但二维理论又存在非物质性的问题，因为我们所在的尺度看到的是四个维。
The problem with a two-dimensional theory is that it is unphysical, as we see four dimensions at our scales.
所有这些与分形学之间的联系还是不可知的，但是我在研究中已经发现它们之间确实存在共性，即都具有非整数维(在同样尺度下)。
No relation of all this to fractals is known, but in my work I've found that they do have a common property, that is, a non-integer dimension (at some scale).
微尺度力学和MEMS系统中的低维材料性能研究是当今国际多学科交叉研究的热门课题。
The study about tiny scale mechanics and material performance in MEMS system today is a hot topic in the intercross investigation among many international subject.
首先，利用奇异摄动理论对再入飞行器状态变量进行两个时间尺度的划分，将系统状态方程分解成两个低维子系统。
Firstly, the state variables of the reentry vehicle are decomposed into two sub-systems of different time scales using the singular perturbation theory.
美术馆的室内设计是轻松快乐和令人惊喜的，通过材料、变化的空间尺度、颜色及质地呼应了维尔贝克的历史建筑。
The galleries have been designed as a place of delight and surprise, reflecting the historic architecture of the Welbeck Estate through their materiality, changing scales, colour and texture.
然后，应用最优控制理论得出慢时间尺度上的解，并将其作为降维后的最优参考轨迹；
Then, through solving the slow time-scale problem by optimal control theory, the optimal reduced-order reference trajectory is obtained.
在风向逐渐或骤然改变情形下，计算的时间响应尺度与海上观测符合，而且演化中的二维谱结构得到良好刻画。
In the case of gradual and abrupt shift of wind direction, computed response time scales agree with field measurements and the evolving two dimensional spectral structures are well depicted.
论文基于这一思想，从二维平滑函数出发，并根据尺度呈级数变化的特点，导出了一组多尺度小波滤波器。
According to the peculiarity that the scale exhibit progressional variety, this paper deduces a group of multiscale wavelet filter from two dimensions smooth function.
揭示中国古代楼阁群体组合中的视觉控制，是综合了建筑三维尺度以及建筑具体构成的比例控制。
The Visual control is the proportion control of the three dimension scale and the detail compose in the Chinese ancient storeyed Building Group compose.
采用线性稳定性理论和多重尺度方法，研究三维可压缩的非平行流边界层稳定性问题。
The compressible linear stability theory and the method of multiple scales are used to study the problem of three dimensional nonparallel flow stability for boundary layers.
种群格局信息维数能够刻划格局强度的尺度变化程度，揭示出种群个体分布的非均匀性状况。
The information dimension of population patterns quantifies the scale variation degree of pattern intensity, and discloses the unevenness of individual distribution.
给出了一个基于一维定常积云模式的对流涡度参数化方案，并和天气尺度运动的计算结果作了比较。
A vorticity parameterization scheme for cumulus convection is derived by using a one dimensional steady cumulus model. The result is compared with that determined by synoptic-scale variables.
本文认为陈维崧是依据“仁”的尺度对民俗文化关照，主要是批判与顺应两种态度。
The paper acclaimed that Chen Weisong' s attitudes towards the folklore culture were mainly according to his inner criterion, which including two kinds: criticizing and accepting.
认为在宇宙尺度上，任何时刻，三维空间是均匀的和各向同性的。
That the scales in the universe, at any time, three-dimensional space is homogeneous and isotropic.
将SAR图像的特点与分形理论相结合，提出了一种新的基于区域自选的多尺度分形维数边缘检测方法。
With the combination of SAR image features and fractal theory, a new method of edge detection by calculating the fractal dimension multiscalely is proposed.
小波变换具有多分辨率和多尺度特性，特别适合于二维图像信号的处理，目前已应用在静止图像的压缩标准中。
While wavelet transform is suitable in image compression due to its multi-resolution and multi-scale analysis property, and is used in the standards of image compression.
给出了三维黑洞温度，研究了该时空时间尺度变换的补偿效应。
The temperature of a three dimensional nonstatic black hole is given. The compensate effect under time scale transformation in the space time is studied.
探讨了基于DEM的VLL物方影像匹配方法、多尺度表达的数字高程模型，以及自适应窗口大小和变化阈值的确定等用于三维变化检测的关键技术。
And many key techniques such as VLL matching, multi-scale DEM, self-adapted matching window and thresholds for the framework are discussed and investigated deeply.
结果表明，尺度-小波能量谱和时间-小波能量谱相比有较好的分类效果和较低的特征维数。
The result shows that, compared with the time-wavelet power spectrum, the scale-wavelet power spectrum has a higher recognition accuracy and smaller dimension of feature vector.
对断裂尺度分布的分形维数而言，损伤演化过程是一个增维过程。
For the fractal dimension of the fracture scale distribution, the damage evolvement process is a process of increasing dimension.
该细胞是细胞的三维尺度模型。
基于归一化尺度计盒维数方法研究了超声波分形特征。
Fractal properties of ultrasonic signal are researched based on normalized scale box-counting dimension method successfully.
实验表明此方法适用于几何尺度较小或温度梯度较小的三维位相物体温度场的散斑照相测量。
The experiment shows that this method is suitable for the measurement of the phase object with the small sectional size and the small temperature gradient.
采用计盒维数方法对霜层生长图像分析表明，充分生长的霜层在一定尺度范围内具有分形特征。
The Analyses on frost image by box-counting method express that full growth frost was a fractal structure ranging in some scale.
将分形用于自然纹理描述，指出了单一分形维数测度用于纹理分析的局限性，并提出了尺度分维的新概念。
The limitations of single fractal dimension for texture analysis are pointed out and a new concept of scale fractal dimension is proposed.
计算得到了上游壁面涡的特征尺度，结果表明上游壁面涡具有高度的三维性，其特征尺度依赖于流速比和环境水深。
The computed characteristic scales of the upstream vortex show distinguished three-dimensionality and vary with the velocity ratio and the water depth.
种群格局关联维数是种群个体空间关联尺度变化规律的反映，表明了种群个体的空间相关程度。
Correlation dimension of population pattern could reflect not only the scaling variation properties of spatial correlation of individuals, but also the spatial occupation degree of population.
多维尺度分析是模式识别与数据挖掘领域一个有力的降维工具。
Multidimensional scaling is a powerful tool for dimensionality reduction in the field of pattern recognition and data mining.
在BFGS变尺度算法中所用的一维搜索方法是二次插值算法。
The one dimension search method of second differential algorithm is used in the Variable metric method of BFGS.
在此基础上，讨论了断裂尺度分形维数与地壳活动性的关系。
Based on this, the relation between fracture fractal dimension and the Earth crust activity was discussed.
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