维数

A dynamical system is just a finite dimensional representation of the system quiver Q with dimension vector .

一个动力系统就是系统箭图Q的一个维数向量为的有限维表示。

The floc structure of pDMDAAC-FA is denser and solider than that of PFS.

得到pDMDAAC-FA、PFS的二维分形维数分别为1.7017、1.6928。

It should be noted that here we only concern about the four dimensional case, neglecting other dimensional black holes.

需要说明的是本文只关心四维黑洞情形，不考虑其它维数的黑洞情形。

It is shown that many of the existing integral transforms (including their logically equivalents) such as chirplet transform, dispersion transform, wavelet transform, chirp-Fourier transform, short-time Fourier transform, Gabor transform, Fourier transform, cosine transform, sine transform, Hartley transform, Laplace transform, z transform, Mellin transform, Hilbert transform, autocorrelation function, cross-correlation function, and the energy and mean of a signal, can each be considered as a special case of the FMmlet transform with specific parameters. In fact, an inventory of subspaces of FMmlet transform runs into countless numbers. The subspaces mentioned above are merely a few among a zoo of subspaces. They are essentially obtained by cutting the transform space of FMmlet transform at different positions, and can be likened to the computed tomography in medical diagnosis. Through these subspaces we actually see different slices or profiles of the FMmlet transform.

将现有诸多变换置于统一的 FMmlet 变换中加以审视，发现 chirplet 变换、频散变换、小波变换、 chirp-Fourier 变换、短时 Fourier 变换、 Gabor 变换、 Fourier 变换、余弦变换、正弦变换、 Hartley 变换、 Laplace 变换、变换、 Mellin 变换、 Hilbert 变换、自相关函数、互相关函数、能量和均值等，均为 FMmlet 变换在其参数取特定值时的特例；上述诸变换之间的差别，主要在于变换空间的维数有别，以及在不同空间维上取值的不同；这些变换有如医学诊断中的 CT，均由压缩 FMmlet 变换域空间所致，可以说我们通过这些变换看到的，是 FMmlet 变换的不同剖面。

Direct and accurate calculation on three-dimension watershed geomorphology is one of key issues in current fractal geomorphology.

实现具有三维立体特征的流域地貌分形维数直接准确计算，是目前分形地貌学研究所面临的主要问题之一。

An estimate of the Hessian of the Lagrangian is updated at each iteration using the BFGS formula.

由于自变量的维数很高，这样的问题是被分解成多个低维子问题来求解的。

Firstly, Wavelet-Galerkin algorithm for solving the first kind of singular integral equation with the Hilbert kernel is proposed, we use the characteristic of periodic wavelet on L~2([0,1]) and Hilbert kernel to solve and make stiff matrix lower dimensions and become sparser through thresholding,thus the cost of computation is reduced. Because of the singularity of Hilbert kernel we use Tikhonov regularization method to solve the system of stiff equation. At last the convergence and numerical result of approximate solution are given. Secondly, an approach of regularization based on Fourier is presented for sideways heat equation; we give the theory proof and error estimate.

首先，提出了含Hilbert核的第一类奇异积分方程的小波伽辽金(Wavelet-Galerkin)数值算法，该算法中利用了L~2([0，1])上的周期小波和Hilbert核的特点进行处理，使得刚性矩阵维数降低并且通过阈值使得它更加稀疏，减少了计算量；由于Hilbert核的奇异性，通过Tikhonov正则化方法求解所得到的刚性方程组，给出了收敛性和数值结果；其次，对标准的一维逆热传导方程给出了一种基于Fourier正则化方法，给出了理论证明及其误差估计，解决了文献中算法与理论误差估计的不相匹配的现象，该正则化方法不仅保留了测量数据的部分高频成份，且与文献中的算法具有同样的计算量和误差估计。

First image and inverse image of refinement of semi-topogenous order on L been defined by GOH.

并由此得到一维非退化扩散过程样本轨道的象集和逆象集的Hausdorff维数。

Aiming at the dual affects to classification results by each input data, this method has punish item be fuzzy, compensates weight to classification, reconstructs the optimization problem and its restrictions, reconstructs Langrage formula, and presents the theories deduction. This method is applied to the credit evaluating system of personal loan.

1引言支持向量机(Support Vector Machine，SVM)是20世纪90年代中期在统计学习理论(Statistical Learning Theory，SLT)的基础上提出的一种新的机器学习方法，它基于VC维理论和结构风险最小化原理，在很大程度上克服了传统机器学习中的维数灾难以及局部极小等问题[1，2]。

The relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar-functions of generalized Brownian Sheet is obtained.

讨论了N指标d维广义Brownian Sheet极函数的特征，得到了满足Lipschitz条件的连续函数类与广义Brownian Sheet的极函数类之间的关系，给出了广义BrownianSheet不动点的Hausdorff维数和Kolmogorov下熵指数的一个不等式。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。