余弦定理

We proposed and proved three theorems through which the theoretical formula of cosine transform spectrum of gravity anomalies of the point mass and the vertical rectangular-cylinder was deduced in order to obtain the general equation of gravity anomalies.

为获得重力异常余弦变换谱的通式，提出并证明了3个定理；利用它们推导了点质量和直立矩形柱体的重力异常余弦变换谱理论公式，同时给出了重力异常余弦变换谱通式。

We proposed and proved three theorems through which the theoretical formula of cosine transform spectrum of gravity anomalies of the point mass and the vertical rectangularcylinder was deduced in order to obtain the general equation of gravity anomalies.

为获得重力异常余弦变换谱的通式，提出并证明了3个定理；利用它们推导了点质量和直立矩形柱体的重力异常余弦变换谱理论公式，同时给出了重力异常余弦变换谱通式。

The maths that theorem of cosine of article solicit comments uses education to talk how to foster 5 years to make high post student uses consciousness and capacity.

本文就正余弦定理应用教学来谈谈如何培养五年制高职学生的数学应用意识和能力。

Discrete Cosine Transform has become one of the widely used transform techniques in digital signal processing.

离散余弦定理已经成为数位讯号处理中被广泛应用的转换技巧之一。

The law of cosines unilaterally has many applications in it, presently specifically chooses the good problem solving method on the concrete question.

正余弦定理都在其单方面有很多应用，现就具体问题具体选择出较好的解题方法。

The sine, the law of cosines connotation is rich, versatility.

正、余弦定理内涵丰富，用途广泛。

The magnitude of opened angle at a point pi in the contour can be easily calculated by the law of cosines, and its local extreme correspond to the sharper changes of the contour of the mode.

其轮廓上点p处的张角可用余弦定理很方便地求出，而张角的极值点则对应于轮廓急剧变化的地方。

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 total of these two sorts of functions is called S-functions The indicial function, sinusoidal function, cosinusoidal function, hyperbolic sinusoidal function, hyperbolic cosinusoidal function, trigonometric function of n-order and hyperbolic function of n-order etch are all belong to S-functions.

指数函数、正弦函数、余弦函数、双曲正弦、双曲余弦、n阶三角函数和n阶双曲函数等。都是S－函数的特殊形式。文中证明了关于S－函数及其各阶导数的性质的三个定理。

In chapter four"The application of generalized sampling theorem to data compression", the qaulity of approximation coefficients is proved and a methodology of discrete cosine transformation combined with ununiform sampling is put forward.

第四章&广义采样定理在数据压缩中的应用&，对广义采样定理一中的展开式系数性质进行了证明，在此基础上提出了一种结合非均匀采样的离散余弦变换方法。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。