维数

In our algorithm, 3D object patch in which user is interested is embedded to the circular disk on the plane. We must consider similarity between 3D patch and 2D disk.

本论文之摊平方式，主要是将使用者选定好之三维多面体表面区域，摊平至二维圆盘上，圆盘之圆周其实是一个多边形，边数和边长分别来自於三维物体边界之边数和边长比例。

E〓 is endowed with a new metric D, such that becomes a complete metric space. After that a locally convex complete pseudonormed space is constructed. Finally, E〓 is embedded into isometrically, and isomorphically.

在n维非紧模糊数空间E〓上引入一个新的度量D，使得成为一个完备的度量空间，然后我们构造了一个局部凸的完备赋准范空间，并将n维非紧模糊数空间等距同构地嵌入到空间之中。

Chaper 3 is general description of ADA encryption. Chapter 4 deals with the transform domain encryption. Includes the element of perfect and quasi-perfect transform domain encryption, and presents two type new schemes. Chapter 5 deals with asynchronous ADA encryption. Extends the general theory and model of asynchronous ADA scrambling, and introduces two type phase-distortion-free a synchronous ADA schemes. Chapter 6 is about new direction of ADA encryption. Includes TASI scrambling, transform domain dummy insertion scrambling, noise coving scrambling and other multi-dimension ADA scrambling, and proposes an adaptive dummy spectrum insertion asynchronous scrambling and a new adaptive noise-coving DFT scrambling algorithm. Chapter 7 is on permutation key. presents part results on permutation features, selecting criterion and constructing method. Chapter 8 introduces the hard and software design of a common ADA encryption/decryption system, and presents the experimental results on several proposed ADA encryption schemes.

第一章为绪论；第二章为语声信号、及其处理基础；第三章为模数模加密的一般描述；第四章为变换域加密研究，包括变换域加密机理，变换域完善与准完善保密研究，提出两种新的变换域加密方案；第五章为异步模数模加密研究，扩充了异步模数模加密的一般理论，介绍了两种新的无相位失真异步加密方案的原理与实现方法；第六章对模数模加密新方向：TASI应用途径、变换域伪谱插空置乱、噪声掩盖、多维置乱加密的原理和方法进行介绍，提出了自适应伪频插空异步模数模置乱算法与自适应DFT系数噪声掩盖置乱新算法；第七章为置换密钥性质、筛选准则以及构造方法研究的部分结果；第八章介绍了通用模数模加/解密实验系统的硬件、软件研制概况，并给出了几种加密方法的实验结果。

This paper analyzes the property of FNT, the characteristics of Kernel Matrixes and the relationship between Kernel Matrixes of two-dimensional Fermat number transform whose modulus are odd prime and image data, and presents and proves the deduction of the theorem which demonstrates the relationship among different transform matrixes corresponding to different roots of unity under the same odd prime modulus of FNT, and reveals the essence of FNT whose modulus are odd prime.

分析二维Fermat数变换性质、正反变换核的特点、二维模为奇素数的二维Fermat数变换正反变换核以及与图像数据的关系，提出了不同单位根对应变换矩阵间的关系定理的推论，证明了该推论中模为奇素数的二维Fermat数变换的不同单位根对应的变换矩阵之间的关系，揭示了模为奇素数的二维Fermat数变换的本质，在构造离散图象数据Fermat数变换时为单位根的选择奠定了理论基础。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

Fractal dimension structure of the Cosmos are explored, and the mathematical foundation, which include the expressions of fractal dimension differential and calculus, regular space integral solutions of fractal dimension differential equations, the fractal calculus definitions of fractal measure as well as the measure computational equation of self-similar fractal, of fractal dimension calculus and fractal measure are given.

摘 要：探讨了宇宙分维构造的形式，给出了分维微积分及分形测度的数学基础，包括分维导数及分维微积分的表述形式、分维微分方程的规整空间积分解、分形测度的分维微积分定义及自相似分形的测度计算方程。

In this paper,we mainly make a deep and systematic study of sample path prop-erties for high and infinite dimensional Gaussian processes,especially for high andinfinite dimensional Wiener process in stronger norm-Holder norm than ever(everbefore,there used to be uniform norm and the process was limited to one dimen-sion).We not only deal with all kinds of functional moduli of continuity,but alsoconcern with different forms of functional limit theorems of C-R increments.

本文主要对高维的以至无穷维的Gauss过程、特别是Wiener过程的样本轨道性质在较以往更强的范数—〓范数下作了系统深入的研究（以往通常采用一致范数，过程限于一维），研究的内容不仅包括各种形式的泛函连续模，而且还包括各种形式的C-R增量的泛函极限定理。

First the three-dimensional Hailmuhz equation of magnetotelluric field is split into two 2D equations which could be changed into 1D equation by Fourier transformation method. The two zootomic coefficients of the equation are found out by the derivation of vertical component of electromagnetic field being sufficient the equation and the boundary condition. The resolution of 1D equation can be confirmed.

首先将大地电磁场满足的三维亥姆霍兹方程降维分裂成两个二维响应方程，然后对每一个二维方程进行傅里叶变换，使二维方程变为一维方程，通过大地电磁场垂向方向的导数在地面上所满足的边界条件，确定外推方程中的两个待定系数，从而得到一维外推方程的解。

Results: in contrast with model group, SSM can (1) increase the survival rate of ARF in rats, cut down Scr and BUN at 24hr, improve renal function, slightly surpass Vp in its therapeutic effect;(2) mitigate the extent of renal pathologicchanges, decrease the numbers of renal tubule necroses and casts;(3) protect renal ultrastructure such as microvilli, mitochondria, endoplasmic reticulum of TEC, podocytic process of glomerulus epithelial cell,endothelial cell etc, better than Vp;(4) enhance SOD activity, lower MDA contents in renal cortex;(5) enhance NO contents in serum, reduce ET levels in plasma;(6) evidently cut down TNF- a contents in serum, superior to Vp;(7) antagonize calcium overload in TEC;(8) alleviate renal pathological changes in ARF metaphase (at 3d), advance regeneration and recovery of TEC, restore renal structure in ARF convalescence (at 5d), and better than Vp;(9) increase the expression of TEC PCNA and prepro EGFmRNA in ARF metaphase.

结果：与模型组相比，SSM能(1)提高ARF大鼠的存活率，降低24hr时Scr及BUN，改善肾功能，其疗效略优于维拉帕米；(2)减轻ARF肾脏病变程度，减少24hr肾小管坏死数及管腔内管型数；(3)对肾脏的超微结构如肾小管上皮细胞微绒毛、线粒体、内质网、肾小球上皮细胞足突、内皮细胞等形态结构均有一定的保护作用，其疗效略优于维拉帕米；(4)提高肾皮质SOD活性，降低MDA含量；(5)提高血清NO水平，同时降低血浆ET含量；(6)显著降低血清TNF-α的水平，疗效明显优于维拉帕米；(7)拮抗小管上皮细胞[Ca~(2+)]_i的升高；(8)使ARF中期(第3d时)肾组织病变较同期其它两组明显减轻，并使肾小管细胞再生修复提前，至ARF恢复期(第5d时)肾组织结构恢复重建良好；作用明显优于维拉帕米；(9)促进ARF中期肾小管上皮细胞PCNA的表达及EGF前体mRNA的合成，从而增加EGF的合成释放，而维拉帕米无此作用。

However,there have been no papers which have investigated Minkowski and Minkowski slant helices and Minkowski conical geodesic curves so far as.In this paper,our major study is to give the definition of Minkowski general helix and Minkowski slant helices and Minkowski conical geodesic curves in indicators 1 in pseudo-Euclidean three-space (that is, three-dimensional Minkowski space), and study the definition of equivalence Minkowski general helix, By considering geometric invariants of these space curves, we can estimate the order of contact with those special curves for general space curves.

本篇文章主要研究在指标数为1的3维伪欧氏空间(即三维Minkowski空间)中，我们给出Minkowski一般螺线、Minkowski斜螺线和Minkowski锥面测地线的定义，研究Minkowski一般螺线的等价定义，给出Minkowski斜螺线和Minkowski锥面测地线作为三维Minkowski空间中的特殊曲线所特有的性质，并通过考虑三维Minkowski空间曲线的几何不变量，估计Minkowski斜螺线和Minkowski锥面测地线这两种特殊曲线和一般Minkowski空间曲线切触的阶数。

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。