Other works conducted by author during past years are also reported in this dissertation: Two modified training algorithms for feedforward network are proposed, one of which uses Cauchy target function and the other adopts an adaptive learning scheme.
除了上述工作之外，在攻读博士学位期间，作者还开展了如下一些研究：提出了两种针对标准BP算法收敛速度慢的改进算法，其中一种方法是将目标函数及激性函数作了修改，而另一种方法则具有自适应学习率。
Pressure effects on the Cauchy relations and the normalized elastic constants of hcp lithium are also discussed in this paper.
还討论了压力对Cauchy关係和相对弹性常数的影响。
Authors have predicted that a nonscalar curvature singularity will be formed at the Cauchy horizon of 1 + 1 dimensional charged dilaton black hole for the case of infalling null dust.
作者预告，对于入射的零质量尘埃的情况，1＋1维带电的膨胀子黑洞的Caochy视界将出现非标曲率奇性。
We start by obtaining a flagged form of the Canchy determinant and establish a correspondence between this determinant and nonintersecting lattice paths, from which it follows that Cauchy identity on Schur functions.
首先我们得到了一个带标志的Cauchy行列式，建立了这个行列式和不交格路径丛的对应，从而得到了关于Schur函数的Cauchy等式。
In this paper, taking Cauchy inequality for example, we discussed some problems on inequalities teaching in middle schools.
以经典的柯西不等式为例，从不等式的证明、推广以及它们的一些应用，对在中学数学教学中的一些问题进行讨论
Cauchy—inequality is an extremely important inequality. Ingeniously applies it or its promoted type nimbly, may cause some more difficult problem to be easily solved.
摘要柯西不等式是一个非常重要的不等式，灵活巧妙地应用它以及它的推广式，可以使一些较为困难的问题迎刃而解。
Secondly, through integrating by parts and using Cauchy inequality, thanks to a lemma of Gronwalls type, an energy inequality is got and a priori estimate is established.
接下来经过分部积分和Cauchy不等式，并利用Gronwall型引理得到一个能量不等式，对解的范数给出先验估计。
First of all, Cauchy inequality is used to obtain a basic inequality. Secondly, the functions of basis are made by Galerkin method, and the error estimates of eignevalues are obtained by Cauchy inequality. At last, the computational method of the approximate value of the eigenvalues turns out immediately, and accuracy of the-th approximate value is estimated by the n-tb approximate value.
首先利用Cauchy场不等式证明了一个基本不等式；其次采用Galerkin方法来构造适当的基函数，并利用Cauchy不等式给出了其特征值计算的误差佑计式；最后得到计算梁横向振动问题的特征值的近似值的算法，而且可以用第n次近似值来估计第n-1次的近似值的精确度。
Secondly, through integrating by parts and using Cauchy inequality, thanks to a lemma of Gronwall's type, an energy inequality is got and a priori estimate is established.
接下来经过分部积分和Cauchy不等式，并利用Gronwall型引理得到一个能量不等式，对解的范数给出先验估计。
Therefore, in order to simplify the proving process of these inequalities. Though reading a lot of relevant resource, we begin with the basic concept of math, and use an ingenious way――probabilistic method, which means that according to the main features of inequality theory, combining the basic concepts and formulas of probability, through creating one suitable probability model, giving some concrete meanings of random events or random variables, proving through probability theory, we discuss the Cauchy inequality, Class inequality, Jensen inequality, and several common inequality`s proofs.
因此，为了简化这些不等式的证明过程，通过阅读大量的相关资料，本文从数学的基本概念入手，运用了1种巧妙的方法——概率方法，即根据不等式的主要特征，结合概率论的1些基本概念和公式，通过建立1个适当的概率模型，赋以1些随机事件或随机变量的具体含义，再利用概率论的理论加以证明，讨论了柯西不等式，级数不等式，詹森不等式和几个1般不等式的证明。
In this paper, quadratic form theory, the European space inner product nature and Jensen inequality are three ways to prove cauchy inequality, and bthe relation between Cauchy inequality and higher mathematics was illustrated briefly.
本文运用二次型理论、欧式空间中内积性质和詹森不等式三种方法证明柯西不等式，并简要说明柯西不等式与高等数学之间的联系。
This paper discusses the Noether theorem of complete singular integral equation which containsboth the convolution kernel and the Cauchy kernel, and comes up with the Noether theoremwhich is similar to the Fredholm integral equation, the convolution equation and the singularintegral equation.
本文讨论了既含卷积核又含Cauchy核的完全奇异积分方程的Noether定理，得到了与Fredholm积分方程、卷积型积分方程、奇异积分方程相类似的Noether定理。
Then it was deeply discussed that one of the generalized Cauchy distributions, also called Lorentz distribution, could be used to model the coefficient priors in the sparse coding framework.
接着，从理论分析的角度论证了将标准Cauchy分布的单参数推广形式——Lorentz分布——作为基函数系数先验概率模型的可行性。
Actually, such a generalized Cauchy distribution was the Pearson VII probability distribution. In this dissertation, the Lorentz distribution was regarded as a generalized Cauchy distribution with only one scale parameter; while the Pearson VII distribution was regarded as a generalized Cauchy distribution with a scale and a shape parameter both.
因此，本文提出应在Lorentz分布的密度函数中再增加一个能够反映分布函数尾部特征的形状参数，希望通过该参数的可调节性进一步改善稀疏编码算法的自适应性。
Based on the discussion of displacement struture, we describe the properties of inversion formulas and the factorization forms, and give an fast algorithm for the paired Cauchy matrix based on LU factorization.
并在深入探讨位移结构性质的基础上推广出相关的逆矩阵的性质与因式分解的性质。
Firstly, by constructing an abstract operator, the original problem can be transformed into a Cauchy problem for an abstract operator equation.
首先，通过构造了一个抽象算子，将原问题转化为一个抽象算子方程的Cauchy问题。
On the basis of the definition of matrix traces, this paper discusses their characteristics at first and then according to the norm of the F of square matrix and Cauchy-Schwarz inequality gives how to prove the zero matrix, unsimilar matrix, number cloth matrix, column matrix idempotent matrix and non-equality matrix.
根据矩阵迹的定义，首先给出了矩阵迹的性质，然后依据方阵的F—范数定义Cauchy—Schwarz不等式，给出了零矩阵，不相似矩阵，数幂矩阵，列矩阵，幂等矩阵及矩阵不等式的证法。
Thus, based on the higher-order Cauchy-Born constitutive model and the generalized parametric constitutive law for van der Waals force developed here, a series of mechanical properties, compression buckling and adhesion behaviors for single-walled carbon nanotubes are studied respectively in the present thesis.
因此，基于所发展的高阶Cauchy-Born广义连续体本构模型以及范德华力广义参变本构模型，本文分别研究了单壁碳纳米管的一系列相关力学特性、压缩变形机理以及平行或交叉排列的碳纳米管间的黏附行为。
It includes luol theorem, Lagrange theorem and cauchy theorem, Taylor theorem.
它包括罗尔定理、拉格朗日定理、柯西定理、泰勒定理。
We particularly mention [13], where thenonlinear partial differential equation〓(4)was given as a model of the propagation of longitudinal deformation waves in anelastic rod, and [55]where the generalized IMBq equation with several variables andthe IMBq equations are derived in considering the problem of lattice vibrations.
在第二章和第三章中，我们研究广义IMBq方程的Cauchy问题〓（9）整体解的存在性和不存在性，并在小初值情形下讨论解的渐近性。