查询词典 approximation methods in physics

In this paper, the elemntary knowledge of oblique circulant matrix is described briefly and three inverse eigenvalue problems which a-re denoted by Ⅰ,Ⅱ,Ⅲ and best approximation problem which is denoted byⅣ on oblique circulant matrix are presented.

本文介绍了斜循回方阵的基本内容，提出了斜循回方阵的特征值反问题Ⅰ，Ⅱ，Ⅲ及其最佳逼近问题Ⅳ，给出了它们有解的充分必要条件及求解算法，并举出了相应的数值例子。

A fast algorithm for calculating the inverse and Moore-Penrose inverse of the permutation factor circulant matrix is presented. Then, a fast algorithm for the product of the permutation factor circulant matrix is given. Finally, The least-square solutions of inverse problems and the optimal approximation problems for the permutation factor circulant matrix are discussed.

首先给出了一种求n阶置换因子循环矩阵的逆阵、自反g-逆、群逆、Moore-Penrose逆的快速算法，然后给出了计算两n阶置换因子循环矩阵之乘积阵的一种快速算法，最后给出了其反问题的最小二乘解的存在性定理及它的一般表示，并证明了逼近矩阵的存在唯一性且给出它的具体表达式。

When scaled factor circulant matrices are nonsingular, we can find the single solution of the scaled factor circulant matrix equation; When scaled factor circulant matrices are singular, we can find the special as well as the general solution of the scaled factor circulant matrix equation; There is only an error of approximation when the fast algorithm is implemented on computers, and only the elements in the first row of the scaled factor circulant matrix and the constants in the diagonal matrix are needed by the fast algorithm.

当鳞状因子循环矩阵非奇异时，该快速算法求出线性方程组的唯一解；当鳞状因子循环矩阵奇异时，该快速算法求出线性方程组的特解与通解。该快速算法仅用到鳞状因子循环矩阵的第一行元素及对角矩阵中的对角上的常数进行计算。在计算机上实现时只有舍入误差。

Application on circular cylinder particle size distribution based on anomalous diffraction approximation.

反常衍射近似在测量圆柱形粒子粒径分布中的应用。

The phase of optical wave can be recovered by the intensity transport equation under the paraxial approximation For the optical system with diffraction limit, it is difficult to get the boundary radical slope of phase and sample in the circular domain boundary when using the intensity transport equation to recover the phase, consequently, we reviewed an algorithm mentioned in the reference ［4］, namely, the equation, computation domain and boundary condition are changed, then the phase is reconstructed by the multigrid method and corrected at last Moreover, the experiment system is set to testify the algorithm, and the recovered phase from the intensity data detected by CCD is compared with the result from phase retrieval algorithm, it is found that the phase reconstruction error can reach 017 λ in the case of non-uniform intensity distribution, as a result, the method is suitable for the phase recovery with low wavefront sensing accuracy.

在傍轴近似条件下，可以利用光强传播方程对畸变波前进行相位恢复。对于衍射受限的光学系统，很难获得相位的边界径向斜率值作为边界条件，此外，要获得精确的圆域边界采样值也并非易事。为了克服上述困难，进一步研究了相位恢复改进方法，即改变了方程的表示形式、计算区域和边界条件，并用多重网格法进行求解获得重构相位，最后再将其修正。为了验证算法的精确性，搭建了实验系统对算法进行实验验证，将由CCD探测的光强分布进行计算得到的相位分布与相位恢复算法的结果进行比较，证明在光强分布非均匀的情况下，该方法恢复的相位均方根误差能够达到017 λ，可以适用于波前传感精度要求不是很高的相位恢复。标签自适应光学相位恢复相位修正光强传播方程 adaptive optics phase retrieval phase correction intensity transport equation

Common Reflection Surface stack is a brand-new and special ZO imaging method, the theory of CRS stack stems from paraxial ray theory, the biggest difference between CRS stack and conventional ZO imaging method is that it consider a reflector R as a circular reflector segment Cr placed in the vinicity of reflector R, Cr can be seen as the second order approximation of the reflector. The CRS traveltime surface is the multi-coverage reflection response of the reflector mirror assigned to R.

共反射面元（CommonReflection Surface=CRS）叠加技术是一种全新的、特殊的零偏移距剖面成像方法，CRS迭加理论源于傍轴射线理论，它与普通的零偏移距剖面成像方法的最大区别是它认为地下反射层是由许多个小反射弧段互相叠合组成的，认为来自某反射点附近的一个邻域内的反射信息都可以对该反射点的成像作出贡献，因此对该反射点进行零偏移距成像时就应该聚焦更多的能量参与迭加。

Focusing on the concept of the climate levels and space reconstruction, we establish a local approximation prediction model with the compound configuration, using the north Indian Ocean sea surface temperature、 Asian zonal circulation index and 37 stations′ winter precipitation anomaly in Inner Mongolia and then use this model to test the predictability of winter precipitation anomaly.

根据气候"层次"概念和重构状态空间理论，利用北印度洋海温、亚洲纬向环流指数以及内蒙古地区的37个测站逐月降水距平百分率的历史资料，建立具有复合结构的局域相似预测模型，并用该模型对内蒙古地区的冬季降水进行预测试验。

It includes the classical mechanics as its approximation.

经典力学是量子力学的一种近似。

Classical Statistical Mechanics; Hamiltonian and Ideal Gases; Factoring the Partition Function with the Semi-classical Approximation; PVTN Properties via Configuration Integral from Intermolecular Effects; Grand Canonical Ensemble I

经典统计力学；Hamilton函数与理想气体；半经典近似微分函数因数；对分子间作用，作定积分而得的PVTN性质；巨正则效果I。

The results show that the most close-packed surface (111) orientation of FCC metals which have the lowest surface energies will grow preferentially, the surface energies for the all lattice surfaces increase linearly with increasing including angle between the surfaces and (111), which are consistent with the experimental and the linear muffin-tin-orbital-atomic-sphere-approximation results.

结果表明，FCC金属的密排面（111）的表面能最小，则该晶粒取向优先生长，与实验结果和第一原理的LMTO－ASA计算结果一致；各个晶面的表面能均随着其它晶面与（111）晶面的夹角的增长而呈线性增长关系，因此利用（111）面可推导出其他各面的表面能量。

The studies on the developing of new media are very important to the increasing of the area density of HDD and to the implementation of hybrid recoding technology.

光磁混合记录方法，是一种可以突破超顺磁极限的限制，并进一步提高硬盘记录密度和读写速率的一种新型超高密度信息存储方式。

In io, mTOR inhibition promotes T cell anergy under conditions that would normally induce priming.

体内研究中，在正常可激发免疫反应的条件下，抑制mTOR可促使T细胞无能。