查询词典 fundamental curve

Rational planar curve; rational space curve; rational ruled surface; moving curve/surface;μ-bases; singularity; self-intersection curve; moving curve/moving surface ideal; ideal-theoretic/set-theoretic generators

基础科学，数学，几何、拓扑平面有理曲线；空间有理曲线；有理直纹面；动曲线/曲面；μ基；奇点；自交线；动曲线/动曲面理想；集论/理想论生成元

First,The properties of the spherical Bezier Curvesproposed by Ken Shoemake(Spherical Bezier curve of first kind)are listed,such asEndpoint property,Symmetry property,Invariant property under solid motion,Spherical convex hull property,etc.,and the fact that this kind of spherical BezierCurve is devoid of subdivision property is pointed out;Based on subdivision,theconcept of a new kind of spherical Bezier curve(Spherical Bezier curve of secondkind)is proposed.This kind of spherical Bezier curve is continuous differentiable.Furthermore,generalization of Bezier curve on more comprehensive manifolds isdiscussed.2Spherical Chaikin algorithm and general spherical corner-cuttingalgorithm.

首先，文中列举了Ken Shoemake提出的点点生成的球面Bezier曲线(第一类球面Bezier曲线)的性质，如端点性质、对称性质、运动不变性质、球面凸包性质等，并指出这种球面Bezier曲线没有剖分性质；基于细分，文中给出了一种新的球面Bezier曲线(第二类球面Bezier曲线)的构造方法，指出这种曲线是连续可微的；作为这些理论的应用，文中改进了Ken Shoemake提出的球面插值曲线构造方法；进一步，文中探讨了Bezier曲线在更广泛的流形上的推广方法。2球面Chaikin算法和一般的球面割角算法。

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的&良性&分布与高阶相关性(correlation of order κ)，这两类序列具有&优&的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

The polarization curve is not sufficient for a reliable and unique validation of a PEMFC model since different parameters can lead to an identical polarization curve. A three-step validation approach is proposed for a complete and unique validation. These three steps are:(1) validated by the global polarization curve,(2) validated by the local current density distribution curve, and (3) validated by the cathode over-potential and anode over-potential versus current density curve. The results from the comparison of four flow-fields show that the PEMFC performance of the flow-fields decreases in order by interdigitated, metal foam, pin-type and parallel.

通过PEMFC参数敏感性研究发现，PEMFC性能受多种参数的影响，这些参数可分为非敏感性参数、敏感性参数和高敏感性参数；与阳极侧参数相比，PEMFC性能对阴极侧的参数更敏感；不同参数值的组合可以得到几乎完全相同的极化曲线，因此电池的极化曲线不足以用于验证数学模型的唯一性与可靠性；为验证PEMFC数学模型的唯一性与可靠性，提出了模型验证的三步法：极化曲线验证、局部电流密度验证和阳极总过电位与阴极总过电位验证。

Based on the existed theory of mareoids and fuzzy matroids, this thesis studies the closed regular fuzzy matroid and its fundamental sequence, the fuzzy base and its algorithm of closed fuzzy matroids, the fuzzy circuit and its algorithm of closed fuzzy matroids and so on. The main contributions of this thesis are as follows: 1 The necessary and sufficient condition of closed regular fuzzy matroid and a property of its fuzzy dual matroid are found by studying some properties of closed regular fuzzy matroid. 2 By studying some properties of fuzzt bases of closed fuzzy matroid, the necessary and sufficient condition of judging fuzzy bases of closed fuzzy matroids and some corollaries are found. In the end, an algorithm of obtaining a fuzzy base is given. 3 By studying some properties of fuzzt circuits of closed fuzzy matroid, some necessary and sufficient conditions of using its fundamental sequence to express fuzzy circuits are found. An algorithm of obtaining a fuzzy circuit is given. 4 By studying the fundamental sequence of closed regular fuzzy matroid, some necessary and sufficient conditions of fundamental sequence of closed regular fuzzy matroid are found.

本文在现有拟阵和模糊拟阵理论的基础上，研究了闭正规模糊拟阵及其基本序列，闭模糊拟阵的模糊基及算法、模糊圈及算法等内容，现分述如下： 1研究了闭正规模糊拟阵的一些性质，得到了闭正规模糊拟阵的充要条件及其模糊对偶拟阵的一个性质； 2研究了闭模糊拟阵模糊基的性质，找到了闭模糊拟阵模糊基的充要条件和几个推论，最后还给出了求模糊基的算法； 3研究了闭模糊拟阵模糊圈的性质，找到了用基本序列来表达模糊圈的几个充要条件，并给出了求模糊圈的算法； 4研究了闭正规模糊拟阵的基本序列，找到了闭正规模糊拟阵的基本序列的几个充要条件。

This problem is also important and valuable in Nonlinear Optics. It will be very helpful to understand how the aberrations affect the course of three- wave mixing, such as the change of conversion efficiency, the distribution of intensity and phase.Small signal solution of aberrated second harmonic generation is deduced from three-dimension three wave coupling functions. The numerical work gives out lot of results of different aberrations. The effects of the fundamental waves aberrations, which will change the conversion efficiency, distribution of intensity and phase in the frequency conversion, is analyzed. It shows that when walk-off and diffraction effects could be ignored approximately estimation of the phase distribution of second-harmonic wave could be done. The far field divergent angle and second moment radius of harmonic wave will vary with the aberration of fundamental wave, but the far field divergent angle will be obviously smaller than that of fundamental wave. The phase distribution of both fundamental and harmonic wave is measured using Hartmann-Shack wave front sensor in the experiment with 1064nm and 790nm lasers, respectively. Results are given.

首次从三维三波相互作用方程组推导得到了位相畸变光束倍频的小信号解；通过建立国防科学技术人学研究生院学位论文三维数值模型，编写相应仿真程序，首次得到了位相畸变光束倍频过程的大量计算结果，深入细致地研究了位相畸变光束经非线性光学频率变换后谐波的转换效率、光强分布、位相分布以及影响它们的各种因素；得出谐波的远场发散角和光斑二阶矩的变化规律会因为基波像差的不同而不同，但谐波的远场发散角明显地比相应基波的小的结论；得到了在走离效应和衍射效应等影响许多因素可以忽略的情况下，位相畸变传递到二次谐波的估算式；举例分析了KDP三倍频方案中，基波位相畸变对二次谐波和三次谐波的影响；实验工作中，用哈特曼一夏克传感器分别对IO64nm倍频过程和790飞秒超短脉冲倍频过程中的基波和谐波的位相分布进行了测量，给出了相应结果。

Small signal solution of aberrated second harmonic generation is deduced from three-dimension three wave coupling functions. The numerical work gives out lot of results of different aberrations. The effects of the fundamental wave's aberrations, which will change the conversion efficiency, distribution of intensity and phase in the frequency conversion, is analyzed. It shows that when walk-off and diffraction effects could be ignored approximately estimation of the phase distribution of second-harmonic wave could be done. The far field divergent angle and second moment radius of harmonic wave will vary with the aberration of fundamental wave, but the far field divergent angle will be obviously smaller than that of fundamental wave. The phase distribution of both fundamental and harmonic wave is measured using Hartmann-Shack wave front sensor in the experiment with 1064nm and 790nm lasers, respectively. Results are given.

首次从三维三波相互作用方程组推导得到了位相畸变光束倍频的小信号解；通过建立三维数值模型，编写相应仿真程序，首次得到了位相畸变光束倍频过程的大量计算结果，深入细致地研究了位相畸变光束经非线性光学频率变换后谐波的转换效率、光强分布、位相分布以及影响它们的各种因素；得出谐波的远场发散角和光斑二阶矩的变化规律会因为基波像差的不同而不同，但谐波的远场发散角明显地比相应基波的小的结论；得到了在走离效应和衍射效应等影响许多因素可以忽略的情况下，位相畸变传递到二次谐波的估算式；举例分析了KDP三倍频方案中，基波位相畸变对二次谐波和三次谐波的影响；实验工作中，用哈特曼-夏克传感器分别对1064nm倍频过程和790飞秒超短脉冲倍频过程中的基波和谐波的位相分布进行了测量，给出了相应结果。

The thesis takes the fundamental education as its focus, and the new public management theory as its logic support, and applies the case research method to analyze the background under where the current western countries" fundamental education administrative system is brought out, and discuss the this system"s establishment process, and finds out policy suggestions appropriate for Chinese quasi-marketing reform on fundamental education which are expected to provide more theorise reference for the decision-makers of Chinese fundamental education.

本文研究定位于基础教育，以新公共管理学理论基础为逻辑支撑，运用案例研究方法，分析当代西方国家基础教育管理体制制定的背景，探讨制定过程，总结西方国家基础教育管理体制制定过程的共性和个性，挖掘其对我国基础教育准市场化改革的政策建议，期望对国内基础教育政策决策者提供理论参考。

Algebraic curve is commonly used in CAGD. Traditional curve interpolation is in various forms of spline fuction. Although better result can be obtained by spline curve, the former two of elliptic, hyperbolic and parabolic shapes can not be represented by spline curve. An exploring research in this aspect is made in this thesis.

代数曲线是CAGD中经常用到的曲线，以往的曲线插值基本上是采用样条函数的形式，采用这种形式虽然能够获得很好的效果，但样条函数所能表达的形状都是抛物线型，对椭圆型与双曲线型曲线的表示是无能为力的。

The cubic algebraic curves (the Bezier curve and B style curve, etc belong to the parameter curve) is apter to realize the curve transition and fitting to dispersed data than the cubic parametric curves.

比如参数曲面与平面的交线就是一条平面代数曲线；平面参数曲线的等距曲线也是一条代数曲线。

Finally it offers the analysis of the fault-tolerance system as well as its test verification.

这样，运行于空间环境中的系统的设计目标就是在保证系统实时性

However, it is still difficult to find out the real reason of the increase of the keratinized gingiva during the orthodontic extrusion whether it is due to the proliferation of the gingival tissue or to its elastic nature, that is because the proliferation of the fibroblasts as well as the connective tissue changes in volume and the intra-fibers spaces were all immeasurable in most of the studies.

然而，仍然难以找到真正的原因增加的角化牙龈在正畸挤压它是否是由于扩散的牙龈组织或其弹性性质，这是因为增殖的成纤维细胞以及作为结缔组织的变化量和内部纤维空格都是不可估量的，大多数的研究。