查询词典 hilbert modular form

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In this paper,at first we transformed the nonlinear elliptic system of 2m first order equations into the complex form, then by use the results on the Riemann-Hilbert problem for nonlinear elliptic complex equation of first order, the method of continuity, the Schauder fixed-point theorem and the Leray-Schauder theorem, we proved that the modified Riemann-Hilbert boundary value problem for the complex system with some conditions is solvable.

本文先将较一般的多个未知函数的一阶椭圆型实方程组化为复方程组，然后讨论这些复方程组在某些条件下的一些边值问题的可解性。这里所考虑的方程组既包含线性的，也包含非线性的，比广义超解析函数所满足的方程组还要广，又本文主要研究较一般的Riemann-Hilbert边值问题，先给出这种边值问题解的先验估计式，然后用参数开拓法及Leray-Schauder定理证明这种边值问题的可解性结果。

Also prove that every bounded linear approximately local Hilbert space representation of a abelian von Neumann algebra is a representation,every bounded linear approximately 2- local Hilbert space representation of a von Neumann algebra is a representation.

同时证明了交换von Neumann代数的有界近似局部表示是表示，每个von Neumann代数的有界近似2—局部表示是表示。

There is a bijection between the set of all the projections on Hilbert space H and the set of all the closed subspaces of Hilbert space H.

我们都知道Hilbert空间上的正交投影和Hilbert空间的闭子空间是一一对应的。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

Fractional Hilbert transform, a generalization of Hilbert transform from integral order to fractional order, extends the application fields.

基于广义Hilbert变换将传统的Hilbert变换由整数阶向分数阶的推广，其应用领域也得到了扩展。

Hilbert space and generalized Fourier series in Hilbert space,etc.

Hilbert空间与广义Fourier级数，主要讲授内积空间内积空间中的正交系，投景定理，与广义Fourier级数。

The method ofsolution for linear discrete Hilbert boundary value problem on the unit circleis illustrated and it is proved that,in case of the index〓,the solutionsof the discrete Hilbert problems are stongly convergent to the solution of theoriginal problem.

我们给出了单位圆上线性离散Hilbert边值问题的解法，并且证明了当问题的指标k=0时离散Hilbert边值问题的解强收敛于原Hilbert边值问题的解。

Chapter 2 converts the solutions of saddle point problems in Hilbert spaces intothe equilibrium points of some dynamic system by means of the projection method,and gives some conditions of global asymptotic stability by extending the LaSalleinvariance principle to Hilbert spaces.

第三章把约束鞍点问题转化为等价的无约束问题，然后利用投影法构造了一个神经网络模型进行求解，并利用第二章结论证明了在适当条件下，模型大范围收敛于问题的精确解。

The different width and length of Hilbert curve geometries were investigated by finite element method. The computation results show that the DGS rejects the signal at two frequencies 2.43 GHz and 7.11 GHz from 0~9 GHz with more than -15 dB suppression. Q factors of the Hilbert curve DGS is bigger than that of conventional DGS.

通过有限元法对不同Hilbert曲线宽度和长度的DGS结构微带线进行计算，计算结果表明，该结构在0~9 GHz频段内表现出2.43 GHz和7.11 GHz这2个谐振频率，对应频率的通带反射损耗低于-15 dB，并且阻带特性在谐振频率处比传统DGS微带线有更高的 Q 值。

For every one of my New Year resolutions, I have been a backslider for years.

说到我的新年决心，我每年都做

With empathy and focus on a feeling level, we can all relate to the common ground of mutuality of emotions.

有了同情心和感觉上一级的重点，我们都可以涉及到相互的情感共同点。