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Based on the speciality of the spectral function, we provide the sufficient conditions such that the spectral function are K—increasing (strictly K—increasing) in Euclidean Jordan algebra, and establish the relationship between the spectral scalar solution set and the K— efficient solution set of the Euclidean Jordan algebra vector optimization problem.

基于谱函数的特殊性,刻画了谱标量函数满足K-增性的充分条件,继而建立了谱标量解集与欧几里德若当代数向量优化问题K-弱有效解集和K-有效解集的包含关系。

Meanwhile, the relationship between the trace scalar solution set and the Bo properly K—efficient solution set of the Euclidean Jordan algebra vector optimization problem is es- tablished.

同时,还建立了特殊谱标量解集——迹谱标量解集与Bo恰当K-有效解集的包含关系。

Given a mesh, we first solve a Poisson equation to construct a scalar field and use it to generate some critical points. The cutting paths between the critical points and the boundaries are solved in the Poisson scalar field using the deepest descent method. For meshes with nonzero-genus, we construct a Harmonic scalar field, and connect the saddle points with the boundaries based on the Morse theory.

对于给定的任意网格,通过求解泊松方程构造标量场来选取临界点,并采用最速下降法给出临界点到边界或者初始点的切割路径;对于亏格不为零的网格,基于Morse理论,通过构造一个调和标量场来得到鞍点,并将它们连接到边界。

The predictions derived from our relation are in reasonable agreement with those given by many other different approaches.Based on the main assumption that a_0(980) and D*_(2317) belongto 1~3 P_0 multiplet, in the framework of Regge phenomenology andmeson-meson mixing, we suggest that a_0(980), K_0*( 1052), f_0( 1099) and f_0(530) constitute the ground scalar meson nonet.

另外,我们假定a_0(980)和D_~*(2317)态是通常的1~3P_0介子态,在Regge唯象和介子混合的框架下,我们对基态标量介子九重态可能安排进行了讨论,我们建议a_0(980),K_0~*(1052),f_0(1099)和f_0(530)组成基态标量介子九重态。

It isshown that there exists a well-defined nonlinear phase operator for the complexscalar fields,whose Weyl correspondence also manifestly exhibits entanglementbetween the positive and negative quanta of the complex scalar fields.

我们显示了对复标量场,存在定义得很好的非线性相位算符,其Weyl对应也明显地展现了复标量场的正负量子间的纠缠。

The performance of the proposed method is compared with that of the well-known vector standard filters such as the VMF, progressive switch median filter, scalar median filter ,minimum distance between central sample and scalar median in its neighborhood vector median filter and the basic vector directional filter.

结果表明,DMNVM滤波性能明显优于现有的VMF、递进开关中值滤波、标量中值滤波、与标量中值距离最小向量滤波和方向矢量中值滤波;同近年提出的自适应向量滤波比较,AVMF客观指标平均绝对误差协MAE、均方误差和标准色差分别是DMNVM的1.81、2.59和2.17倍,这说明DMNVM的滤波性能有显著提高。

Vector algebra, Vector product, Scalar product, Gradient, Divergence, Rotation, and several theories

掌握矢量代数运算,矢量积,标量积,掌握标量场与矢量场的特性参数及相应的定理。

In order to derive the qq-qq interaction, we generalize the Fierz transformation from SU(N ≤4) scalar and pseudo scalar to SU tensor and point out that the qq — qq interaction may be useful in an extended quark potential model calculation.

为了得到三体夸克-夸克对之间的相互作用,我们将著名的Fierz变换从SU(N<4)的标量和赝标量推广到任意的SU张量。

This paper focuses on four important aspects as follows. The first one is the establishment of variational quations which provides the mathematics theories for the finite element method of HMT; the second one is for the study of scalar/node and vector/edge finite element method; the third one is about how to solve faster for the large-sacled matrix system of scalar/node and vector/edge finite element; and the last one is achieving the forward modeling with high precision of HMT method.

主要包括四部分:建立与高频大地电磁法边值问题相等价的变分问题,为有限元数值计算奠定数理基础;标量/矢量有限元方法的研究;加速标量/矢量有限元矩阵系统方程迭代求解技术的研究;实现高频大地电磁参数精确快速正演模拟的研究。

The results show that our approaches lead to lower complexity which contributes to the efficient implementation of elliptic curve scalar multiplication.

改进以后的结果表明,计算标量乘nP的总的运算量减少,能更加有效地计算标量乘。

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