维数

In order to determine the fractal dimension of the interface, structures with different rotation radii are set in the transition region. By using above regulation, the number of surface molecules of each rotation structure with certain radius can be obtained, then correlate these molecule numbers with the corresponding radii, in a logarithmic coordinate system the asymptotic slope of the correlated curve is the fractal dimension of the liquid-vapor interface.

为了确定界面的分形维数，在气液过渡区中作出不同回转半径的结构，利用（2～5）/1.2r〓规则找出其中所包含的气液界面上的分子数，然后将这些分子数与回转半径关联，在双对数坐标中此关联曲线的渐近斜率便是气液界面的分形维数。

For higher codimension, the situation becomes more complicated. Due to the counterexample of Lawson-Osserman [31], the higher codimension Bernstein type result is not expected to be true in the most generality.

在余维数为1的情况，这个结果以被推广到(n+1)-维欧氏空间中(n≤7)，以及在某种增长性限制下，这个结果被推广到任意维数欧氏空间中，这些结果可以参考[17]及其参考文献中所提到的文献。

A new approach for pattern recognition of ultra-high frequency signals of transformer partial discharge based on multi-scale analysis of wavelet packet and grid dimensionality is proposed, in which the multi-scale transform of wavelet packet is used to extract wavelet coefficients of UHF PD signals and by means of improving difference box-counting method the grid dimensionality of multi-scale wavelet coefficients is calculated and the multi-scale grid dimensionality is taken as the characteristic quantity that is used in the recognition of UHF PD signals.

提出了一种基于小波包多尺度分析和网格维数的变压器局部放电超高频信号模式识别的新方法，采用小波包多尺度变换提取局部放电超高频信号在多尺度上的小波系数，通过改进差盒计数法计算多尺度小波系数的网格维数，并将多尺度网格维数作为特征量用于局部放电超高频信号的识别。

In addition, the paper analyzed the influence of fractal dimension values on the compaction characteristics, and indicated that the fractal dimension values was the representation of gradation, the gradations with different fractal dimension values had different compaction process and energy dissipation, but the trend of compaction curve was consilient.

通过分析分维值对级配压实特性的影响，认为分维数是级配的表征，不同分维数级配的压实过程以及压实耗能也不一样，但其压实曲线变化趋势一致。

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。

The porosity and pore size distribution of HVFA pastes and concretes were determined by autoscan porosimeter. The results show that excessive fly ash content and comparatively high water-cementitious materials ratio will cause a big increase in porosity and harmful pore in HVFA pastes.

首次把X射线小角散射技术用于测定高掺量粉煤灰水泥浆体气孔—固体界面的分形维数，并就粉煤灰掺量、水胶比对气孔—固体界面分形维数的影响进行了分析，发现过高的粉煤灰掺量和较大的水胶比均会使分形维数大幅度增加。

The desulfurization experiments of CaO samples with various fractal dimensionswere carried out in the TGA to investigate the influences of fractality on the sulfationreaction, and the evolution of pore structures during the reaction. Under certainsulfation conditions, the calcium conversions of the CaO samples increase with theincrease in fractal dimension when fractal dimension is less than 2.68, and decreaseswhen it is more than 2.68. In the range of the experiment temperatures, the calciumconversion for a sample with a lower fractal dimension increases with the increase inthe temperature, and for a sample with a higher fractal dimension there exist anoptimum temperature at which the sample can reach the highest calcium conversion.

选用具有不同分形结构的CaO试样进行了硫化实验，研究孔结构的分形特性对硫化反应的影响以及硫化过程中分形孔结构的变化特性，实验结果表明，在一定的分形维数范围内，随着分形维数的增加，钙利用率增大，但分形维数超过一定值时(约为2.680)，钙利用率反而降低。

The crack and stress-strain of Chinese White Poplar were studied by the box counting method. The results showed that the cracks were obvious fractal and that the value of dimension D was determined to be between 1.2～1.5 by studying the crack propagation in the two dimensions. By comparing the crack propagation over a period of time, we found that the value of D increased as the crack increased.

运用数盒子法对裂纹发育带在二维平面内的分布进行了分形特征研究，发现木材裂纹具有明显的分形规律，分形维数为1.2～1.5；通过比较不同时间段的裂纹发育情况，发现裂纹的分形维数随着裂纹的扩展呈增加的趋势。

A time-delay reconstruction of a phase space equal to the original system has been made by analyzing of observed time series of current signal and vibratory signal, and the methods of choosing properly the embedding dimension and delay-time for phase space reconstruction have been studied in detail.

本文利用振动信号和电流信号时间序列，采用时间延迟法，重构了系统的等价相空间，并详细研究了嵌入维数及时间延迟的选择对重构相空间的影响，计算了铣削加工典型过程的Lyapunov指数谱，分析了系统的混沌特性；同时采用P-G算法，计算了混沌动力系统的奇异吸引子的分维数，分析了分维数与系统状态的关系，定量地指示出系统的混沌程度，同时也反映出系统的不可预报程度。

Finally, fractal characteristic is researched in the thesis. Fractional Brownian motion characteristic of sea clutter is validated and fractal dimention of sea clutter without taget and sea clutter with target are calculated by box-dimention method.Target detection based on fractal dimention is analyzed in brief and sea clutter multi-fractal characteristic is analyzed by MF-DFA.

最后，本文对海杂波分形特性进行了研究，验证了海杂波符合分数布朗运动的特性，通过盒维数法计算纯海杂波和目标海杂波的分形维数，简要分析了基于单重分形维数的目标检测，并采用MF-DFA对海杂波多重分形特性进行了研究分析。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。