查询词典 symmetric difference

In this paper, the inertial theorem of real symmetric matrix has been proved by three methods in three aspects: the relationship between real symmetric matrix and real quadratic form, the relationship between real symmetric matrix and symmetric bilinear function of real linear space.

从实对称矩阵与实二次型的联系、实对称矩阵与实线性空间的对称双线性函数的联系以及将实对称矩阵作为研究主体这三个角度，介绍实对称矩阵的惯性定理的三种证明，以期加深对实对称矩阵的惯性定理的理解。

The solution group such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are successfully found.

构造了一种迭代法系统地研究了问题Ⅴ的一般解组、对称解组、中心对称解组、自反矩阵解组、双对称解组、对称次反对称解组及其最佳逼近等问题，并成功地解决了这些问题。

Non-symmetric kernel density estimation is first used for life-table graduation in order to solve boundary bais of symmetric kernel used in the standard kernel density estimator,and compare the symmetric kernel graduation with non-symmetric kernel graduation and obtain the satisfied result.

针对以地称核修匀方法存在着边界偏差这种现象，将非对称核密度估计用于生命表数据修匀中，提出了非对称核修匀方法，并与对称核修匀方法进行比较，得到了令人满意的结果，从而使核修匀方法得到了进一步的推广。

In this paper we separate the Hamiltonian into three parts: a spherical symmetry Hamiltonian; a z-component of the angular momentum operator, and a non-spherical symmetric potential as the perturbation operator, and provide a propose method by separating the potential containing squared magnetic field B^2 into two parts spherical symmetric and non-spherical symmetric ones so that the first-order energy correction due to the non-spherical symmetric potential is zero, and the second-order correction due to B^2 can be obtained by a simple variational method.

采用变分法和微扰法相结合的方法，把高强度磁场中氢原子的哈密顿H分为三部分：球对称哈密顿；z分量角动量算符相应部分和非球对称势微扰，并用一种特别规定的分解法将哈密顿H中含磁场平方项的势能分解为球对称与非球对称两部分，且使非球对称部分引起的一级修正能量值为零，并采用一种简便的变分法直接求出B^2对能级的二级修正值。

In many practice problems such as to know the resonnance frequency of a structure and to know the critical value for the stability of a dynamical system,often need to compute the eigenvalues of a symmetric matrix. The chief method to compute the eigenvalues of a symmetric matrix is first to transformate the matrix to a symmetric tridiagonal matrix similarly and orthogonally, then to use the QR method with shift to the symmetric tridiagonal matrix.

很多实际问题，如求结构振动的固有频率，动力系统稳定性的临界值等常常归结为计算对称矩阵的特征值，而首选的计算方法是先把该矩阵正交相似变换成一个对称三对角矩阵，再对这个对称三对角矩阵用带位移的QR方法。1968年J.H。

Problem III Given find such thatProblem IV When Problem I or II or III is consistent, let Se denote the set of its solutions, for given , find , such thatwhere is Frobenius norm, S is Rn×p or a subset of Rn×p satisfying some constraint conditions, such as symmetric, skew-symmetric, centrosymmet-ric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric.

问题Ⅳ 设问题Ⅰ或Ⅱ或Ⅲ相容，且其解集合为SE，给定X0∈Rn×p，求X∈SE，使其中‖·‖为Frobenius范数，S为Rn×p或为Rn×p中满足某约束条件的矩阵集合，如对称矩阵、反对称矩阵、中心对称矩阵、中心反对称矩阵、自反矩阵、反自反矩阵、双对称矩阵、对称次反对称矩阵等。

R~, find∈S_E, such that ProblemⅤGiven, find [X_1,X_2,…,X_l](where X_i∈S_i,i=1,2,…,l), such that A_1X_1B_1+A_2X_2B_2+…+A_lX_lB_l=C ProblemⅥWhen ProblemⅤis consistent, let SE denote the set of its solutions, for given,find, such that where||·|| is Frobenius norm, S and S_i are the matrix set satisfying some constraint conditions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric.

R~，求∈S_E，使得问题Ⅴ给定，求[X_1，X_2，…，X_l](其中X_i∈S_i，i=1，2，…，l)，使得 A_1X_1B_1+A_2X_2B_2+…+A_lX_lB_l=C 问题Ⅵ设问题Ⅴ相容，且其解集合为S_E，给定矩阵组，求，使得其中||·||为Frobenius范数，S，S_i为满足某种约束条件的矩阵集合，如对称矩阵、反对称矩阵、中心对称矩阵、中心反对称矩阵、自反矩阵、反自反矩阵、双对称矩阵、对称次反对称矩阵等等。

Finite commutative group; Symmetric bicharacter; Lie color superalgebra ; Left color symmetric algebra ; Left color symmetric structure

基础科学，数学，代数、数论、组合理论有限交换群；对称双特征标；着色李超代数；左着色对称代数；左着色对称结构

The conditional symmetry instability is the intermediate process between the stable and instable states of the atmosphere. The evolution of the atmosphere from the stable to unstable state or from unstable to stable state comes through two stages. The convective-symmetric instability circulation is related with the state and type of the instability. When the conditional instability lies in the lower level and conditional symmetric instability in the upper level, the circulation will have vertical updrafts in the lower level and slantwise updrafts in the upper level. The release of conditional symmetric instability gives rise to a mesoscale rain belt.

结果表明：条件对称不稳定是大气稳定状态和条件不稳定状态之间的中间纽带，大气由稳定向不稳定或者由不稳定向稳定的演变均通过条件对称不稳定来实现；对流对称不稳定环流的形成与不稳定层的配置有关，当低层为条件不稳定而高层叠加深厚的条件对称不稳定时，对流对称不稳定环流低层出现垂直上升气流，高层出现范围较广的倾斜上升气流，对称不稳定能量释放产生中尺度云带。

The conclusion of this article contains:(1) The climatology symmetric index and antisymmetric index which represent the uniform system of ocean and atmosphere is defined according to the unique kinetic character of the large-scale fluid. The symmetric mode, a state mode, and antisymmetric mode, a propagate westward mode, of ocean and atmosphere are distinguished clearly from each other. Also, the primary part which determines the symmetric mode emerges from non-divergenct wind and the dominant part which contributes to the antisymmetric mode mostly is irrotational wind. The article also compares the disparity of the climatology distribution of SST and sea surface wind field between 1948-1975 and 1976-2005. The SST of both the tropical Indian Ocean and the tropical Pacific after 80's is warm than before 80's .

主要结论如下：(1)热带太平洋气候平均态所包含的海-气相互作用的资料分析根据海洋和大气的运动特性，定义了表征海洋大气系统的对称模态和反对称模态指数，通过两个指数对热带太平洋和印度洋关于赤道对称和反对称的两个模态进行区分，发现关于赤道反对称的海-气耦合模态主要包含了大气散度分量和海洋SST的相互作用；关于赤道对称的海-气耦合模态主要包含了大气旋度分量和海洋SST的相互作用，并从资料估算了该耦合模态向西传播的速度。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。