查询词典 gradient of scalar field

In this thesis, we totally depict the spectrum of the Laplacian on theclosed hypersurface with constant mean curvature and constant scalar curvaturein S~4, i.e., compute all eigenvalues of such closed hypersurface.

本文完整地刻画了S~4中具有常平均曲率和常数量曲率的闭超曲面上Laplace算子的谱，即计算出这类闭超曲面的各阶特征值。

In computer graphics, an input device that provides a scalar value.

在计算机图形学中，提供标量值的一种输入设备。

An integral expression for the time domain output response of traveling wave electrooptic phase modulator is derived by using the scalar wave equation and Fourier transform technique.

从标量波动方程出发，采用傅里叶变换的方法，导出了行波电光相位调制器的时间域输出响应的计算公式。

Nabla operators applied on the scalar Green's function are applied on electric and magnetic fields using integration by parts.

利用分部积分将作用在标量Green函数上的Nabla算子转移到电磁场强上。

From K-G Equation and Dirac equation,using 2-D invariant line element, the radius equation and event horizon formula of particles are obtained.A simpler method to the research of quantum effect of the scalar and vector particles in black hole with spherical symmetry is singgested.

分别从K-G方程和Dirac方程入手，利用简化后的二维不变线元，直接给出了粒子的径向方程和视界面方程公式，为研究球对称黑洞中标量粒子和矢量粒子的量子效应提供了一个更简单的方法。

In the framework of Filippov solutions and on the basis of Lipschitz continuous and regular scalar Lyapunov functions, this dissertation discusses the stability problems of nonlinear systems with discontinuous right-hand sides with respect to a given point or a closed invariant set, and have some related results.

本论文在Filippov解的意义下，基于Lipschitz连续且正则的标量Lyapunov函数，讨论了右端不连续的非线性系统相对一个给定的点或相对于闭不变集的稳定性问题。

It is proved that every Lie derivation of nest algebra is the sum of an associative derivation and a general trace. Every Lie isomorphism between nest subalgebras of a factor von Neumann algebra is the sum of an isomorphism and a general trace or the sum of a negative anti-isomorphism and a general trace. Lie invariant subspace of linear mappings on Banach algebras is introduced, and linear maps from nest subalgebra of a factor von Neumann algebra into itself which satisfy the property that the space of derivations is their Lie invariant subspaces are characterized. Simultaneously, it is shown that such maps are Lie derivations modulo the set of scalar multiple of the identity.

得到Lie导子的特征表示，即套代数上的任何一个Lie导子都是内导子与广义迹之和；给出了Lie同构和同构及反同构之间的关系，即因子von Neumann代数中套子代数之间的任何一个Lie同构要么是同构与广义迹之和要么是负反同构与广义迹之和；引入了Banach代数上线性映射的Lie不变子空间，并给出von Neumann代数中套子代数上以导子空间为Lie不变子空间的线性映射的一个刻画，同时也表明在模去数乘恒等映射的意义下，以导子空间为Lie不变子空间的线性映射就是Lie导子。

Directional data ; Interpolation ; Inverse distance weighted ; Scalar data

方向数据；插值；反距离权；标量

The formula group for the design of multi-phase micro Fresnel lens according to scalar diffraction theory was given and the transmission theory of spherical wave were used to deduce the relation of focal distance of the micro lens with spectrum resolution. According to the relation spectrum resolution is inverse proportional to focal distance given a certain incident wavelength and phase number, and the theoretic formula is consistent with reported experimental result.

光谱分辨率是评价衍射微透镜分光特性的主要指标，根据标量衍射理论，给出了多台阶位相型菲涅尔透镜的设计公式，并利用球面波的传输理论推导了微透镜主焦距与光谱分辨率之间的函数关系，得出在入射波长和位相台阶数一定的情况下，光谱分辨率与中心焦距之间呈反比；理论推导的结果与已发表的实验结果一致。

In any case Scalar wave domain ;is generally between the earth and the ionosphere .

在任何情况下，标量波域；）一般为地球和电离层。

Alternatively, the con- trollers can use the synchronous rectifier itself or loss- less inductor current-sensing methods to provide overload protection with lower power dissipation.

另外，康威特罗勒斯可以使用同步整流器本身或亏损减少电感电流检测方法，以提供低功耗过载保护。

Mr. Dauber's other Schatz hangs in his home movie studio.

多伯把沙兹的另一件作品挂在家里的电影室。