点群

基于极化变换的点群综合几何质量评估

Quality Assessment of Point Group Geometry Generalization with Polarization Transformation

本文用点群研究共轭环烯分子的结构。

The study of molecular structures of the conjugated cyclenes with point group method was based on the hypothesis that all conjugated cyclenes ' carbon atoms were arranged at one same surface .

基于CIRCLE特征变换的点群选取改进算法

An improved algorithm of point cluster selection based on circle characteristic transformation

构建Delaunay三角网对空间随机点群目标进行表达。

To represent point-cluster , the study builds Delaunay triangular network .

基于Voronoi图的点群目标普适综合算法

A Generic Algorithm for Point Cluster Generalization Based on Voronoi Diagrams

3m点群晶体纵向压电性能的研究

Crystal Orientation Dependence of Longitudinal Piezoelectric Properties for 3m Point Group Crystals

它们属于D∞h点群.具有特殊的结构，用电子布居分析和振动模式分析来研究这种特殊结构。

They belong to the D ∞ h point group and have unique structures . The electron population and vibrational mode analysis were carried out to study their unique structures .

一种利用实验测量和数值计算确定3m点群晶体弹性系数的方法

An Alternative Method in Measurement of Elastic Constants of a Crystal with 3 m Symmetry

ZnO是一种具有六方纤锌矿结构的Ⅱ-Ⅵ族自激活的宽禁带半导体材料，是P6mm点群对称的六角晶系纤锌矿晶体。

ZnO is self activated wide band gap semiconductor material composed of ⅱ - ⅵ elements with P6 mm point group symmetry hexagonal wurtzite crystal structure .

d~5系C（2h）点群强场方案和MnCl2·2H2O的吸收谱

The Strong Field Scheme of Point Group C_ ( 2h ) for System d ~ 5 and the Absorption Spectrum of MnCl_2 · H_2O

相变温度上下晶体点群分别为4mm和m。

The point groups above and below the transition temperature are Amm and m respectively .

在有限素整数域Fp上定义了一条椭圆曲线及点群运算规则，并由此构造出一种椭圆曲线密码体制。

An elliptic curve is defined over a finite field GF ( p ) for a given set of operation rules .

点群10mm十次对称二维准晶中的两类接触问题

Two kinds of contact problems in decagonal quasicrystalline materials of point group 10 mm

正交mm2点群双轴晶体倍频最佳相位匹配角的计算方法

The Calculation Methods of the Second Harmonic Generation Phase Matching Angles in Orthorhombic mm2 Group Biaxial Crystals

在反铁电晶体NH4H2PO4（ADP）顺电反铁电相变中，对称性所属点群也随之发生相应的改变。

In the paraelectric-antiferroelectric phase transition of antiferroelectrics NH_4H_2PO_4 , the symmetry of crystalloid changes .

90年代，陈金全等人在点群的表示理论上提出了一种新的方法，对称化玻色表象方法（SBR）。

In1990s based on the eigenfunction method of representation theory of groups , a new method , the symmetrized boson representation ( SBR ) method , was brought forward .

另一套为已知晶系情况下应用CBED测定晶体点群的实验流程图，它适用于已有X射线衍射或选区电子衍射数据的情况。

The second is a special flow chart for point group determination by CBED when the crystal system of the specimen have been determined by XRD or SAED .

用轴矢量R作为序参量来描述反铁电相便是对称性的变化，对于已得到的晶体相变前后的对称点群，应用居里原理，得到了理想结果。

An axial vector R is selected as the order parameter to reflect the change of symmetry in anti-ferroelectric phase transition . According to Curie principle , the satisfying results are obtained relative to the change of symmetry group in the phase transition .

一些基于椭圆曲线的密码协议比如ECDSA签名验证，就需要计算双标量乘法kP+lQ，其中P、Q为椭圆曲线点群上的任意两点。

Some elliptic curve based on cryptographic protocols , such as ECDSA signature verification , require computation of multiple scalar multiplications of kP + lQ , where P and Q are points on an elliptic curve .

寻找对椭圆曲线公钥体制（ECC）有用的椭圆曲线，关键在于求有限域上椭圆曲线有理点群的阶。

The key to finding a useful elliptic curve for Elliptic Curve Cryptosystem ( ECC ) is to compute the order of elliptic curve rational points group over a finite field .

超椭圆曲线密码体制所基于的除子类群，又称Jacobian群，其结构与运算比有理点群要复杂得多。

The divisor class group , often called Jacobian group , based on which hyperelliptic curve cryptosystems are constructed , is much complicated than the elliptic curve rational point group .

指出它们均具有C（2v）局部对称性，并从晶体场点电荷模型出发对具有C（2v）对称性点群的分子进行了配位场半定量计算。

They belong to C_ ( 2V ) local symmetry . From the point of view of point-charge model the ligand field semi-quantitative calculation is applied to molecules with C_ ( 2v ) point group symmetry .

本文介绍了双轴晶体五种点群有效二阶非线性系数d（eff）~Ⅰ、d（eff）~Ⅱ在光率体主轴坐标平面上的解析表达式。

The paper introduces the analytic representation of the effective second nonlinear coefficients for 5 groups of biaxial crystals in the coordinate planes of optical ellipsoid .

X射线衍射实验发现，在1100℃以下烧结得到X1型物相，属单斜晶系，空间点群为P21/c；

It is discovered on the basis of XRD research that the samples calcined at lower temperature than 1100 ℃ belong to a X1 type which is the monoclinic crystal and its space group is P21 / c.

本文从基本的压电Christoffel方程出发导出三角晶系3m点群压电晶体弹性常数的表示式。

Based on the fundamental piezoelectric Christoffel 's equation , we derived the expression of the elastic constants for piezoelectric crystal with trigonal symmetry point group 3 m.

从总能量、配体场分裂、迁移自旋密度数据和π键形成的强度确定它应是属于Th点群。

From the data of total energy , Ligand-field splitting , transferred spin density and strength of π donor-bond , it is found that the geometry of Mn ( H_2O ) _6 ~ ( 2 + ) should belong to T_h point group .

并根据一级空间色散唯象理论，讨论了Td点群类晶体，[ζζ0]方向纵、横声学支声子发生耦合的现象与原由。

The origin of the coupling between LA and TA phonons propagating along (ζζ 0 ) axis in the crystal of point group Td was investigated according to " the first-order spatial dispersion " phenomenological theory .

ADP（磷酸二氢铵）和KDP（磷酸二氢钾）晶体都属于42m点群，是20世纪早期的著名压电晶体，具有易于大尺寸生长的优点。

ADP ( ammonium dihydrogen phosphate ) and KDP ( patassium dihydrogen phosphate ) are classified as 42m point group which both are the famous piezoelectric crystals in earlier last century .

首先利用群论，将Td点群中以五个d轨道为基函数的五维可约表示向不可约表示约化，得到d轨道在正四面体场中的能级分裂；

First of all , when the five-dimension reduction representation with the five d orbits wave-functions as the base functions is converted to an un-reduction representation , the energy splitting in tetrahedron crystal field can be obtained .

本文设计了两套应用会聚束电子衍射（CBED）测定晶体点群的优化实验流程图。

In this paper , two sets of flow charts for point group determination by convergent beam electron diffraction ( CBED ) were given .