查询词典 Hilbert

They state that the state space of a system is a Hilbert space and the observables are Hermitian operators acting on that space, but do not tell us which Hilbert space or which operators.

它们规定系统的状态矢量空间是希耳伯特空间以及可见的是作用于空间的哈密特操作者，但是不告诉我们哪个是希耳伯特空间或哈密特操作者。

After deduced that the moist atmospheric equations in Hilbert space is a very special operator equation, the existence theorems of the gloal absorbing set and the global attractor are obtained by use of the properties of operators, and the property that the asymptotic behavior of solutions shows itself on the structure of attractor and the nonlinear adjustment to the diabatic heating ...

最后指出了几个简化方程组与原方程组在解的长期行为上的根本不同，从而给出长期天气或气候研究中简化方程组必须遵循的原则。

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。

In this thesis, we discuss some algorithms for giving the zeros of maximal monotone operator in a Hilbert space and the alternating direction method for the variational inequalities.

本论文主要讨论了求解Hilbert空间上极大单调算子的零点的数值算法以及有限维空间上的变分不等式的交替方向方法。

The conception of'physical wavelets'was first introduced by Gerald Kaiser, who had expended real signal to complex Hilbert space by analytic signal transform.

Gerald Kaiser首度提出了"物理小波"的概念，并通过解析信号变换将这一概念拓展到Hilbert空间。

Comparing EMD method with traditional FFT method in the analytical process, Hilbert-Huang transformation is found to be superior in performance. Structural response of the warship subjected to underwater explosion is simulated numerically, and EMD method is applied to analyzing the structural impulse signals.

该方法不把信号分解成正弦或余弦函数，因此既能分析线性稳态信号又可用于非线性非平稳信号的分析，且避免了高频干扰结果的出现，被认为是近年来对以Fourier变换为基础的线性和稳态谱分析的一个重大突破。

In the second chapter, we study the concepts of resolvent operator associated with-monotone operators in Hilbert space.

第三章，我们在Banach空间中引进一类H-增生算子，并给出了一类新的-增生算子的概念。

By using nonconforming element and Bramble-Hilbert-Xu Lemma, Laplace approximating eigenvalue is given by the means of asymptotic expansion and the main error terms are presented ,too.

利用Bramble Hilbert Xu引理对Laplace特征值用一个非协调元作对称展开，给出该单元在研究Laplace特征值问题时的误差主项，并进一步给出外推结果，最后给出数值验证。

This particular formula involves a special function,which is the uniformly bounded solution to a scalar Riemann-Hilbert problem,and which is asymptotically equal to the constant "1" except at the origin.

这个特殊的公式包含了一个特殊函数，这个特殊函数实际上是一个一维Riemann-Hilbert问题的一致有界的解，并且除了在原点，它的取值都渐近地等于常数"1"。

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

This matter overthrew all basises I learned from Sunday school .

这件事把我从周日学校学到的所有道理都颠覆了。

It's one of the cruel ironies of aging: if you want to remember your favorite restaurants, the less you should eat at them.

这是一个老化的残酷讽刺：如果你想记住你最喜欢的餐馆，你应该更少吃到它们。