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1·Using the Hilbert space filling curve.

使用Hilbert空间填充曲线。

2·We discuss at length the properties of a very important class of kernels which lead to the key notion of Reproducing kernel Hilbert Space (RKHS).

我们将详细的讨论核心课程中十分重要的特质，其引导出再生核希尔伯特空间理论(RKHS)中一个非常关键的概念。

3·In this paper we present a new characteristic of norm continuous semigroups on a Hilbert space and greatly simplify the proof about the known characteristic.

给出Hilbert空间中范数连续半群的一个新特征，同时极大地简化了已有结果的证明。

4·Generalized coherent states of a non harmonic oscillator in a finite dimensional Hilbert space are constructed and some quantum statistical properties are studied.

在有限维希尔伯特空间中构造了非简谐振子的广义相干态，并研究了其量子统计特性。

5·A new perturbation result on the Hilbert space for the eventually norm-continuous semigroups is obtained, which makes the perturbation of the semigroups more abundant.

讨论描述希尔伯特空间最终范数连续半群特征的一个算子方程的解，给出这个解的一个显式表达式。

6·We first provide the background to the concept of Hilbert space, introduce RKHS, and then clarify the relation between smoothness and apriori knowledge on the solution in RKHS.

因此我们首先需了解希伯特空间背景的基本观念，接着针对RKHS的解释说明平滑算法和先验算法之间的关系。

7·This paper presents a approximate proximal algorithm finding the zero of a maximal monotone operator in Hilbert space, whose error criterion is weaker than that in the literatures.

给出求解单调变分不等式问题的一个近似邻近点算法，在不需要任何中间步骤的条件下证明算法的收敛性。

8·Interpreting not in the quantum sense means taking songs as an arrow in a multidimensional Hilbert space called semantic space, where words with the same meaning are grouped together.

在量子语境中的解释“不”意为把“song”作为在称为语义环境的多维希尔伯特空间中的标志，所有有相同意思的单词都集中在这个标志附近。

9·The local straightness theorem for the ordinary differential equation in Hilbert space was proved and the results were extention of corresponding results for ordinary differential equation.

证明了Hilbert空间微分方程的局部直性定理，所得结果是常微分方程相应结果的推广。

10·For your convenience, we provide an implementation for another space filling curve, the Hilbert curve (see the Resources section for information on the Hilbert curve) in the download section.

为了方便，我们在下载一节中提供了另一种空间填充曲线，即Hilbert曲线的实现(请参阅参考资料一节以了解关于Hilbert曲线的信息)。