可变换性

Chaikin algorithm is the simplest discrete curve modeling method.In thepaper planar Chaikin algorithm is generalized into sphere,and the practicability ofthe algorithm as well as the continuous differentiable property of the generatingcurve is proved.It is shown that the curve generated by Chaikin algorithm is apiecewise spherical Bezier curve of second kind of order two.Furthermore,generalspherical corner-cutting algorithms are discussed,and it is pointed out that thecurve generated through corner-cutting has"Spherical Variation DiminishingProperty".3Curve interpolation method restricted on a smooth surface based ontransformation.

Chaikin算法是最简单的离散曲线造型方法，文中将Chaikin算法推广到球面，证明了算法的可行性和生成曲线的连续可微性，指出球面Chaikin算法得到的曲线是分段的二次第二类球面Bezier曲线，并给出了用球面Chaikin算法构造球面插值曲线的算法；进一步，文中讨论了一般的球面割角算法，指出由球面割角算法得到的曲线具有"球面变差缩减性质"。3基于变换的约束在光滑曲面上的曲线插值方法。

In modern science, it is "the invariability under transformations" reached in the course of scientists\' interiority using the instrument of symmetry that makes science to be of public intelligibility and acceptability.

在现代科学中，科学家们自觉地运用对称性工具实现"内在化"而得到的"变换下的不变性"，使得科学具有了公共可理解性与可接受性。

The paper summerizes several general pratical new techniques, such as the analyzers of program profiles, maximum potential parallelism, array privatizability, loop parallelism; the visualizers of the statement data dependence graph, procedural callgraph, loop iteration space graph and interactive tools of array privatization and unimodular transformation; the automatic techniques of array privatization combined data dependence and coverage, the computation of parallelizing unimodular transforming matrix for mult-nested loops, enhanced unimodular transformation with array reduction recognition, non-loop level parallelism revealing technique, dynamic dataflow analysis and optimization of cross-loop local cache reuses, etc.

本文从而概括了若干具有一般性的实用新技术，如：程序计算量分析、最大潜在并行性分析、数组私有化分析、循环并行性分析等动态程序分析技术；语句数据相关图、过程调用图、循环迭代空间相关图、交互数组私有化、交互幺模变换等可视化语义交互分析变换技术等等；总结了若干自动并行化新技术，如：结合相关和覆盖的数组私有化方法、对多层嵌套循环计算幺模并行化变换矩阵的循环幺模变换方法、结合数组规约识别增强幺模变换的技术、发掘非循环级并行性的技术、动态数据流分析技术、优化利用循环间Cache数据局部性的技术等等。

The method optimizes the features according to the class separable criterion of margin of within-class and among-class distance and selects the optimized feature vector combination based on four kinds of features,such as gray histogram feature,wavelet transform feature,gray level co-occurrence matrix feature and moment invariants feature,with 26 dimension feature vectors in all.

针对冷轧板带材常见表面缺陷图像识别的特点，提出了板带材表面缺陷多特征优化组合方法，该方法以直方图统计特征、小波变换特征、灰度共生矩阵特征、不变矩特征等4类特征共26维特征向量为基础，依据类间类内距离差的类别可分离性判据对特征进行优化，选出最优特征向量组合。

Module history and module family data were saved in the form of ordered three-dimensional group, and then the extensibility and transformation of module-matter-element were studied.

该方法首先在物元模型的基础上，结合模块自身特点，建立了模块物元与模块族物元，以有序三元组的形式规范化地保存了历史模块和模块族数据，并研究了模块物元的可拓性及其变换。

By establishing the correspondence between the primitive operation in polynomial and clause solution in SAT,an efficient algorithm has been built to obtain all solutions which satisfied the problem.

利用一个简单的变换，将可满足性问题转化为多项式形式，然后根据命题逻辑的性质以及多项式的性质，得到一个求解出SAT问题所有解的算法。

The solvability of quadratic matrix inequalities of singular H∞ control problems with infinite zeros is studied in this paper. It is proved that the quadratic matrix inequality can be solved directly via the generalized eigenvalue problems. The previous method of solving the quadratic matrix inequality involving complicated decompositions and transformations of the systems is avoided.

摘要研究具有无穷远零点的奇异H∞控制问题的二次矩阵不等式的可解性，证明了通过求解广义特征值问题，可以直接求得二次矩阵不等式的解，从而简化了原需通过复杂的系统分解和变换来求解二次矩阵不等式的方法。

This dissertation studies some topics in soliton and integrable system,which mainly include as follows:exact solutions especially travelling wave solu-tions and solitary wave solutions,Painlevēproperty,transformation,similarity reduction,symmetries and their Lie algebra structure,generation ofsoliton hierarchy and their zero curvature representation,Hamiltonian struc-ture,Lax or Liouville integrability,nonlinearization of Lax pairs,applications ofWu's method and symbolic computation.

本文研究内容涉及到孤立子和可积系统的多个方面：精确解特别是行波解和孤波解，Painlevē性质、变换、相似约化、对称及其Lie代数结构、孤子族的生成及其零曲率表示，Hamilton结构，Lax和Liouville可积性、Lax组的非线性化以及吴方法和符号计算在上述研究中的应用。

The relative transformation can improve the distinguishing ability between data points and reduce the impact of noise and sparsity of data.

相对变换可以提高数据之间的可区分性，并能抑制噪音和数据稀疏的影响。

The Chinese light verbs supported by neuromechanism can explain the generative question in Chinese interchangeable phrases, causative structures, reverse factitive structures and verb-complement structures. All these questions can be marked by causative in the lexical feature and moving in syntax. All the conclusions demonstrate that we can unify the explanations of Chinese syntax and lexicon by light verbs. Therefore light verbs are the interface among brain, lexicon and syntax.

具有神经基础支持的汉语轻动词理论可以解决汉语可变换位置词组、使动句、反转型使役句以及动补结构等句子的生成问题，而这些问题在轻动词词汇特征上可以用&致使&性来统一标示，在句法特征上可以用&移位&来统一操作，从而表明汉语轻动词可以实现词法句法的统一解释，轻动词研究是大脑、词库以及句法研究的结合点。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。