四维的

The adjoint operator method and the theory of normal form are used to investigated the normal forms in the four dimensional nonlinear systems with cubic nonlinearities. We give two methods to compute the normal form for the four dimensional nonlinear systems. The corresponding Maple programs are also given in the appendix. The results obtained in this dissertation have a completely agreement with the results obtained in other papers.

利用共轭算子法和规范形理论研究了含有三次非线性项的四维系统的规范形，给出了计算四维非线性规范形的两种算法，给出了相应的Maple符号推导程序，所得到的结果与其它文献所得结果完全一致。

But from the point of view of the relativity theory, time as well as space is changed by passing from one c.s. to another, and the Lorentz transformation considers the transformation properties of the four-dimensional time-space continuum of our four-dimensional world of events.

但是从相对论的观点看来，时间和空间从一个坐标系过渡到另一个坐标系时都是要改变的，而洛伦兹转换就是考察事件的四维世界的四维时空连续区的转换性质的。

It is not one dimension time of three dimensional space of superstring theory.

提要：本文再次说明时间四维空间六维，不是超弦理论的三维空间一维时间。

In most cases, time-lapse seismic is taken by repeated 3D seismics,so it is also called 4D seismics.There are many other time-lapse observation methods besides the 3D time lapse seismic such as time lapse 2D seismics,time-lapse cross hole seismic,time-lapse VSP etc.

由于大多数情况下，时移地震都是通过重复三维地震进行的，因此国内外很多学者也将其称为四维地震，除三维时移观测外，还有很多其它的时移观测方法，如时移二维地震、时移井间地震、时移VSP等。

Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin).

大 约在一百年以前，庞加莱已经知道，二维球面本质上可由单连通性来刻画，他提出三维球面（四维空间中与原点有单位距离的点的全体）的对应问题。

It is found thatthe fractal dimension D=1.25 corresponds to the lowest criticalcoupling constant αc=1.9,D=1.73 corresponds to the highest criticalratio of dielectric constants ηc=0.163,and when D≤1.145 bipolaronscan not exist at any rate.In chap,4,we will propose a novelapproach to the calculation of the exciton ground-state energy for thestrong-coupling case.Different from all previous methods,the wavefunction of the phonon part is assumed to take a form related to thewave function of the relative motion.We obtain the exciton energy bysolving the derived integrodifferential equation rather than select ahydrogen-like form to minimize the energy expectation.

结果发现，分数维的维数D＝1.25对应最小的临界的电-声耦合常数(αo＝1.9)，D＝1.73对应最大的临界的介电常数比(ηc＝0.163)，当分数维的维数D≤1.145时，双极化子无论如何也不可能存在，在第四章中，我们将提出一种新颖的变分方法来计算强耦合的激子-声子系统的基态能，不同于以前所有的方法，我们取声子的波函数与相对运动波函数有关的形式，而不是假定一个固定的关于相对运动坐标r的函数形式，得到相对运动波函数所满足的非线性的微分积分方程，我们数值求解这个微分积分方程得到系统基态能，而不是选择一个类氢原子的波函数变分使得能量的期待值最小。

From this point of surface as methord, this article studies the method of 4-dimention decompounds used by De Style and Mies van der Rohe in early 20 century and the methord of 4-dimention continuum used by Rem Koolhaas and others from late 20 century.

本文从表皮作为方法的角度探讨20世纪初以风格派和密斯·凡·德·罗等建筑师为代表的四维分解法和从20世纪后期至今以雷姆·库哈斯等当代建筑师为代表的四维连续法。

According to this background, this house is a great attempt from four-dimensional decomposition to four-dimensional continuum .

这个住宅设计是从四维分解到四维连续的一种大胆尝试，并引入拓扑学的基本方法处理动态空间。

Quaternions extend the concept of rotation in three dimensions to rotation in four dimensions.

四元数将三维中旋转的概念扩展到四维中的旋转。

For when Pope Hadrian IV had died in 1159, the cardinals elected two popes together, namely Roland of Siena, who took the name of Alexander III, and Octavian of Rome who though he was nominated by fewer cardinals, nevertheless with the support of the emperor Frederick usurped the name of Pope Victor IV.

时，教宗哈德良四死於1159年，两名枢机主教当选为教皇在一起，即罗兰锡耶纳，谁的名字了亚历山大三世和屋大维的罗马尽管他是谁提名的少红雀，不过的支持下，皇帝弗雷德里克篡夺教皇的名字维克多四。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。