查询词典 hilbert space

In this paper,four aspects of the above problems were studied:Firstly, the problem of solving continuous linear operator equation inseparable Hilbert space is studied .

通过把第一类连续不适定算子方程转换为等价的无穷维方程组，然后利用投影法，给出了解存在唯一的充要条件；给出了连续线性不适定算子方程解析解，解决了不适定情况下解的表示问题，由此给出了算子方程的数值求解公式；进一步证明了，在解不唯一情况下，此表达式给出的解为算子方程的最小范数解，同时表示出了连续线性不适定算子方程的解集。

In order to construct the spectral decomposition of the Frobenius-Perron operator for a general Chebyshev maps We define a suitable dual pairs or rigged Hilbert space, which provides mathematical meaning for the spectral decomposition.

为了构建广义Chebyshev映射在Frobenius-Perron算子下的一种谱分解。

We have obtained the following main significant results:(1) A master constraint operator for LQG is constructed, which is shown to be self-adjoint in the diffeomorphism invariant Hilbert space. Thus it lays a foundation for the master contraint programme in LQG;(2) The Immirzi parameter ambiguity in LQG is fixed by introducing supersymmetry, which leads to the conclusion that in the case where matter fields are coupled LQG might prefer supersymmetry in low energy;(3) The current accelerating expansion of our universe is successfully explained in the context of 5-dimensional Brans-Dicke theory, which gives a natural strategy to solve the dark energy problem.

重要成果包括：(1)构造出圈量子引力的Master约束算符，并证明了其自伴性，从而为应用Master约束方法解决量子动力学的难题奠定了基础；(2)通过引入超对称合理地固定了Immirzi参数，得出了在与物质场耦合的低能情况下圈量子引力可能偏爱超对称的结论；(3)用五维Brans-Dicke理论成功地解释了当今宇宙的加速膨胀，从而给出了一个自然解决暗能量问题的方案。

Relationship between the dual form and primal form of solution based on SVM method in a frameable reproducing kernel Hilbert space is studied.

在基于标架型的再生核希尔伯特空间中，研究了SVM算法下，解的对偶形式和原形式之间的关系，进而将SVM算法与最小二乘法相结合，讨论了支持向量机的半参数估计。

In Chapter 6, we study a kind of system of nonlinear variational inequalities and its related auxiliary problems in real Hilbert space.

针对一类非线性变分不等式系统，我们研究了其相关辅助问题，建立了辅助问题解的存在性定理。

And the series of the sampling difficulty coefficient is made in the Hilbert space.

关于试题难度系数的研究，国内学者已提出了一些模型。

Where is the state valued in a Hilbert space , is a

在此论文中，我们也将考虑关于的其它一些相关问题，诸如，能观性，唯一延拓性质，等等。

It not only explores a novel application of the reproducing kernel Hilbert space theory, but also provides a new view on solving the differential equation.

本文的研究拓宽了再生核理论的适用范围，为波动方程的求解问题提供了新的框架。

In Chapter 2, we study Isosceles orthogonality and Pythagorean orthogonality, which are natural extensions of orthogonality in Hilbert space.

首先给出Isosceles正交性的性质，揭示了这种正交性与等距算子的密切联系。

In the reproducing kernel hilbert space, It proved one-one mapping between positive regularization operator and kernel function.

本文在重构核希尔伯特空间中论述了正规化理论与核方法的一一对应关系。

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