查询词典 theorem on embedding

This paper investigates alternating iterative method and generalized alternating method for the solution of a large linear system, extend the convergence theorem and comparison theorem for generalized or alternating iterative method when the coefficient are Hermitian positive definite systems.

本文主要研究了大型线性方程组的交替迭代法及迭代法的各种变形，给出了当系数矩阵为Hermitian正定矩阵时各类迭代法的收敛原理及其相应的比较理论。

This paper weakened the Liouville s theorem conditions,and gives the Liouville theorem of a promotion.

弱化了刘维尔定理的条件，给出了刘维尔定理的一个推广。

A three solutions theorem of nonlinear operator equation in Hilbert space was given by Sun Jing-xian in 1983,in this paper,the theorem was expanded to general Banach space by using gradient method ,and some conditions was weakened,such as the local Lipschitz condition s transformation to the bounded character of F and so on.

依据H ilbert空间中非线性算子方程的一个三解定理，本文运用最速下降法将这个定理推广到了一般的Banach空间，并且减弱了原定理的某些条件，如将局部Lipschitz条件减弱为F的有界性等

By employing the local Lipschitz condition and Picard sequence, the local existence-uniqueness of solutions of stochastic functional differential equations of Ito-type is firstly obtained. Furthermore, a continuation theorem for stochastic functional differential equations of Ito-type is given by using stochastic analysis technique and the quasi-boundedness condition. Finally, by establishing some delay differential inequalities and using properties of H_m-functions, a stochastic version of Wintner theorem and the global existence-uniqueness of solutions of stochastic functional differential equations of Ito-type are given. The results generalize the earlier publications.

首先，利用局部Lipschitz条件和Picard序列，获得了伊藤随机泛函微分方程解的局部存在唯一性；其次，利用随机分析技巧和拟有界条件，建立了伊藤随机泛函微分方程解的延拓定理；最后，通过建立一些时滞微分不等式和利用H_m-函数的特性，得到了Wintner定理的随机版本和伊藤随机泛函微分方程解的全局存在唯一性，推广了已有的一些结果。

Firstly, the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay under the uniformly Lipschitz condition, linear grown condition and contractive condition can be directly derived; And the moment estimate of the solution and the estimate for error between the approximate solution and the accurate solution can be both given; If the uniformly Lipschitz condition is replaced by the local Lipschitz condition, the existence and uniqueness theorem can be gained; Meanwhile, the existence and uniqueness of the global solution in the interval 0,+∞ can also be obtained; Secondly, L~p-exponential estimate of the solution for neutral stochastic functional differential equations with infinite delay can be studied; At length, the theorem of the local solution about neutral stochastic functional differential equations with infinite delay only under the local Lipschitz condition and the contractive condition can be established.

首先，在一致Lipschitz条件，线性增长条件和压缩性条件下，直接得到了具无限时滞中立型随机泛函微分方程解的存在惟一性，并给出了解的矩估计，近似解与精确解之间的误差估计；将一致Lipschitz条件替换为局部Lipschitz条件，也得到了具无限时滞中立型随机泛函微分方程解的存在惟—性，同时，也给出了在整个区间0，+∞上具无限时滞中立型随机泛函微分方程解的存在惟一性定理；其次，也讨论了具无限时滞中立型随机泛函微分方程解的L~p指数估计；最后，在局部Lipschitz条件和压缩性条件下，建立了具无限时滞中立型随机泛函微分方程局部解的存在惟一性定理。

First,we consider the lower semicontinuity property fora functional with linear growth in LDΩthe second, in the SBD space,we discussthe lower semicontinuity of an integral functional that the integrand is a Carathéodoryfunction and that satisfies a symmetric quasi-convex assumption, by the compactnesstheorem of the SBD space,blow-up method and Morrey theorem,prove that integral functional is lower semicontinuous with respect to L~1- convergence;then by using theone-dimentional sections method and the structure theorem of the BD functions, dis-cuss the lower semicontinuity of the integral functional in the whole BD space.

首先我们考虑LD空间满足线性增长的积分泛函的下半连续性；其次在SBD函数空间讨论了被积函数为Carathéodory函数时的积分泛函在满足对称拟凸条件时的下半连续性，主要利用SBD函数空间的紧性定理和blow-up方法以及Morrey定理等给出了积分泛函关于L~1-强收敛的下半连续性；然后利用BD函数的一维截断方法和结构定理，讨论了在BD全空间上的积分泛函的下半连续性。

The theoretic results on conventional theorems are far from the experiment results. Through discussing on ABA mapping, we obtain the general collage theorem and local collage theorem for ABA mapping.

本文从分析ABA映射的Collage定理入手，导出了ABA映射的广义Collage定理和ABA映射的局部Collage定理，并提出了符合实际情况的概率模型。

The main work and innovation1 In general , a image compression method has different effect to different image . Some are fit for image which has much high frequency . Some are fit for image which has much low frequency .This paper analysis the applicability of fractal algorithm . In this dissertation , an improved algorithum is given . The basic algorithum without eight change and the joint use of quantitative coding , The compression ratio and PSNR can be adjusted , and it can get more quickly speed of coding .2 To a group of exact fractal code , the decoding image can be any resolution .With this characteristic ,choose the proper domain block and range block,this paper get an algorithum which can get higher decoding PSNR and speed than the basic fractal algorithum.3 Give a new method to calculate the scale factor . The calculation of basic algorithum is complex and enormous . The factor of scale is an important variable of the basic algorithm. Now there are two methods to calculate the factor of scale .A new method was given to calculate the factor of scale. The calculation load and complexity are reduced by the new method. Compared with the basic algorithm , the method can reduce coding time.4 The basic fractal algorithum is based on the Collage theorem and contraction mapping theorem . A mathematic model based on basic fractal algorithum is given .

本文的主要工作及创新点主要包括以下几点：1一般情况下，一种图像压缩的方法对不同特点的图像，压缩效果会有所不同，本文利用分形压缩编码对不同特点的图像进行编码，分析了分形编码对不同图像的编码适用性，利用去掉8种变换的分形编码算法与简单的均匀量化编码方案相结合，得到了一种可以调节压缩比与解码质量的分形编码方案，该提高编码速度6倍以上。2分形编码的特点之一是分形解码的分辨率无关性，即对于一组分形编码可以将其解码到任意分辨率下，本文利用分形编码的这一特点，结合不同的量化编码方案，选择合适的定义域块与值域块及适当的编解码分辨率，得到了一种提高解码质量，编码速度提高12倍以上的加速算法。3比例因子是基本分形算法中的一个重要变量，目前有两种计算比例因子的方法，文中给出了一种新的求比例因子的方法，该方法简化了求比例因子的计算，从整体上减小了基本分形算法的计算量，简化了算法4分形压缩的数学基础是不动点定理与拼贴定理，本文根据基本的自动分形编码方法，建立数学模型对其进行推导，得到了用普通数学的极限理论解释分形编码的数学表达式，从而对由基本分形编码得到的解码图像中的像素点的值给出了确定的表达式。

Proposed in the p aper are the ordered monotony property of MFNNs when the transfer function is mo notone, the continuous mapping theorem, and non-approximation theorem to functi on.

给出了单调传递函数的MFNNs按序单调特性、连续映射定理以及非函数一致逼近定理。

In this paper,we presented a succinct method to obtain the unitary matrix in the representation transformation by the theorem form,gave the reasonable demonstration,and simultaneously confirmed the theorem accuracy by a concrete example.

以定理的形式给出了表象变换中获得幺正矩阵的一种简洁方法，并给予了合理的证明，同时结合具体实例验证了定理的正确性。

Listen,point and check your answers.

听，指出并且检查你的答案。

Warming needle is one of effective treatment methods for knee arthralgia aggravated by cold,and it is simple,safety,so it should be developed in clinical acupuncture and moxibustion extensively.

但以本院科针灸门诊在2005年1月—2006年6月期间共收治膝痛患者100余例，经过临床的诊断后，其中施以温针治疗的48例，疗效显著，报道如下。1临床资料本组病例48