函数

By substituting stream function into differential equation, its validity is proved in mathematics and the analytical expression of helical solitary vortex function is also obtained.

将获得的流函数回代到涡与流函数微分方程中，在数学上验证了这些流函数解的正确性。

Moreover, we get the sufficient and necessary condition of in Orlicz spaces.Chapter 3 Extreme points and strongly extreme points in Orlicz spaces equipped with the generalized Orlicz norm: In this paper, the conceptions of the generalized Orlicz norm and the generalized Luxemburg norm are introduced, and the criteria of extreme points and strongly extreme points of Orlicz function spaces equipped with the generalized Orlicz norm are obtained. Moreover, criteria of space strictly convex and mid-point locally uniform convex are given.

第三章 赋广义Orlicz范数的Orlicz函数空间的端点和强端点：本章在Orlicz空间推广了Orlicz范数和Luxemburg范数，引入了广义Orlicz范数和广义Luxemburg范数的定义，并给出了赋广义Orlicz范数的Orlicz函数空间的端点和强端点的判据，进而得到了赋广义Orlicz范数的Orlicz函数空间严格凸和中点局部一致凸的充要条件。

Convex analysis part will study convex set, convex function and its subdifferential, Lipschitz function and its G-subdifferential in infinitive dimension.

第一，凸分析部分，包括无限维空间的凸集、凸函数和凸映射，凸函数的次微分，Lipschitz函数的G-次微分。

In the POPF model, wind farm is modeled by the probabilistic wind farm model considering the reactive power-slip characteristic, and the inequality constraints include not only the unit output constraints, the ratio constraints, the voltage constraints and the line current constraints but also the reactive compensation capacity constraints in wind farm and the system climbing capacity constraints per minute. By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth Newton-type method based on the subdifferential.

概率最优潮流模型中，风电场采用考虑无功功率—滑加热器差特性的风电概率模型，不等式约束中除了机组出力约束、有载调压变压器变比约束、电压约束和支路电流约束，也考虑了风电场无功补偿容量约束、系统的分钟级爬坡能力约束；使用非线性互补函数将概率最优潮流的KKT条件转化为一组包含有不光滑函数的非线性代数方程组，然后基于一次二阶矩法确定了以待求量的数字特征表示的POPF模型，由于该模型包含不光滑函数，因此采用基于次微分的半光滑牛顿型方加热器法求解。

This thesis will be expanded from two aspects: first, delta-sequence obtained by cubic spline interpolation cardinal function showed the properties of symmetry, Riesz basis and interpolation. Non linear convection diffusion equation (Burgers′equation) was used as an example. Then we modified this delta-sequence to improve the attenuation, the same example was used in numerical application.

在小波方法与PDE算法相结合方面，本文主要从两方面入手：首先是以样条插值基函数为基础构造δ-序列核，以非线性对流扩散方程为例给出了一种数值算法；进而对三次样条插值基函数进行改进，构造新的具有更快衰减性质的δ-序列核，同样以非线性对流扩散方程为例验证了新函数在数值求解中的有效性。

In the even-odd method, according to the symmetry properties of odd and even functions, the function to describe the surface distribution of a flat is decomposed to four components: even-odd odd-even even-even and odd-odd functions, the absolute distribution of three flats are obtained by solving every component.

奇偶函数法根据函数的奇偶特性，将平面面形函数分解为：偶奇、奇偶、偶偶和奇奇函数，再分别求出各项，从而得到三个平面的绝对面形。

We transforms the special linear system of strict inequalities into three kinds of minimax problems, and then solves it with the aggregate function method assisted with some corresponding method. At last the numerical experiment is done under the environment of matlab.

我们将其转化为三种形式的Minimax问题，对转化后的三种Minimax问题，用凝聚函数法分别将其目标函数光滑化，并分别用带Armijo不精确线搜索的最速下降法、带自适应参数修正的凝聚函数法以及既约梯度法来求解。

The derivative of a function can be interpreted either as a function whose value at x is equal to the gradient of the tangent line to the graph of y=f at x, or, alternatively, as a function that describes the instantaneous rate of change of y with respect to x at the point x.

一个函数的导数可以理解为一个函数的值无论是在x是等于切线的梯度的y图二F在x，或者，或者，作为一个函数描述瞬时速度y的变化的关于x的点x在f关于x的也可以表示为导数

If virtual functions are used, the function pointer points to a two-instruction 'thunk' to determine the actual function to be called.

如果使用虚函数，函数指针指向两个指令'thunk的'以确定实际的函数被调用。

The transformation of function plays an important role in high school mathematics textbooks.

函数图像的变换，其实质是用图像形式表示的一个函数变化到另一个函数。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。