部分函数

Thismethod adopted affine transformation model and a Lie derivative-based analytical algorithm.We introduced the process and characters in extracting information of biological visionsystem, studied the feasibility of the generalized Gabor function used as receptive fieldfunction in extracting information and analyzed affine transformation group and Liederivatives. Finally, we deduced the mathematical denotation for Lie derivatives, i.e. theinfinitesimal generator of the geometric distortion in affine transformation.

对生物视觉信息提取的过程及特点进行了介绍，其中主要研究了广义Gabor函数作为感受野函数提取初级视觉信息的可行性；对仿射变换作为外界图像信息在视觉成像系统上的投影模型的原理进行了初步讨论；对Lie变换群微分算子用于提取仿射变换不变量的分析方法作了剖析，并推导了该方法中关键部分——仿射变换Lie微分算子的具体表达式，也就是几何变形无限小微分算子的计算表达式，使下一步编程实现该方法成为可能。

Solvability of (0,δm),(o,m1,Am2,/m3)-interpolation problems on π-antiperiodic function and some of 2-oeriodic situation were discussed, and some fundamental problems on ;π-antiperiodic function were considered in this aspect.

讨论以π为周期的反周期函数的(0，δ~m)，(0，δ~p)插值问题，(0，m_1，m_2，m_3)插值问题及部分双周期情形解的存在性，其中也包含了许多反周期函数的基本问题的讨论。

Then we propose a new kind of kernel function—autocorrelation kernel function.

核学习方法中核函数的研究：核函数是核学习方法的核心部分。

The relationship between the partial spectra of a Boolean function and the spectra of its sub-functions is discovered.

本文揭示了布尔函数部分点谱值和其子函数谱值的关系。

Take the method of "subarea" and "conjunction" to segment the whole request model to three parts. Making use of boundary continuousness between medium and lining structure at stress and displacement, construct a wave function that can satisfy the stress boundary condition at horizontal surface by the scattering of SH-waves in circular part. And then, availing of the wave function, conjoin the circular part into the semi-circular hollow space at common boundary. The problem can be reduced to solve the question that can only meet the condition of "conjunction". Finally, the solution of the problem can be summarized to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations.

采用"分区"与"契合"的方法，将整个求解区域分割成三部分，利用介质与衬砌结构在边界上的应力、位移的连续性，构造一个可以自动满足水平界面上应力边界条件的圆域对SH波散射的波函数；再利用这一波函数将圆域与半圆形凹陷半空间的"公共边界"进行"契合"，将问题简化成对一个只需满足'契合'边界条件的散射问题的求解；最终归结为对一组无穷代数方程组的求解问题，利用截断有限项的方法对其进行计算。

On the second part, we investigate a decomposition formula of spectrum of a class of m-valued logical functions.

第二部分研究环上逻辑函数的谱分解式及其在多维广义Bent函数构造中的应用。

In the first four sections of this paper, these basic knowledge and calculational methods for the study of potential energy function are simply introduced. 9-parameter Murrell-Sorbie analytical potential energy function that can accurately describe especial potential energy function of diatomic molecule is obtained through calculations and analysis for the first time.

本文前面部分在简单介绍与分子势能函数研究相关基础理论知识和计算方法的基础上，通过计算、分析比较，首次得到了能够正确描述双原子分子特殊势能曲线的九参数Murrell-Sorbie解析势能函数。

Compared with the initial value problems of scalar conservation laws with smooth flux function, the global weak entropy solutions for the initial-boundary value problems of scalar conservation laws with weak discontinuous flux function include the following new interaction types: a rarefaction wave collides with the boundary and is absorbed compltetely or partially by the boundary; a rarefaction wave collides with the boundary and the boundary will reflect a contact or non-contact shock wave; a contact or non-contact shock wave collides with the boundary and is absorbed by the boundary; a contact or non-contact shock wave collides with the boundary and a new non-contact shock will rebound from the boundary simultaneously or later.

与具有光滑流函数的单个守恒律的初始值问题相比，具有弱间断流函数的单个守恒律初边值问题的整体弱熵解中包括下列新的相互作用类型：稀疏波碰到边界并被边界部分或全部吸收；稀疏波与边界相撞，边界反射出一个接触或非接触激波；接触或非接触激波碰到边界并被边界吸收；接触或非接触激波与边界相撞，边界同时或稍后反射出一个新的非接触激波。

Using the method of blow up lower and upper solutions, the existence and boundary behavior of positive boundary blow up solutions for some elliptic systems of competitive type with singular weight functions are obtained, here the singular weight functions are permitted to be bounded in some parts of the boundary, and to go to infinity or even oscillate in other parts.

利用爆破上、下解方法，本文建立了带奇异权函数的竞争型椭圆方程组正的边界爆破解的存在性和边界行为，这里奇异权函数可以在边界的某一部分有界，而在其他的部分趋于无穷或者震荡。

First, we consider nonholonomic chained systems with modeling error, in this section,based on back-stepping , using the so-called adding a integrator , state-scaling technique , we design discontinuous feedback law,such that the trival solution of the closed-loop systems global strong stable; Second,we consider high-order nonholonomic chained systems with modeling errors and external disturbances, in this section,using input/state-scaling and integrator backstepping methods , we design discontinuous feedback law and give out the switching strategy, such that the closed-loop systems global /C-exponential stable; Finally, we consider a class of more general power chained form systems with particular drift-terms, in this section , using Lyapunov method, we design time-varying feedback law , such that the closed -loop systems p—exponential stable.

第一部分考虑的模型为带有模型误差的高阶非完整链系统，我们运用加幂积分器、State-scaling技巧以及基于Back-stepping方法构造出不连续反馈律，从而使得所讨论系统的闭环系统的平凡解全局强稳定；第二部分考虑的模型为带有模型误差的不确定高阶非完整链系统，这一部分我们运用input／state scaling和integrator backstepping方法构造出不连续反馈律，并给出切换策略，使得所对应的闭环系统全局κ-指数稳定；第三部分考虑的系统是形式更为一般的且带有特殊形式漂移项的幂链系统，利用Lyapunov函数方法，设计出时变反馈律，从而使得相应的闭环系统ρ-指数稳定。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。