零函数

The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

In this role, the epsilon takes a 0-ary function/functor.

在这种情况下，空串使用一个零元函数/函数对象。

Definition 1 If the limit of function is zero as, then is called an infinitesimal as.

定义 1 如果函数当时的极限为零，那么称函数为当或

If deg f = n, then Rfc is an empty set. For all the functions of degree 2, Rf have at least 2n-1 vectors, when Rf is a linear subspace, the relationships between Rf and Lf are discussed . Boolean functions have no nonezero linear structure if and only if there are n linear independence vectors in f, the correlation of the vectors in ?

证明了，若degf=n，则R_f~c为空集，对于所有的二次布尔函数而言，均有R_f~c中的元素个数大于等于2~(n-1)，给出了R_f构成线性子空间时，R_f和L_f之间的关系，还给出布尔函数不含有非零线性结构的充分必要条件是ζ_f中含有n个线性无关的元素。

The basic idea was to discrete the structure and find the load function according to the energy criterion of buckling and the principle of random displacement method. As the critical load is the minimum of the load function, a problem of frame buckling can be transformed into an optimization problem. Therefore, the critical load can be found through solving the optimization problem.

先将结构离散为一个有限自由度系统；然后根据有限自由度系统平衡稳定性的能量准则和随机位移法的基本原理，建立符合能量准则的载荷函数，该函数不为零的最小值即为临界载荷，由此将稳定问题转化为无约束的多维优化问题；最后应用遗传算法求出相应于最优解的目标函数值。

The aim of this paper is to answer the query on the foundation of quantum mechanics advanced by Tao Zongying in articles,Acta Mathematica Scientia,1982,2(2):183～192 and Acta Photonica Sinica,1997,26(9):769～770.It is shown,based on the globalism concept in quantum mechanics,that Landau and Lifshitz′s momentum probability distribution function of a particle in a one dimensional infinitely deep square potential well is correct,and that Pauli and other′s distribution function is incorrect.The problem of mome...

本文回答了文献1～2对量子力学提出的疑问基于量子力学的整体性概念指出，Landau和Lifshitz给出的一维无限深方势阱中粒子的动能概率分布函数是正确的，Pauli等人给出的概率分布函数是不正确的从量子测量理论的角度讨论了一维谐振子的动量概率分布问题，并且指出势能大于本征能量的概率不为零并不表示存在负动能的概率分布区域

The preliminary chromatogram data were resolved with Mallat algorithm of wavelet analysis theory. This method that resetting the high frequency signals, reconstructing low frequency and then correcting the background signals in the original signal was to avoid the data skewness with negative digital points after background correction and achieve the baseline correction; according to the study and analysis of simulated data including curve background and real data of the needle-plate and free metal partials insulation defects, the method is effective; the best wavelet function of the background correction is Db5 and the best resolution times of the background correction is 8 for chromatogram data of SF_6 decomposition products, based on the calculation with different wavelet functions and resolution times.

在初步获取的气相色谱数据基础上，运用小波分析技术中的Mallat算法对色谱数据进行小波分解，采取将高频信号置零，重构低频背景信号，再用原始信号扣除背景信号的方法，并对背景信号进行纵向平移以避免扣除后出现负数据点造成色谱峰失真的题目及达到色谱图基线校正的目的；通过对含曲线背景信号的模拟色谱数据和针-板、自由金属微粒缺陷下的真实数据的计算研究表明，该方法的应用是有效的；并通过对不用小波函数和不同分解次数的背景扣除计算，确定了SF_6气体放电分解组分色谱背景扣除所选用的最佳小波函数为Db5小波和最佳分解次数为8次。

Furthermore,a cost function which can null the noise compontnt of signal vector is presented.

设计了一个代价函数，满足此代价函数就可使信号向量在噪声子空间的投影为零。

One of the two parameter group can be obtained directly by taking its corresponding nonnegative functions to be zero and another parameter group can be obtained through learning according to its corresponding nonnegative functions—performance index.

其中的一组可调参数可通过令相应的非负函数为零直接求得，而与另一组可调参数相对应的非负函数就是用于这组参数学习的性能指标。

Section two elaborates the structure of a simple model on static yield curve of zero-coupon bond. According to the difference of constitution principle, the dissertation divides the numerous static models into direct ones and indirect ones. On the basis of setting forth the different constitution thoughts of two methods, it compares the merits, shortcomings, and the application scopes of the two methods. Spline model is the most common indirect method, and is the study emphasis of this section, especially its three key approaches that are defining the rank of function, the subinterval number to be divided, and knot of each subinterval, which are fully elaborated in the dissertation.

第二节阐述了现行静态零息票债券收益率曲线简单模型的构造，根据构造原理的不同，论文把众多静态模型划分为直接法和间接法两大类，在简述两种方法各自不同的构造思想的基础上，对两种方法的优缺点及适应范围进行了比较；分段样条函数模型作为最常用的间接法，是本节研究的重点，尤其是对它的三个关键环节：确定函数的阶数、确定所分的段数、确定各段的分解点，论文更是给予了充分的论述。

If you are unfortunate enough to the lovelorn, please tell me, I will help you out, really, please contact me!

如果你不幸失恋了，请告诉我，我会帮助你摆脱困境，真的，请联系我啦！

China's plan to cut energy intensity by 20 percent and pollutant discharges by 10 percent between 2006 and 2010 is a case in point.

中国计划在2006年到2010间降低20%的能源强度和减少10%的主要污染物排放，就是一个这样的例子。