查询词典 extremum conditions

By the alternative theorem, the optimality conditions of vector extremum problems with generalized inequality constraint are established in linear space.

在线性空间中，定义了广义次似凸映射的概念，并讨论了它的一些性质，建立了此映射的择一定理。

Extremum of the free multi-function method, multi-function conditions for extremum method.

多元函数自由极值的求法，多元函数条件极值的求法。

The optimality conditions of vector extremum problems with generalized inequality constraint are obtained by the theorem in ordered linear topological space.

运用此定理，在序线性拓扑空间中获得了带广义不等式约束的向量极值问题的最优性条件。

Under the G-differentiable ,using the alternative theorem of generalized subconvexlike map and other some conclusions in locally-convex Hausdorff topological spaces, the optimality conditions of vector extremum problems with set constraint are established.

在局部凸Hausdorff拓扑空间中，在G-可微的意义下，运用广义次似凸映射的择一定理和其他一些结论，建立了带集合约束的向量极值问题的最优性条件。

The sufficient conditions for guaranteeing the permanence of the system and the existence and uniqueness of periodic solution having globally asymptotical stability are obtained by using the extremum principle,fixed point theorem and V function method s together.

讨论一类具 Holling 类功能反应和放养的捕食链非自治扩散系统，应用极值原理和不动点定理及 V函数法，得到该系统的一致持久性以及存在唯一全局渐近稳定周期解的充分条件。

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

Applying the theorem of alternative of subconvexlike map and other some conclusions, the optimality conditions represented by gradient for the vector extremum problems with generalized inequality constraint are obtained.

在线性拓扑空间中，引入了G-可微函数的梯度的概念，运用次似凸映射的择一定理和其他一些结论，获得了带广义不等式约束的向量极值问题的一种含有梯度的最优性条件。

By the time of its fall, most of the prisoners were writers who had written against the corruptions of the government.

到它被攻陷的时候，里面多数的犯人是写了反对政府贪污文章的作家。

The most obvious variation to ovum morphological character was that the color was changed from light green to sepiaceous in embryonic development, and all the ovums were almost hatched after 96h.

在胚胎发育过程中卵的形态特征最明显的变化是颜色从淡绿到深褐色，卵在发育96h后卵基本全部孵化。