查询词典 differentiable function

Applied Green's function, the differential equations will be transformed into the equivalent of integral equations, sufficient conditions for existence and uniqueness of positive solutions for fourth-order nonlinear singular continuous boundary value problems with p-Lapacian operator are obtained.

文中，利用格林函数，将微分方程转化成等价解的积分方程，给出了该奇异非线性四阶p-Lapacian微分方程边值问题的正解的存在及惟一性的一个充要条件。

Then by matching the traction along the branches and the boundary of the strip, Cauchy singular equations were obtained, in which the point dislocation and the distributed dislocation density served as the unknown function.

根据板条边界和裂纹面上的应力边界条件，建立以集中位错强度和分布位错密度为未知函数的Cauchy型奇异积分方程，利用半开型积分法则将该奇异积分方程化为代数方程求解。

Green function is an important tool in the study of boundary value problems of ordinary differential equations.

0引言Green函数是研究非线性常微分方程边值问题的一个重要工具。

First we give the characterization of subsets on which every real-valued convex function bounded above is continuous on the space, and give the βperturbed optimization in Banach space by introducing new locally convex topology.

给出了广义实值凸函数在集合A上有上界则连续的一类子集的特征性刻画；并且通过引入新的局部凸拓扑的方法，给出任意Banach空间的β扰动优化。

First we give the characterization of subsets on which every real-valued convex function bounded above is continuous on the space, and give the fi-perturbed optimization in Banach space by introducing new locally convex topology.

给出了广义实值凸函数在集合A上有上界则连续的一类子集的特征性刻画；并且通过引入新的局部凸拓扑的方法，给出任意Banach空间的β扰动优化。

In chapter four, we prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its excess is bounded by some function of its conjugate radius.

第四章，我们证明了对于Ricci曲率具负下界的完备开Riemannian流形，当其共轭半径有正下界且它的Excess被其共轭半径的某个函数所界定时，它就有有限拓扑型。

FR conjugate gradient methods with perturbations are proposed. The global convergence property of the first method is proved under the condition of main directions' sufficient descent. Whereas, in the proof of the convergence for the other two methods, we only need main directions' descent. Importantly and quite interesting, boundedness conditions such as objective function being bounded below, boundedness of level set are not needed. Chapter 5 presents a version of Dai-Yuan conjugate gradient method with perturbations.

在主方向充分下降的条件下证明了第一个方法的全局收敛性，而后两个方法的收敛性是在主方向下降的条件下证明的，这些收敛性证明的一个共同特征就是不需要目标函数有下界或水平集有界等有界性条件，第5章采用Wolfe或Armijo步长规则提出了带扰动项的Dai-Yuanabbr。

Suppose that f is a real-valued ω〓-lower semicontinuous function defined on a ω〓closed bounded subset A〓 of the dual E〓 of a locally convex space E, which is bounded below on A〓, and suppose every ω〓 closed convex subset of C〓≡ω〓-clcoA〓 is the ω〓closed convex hull of its w〓-β-exposed points.

假设X是一个局部凸空间，X〓是其对偶。A〓是X〓上的ω〓有界闭子集，f是A〓上的ω〓-下半连续实值函数且在A〓上下有界。

We prove that a bounded hyperconvex domain D is Bergman complete if the pluricoinplex Green function is symmetric.

我们证明了若一个有界超凸域的多复变量Green函数是对称的，则其是Bergman完备的。

We prove that a bounded hyperconvex domain D isBergman complete if the pluricomplex Green function is symmetric.

我们证明了若一个有界超凸域的多复变量Green函数是对称的，则其是Bergman完备的。

Alternatively, the con- trollers can use the synchronous rectifier itself or loss- less inductor current-sensing methods to provide overload protection with lower power dissipation.

另外，康威特罗勒斯可以使用同步整流器本身或亏损减少电感电流检测方法，以提供低功耗过载保护。

Mr. Dauber's other Schatz hangs in his home movie studio.

多伯把沙兹的另一件作品挂在家里的电影室。