条件极小

Moreover, With assumption of symmetry on the domain, we show the effect of the domain topology on the number of minimal nodal solutions and give a characteristic of the number of solutions.

进一步，在假设区域具有某种对称性的条件下，研究对称性对极小变号解个数的影响，并给出解的数量的刻画。

Given a finite training sample set, according to the proposal of establishing a Local Most Entropy probability density function to estimate the number of cluster a method for estimating 〓 is proposed, where a complicated method based on Maximum Likelihood Cross-Validation is replaced by Chebyshev inequality.

为改善BP算法的收敛速度慢、易陷入局部最小的问题，提出了带一类非线性特性动量项的变步长BP算法，构造了一个能自适应升降温的动量项非线性强度函数，在编程中又采用了有条件引入非线性特性动量项的措施，大大提高了搜索过程跳出局部极小、快速稳定收敛的能力。

So before applying Mather's theorem of connecting orbits to concrete Hamiltonian system, we have to check whether the set W〓 is empty or not, and which cohomology classes are C-equivalent. In present paper, by investigating the topological structure of action minimizing sets near a co-dimensional one torus which is preserved under generic perturbations and becomes hyperbolic in nearly integrable Hamiltonian system.

与传统的Poincaré-Melnikov方法相比，我们方法明显优越之处在于，一方面我们的方法不仅可以得到双曲环面之间的异宿轨道，而且当该环面附近的其它环面破裂时，可以得到不同Mather集之间的连接轨道，另一方面，我们把异宿轨的存在性的证明转化为双曲环面极小同宿轨的某种弱孤立性的证明，所需条件比Poincaré-Melnikov方法弱得多。

The compound pendulum of alterable centroid has extremum of period which can be searched for by the golden section method and the Fibonacci method under laboratory condition.

钟摆式复摆的质心可以变化，因此具有极小周期点位置，在实验室条件下，这个极值点可以采用黄金分割法和Fibonacci法来搜索。

Thereinto the concavity and convexity of functions is important condition in minimax theory.

其中函数的凹凸性是极大极小定理的重要条件。

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。

We can costruct an exterior n-form ξ for every hypersurface M in Euclidean space Rn+1. The submanifold M is minimal if and only if is closed (dξ= 0), then ξ is calibration and M is ξ-submanifold.

我们证明了对于欧氏空间R~(n+1)中每一超曲面M，可以构造η-微分式ζ，而超曲面极小的条件恰是ζ为闭形式，即dζ=0的条件。

In order to study vector-valued optimization problem, in chapter 5, a class of vector -valued function, that is, uniformly same-order set-valued function is introduced , which includes the separated functions as its proper subset; without hypothesis of convexity, new minimax theorem and saddle point theorem for uniformly same-order set-valued function are established. Next, by employing Ky Fan\'s lemma and H-KKM mapping , several existence results for generalized vector equilibrium problem established.

为了研究向量优化问题，作为可分函数的推广，第五章引入了一致同阶集值函数类，在没有凸性条件的假设下，对一致同阶集值函数建立了新的极小极大定理与鞍点存在定理；利用H-KKM映射，对一般向量均衡问题建立了(来源：A73BcbC论文网www.abclunwen.com)几个存在性定理；最后讨论了集值向量均衡问题系统，利用集值映射的拟凸性，在较弱的条件下证明了解的存在性。

In this paper,some characterizations of solutions for a system of vector variational inequalities are derived under the a.

该文研究了一类向量变分不等式组，在PPM条件下，对其解进行了一些刻画此外，给出了该向量变分不等式组的一个间隙函数，并在强单调条件下，证明了它是弱尖极小的。

In this paper, some characterizations of solutions for a system of vector variational inequalities are derived under the assumption of PPM (where F and-F are both pseudomonotone). Moreover, a gap function for this system of vector variational inequalities is suggested and proved to be weak sharp minima under strong monotonicity.

该文研究了一类向量变分不等式组，在PPM条件下，对其解进行了一些刻画此外，给出了该向量变分不等式组的一个间隙函数，并在强单调条件下，证明了它是弱尖极小的。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷