查询词典 calculus of classes

We present the preliminary knowledge in Chapter 2,which includes the main properties of Sobolev Functional Space,the calculus on the Banach Space and the existence and uniqueness of the solutions of parabolic equations.

第二章给出了本文的预备知识，即Sobolev函数空间基本性质和Banach空间上的微分学，以及抛物型方程解的存在唯一性。

The stability and convergence for spectral methods and spectral element methods are presented, with the aid of the knowledge of functional analysis and calculus and with the help of the theorem of Lax-Milagram, the stability and convergence for steady problems, evolution equations and Navier-Stokes Equations are analyzed in detail.

利用泛函分析和微积分的基本知识，运用Lax-Milagram定理等，从理论上比较详细地分析了谱方法和谱元方法在定常问题、非定常问题以及求解Navier-Stokes方程方面的稳定性和收敛性问题，得出了Navier-Stokes方程谱近似的稳定性条件和收敛性准则。

The term originates from functional programming and lambda calculus, where a lambda abstraction defines an unnamed function.

这一术语来源自函数式编程和 lambda 运算，lambda 抽像定义了一个匿名函数。

The functional by variational calculus leads to a set of elliptic partial differential equations,in particular,Poisson equations,which is possibly solved by numerical methods.

利用变分法可以从这个二次误差指标函数导出一组椭圆形偏微分方程泊松方程，这类方程有相当成熟的数值解法。

The basic features of digital baseline estimation for multi-channel pulse height analysis are introduced. The weight-Junction of minimum-noise baseline filter is deduced with functional variational calculus. The frequency response of this filter is also deduced with Fourier thansformation, and the influence of parameters on amplitude frequency response characteristics is discussed.

介绍了用于多道脉冲幅度分析的数字基线估计方法的基本特点，利用泛函变分方法推导了最小噪声基线滤波器的计权函数，利用Fourier变换导出了数字基线估计的频率响应，探讨了参数取值对其幅频特性的影响。

The variational problems of the complete functional in calculus of variations are studied deperding on the arbitrary arguments,arbitrary multivariable functions and arbitrary-order partial derivatives of multivariable functions.

研究变分法中依赖于任意个自变量、任意个多元函数和任意阶多元函数偏导数的完全泛函的变分问题；提出并证明了完全泛函的变分问题的定理，采用偏微分算子，给出了完全欧拉方程组。

The main results are as follows: the relations between local fractional integrated semigroups and the corresponding Cauchy problem, global fractional integrated semigroups and regularized semigroups are given; introduction of the notion of regularized resolvent families, and the generation theorem and analyticity criterions for regularized resolvent families are obtained; the spectral inclusions between fractional resolvent family and its generator, and the approximation for fractional resolvent families in the cases of generators approximation and fractional orders approximation; elliptic operators with variable coefficients generating fractional resolvent family on L^2 by using numerical range techniques; and the L^p theory for elliptic operators with real coefficients highest order are obtained by Sobolev''s inequalities and the a priori estimates for elliptic operators; and a kind of coercive differential operators generates fractional regularized resolvent family by applying the Fourier multiplier method, functional calculus and some basic properties of Mittag-Leffler functions.

主要结论是：给出了局部分数次积分半群和相应的Cauchy问题的关系以及分数次积分半群和正则半群的关系；引入了正则预解族的概念，并给出了其生成定理和解析生成法则；给出了分数次预解族与其生成元的谱包含关系，并研究了在生成元逼近和分数阶逼近两种情况下相应的预解族的逼近问题；利用数值域方法证明了具变系数的椭圆算子在L^2上生成分数次预解族；利用Sobolev不等式和椭圆算子的先验估计证明了具变系数的椭圆算子在其最高项系数为实数时在L^p上生成分数次预解族；运用Fourier乘子理论、泛函演算和Mittag-Leffler函数证明了一类强制微分算子可以生成分数次正则预解族，并给出了该预解族的范数估计。

Calculus of Thermodynamics; Gibbs Fundamental Equation; Graphical Interpretation of Fundamental Surface

热力学微积分；Gibbs基本方程；基本表面的图示说明。

Their solutions are described by the fundamental theorem of the calculus,which reads as follows.

意思是：它们的解由微积分基本定理所描述，可写出如下。

The Fundamental Theorem of Calculus in Higher Dimensions; Additive Measures, Stokes Theorem and the Divergence Theorem

微积分在多维中的基本定理：加性测度，斯托克斯定理以及散度定理

Yet, Edith says, there was always money in the bank.

但是Edith说，她的银行户口里面总是有钱。

We have created a series of files that resolve this problem--one for each day of the 40 days of purpose.

我们制作一系列的档案去解决这问题---一个为标竿40天中的每一天。