轭

So an inner product space is automatically a normed linear space, and a Hilbert space is automatically a Banach space.

我们定义了线性映射的厄米共轭：对所有的，，(1)从而定义了中的内积：对(2)注意，由(1)可见与不同。

This paper discusses the nonlinear inversion algorithms instructively andmainlystudytwokinds ofnonlinearinversionalgorithms: SimulatedAnnealingConjugate Grads and Artificial Neural Network Genetic Algorithms, these two methods can decrease the iteration times and avoiddroppinginto the local extremum, we do the model calculation and confirm thevalidityofthealgorithm.

对非线性反演算法进行了有益的探讨，主要研究了两种非线性混合优化反演算法：模拟退火共轭梯度混合反演和神经网络遗传反演算法，两种混合算法都达到了减少迭代次数、避免陷入局部极值的目的，并进行了模型试算，验证了算法的有效性。

By improving and rebuilding the previous mid-latitude model, we extend the model to high latitude and low latitude, respectively. The extension to high latitude mainly includes the effects of convection electric field and particle precipitation. The low-latitude extension primarily takes account of the configuration of magnetic field and interhemispheric coupling.

在对原有中纬电离层模型改造和重建的基础上，将该模型分别向高纬和低纬扩展，模型向高纬的扩展主要考虑了对流电场和粒子沉降的影响，模型向低纬扩展主要考虑了磁场位形、共轭半球的影响。

And I intreat thee also, true yokefellow, help those women which laboured with me in the gospel, with Clement also, and with other my fellowlabourers, whose names are in the book of life.

4：3 我也求你这真实同负一轭的，帮助这两个女人，因为他们在福音上曾与我一同劳苦。还有革利免，并其馀和我一同作工的。他们的名字都在生命册上。

And I intreat thee also, true yokefellow, help those women which laboured with me in the goel, with Clement also, and with other my fellowlabourers, whose names are in the book of life.

4：3 我也求你这真实同负一轭的，帮助这两个女人，因为他们在福音上曾与我一同劳苦。还有革利免，并其馀和我一同作工的。他们的名字都在生命册上。

Every reducible subspace of $T$ is invariant subspace of $T$ too.

人们自然相信，有不变子空间的算子可能有共轭。

The well-known invariant subspace problem is A long-standing problem in operator theory,which has been to determine whether every operator $T$ on a Banach space $X$ must have a nontrivial invariant subspace.

不变子空间问题是一个尚未解决的问题， Enflo反例所给出的没有不变子空间的算子不为任何算子的共轭。

The main results are:(1) these entropies are all invariant with respect to equiconjugacy.

主要结果是：(1)证明了这些熵都是等度拓扑共轭不变量。

The one order differential model and convolutional model of impedance formula of amplitude versus offset inversion were established. Impedance inversion formula from AVO was derived based on Bayesian framework. Methods of using Huber function as prior model parameter distribution and covariance matrix from well log as constrains were developed. The P-wave impedance, S-wave impedance and density were calculated by the conjugate gradient algorithm.

为此建立了振幅随偏移距变化波阻抗反演公式的一阶差分模型及褶积模型，推导了基于贝叶斯理论的AVO波阻抗反演公式，给出了采用Huber分布作为模型参数的先验分布及测井数据的参数协方差矩阵作为约束条件的实现方法，并利用共轭梯度法计算了纵、横波阻抗及密度。

In the ***, all types and fundamental principles of Radon transform are summarized systematacially. This *** starts from the general linear Radon transform, and then researches how to use the damped least square method to find the solution of the forward transform. However, the least squares smoothing effect will lead to a certain degree of trails in the data of Radon domain, which led to the application\'s limitations. After that the implementation in Radon domain and relative merits of linear Radon transform, parabolic Radon transform and polynomial Radon transform which have time invariance are introduced, the conjugate gradient method that can solve numerical solution is also given. And then the high resolution Randon transform is discussed, it introduces the regularization theory and Bayes principle into inversion, which successfully remove the negative affect caused by discrete Radon transform. Finally, we introduce the optimal weighting similar coefficient Radon transform, which adapt to the time variant quality of hyperbolic Radon transform.

本文系统总结了Radon变换的各种类型及其基本原理，从τ- p变换(即一般线性Radon变换)出发，研究利用阻尼最小二乘平方法求解其正变换，但是最小平方法的平滑作用会导致Radon域数据存在一定程度的拖尾效应，给这种方法的应用带来了很大的局限性；然后先容了具有时不变性的线性、抛物和多项式Radon变换在频率域的实现及其优缺点，给出了求解其数值解的共轭梯度算法；接着讨论了高分辨率Radon变换，它把正则化思想和贝叶斯原理引进到了反演中，很好的克服了离散Radon变换产生的截断效应对结果的不利影响；最后先容了适应双曲Radon变换时变性质的高分辨率最优相似系数加权Radon变换。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！