解空间

Then, we investigate iterative methods in Hilbert spaces for solving such problems in the second part.

本文在第二部分讨论了Hilbert空间中均衡问题的近似迭代解。

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。

The sufficient condition of stochastic delay population system with diffusion is obtained in Hilbert space.

利用Ito公式和Burkholder-Davis-Gandy定理及Gronwall-Bellman不等式，通过构造一个有界的柯西列，给出了Hilbert空间中随机时滞种群扩散系统解的存在性和唯一性的充分条件，文章所得到的结论是目前现有结果的推广。

On the basis of least potential energy theory the stability and convergence are analyzed and discussed in Hilbert space, and the basic condition ensuring uniqueness and convergence of solution is given.

在Hilbert空间内，从最小势能原理出发对非协调数值流形方法的稳定性和收敛性进行了分析和讨论，得到了保证非协调流形元解唯一存在和收敛的基本条件，完善了非协调数值流形方法的理论基础。

Owing to the monotonic mapping of fuzzy structured element established the homeomorphic property between fuzzy number space and the family of standard bounded monotone function, so, we can transform the study of any properties in fuzzy number space to the corresponding one in the family of standard bounded monotone function, e.g.

本项目针对矿井下采空区岩石陷落形成的多孔隙介质空间的极度不规则性，建立一种以模糊值函数分析学为基础的、更接近于刻划采空区内气体流动实际状况的模糊微分方程及各种边值问题，进而得出解算复杂采场气体模糊渗流问题的数学方法。

Arkeryd [5], then we use the results about moment and entropy given in [6], andprove that there exists a space homogeneous solution in L~1(R~3) to this equation withunbounded collision frequency.

Arkeryd紧性方法[5]的启发，根据[6]中给出的熵与矩的结果，在碰撞机率无界的情况下，证明了线性半导体Boltzmann方程在L~1(R~3)空间中存在均匀解。

The concept of hyperspace is used to imagine these solutions.

多维空间的概念就是用来推测这些问题的解。

The result shows that particle swarm optimization performs better in this case, which implies that the two methods traverse the problem hyperspace differently.

优化结果说明在这个例子中粒子群优化有更好的表现，这也说明两种方法在问题的多维空间中搜索最优解的方式不同。

From theoretical viewpoint,Support Vector Machinesolution corresponds to the center of the lar- gest hypersphere inscribed in the version space,and Analytic Center Machinesolution corresponds to the ana- lytic center of the largest hypersphere inscribed in the version space.

1问题的提出支持向量机以其优越的泛化性能在机器学习和优化领域日益受到重视并得到广泛应用，其解对应于样本空间最大超球体的中心。

The existence of classical solutions to non-divergence quasilinear parabolic equation of second order has been proved by basic knowledge of non-linear functional analysis and implicit function theorem in banach spaces.

用非线性泛涵分析的基本知识和Banach空间上的隐函数定理证明了非散度型拟线性抛物型方程古典解的存在性。

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。