-crossing decision process, a hyperbolic tangent function is used to substitute the symbol function, governing softly the varieties of gray levels of pixels beside the zero-crossing of edges.

为了克服二值的零交叉决策过程导致的虚假的分片常数图像，利用双曲正切函数代替符号函数，柔和地控制边缘的零交叉点两侧像素的灰度值变化。

Current tuning is introduced, and the speed open-loop transfer function is established based on current closed-loop. A mathematical inequation about the speed open-loop transfer function is deduced, then the measured amplitude-frequency data is introduced in the inequation, thus the mathematic expressions about moment of inertia and mechanism time constant are obtained.

引入了电流校正环节，建立了基于电流闭环的速度开环传递函数，推导了关于该速度开环传递函数的数学不等式，再将实际测得的幅频特性代入此不等式中，得到了关于转动惯量和机械时间常数的数学表达式。

By introducing special stress functions, we find solutions of eighth order homogeneous linear equation set with complex functions method and approach of undetermined coefficients, deduce calculation formulas of bi-material elastic constants for two dissimilar orthotropic composite materials. The expressions of stress intensity factors near finite interface crack tip subjected to symmetric loadings are derived. A engineering application numerical example is given.

通过引入特殊的应力函数，采用复变函数方法和待定系数法求解了八阶齐次线性方程组，推出了两种相异正交异性复合材料板的双材料弹性常数的计算公式，得到了受对称载荷作用的界面裂纹尖端应力强度因子的计算公式，给出了一个工程应用算例。

For intramolecular electron transfer reactions in solution,the fluctuations of the intramolecular vibrational modes are much faster than that of solvent mode.Thus,the reaction-diffusion equation is commonly used to describe the motion of solvent,with a sink function to treat the vibrational high-frequency mode.Based on this theory-so -called the Sumi-Marcus theory,we proposed an imaginary-time split operator approach to solve the reaction-diffusion equation.The approach is applied to evaluate the intermolecular ET rate between oxazine 1 and N,N-dimethlaniline.By measuring the two average survival times of the donor state probability and the rate constant in long time limit,the full kinetics of the ET is revealed with a variety of sink functions.

对于扩散控制的溶液中的电子转移反应，分子内振动模的运动比溶剂运动快很多，Sumi-Marcus理论提出用反应扩散方程(reaction-diffusion equation)处理溶剂的扩散运动，而分子内的振动用sink函数来表示，我们基于此理论发展了用虚时间分裂算符的方法(imaginary-time Split operator approach)解反应扩散方程，并将其应用于嗪1(oxazine 1，OX1)和N，N-二甲基苯胺分子之间的电子转移反应，Sink函数采用几种不同的微扰表达式，通过计算得到给体几率衰减的两种平均速率和长时间极限下的速率常数，揭示了该体系电子转移过程中的一些动力学性质。

Then, based on the mean curvature, Gaussian curvature and the function of principal curvature, the minimal loci of the principal normal surfaces of curves, the curves with constant Gaussian curvature and the two curves of which the ratio of their functions is constant can all be obtained, as well as the properties of geodesic curve and lumbar curve.

再根据平均曲率、高斯曲率及主曲率函数，能得到曲线的主法线曲面的极小轨迹、常高斯曲率曲线及两个主曲率函数之比为常数的曲线。还给出曲面上测地线和腰曲线的性质。

By means of input - output production function, the Constant Elasticity of Substitution production function of rank two is established in this paper, so it provides a method of assessment on the driving function of construction investment to urban economy, which meets the characteristics of urban construction and overcome the limitation of statistical material.

将CES生产函数应用于城市建设经济分析，推导并建立了用于测定城市建设投资的二级常数替代弹性CES生产函数模型，提供了从数量角度研究城市建设投资对城市经济拉动的方法，反应了城市建设的特殊性，克服了城市建设投资统计资料不健全的缺陷，弥补了以往对城市建设投资规律认识的不足。

An extra force is produced using the piecewise-constant MS model during the segmenting. In each time step, the additional force is added to reinitialize the level set function, advance the speed of the curve evolution. Otherwise, a nonlinear function Ψ is introduced to instead of u+ and u-for edge preserving in MS model.

该方法在分割过程中利用分段常数MS模型产生一种驱动力，在每个时间间隔加入这种驱动力来推动水平集函数的进化，提高曲线演化速度；另外，通过在MS模型中引入一个非线性函数Ψ代替u+和u-实现保边。

Secondly, based on the different structure characteristics and additional conditions, we study several kinds of inverse problems of pseudoparabolic equations. One is a kind of pseudoparabolic inverse problem of identifying a constant coefficient solved by combining the formal solution of the problem and the additional condition properly. The second is the pseudoparabolic inverse problems of identifying an unknown boundary function and an unknown source term solved by using the Riemann function method to get the formal solution of the problem and then using the additional condition to transform the problem into a Volterra integral equation of the second kind. The third is a kind of backward heat flow problem of nonlinear pseudoparabolic equation solved by combining the Riemann function method and the fixed point theory properly.

其次，根据不同模型的结构特点和附加条件，研究了几类伪抛物型方程的反问题：一是利用问题的形式解并结合附加条件，解决了一类伪抛物型方程常数系数的反问题；二是利用Riemann函数方法获得问题的形式解，利用附加条件将问题转化成求解第二类Volterra积分方程问题，解决了一类伪抛物型方程未知边界值的反问题和未知源项的反问题；三是将Riemann函数方法和不动点定理相结合，解决了一类非线性伪抛物型方程的后向热流问题。

In comparison, it is proved that the wave functions occuring in the two formalisms are identical, apart from a constant multiple which represents the scalar product of the wave functions of a bare nucleon and a dressed nucleon.

这个常数倍即是物理核子及裸核子的波函数的内乘积。第二，我们讨论了一般的含有二个h函数的Chew-Low方程的解，方程的形式使它们在实轴上在(1，∞)及(-1，-∞)二段上不连续。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。