超几何的

By using the expansion of spherical wave functions for a cylindrical wave function and with the help of the theory of hypergeometric functions, the Sommerfeld type integral contained in the electromagnetic fields is expressed as a rapidly and absolutely convergent series of spherical wave functions; and the coefficients of the series are the Legender Polynomials with the complex argument for the constitutive parameter.

应用圆柱波函数的球面波展开式和超几何函数理论，场分量中的索末菲尔德型积分被表示成快速、绝对收敛的球面波函数系展开式；展开系数是以物性参数为复宗量的勒让德多项式。

By using the expansion of spherical wave functions for a cylindrical wave function and with the help of the theory of hypergeometric functions, the Sommerfeld type integral contained in the electromagnetic fields is expressed as a rapidly and absolutely convergent series of spherical wave functions; and the coefficients of the series are the Legender Polyno...

应用圆柱波函数的球面波展开式和超几何函数理论，场分量中的索末菲尔德型积分被表示成快速、绝对收敛的球面波函数系展开式；展开系数是以物性参数为复宗量的勒让德多项式。

An analytical model describing the dispersion with an exponential dispersion function is built, which be transformed into CDE problem with variable coefficient, using hypergeometric function and inversion technique, an analytical solution for two type boundary conditions is obtained.

文章对于具有指数弥散函数的弥散过程建立了对流-弥散微分方程模型，应用积分变换将问题转化为具有变系数的常微分方程问题；对于两种类型的边界条件，应用超几何函数和反演技术得到了问题的解析解，并分析了指数弥散过程和常数弥散过程的不同性质。

Dirac equation can be separated into an angular equation and a radial equation with the help of separation variable.

通过分离变量得到Dirac方程相应的角向方程和径向方程，得出了用广义连带勒让德多项式表示的归一化角向波函数和用合流超几何函数表示的归一化径向波函数；获得了精确的束缚态能谱方程并对结果作适当讨论与结论。

On this basis, it deeply analyzesed the spatial geometry structure of hyper spectral data lattice distribution, concluded that high\|dimensional space of remote sensing hyper spectral data belong to low\|dimensional geometry structure \|"hyperplane" shape, and anomaly point group which includes alteration information usually dissociates out the "hyperplane".

在此基础上，对高光谱数据点阵分布的空间几何结构进行了深入的研究分析，推断出遥感高光谱数据集合的高维空间属于低维几何结构"超平面"形态，而包含蚀变信息在内的异常点群通常会游离在"超平面"之外。

The theory of orthogonal symmetric polynomials (Jack polynomials, Macdonald's polynomials and others) and multivariate hypergeometric functions associated to symmetric polynomials are treated.

对称的正交多项式理论（杰克多项式，麦克唐纳的多项式等）及相关的多元对称多项式超几何函数的待遇。

The stealth warplane for the microwave radar usually have complicated structures with the coating of wave absorption. On the base of calculation and modeling of the geometrical structure of the warplane in real size, the HF RCS of the air crafts under two different polarizations in different direction have been calculated with the FDTD. The result shows that the above mentioned stealth warplane have the obvious characterstics of frequency resonance, polarization and the relatively large RCS in HF Band 10-30dBm2, which can be used as the theoretical reference for selection of working frequency for sky wave OTH Radar and it also means that the sky wave OTH radar has good capability of anti-stealth targets quantitatively.

对微波雷达具有隐身作用的飞机，其形体较为复杂且表面涂敷有强吸波材料在对一种具有隐身几何外形结构实际尺寸飞机进行计算建模的基础上，文中采用FDTD技术得到了两种极化状态下该飞机无涂敷时不同方向上的短波雷达截面RCS值其结果显示了这种隐身几何外形飞机在短波波段有明显的频率谐振特性、极化特性和较大的RCS10-30dBm2，可为天波超视距雷达在选择工作频率时提供理论参考，并定量地说明天波超视距雷达具有较优的反隐身目标能力

The basic principle is that basic geometry shape of openings in the photo is revised; the image can't be distortion by use of projection reconstruction; the corrected image is exerted by open operation and close operation of gray-image; the shape of openings is gained lastly. The perimeter borderline of openings shape is extracted. The quantity of overbreak as well as underbreak is gained by comparing to extracted perimeter and designed perimeter. The same method is applied to other opening sections. Evaluation of overbreak as well as underbreak in the openings can be easily solved in the way of quantitative.

其基本原理是：对野外摄取的洞室的基本剖面形状进行几何校正，然后应用图像学中的投影重建方法使图像不失真，对修正后的图像实行灰度图像的开操作和闭操作运算，得到洞室的基本形状，然后用图像学中的边界提取技术提取洞室的周边界，与洞室的设计形状对比分析，得到洞室在该断面上的超欠挖方量，然后对其它断面采用同样的技术就可评价某一段或整个洞室的超欠挖数量，从定量的角度解决了工程中的超欠挖评价问题。

For m-modal maps with m turning points C1,C2,…,Cm, by defining equivalent scaling factors α_e as the geometric average of all scaling factors α_Ci (i=1,2,…,m),|α_e|=|α_C1α_C2…α_Cm|1/m, global superuniversal relationship between equivalent scaling factors α_e and fractal dimensions d of Feigenbaum-type attractors on all the infinitely many critical points of transitions to chaos is obtained: dlog_|α_e|=β~, where|W| is the basic period of the m-tuply superstable sequences W, and β~ is not only independent of the concrete sequences W, but also independent of the concrete maps.

对于具有m个转变点C_1，C_2，…，C_m的m峰映射，通过定义等效标度因子α_e为所有标度因子α_(i=1，2，…，m)的几何平均，|α_e|=|α_(C_1)α_(C_2)…α_|~(1/m)，得到了等效标度因子α_e与所有无穷多个转变至混沌的临界点上Feigenbaum型吸引子的分维d之间的一个整体性的超普适关系：dlog_|α_e|=β~(e，其中|W|是m超稳序列W的基本周期，超普适常数β~(e不仅不依赖于具体的序列W，而且也不依赖于具体的映射。

The intensity-dependent interaction of the different states:the superposition of thebinomial states,generalized binomial states,hypergeometric states,Polya states,negative binomialstates,the superpositions of the negative binomial states,Glauber-Laehs states,displaced binomialstates and displaced negative binomial states with two-level atoms are studied and the dynamicsof the atomic population inversion and the field second-order correlation function areinvestigated.

对各种量子态：二项式叠加态，广义二项式态，超几何态，玻利亚态，负二项式态，负二项式叠加态，Glauber-Lach态，位移二项式态，位移负二项式态与二能级原子在强度耦合情况下的相互作用中原子与光场的动力学特性做了仔细的研究。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。