函数元素

The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

They are derived from the corresponding components of struct Class by simply removing one indirection from the declarator.

Here is the application：前两个原型声明选择函数，它们从Class结构体中对应的元素中通过简单地从声明函数中去掉一次间接而派生出。以下是应用

The first two prototypes declare selectors. They are derived from the corresponding components of struct Class by simply removing one indirection from the declarator.

前两个原型声明选择函数，它们从Class结构体中对应的元素中通过简单地从声明函数中去掉一次间接而派生出。

The matrix =( xi, xjp having the e-th power of the greatest common P-divisorp of xi and xj as its-entry is called the e-th power GCD matrix on S. The matrix = having the e-th power of the least common P-multiple p of xi and xj as its-entry is called the e-th power LCM matrix on 5. We obtained the following results:(1) is nonsingular for any set S;(2) If S is an FC set, then the determined of has formula Det =Jpe(x1)...Jpe, where the function Jpe is the generalized Jordan totient function;(3) A formula of the inverse of is given when S is an FC set;(4) If S is an FC set, then |.

以_P的e次方为第i行j列元素的矩阵称为定义在S上的e次幂GCD矩阵，记为；以_P的e次方为第i行j列元素的矩阵称为S上的e次幂LCM矩阵，记为，我们得到了如下结果：①定义在集合S上的e次幂GCD矩阵是非奇异的；②若S是R上的FC集，则S上的e次幂GCD矩阵的行列式Det=J_p~e(x_1)J_P~e(x_2)…，J_p~e，其中J_p~e为R上的Jordan函数；③当S为FC集时，得到了的逆矩阵~-1的表达式；④证明了当S是FC集时，整除，即等于与R上另一个矩阵的乘积。

Furthermore, certain member functions of the container create a temporary copy of one or more elements, thereby nullifying them.

此外，容器的某些特定成员函数也会一个或列多元素的临时副本，从而使这些元素失效。

If drop finds its element in the set, it decrements the element's reference count and the number of elements in the set.

如果drop函数在集合中发现了其参数所指向的元素，便将该元素的引用计数器和集合的计数器减一。

If drop finds its element in the set, it decrements the element's reference count and the number of elements in the set.

如果drop函数在集合中发现了其参数所指向的元素，便将该元素的引用计数和集合元素数减一。

If drop finds its element in the set, it decrements the element's reference count and the number of elements in the set.

如果drop函数在集合中发现了其参数所指向的元素，便将该元素的引用计数器和集合元素数减一。

The meshfree method has the advantage over the finite element method on constructing shape function without predefining meshes.

无网格法为近十几年来逐渐日趋成熟的演算法，相较於传统的有限元素法，其具有不需使用网格建立形状函数之特点，让无网格法摆脱有限元素法在处理某些问题遭遇到的限制。

The results show that the variograms of As, Cd, Pb and Zn exhibit anisotropy, which possibly is controlled by the distribution of ore deposits; Hg behaves strong nugget effect, which is influenced by smallscale factors, and the further study should increase the sample density.

结果表明，As、Cd、Pb、Zn元素的变异函数表现为各向异性，其方向性可能主要受矿床分布控制；Hg元素块金效应较大，表明其受小尺度因子影响较大，其进一步分析须增加采样密度。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。