查询词典 hilbert space

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。

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。

Thesolutions compose self-contained inner product space (weight function is constant 1),i.e., they are basic series of Hilbert space; hence any internal waves could beexpanded into generalized Fourier series. With difference method, Sturm-Liouvilleequation is transformed to matrix eigenvalue problem. Each eigenvalue is related to ahorizontal wave number, and relevant solution is a certain mode of internal wave.

其解系构成完备的加权(权函数为1)内积空间，即Hilbert空间，从而内波现象可以展成该解系的广义Fourier级数；采用差分方法，将 Sturm-Liouville 方程转化为矩阵特征值问题，每一个特征值对应一个内波波数，该特征值对应的解则是内波的某一模态。

Dahlquist,Butcher,Burrage and Frank et.al.established early or late B-theory of Runge-Kutta methodsfor stiff problems in Euclidean space with finite dimensions.Afterward,Shoufu Li et.al.extended this theory to general linear methods and stiff problems in Hilbert space andfurther established B-theory of general multivalue methods in Banach space.

Dahlquist、Butcher、Burrage及Frank等人先后建立了有限维空间中刚性问题Runge-Kutta方法的B-理论；李寿佛等人将该理论推广到一般多值方法和Hilbert空间中的刚性问题，进而建立了Banach空间中刚性问题一般多值方法的B-理论。

This kind of problems can be described by the state-space of Co-semigroup in Hilbert space.

这样的系统可以通过Hilbert空间上的C_0算子半群作状态空间描述。

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。

The research of this thesis focuses on spectral complements of operator matrices, the Moore-Penrose inverse and Drazin inverse of projections in a C~*-algebra, Weyl theorem and infimum and generalized infimum of quantum effects on a Hilbert space.

本文研究内容涉及Hilbert空间中算子矩阵的谱补、C~*代数上投影算子的Drazin逆及Moore-Penrose逆、Banach空间上算子的Browder定理和Weyl定理、Hilbert空间中量子效应的下确界和广义下确界四个方面的内容。

And if H is an infinite dimensional Hilbert space, it is an inner derivation; Finally we get the same results when the nest is non-trivial.

首先证明了作用在Hilbert空间上的B上的r-Jordan可导映射是一个可加导子，并且当Hilbert空间是无限维时，它是一个内导子；最后在N≠{{0}，H}的情况下得到了相同的结论。

With Hilbert space filling curve and latent semantic index, MLSQ maps similar data objects in high dimension semantic space into an adjacent range in one dimensional value space, and considers every data object sequence number in one dimensional space as a key. MLSQ distributes the keys to adjacent nodes of structured P2P systems. By embedding the process of searching data points of HSFC into the nodes of structured P2P networks and using the data search mechanism of networks, MLSQ can facilitate to search the data objects in accordance with query requirements.

该方法利用Hilbert空间填充曲线和潜在语义索引，将高维语义空间中相似的数据对象映射到一维数值空间中的邻近区域中，并以每个数据对象在一维数值空间中的序号作为键，将数据对象的索引分布到有组织P2P网络邻近的结点上，通过将HSFC中数据点的查找过程嵌入到有组织P2P网络的结点上，再利用网络的数据查找机制，MLSQ可方便地搜索到符合查询要求的数据对象。

Using two new methods, this paper prores one pertubation theorem on the finite Hilbert space of 2×2 operator matrices, and gereralizes this theorem to the infinite Hilbert space of selfadjoint operators.

给出了有限维Hilbert空间中2×2算子矩阵的数值域扰动定理的两种证明方法，并且将该定理推广到无限维Hilbert空间上的自伴算子。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失