查询词典 hilbert nullstellensatz

Applying the techniques of real radical ideal, P-radical ideal , decomposition of semi-algebraic set in ( [72] ), affine Hilbert polynomial and B-net form of polynomials on simplex, this paper obtains two theorems of real C〓 piecewise algebraic variety dimensions and the real Nullstellensatz in C〓 spline ring.

4：应用多项式在单纯形上的B-网形式以及文献（[72]）中的实根理想，锥根理想，半代数簇分解定理，本文得出了实C〓分片代数簇的二个维数定理和C〓样条空间的实零点定理。

It is one form of Hilbert's Nullstellensatz.

它是Hilbert零点定理的一个形式。

The research of this thesis focuses on the infimum and supremun of self-adjoint operators in a complex Hilbert space with respect to the Gudder order, the infimum and supremun of operators in a complex Hilbert space with respect to the *-order and theΓ-inverse of operators in a complex Hilbert space.

本文研究内容涉及Hilbert空间上自伴算子关于Gudder序的上确界和下确界，Hilbert空间上算子关于~*-序的上确界和下确界以及Hilbert空间上算子的Γ-广义逆这三个方面的内容。

Firstly, Wavelet-Galerkin algorithm for solving the first kind of singular integral equation with the Hilbert kernel is proposed, we use the characteristic of periodic wavelet on L~2([0,1]) and Hilbert kernel to solve and make stiff matrix lower dimensions and become sparser through thresholding,thus the cost of computation is reduced. Because of the singularity of Hilbert kernel we use Tikhonov regularization method to solve the system of stiff equation. At last the convergence and numerical result of approximate solution are given. Secondly, an approach of regularization based on Fourier is presented for sideways heat equation; we give the theory proof and error estimate.

首先，提出了含Hilbert核的第一类奇异积分方程的小波伽辽金(Wavelet-Galerkin)数值算法，该算法中利用了L~2([0，1])上的周期小波和Hilbert核的特点进行处理，使得刚性矩阵维数降低并且通过阈值使得它更加稀疏，减少了计算量；由于Hilbert核的奇异性，通过Tikhonov正则化方法求解所得到的刚性方程组，给出了收敛性和数值结果；其次，对标准的一维逆热传导方程给出了一种基于Fourier正则化方法，给出了理论证明及其误差估计，解决了文献中算法与理论误差估计的不相匹配的现象，该正则化方法不仅保留了测量数据的部分高频成份，且与文献中的算法具有同样的计算量和误差估计。

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。

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。

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。

This studys objective is:(1).To explore the leaf of the Psidium guajava and its extract effect on rotavirus in vitro.(2).to study the leaf of the Psidium guajava effect on rotavirus in vivo.

本研究的目的在于：1、探讨番石榴叶及其提取物体外杀灭HRV的药理作用；2、探讨番石榴叶体内抗HRV的实验研究。

The Coast Guard says it will continue to search waters off Florida's Gulf Coast for three missing boaters.

海岸警卫队宣布他们仍在佛罗里达州附近的墨西哥湾海域继续搜寻三名失踪的船上乘客。