查询词典 cauchy kernel

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。

The boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function uses Cauchy integral formula as the foundation . The singularity of the Cauchy

广义解析函数的Riemann-Hilbert边值问题的边界元方法是以Cauchy公式为基础，Cauchy核具有奇性，这是所面临的困难，可以设法利用Cauchy主值积分来解决，最后给出问题的解。

Secondly,we firstly study the properties of functions with values in a uni-versal Clifford algebra 〓,and we obtain the following very important basictheorems in universal Clifford analysis:Cauchy's integral formula,Cauchy's inte-gral theorem,the mean value theorem,the three versions of the maximum mod-ulus theorem,the Taylor's expansion,the Laurent's expansion and the residuetheorem etc..All of these results generalized the classical results.

第二，本文所讨论的各种函数性质以及所得的结果都在泛Clifford代数〓上所做的工作，它一方面包含了从前在泛Clifford代数〓上所做的工作，所得到的结果更广泛、更漂亮、更自然，另一方面，本文也是迄今为止第一次建立起来了在泛Clifford分析中与经典函数论相对照处基础地位的LR正则函数在特异边界上的Cauchy积分公式、Cauchy积分定理、平均值定理、极大模原理的三种表达形式、Taylor展式、Laurent展式留数定理等深刻的结果。

In chapter 1, we introduce some notions and some classical results related to this paper, such as Cauchy type integral as well as the limiting value of Cauchy integral and so on.

第一章介绍了本文涉及到的知识背景和相关的基本概念：Cauchy型积分，Cauchy主值积分等，以及本文要用到的与它们有关的一些经典结果。

Fast algorithm of minimal norm least square solution for Cauchy linear system;2. For the m×n Cauchy-type matrix with full column rank,the fast algorithm of the minimal norm least square solution to the linear system Cx=b was obtained by construction of a special block matrix and study of the triangular decomposition.

对于秩为n的m×n阶Cauchy型矩阵C，通过构造特殊分块矩阵并研究其三角分解，进而得到了线性方程组C x=b的极小范数最小二乘解的快速算法，所需运算量为O+O(n2)，而通常构造法方程组的方法所需运算量为O(m n2)+O(n3)，用正交化法虽然避免了构造法方程组，但所需的运算量更大些。

Via generalizing the Cauchy method we obtain a new method,called the modified Cauchy method.By means of this method we establish two bilateral _3ψ_3 and _4ψ_4 series summation formulae,two four-term summation and transformation formulae for unilateral _3φ_2-series and bilateral _3ψ_3-series,and two five-term summation and transformation formulae for unilateral _3φ_2-series and bilateral _3φ_3-series,which contain many known results as their special cases,such as non-terminating q-Saalschütz summation formula,Bilateral _6ψ_6 series summation formula of Bailey,non-terminating Watson transformation formula and some transformations of _3φ_2-series etc.

通过对Cauchy方法的推广，我们得到修正的Cauchy方法，采用这个方法分别得到两个双边的_3ψ_3和_4ψ_4基本超几何级数的求和公式、单边_3φ_~(2-)级数和双边_3ψ_(3~-)级数的两个四项求和变换公式和两个五项求和变换公式，它们包括许多已有的结果为特例，如非终止的q-Saalschütz求和公式、Bailey的very-well-poised双边级数_6ψ_6求和公式、非终止的Watson变换公式和一些关于单边_3φ_(2~-)级数的变换公式等。

Then we prove that if the initial data enter into the unstable set, then the solution of the aforementioned Cauchy problem blows up in finite time, and if the initial data enter into the stable set, then the solution of the aforementioned Cauchy problem globally exists.

其次证明了如果初值进入不稳定集，该柯西问题的解在有限时间内爆破；如果初值进入稳定集，该柯西问题的整体解存在。

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

The main conclusions are: Mexican hat wavelet is anisotropic one, and it could detect pointlike singularities very efficiently. Morlet and Cauchy wavelet could be used to detect specific directions, and Cauchy wavelet has better direction selectivity than Morlet one. And it has been used to separate the wave field of Ricker. Its results are basically accurate and computation is more efficient.

主要结论有：Mexcian帽小波是各向同性的，主要用来检测点状信号分量，Morlet小波和Cauchy小波主要用来检测方向信号分量，并且Cauchy小波比Morlet小波的方向性要好，检测结果的分辨率要高；利用二维连续小波反变换，以合成的Ricker子波为模拟信号为例进行波场分离，提高了运算效率，实验结果基本上比较准确，还需要实际地震信号的进一步验证。

By comparing the activity of theα-amylase and the soluble acid invertase in the kernel and the pedicel, the trend of theα-amylase activity in the kernel and the pedicel showed a peak, theα-amylase activity was high in the early stage, it could promoted amylolysis, supply the nutrition for the kernel development; theα-amylase activity was low in the rapid filling stage, it was in favorable to the starch accumulation.

通过比较籽粒和小穗柄中α-淀粉酶和可溶性酸性蔗糖转化酶的活性表明，籽粒和小穗柄中α-淀粉酶活性均呈单峰变化趋势，籽粒发育早期α-淀粉酶活性较高，可以促使淀粉转化，为籽粒的早期的发育提供营养物质；籽粒发育中期为快速灌浆期，淀粉酶活性较低，利于淀粉的积累。

Panorama Many people are dancing in a large sitting room.

在一个大客厅里，许多人在跳舞。

We fully understand how a microwave oven cooks food, it is first necessary to talk ...

我们充分理解一个微波炉煮的食物，这是首先要谈。。。