查询词典 generalized function

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。

For fixed generalized reflection matrix P, i.e., P^T=P, P^2=I, then matrix X is said to be generalized bisymmetric, if $X=PXP$ and $X=X^T$.

对于某个广义反射阵P，满足P^T=P， P^2=I，那么称矩阵X是广义双对称的，如果满足X=PXP及X=X^T。

The solutions of ProblemⅠ,ⅡandⅢare discussed by using the generalized conjugate gradient method. When the equation is consistent, the solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are successfully found; When the equation is inconsistent, the least-squares solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are also found successfully. The generalized conjugate gradient method has the following traits:(1) It can judge automatically the information of solutions.

利用广义共轭梯度法，讨论了问题Ⅰ、Ⅱ和Ⅲ解的情况：当方程相容时，研究了方程的一般解、对称解、中心对称解、自反矩阵解、双对称解、对称次反对称解及其最佳逼近等问题；当方程不相容时，研究了方程的最小二乘一般解、最小二乘对称解、最小二乘中心对称解、最小二乘自反矩阵解、最小二乘双对称解、最小二乘对称次反对称解及其最佳逼近等问题。

Methods We retrospectively studied clinical and EEC features of 80 patients with ICE. Ten patients were diagnosed with juvenile myoclonic epilepsy, 35 has absence epilepsy, 28 had generalized tonic clonic seizure, and 7 had adult-onset idiopathic generalized epilepsy.

回顾性分析80例特发性癫痫患者的临床和常规EEG特征。10例患者诊断为青少年肌痉挛癫痫，35例患者有失神发作，28例患者为全面强直痉挛发作，7例患者为成年期起病的特发性全面性癫痫。

The generalized criterion for minimum zone in the determination of form error of surface is presented on the basis of linear minimax techniques, and the criteria of such surfaces as for cylindricity and straightness with arbitrary direction are derived from this generalized criterion.

本文讨论形状误差最小区城的判别准则和判别方法。根据线性极差极小化问题解的特征，给出形状误差最小条件的统一判别准则。推导出各种形状误差最小区域判别法(包括圆柱度误差和任意方向直线度误差)，并在几何判别的基础上得出代数判别的格式。

The recursive algorithm about Diophantine equations is improved in the common generalized predictive control and generalized predictive poleplacement control.

改进了通常的广义预测控制和广义预测极点配置控制中的Diophantine方程的递推算法。

Accordingly, the development of sports has also experienced the transmutation from body and mind dualistically opposite object generalized sports, to body and mind dualistically opposite subject generalized sports, and to body and mind unified life imitated sports.

与之相适应，体育运动的发展也经历了从身心二元对立的客体化式体育、身心二元对立的主体化式体育到身心统一的生命化式体育的嬗变。

Through establishing the priori estimates for the approximation solutions, we pove the existence of global generalized solution by using the compactness principle and obtain the global property for the generalized solutions in the space L〓. At the last, a new method is used to prove the uniqneness which is a good results, at some extense, under generalize conditions.

运用De Giorgi的最大模估计方法，证明了解的整体上界估计和准衰减型的估计，进一步，在边值和初值具有正的下界条件下，证明了解的一致下界估计，得到了深刻结果。

As an examplc, in the Chebyshev coordinates, we use the Backlund theorem to give a Backlund transformation and a permutability formula between the generalized sine-Laplace equation and the generalized sinh-Laplace equation.

作为一个例子，利用几何的Backlund定理我们给出了广义的sine-Laplace方程和广义的sinh-Laplace方程之间的Backlund变换及其置换公式。

The advantages and disadvantages of balanced truncation, singular perturbational method and generalized singular perturbation are analyzed. A quasi-generalized singular perturbational model reduction method is proposed.

分析了平衡截断法、平衡奇异摄动法和广义平衡奇异摄动法存在的优缺点，提出了一种近似广义奇异摄动模型降阶算法。

A backer of an Afghan law that critics say legalizes marital rape has rejected the international outcry as foreign meddling.

饱受批评的一项法律的拥护者说合法化的婚内暴力不会受国际舆论的干涉。

Years ago, a ancient Egyptian fleet went to the Land of punt for seeking a kind of flavor named "myrrh", and aromatic plants which has dense exotic style for the queen Hatshepsut.

3500年前的一个古埃及的舰队到&彭特之地&寻找一种叫没药的香料。