广义函数空间

词组短语

distribution space

与广义函数空间相关的网络例句 [注：此内容来源于网络，仅供参考]

In the fifth chapter, we use the the methods of function theoryestablised a class of analytic reproducing kernel space, we call it a generalized Arveson space.

在第五章中，我们利用函数论的方法建立了更广泛的一类解析的再生核空间，称之为广义Arveson空间，讨论了它的一些关系，并得到了一些有趣的结果。

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。

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。

On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we define δ-fine partitions for infinite interval and integral of vector-valued functions on infinite interval, and discuss the properties of integral, and characterize its primitives...

主要包括以下五部分内容：在第一部分中，我们介绍了本文所用到的基本概念和引理；在第二部分中，通过定义无穷区间上δ-精细的分法，我们给出了无穷区间上向量值函数的积分的定义，并讨论其性质，还给出了原函数的刻划；在本文的第三部分中，我们着重讨论了无穷区间上向量值函数积分的收敛定理；在本文的在第四部分中，我们首先应用无穷区间上向量值函数积分的收敛定理给出了常微分方程整体广义解的存在性定理，其次应用强积分对Banach空间常微分方程广义解进行了讨论；最后，在第五部分中，我们将模糊积分推广到无穷区间上并给出了其数值计算方法。

Adopting generalized Jordan block and algebra equivalence transform method, all of the transfer functions at different load points can be transformed to state-space description with time variable. The steady robustness of three different mode of control systems were researched by mathematic analysis. It shows that: for the high order inertia controlled object with the characteristic of nonlinear and time-variable that described by the set of transfer functions, the Luenberger function observer established according to its any algebra equivalence state-space description, if some conditions can be met, there would be a matrix of T with n′n satisfied the Sylvester matrix equation TA- FT=GC.

采用广义约当块及代数等价变换方法，可将分段的传递函数描述转换为变参数的状态空间描述，对3种典型控制系统的稳定鲁棒性所进行的理论研究表明，对同一组传递函数描述的具有非线性和时变特性的高阶惯性受控对象，依据其任一代数等价的状态空间描述所构建的Luenberger函数观测器，在满足一定的条件时，存在n′n解阵T满足Sylvester矩阵方程TA- FT=GC。

2The new cloud physical model is put forward the metric geometry.(3)The generalized cloud equations of cloud is derived on the generalized function and the Sobolev space on the Riemannian manifold.

提出了 大气模式中新一代云方案的动力学：(1)基于拓扑的云分类；(2)基于度量几何的云模型(3)利用黎曼流型上的广义函数和索伯列夫空间，系统建立了云之动力学方程组。

Some new basic concepts are proposed in this paper, including the approximation space of generalization, rough approximation axiom, disturbance set axiom, classification principle of rough set, principle of nondeterministic even set, principle classification, bit quantum symmetric classification, of concentration, game classification, quantum logic incomparable set, bit space set, protocol relation, rough set function of protocol relation, rough classification algebra, rough simple algebra, etc., and a guess is also proposed.

提出了广义近似空间、粗近似公理、干扰集公理、粗糙集的分类原则、粗选原则、不确定偶集原则、精选原则、对策分类、量子逻辑分类、bit量子对称分类、不可比集、bit空间集、协议关系、粗糙集函数、粗糙分类代数和粗糙单代数等基本概念，并提出了一个猜想；展示了一些新观点；基于协议关系构造了粗糙商代数和粗糙子代数，给出了回避-归并算法及算例。

Moreover, we will stress on the theory of Schwartz distribution, and then we will deal with the celebrating theory which we call Sobolev space.

进一步，我们将讲授Schwartz广义函数基本理论，在此基础上我们讲授Sobolev空间的基本理论。

Keywords Sobolev space;generalized function;Galerkin method;nonlinear elastic bar;existence and uniqueness of solution

Sobolev空间；广义函数； Galerkin法；非线性弹性杆；解的存在性和唯一性

Moreover, we get the sufficient and necessary condition of in Orlicz spaces.Chapter 3 Extreme points and strongly extreme points in Orlicz spaces equipped with the generalized Orlicz norm: In this paper, the conceptions of the generalized Orlicz norm and the generalized Luxemburg norm are introduced, and the criteria of extreme points and strongly extreme points of Orlicz function spaces equipped with the generalized Orlicz norm are obtained. Moreover, criteria of space strictly convex and mid-point locally uniform convex are given.

第三章 赋广义Orlicz范数的Orlicz函数空间的端点和强端点：本章在Orlicz空间推广了Orlicz范数和Luxemburg范数，引入了广义Orlicz范数和广义Luxemburg范数的定义，并给出了赋广义Orlicz范数的Orlicz函数空间的端点和强端点的判据，进而得到了赋广义Orlicz范数的Orlicz函数空间严格凸和中点局部一致凸的充要条件。

与广义函数空间相关的网络解释 [注：此内容来源于网络，仅供参考]

generalized Bayes decision function：广义贝叶斯决策函数

广义贝叶斯估计|generalized Bayes estimate | 广义贝叶斯决策函数|generalized Bayes decision function | 广义本征空间|generalized eigenspace

distribution rule：分布规则

distribution ratio 分布系数 | distribution rule 分布规则 | distribution space 广义函数空间

distribution space：广义函数空间

distribution rule 分布规则 | distribution space 广义函数空间 | distribution with negative skewness 负偏斜分布

distribution with negative skewness：负偏斜分布

distribution space 广义函数空间 | distribution with negative skewness 负偏斜分布 | distribution with positive skewness 正偏斜分布

generalized eigenspace：广义本征空间

广义贝叶斯决策函数|generalized Bayes decision function | 广义本征空间|generalized eigenspace | 广义本征值|generalized eigenvalue

space of generalized function：广义函数空间

广义函数卷积|convolution of distributions | 广义函数空间|space of generalized function | 广义函数支集|support of distribution