极值函数

Based on the feature of targets, a new small target detection algorithm is presented based on the extremum theory for bi-variate cubic function.

针对这个特点，依据二元三次函数的极值理论，该文提出了一种新的弱小目标候选点的检测方法。

In this paper,the authors deeply discussed the relations between the extremum and the multiple roots for some types of functions,and researched how to use the relations in real world.

就一类函数极值与重根的关系作比较深入的探讨，并对这些关系作一些应用研究。

At the early iteratives, the mutation rate is bigger and the aim is to make particles to explore smaller and isolate region and to avoid the algorithm trapping to the local optimum. While the algorithm runs, the mutation rate will be decreased to reduce the disturbing to the particles. IPSO adopts a new method that congregates some neighboring individuals to form multiple sub-populations in order to lead particles to explore new search space. Additionally, our algorithm incorporates a mechanism with a simple and easy penalty function based on the largest distance between the particle and the boundary of the feasible region to handle constraint.

IPSO采用了一种新型的变异策略，变异概率随着算法的运行是动态变化的：在算法运行初期，变异概率大，其目的是使算法不但能够探测到目标空间中的孤立区域，而且避免搜索陷入局部极值；在算法运行后期，变异概率逐渐变小，以减少对粒子的扰动；算法通过将部分具有邻近距离的粒子聚集成核形成多子群引导种群中粒子的飞行；采用一个简单的基于粒子与可行域边界最远距离的罚函数处理约束的机制，使得算法高效实现。

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。

The Scheutjens - Fleer model on monodisperse polymer adsorption was extended to the situation of polydisperse polymer adsorption by the method of seeking the extremum of the partition function constructed for the system.

采用构作配分函数而后求极值的方法，将Scheutjens-Fleer模型推广到多分散高分子吸附情形，并采用适当的计算方法，解决了长期以来人们难以解决的多分散高分子模型计算上的困难，研究了固液界面区域多分散高分子的微观吸附行为、多分散指数对吸附层性质的影响以及各种微观构象的链段大小的几率分布。

Based on the precision and the cost of the relationship between the use of conditional extremum for the function of several variables method to determine when the first sample for sampling with probability proportion to size,the second-simple random sampling,the two-stage sampling is optimal allocation.

本文根据精度与费用之间的关系，利用求多元函数条件极值的方法，确定当第一级抽样为有放回PPS抽样，第二级抽样为简单随机抽样时，二阶抽样的样本容量最优分配。

The DFP method is proved a officient one in processing unconstrainted optimization problem, so in this thesis, used the idea of mechanical structural optimization for reference analytically and extended modified formula of DFP—matrix to shape optimiation the DFP—Hamilton function method is put forward.

由于变尺度方法是有效的无约束优化方法，本文在分析的基础上借鉴了机械结构参数优化的思想，并将变尺度矩阵的修正公式扩展至形状优化中去，进而提出了变尺度—H函数极值法，并用其解决了梁、柱和复杂曲面的形状优化设计问题，取得了较好的效果。

An modified BFGS algorithm to solve the unconstrained optimization, whose Hessian matrix of the minimum point of the convex function is rank one defect, is presented in this paper.

本文对凸函数在极值点的Hessian矩阵是秩亏一的情况下，给出了一类求解无约束优化问题的修正BFGS算法。

An modified BFGS algorithm o solve the unconstrained optimization, whose Hessian matrix of the minimum point of the convex function is rank one defect, is presented in this paper.

本文对凸函数在极值点的Hessian矩阵是秩亏一的情况下，给出了一类求解无约束优化问题的修正BFGS算法。

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。

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。