查询词典 radon nikodym theorem

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

Using the divergence theorem, converted the area integral of the flux of stress for the surface force to a volume integral of the divergence of stress.

应用散度定理，将通量应力的面积积分转换成应力散度的体积积分。

Moreover, we design a testing method based upon Wald theorem for the specification of model, thus greatly facilitates and extends the specification test of Panel Data model.

此外，本文设计了一种基于Wald定理的模型设定检验方法，极大的方便和拓展的Panel Data模型的设定检验。

For diffusive Predator-Prey model with Holling-Ⅲ functional response without time delay, shooting argument together with LaSalle's Invariance Principle and the Hopf bifurcation theorem are applied to prove the existence of traveling wave solutions and small amplitude traveling wave train solutions.

在数学理论的研究中，行波解可以揭示方程本身的许多重要性质；在实际应用中，行波解可以很好的表现自然世界中的振荡现象。因此，对反应扩散方程行波解的研究具有非常重要的意义。

Finally,usingHodge decomposition theorem,domain variations theory and capacitytheory,we prove that the continuity of very weak solutions of a classof nonlinear elliptic equations on varying domains.

最后，使用Hodge分解、区域拓朴和容量理论，我们证明了一类非齐次半线性椭圆型方程很弱解关于区域的连续依赖性。

Chapter 4 at first concerns a doubly degenerate parabolic inequality.A Liouville-type theorem is obtained by carefully choosing desired test functions for weak solutions of the inequality problem.

第四章首先考虑一类双重退化抛物型不等式，通过适当选用试验函数的办法得到此抛物不等式弱解的Liouville型定理。

Major topics covered are: basic concepts of probability, sample space and events, axioms of probability, random variables, discrete and continuous distributions, joint and marginal distributions, numerical characteristic for random variables, the weak law of large numbers, central limit theorem, basic concepts of statistics, parameter estimate, hypothesis testing and regression analysis.

本课程的基本内容有：随机事件及其概率、随机变量及其分布、多维随机变量及其分布、随机变量的数字特征、大数定律与极限定理、数理统计的基础知识、参数估计、假设检验、回归分析。

By properties of a real function, fixed points problem on two complete metric spaces are discussed.The result generalizes corresponding result of Fisher.Moreover, this result provides a general convergence rate estimate. Meanwhile, we discuss the existence of fixed point on two normed linear spaces under the condition of weak topology, and we obtain a new fixed point theorem.

利用实函数性质，讨论了两个不同度量空间中两个映象乘积的不动点问题，推广了Fisher的主要结果，并给了出逼近不动点的敛速估计；同时，在弱拓扑的意义下，利用分析的方法，讨论了赋范空间中有关映象不动点的存在性，得到一个新的不动点定理。

Akin-Kolyada theorem said that for a weakly mixing system the proximal cell of any point is residual.

Akin-Kolyada定理指出，弱混合系统的每个点的proximal核为通有的，即包含了一个稠密的G〓集。

Due to the moving base existence of the minehunting and the frame structure characteristic of the sonar array, a new modeling thought in which the boat body coordinates is regarded as moving coordinates and the whirligig equation of sonar array compared with the self coordinates is founded on the basis of the Euler's theorem and the coordinate transform is introduced.

由于猎雷艇作为动基座的存在和声纳基阵的框架结构特点，提出了以艇体坐标系为运动坐标系，运用变形的欧拉定理和坐标变换建立声纳基阵相对自身坐标系的旋转运动方程的建模思想；将所建立的矢量形式的动力学模型展开整理，获得了状态矩阵形式的猎雷声纳基阵动力学方程，为系统动力学模型的实用化奠定了基础。

You can snipe the second and third union leaders from this position.

您可以鹬第二和第三工会领袖从这一立场出发。

Aiming at the currently shortage of XML streams quality detecting, this paper proposes a new forecasting method of XML streams quality by least squares support vector machines, which is used the method of XML keys' vector matrix as windows, and vector product wavelet transform to multilevel decompose and refactor the XML streams series, that can fulfill real-time checking demand of XML quality, and ensure constraint, consist- ency and integrality. For even more adapting net load, it proposes a control strategy by weight and adaptive adjustment to ensure XML streams quality.

针对当前XML数据流质量检测存在的不足，提出构建XML键的矢量矩阵作为窗口，利用矢量积小波变换多级分解与重构XML数据流，再结合最小二乘支持向量机对XML数据流质量进行预测的一种方法，满足XML数据流质量重构时实时检测的要求，保证XML数据的约束性、一致性与完整性；为了更好的适应网络负载，采取加权与自适应窗口调整等调度策略充分保证XML数据流的质量检测。