Existence of Moduli for Bi-Lipschitz Equivalence of Analytic Functions

We show that the bi-Lipschitz equivalence of analytic function germs (², 0)(, 0) admits continuous moduli. More precisely, we propose an invariant of the bi-Lipschitz equivalence of such germs that varies continuously in many analytic families f _t : (², 0)(, 0). For a single germ f the invariant of f is given in terms of the leading coefficients of the asymptotic expansions of f along the branches of generic polar curve of f.     

癸酸-十四烷酸二元体系的相变性能

以癸酸(CA)-十四烷酸(MA)二元体系的理论预测相图为指导, 测量了该体系不同组成超声波混合后的步冷曲线, 绘制了该体系的实验相图, 判断出最低共熔温度与组成范围; 采用DSC测试最低共熔组成的相变性能, 采用IR检测最低共熔组成300次热循环前后的波形变化. 实验结果表明, CA-MA二元体系最低共熔组成范围为(76%~82%)CA+(24%~18%)MA, 最低共熔温度为294.45 K, 最大过冷度为274.75 K, 相变过程中无分层现象; DSC和IR的测试结果表明, 组成为78%CA+22%MA的相变焓为149.02 J/g, 开始相变温度为292.80 K, 热稳定性好.     

通用回归分析模型

建立了通用的回归分析模型,它包含了直线、指数线、抛物线、双曲线等众多模型形式,因而具有广泛代表性.分析了通用模型中的常数项对模型曲线形状的影响.结合实例用计算机程序给出了相关参数的数值解法.通用模型与数值解法相结合,突破了回归分析中预先确定简单函数曲线误差大和复杂曲线求解难度大之间的矛盾问题,大幅度提高了计算精度和速度.     

Generalized quaternionic involute-evolute curves in the Euclidean four-space E4

In this paper, a new type of quaternionic partner curves is defined as generalized quaternionic involute-evolute curves or $(0,2)$-quaternionic involute– $(1,3)$-quaternionic evolute curves in the four-dimensional Euclidean space. The relations between the Frenet frames and curvatures of the quaternionic involute-evolute curve couple are introduced. Moreover, the necessary and sufficient conditions for a quaternionic curve to have a generalized involute are obtained.     

新型光谱曲线特征参数与水稻叶绿素含量间的关系研究

利用高光谱信息检测作物叶绿素含量信息是田间作物长势诊断的重要研究内容。利用水稻光谱和叶绿素含量田间实测数据,从作物叶绿素含量不同,光谱曲线峰谷波形有高矮胖瘦形态变化的观点出发,提出光谱曲线峰谷波形中特征边的上升、下降速率以及组成峰谷波形两边的夹角等新型特征量,利用归一化光谱信息,分析了这些变量与水稻叶绿素含量间的相关关系。研究结果显示:(1)可见光波段范围520～740nm之间的归一化光谱反射率与叶绿素含量间呈良好的负相关关系;(2)绿峰反射光谱曲线特征边的变化速率及绿峰两边的夹角等变量与水稻叶绿素含量具有较好的相关性,表明利用这些新型变量开展叶绿素含量高光谱无损监测成为可能,这将为利用高光谱信息开展作物长势与营养诊断提供新的思路和方法。     

On nested code pairs from the Hermitian curve

Nested code pairs play a crucial role in the construction of ramp secret sharing schemes [15] and in the CSS construction of quantum codes [14]. The important parameters are (1) the codimension, (2) the relative minimum distance of the codes, and (3) the relative minimum distance of the dual set of codes. Given values for two of them, one aims at finding a set of nested codes having parameters with these values and with the remaining parameter being as large as possible. In this work we study nested codes from the Hermitian curve. For not too small codimension, we present improved constructions and provide closed formula estimates on their performance. For small codimension we show how to choose pairs of one-point algebraic geometric codes in such a way that one of the relative minimum distances is larger than the corresponding non-relative minimum distance.     

Theoretical study of structure and analytic potential energy function for the ground state of PO2 molecule

In this paper, the energy, the equilibrium geometry, and the harmonic frequency of the ground electronic state of PO₂ are computed using B3LYP, B3P86, CCSD(T), and QCISD(T) methods in conjunction with 6-311++G(3df, 3pd) and cc-pVTZ basis sets. A comparison between the computational results and the experimental values indicates that the B3P86/6-311++G(3df, 3pd) method can give better energy calculation results for the PO₂ molecule. It is shown that the ground state of the PO₂ molecule has C_2v symmetry and its ground electronic state is X²A₁. The equilibrium parameters of the structure are R_P-O=0.1465 nm, d=19.218 eV. The bent vibrational frequency ν₁=386 cm^-1, the symmetric stretching frequency ν₂=1095 cm^-1, and the asymmetric stretching frequency ν₃=1333 cm^-1 are obtained. On the basis of atomic and molecular reaction statics, the reasonable dissociation limit for the ground state of the PO₂ molecule is determined. Then the analytic potential energy function of the PO₂ molecule is first derived by using the many-body expansion theory. The potential curves correctly reproduce the configurations and the dissociation energy for the PO₂ molecule.     

Web‐spline‐based finite element approximation of some quasi‐newtonian flows: Existence‐uniqueness and error bound

This article deals with the web‐spline‐based finite element approximation of quasi‐Newtonian flows. First, we consider the scalar elliptic p‐Laplace problem. Then, we consider quasi‐Newtonian flows where viscosity obeys power law or Carreau law. We prove well‐posedness at the continuous as well as the discrete level. We give some error bounds for the solution of quasi‐Newtonian flow problem based on the web‐spline method. Finally, we provide the numerical results for the p‐Laplace problem. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq31: 54–77, 2015     

Mesures d'indépendance linéaire de carrés de périodes et quasi-périodes de courbes elliptiques

A linear independence measure over Q is obtained for values of some generalized hypergeometric functions at rational points and for the squares of real periods and quasi-periods of elliptic curves in Legendre form y²=x(x−1)(x−1/q) for almost every q∈Z.     

C40富勒烯分子的电子结构与传输特性研究

本文采用密度泛涵理论对富勒烯C40分子进行了结构优化,得到了稳定构型,然后构建了以金原子面为电极的电子输运模型．使用非平衡格林函数方法对构建的电子输运模型进行了电子输运性质的计算,得到了电子透射谱和伏安曲线,并分析了分子器件产生电子输运性质的原因. 研究结果发现：C40富勒烯的化学活性明显强于富勒烯C60和C32分子,在一些分子能级处,该分子为一个良导体．