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 this paper, we study the periodic controllability of linear evolution equations in Hilbert space.

在本文中，我们研究了在Hilbert空间中的线性发展方程的周期能控性问题。

A Lipschitz strictly pseudocontractive map from a nonempty closed convex subset of a Hilbert space into itself was showed to have fixed points, Ishikawa and Mann iterative sequences with errors of a Lipschitz strictly pseudocontractive map was introduced and the iteration processes strongly converges to a fixed point was proved.

证明了在Hilbert空间中的非空闭凸集上Lipschitz严格伪压缩映象有不动点，介绍了Lips-chitz严格伪压缩映像下的的具误差的 Ishikawa和Mann迭代序列并证明了其强收敛性于不动点，其结果把非扩张映像推广到Lipschitz严格伪压缩映象上，改进了一些相关结果。

Let C be a nonempty closed convex subset of a Hilbert space H, P:H→C be a nearest point projection, and T:C→H be a nonexpansive mapping satisfying the weakly inwardness condition, and :C→C be a fixed contractive mapping. Let the implicit iterative sequences {x},{y} and the explicit iterative sequences {x},{y}.

设C为实Hilbert空间H的非空闭凸子集，P：H→C为最近点投影映射，T：C→H为非扩张映象，且T满足弱内向条件，：C→C为压缩映象。t∈(0，l)，定义了2种隐式粘性迭代序列{x}，{y}和2种显式粘性迭代序列{x}，{y}，证明了T有不动点当且仅当序列{x}，{y}，{x}，{y}有界。

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。

And then prove that every approximately derivable maps of nest algebras acting on an infinite dimensional Hilbert space is inner.

并且对作用在无限维Hilbert空间上的套代数上的近似可导映射进行了刻画，证明了它是一个内导子。

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 the product space of unanimity convex Hilbert, we obtained the theory of existence and uniqueness of best approximation element on weakly closed t convex set .

讨论了凸集及凸包的形态学运算的几个几何特性，并使某些文献中的几个错误结论得到修正和完善。

Moreover, when X is a Hilbert space, Miaxoguchi and Takahashi provided the ergodic retraction theorem for general semigroups of asymptotically nonexpansive mapping by using the concept of invariant submean.

进一步，当X是Hilbert空间时，Miaxoguchi及Takahashi引入了不变子平均的概念，在一般拓扑半群上给出了渐近非扩张半群的遍历压缩定理。

Objective:To explore the feasibility of laparoscopy in diagnosing and treating of abdominal diseases.

目的：探讨腹腔镜用以诊断腹部外科疾病及选择治疗方案的可行性。

The lifetime of nylon 1010 and nylon 1010/POSS composites decreased with increasing temperature.

热重-红外联用分析表明尼龙1010在氮气气氛下的降解产物主要为小分子的低聚物，POSS并不改变尼龙1010降解产物的组成。