查询词典 Hilbert

The boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function uses Cauchy integral formula as the foundation . The singularity of the Cauchy

广义解析函数的Riemann-Hilbert边值问题的边界元方法是以Cauchy公式为基础，Cauchy核具有奇性，这是所面临的困难，可以设法利用Cauchy主值积分来解决，最后给出问题的解。

In Chapter 4, on the basis of introducing the theory of linear operator semigroup and the Cauchy problem in Hilbert space, this dissertation has researched the method on solving solution of distributed parameter system, and the model estimation and optimal control of the nonlinear distributed parameter system.

本文第四章在介绍线性算子半群理论及希尔伯特空间中的柯西问题的基础上，研究了分布参数系统的近似解求解方法，一类非线性分布参数系统的模型辩识和最优控制等问题。

This paper use Mirror closed extension to solve the problem of end effect. Mirror closed extension maps the signal into a periodic signal of the ring through the mirror image method, and there is no endpoint, and fundamentally avoids the end effects of EMD and Hilbert transform.

针对这一。。。更多问题，本文利用镜像闭合端点延拓来抑制端点效应，闭合端点延拓法即用镜像法把镜内信号映射成一个周期性的环行信号，不存在端点，从根本上避免了EMD和Hilbert变换的端点效应。

The assertion is known as the closed graph theorem for Hilbert spaces.

这个断语被称为希耳伯特空间的闭图象定理。

So you want to show that a finite rank operator A on a Hilbert space is : compact?

三角函数全体在C上稠密，这个是如何证明的？

By introducing two pairs of conjugate exponent parameters and, and using the improved Euler-Maclaurin＇s summation formula for estimating the weight coefficient, a reverse Hilbert-type inequality with a best constant factor is proved.

本文通过引入两对共轭指数参量与及应用改进的Euler-Maclaurin求和公式以估算权系数，证明了一个具有最佳常数因子的逆向Hilbert型不等式；作为应用，还给出了相应的等价式及一些特殊结果。

In the third, we hit the variational principle, orthogonal decomposition, orthonormal base, Riesz representation theorem and the conjugate operators in the Hilbert space.

第三部分，Hilbert空间的变分原理、正交分解、完备标准正交系的存在性、Riesz表现定理和共扼算子等。

Order Hilbert ill-conditioned linear equations were solved, and the relative error was less than 0.45%. Numerical experiments verified that the method was efficient compared with the efficient methods used commonly nowadays. Numerical experiments results showed that the conjugate vector base method was suited for solving large-scale ill-conditioned linear equations with fast convergence and high precision.

通过对5000阶的Hilbert方程组进行求解，结果的相对误差小于0.45%，并与当前普遍使用有效的方法进行了比较，数值实验结果表明，该算法适合求解大型病态线性方程组，且具有快速收敛，精度较高的特性。

In Chapter 3, we study the conjugate linear operators on Hilbert spaces and normed spaces.

第三章：研究了Hilbert空间和赋范空间中的共轭线性算子。

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 new architectural plan the Garden of Golgotha came to be at the centre of the new city.

Aelia 是高举他自己，并在此城内朝拜罗马诸神。

The continuous nature of peat accumulation means that terrestrial coaly rocks may provide a higher resolution and more complete record of base-level change than the time-equivalent shallow-marine strata, thus enabling the identification of highfrequency cycles that are not recorded in themarine strata.

泥炭积累的持续性质的手段，陆地coaly岩石可提供较高的分辨率和更完整的记录基准面变化的影响时，相当于浅海阶层，从而使确定的高频周期，不记录在themarine 阶层。