Lie symmetries and nonlocally related systems of the continuous and discrete dispersive long waves system by geometric approach

By using the extended Harrison and Estabrook's differential forms approach, in this paper, we investigate the Lie symmetries of the continuous and discrete dispersive long waves system, respectively. Based on this method, two closed ideals written in terms of a set of differential forms are constructed for the dispersive long waves systems. Furthermore, some invariant solutions are presented for such systems. By a direct computation, it is shown that the discrete dispersive long waves system admits a Kac-Moody-Virasoro type and a Virasoro-like type Lie algebra, respectively. Finally, we present an interesting relationship between the continuous case and a modified dispersive long waves system, which can be used to find nonlocal properties for such systems with each other.     

一类非光滑函数的区间扩张

本文指出了文献[1]中的一个错误,并给予修正,同时讨论了一类非光滑函数的区间扩张,它在数学规划有很多应用。所举的例子说明,我们给出的区间扩张函数优于文献[1]中的区间扩张函数。     

由偏微支配的系统的最优控制理论中的奇异摄动方法*

本文介绍了由偏微分方程支配的系统的最优控制理论中有关应用奇异摄动方法时出现的各种问题。考虑了渐近分析来自状态方程。或来自性能指标函数,也考虑了状态方程是定义在摄动域内的情形。     

AN INVARIANCE OF CDF EQUATION

ＡＮＩＮＶＡＲＩＡＮＣＥＯＦＣＤＦＥＱＵＡＴＩＯＮ￥ＴＩＡＮＣＨＯＵＡｂｓｔｒａｃｔ：ＴｈｉｓｐａｐｅｒｐｒｅｓｅｎｔｓａｎｅｗｉｎｖａｒｉａｎｃｅｆｏｒｔｈｅＣＤＦｅｑｕａｔｉｏｎ．Ｕｓｉｎｇｔｈｉｓｉｎｖａｒｉａｎｃｅ，ｔｈｅａｕｔｈｏｒｏｂｔａ...     

SYMMETRIES AND GROUP-INVARIANT SOLUTIONS OF DIFFERENTIAL EQUATIONS

ＳＹＭＭＥＴＲＩＥＳＡＮＤＧＲＯＵＰ－ＩＮＶＡＲＩＡＮＴＳＯＬＵＴＩＯＮＳＯＦＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＴＩＡＮＣＨＯＵＡｂｓｔｒａｃｔ：Ｆｏｒａｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ，ａｔｈｅｏｒｅｔｉｃａｌｐｒｏｏｆｏｆｔｈｅｒ...     

Effect of mechanical force on domain switching in BiFeO_3 ultrathin films

Ferroelectric polarization can be switched by an external applied electric field and may also be reversed by a mechanical force via flexoelectricity from the strain gradient.In this study,we report the mechanical writing of an epitaxial BiFeO3(BFO)thin film and the combined action of an applied mechanical force and electric field on domain switching,where the mechanical force and electric field are applied using the tip of atomic force microscopy.When the applied force exceeds the threshold value,the upward polarization of the BFO thin film can be reversed by pure mechanical force via flexoelectricity;when an electric field is simultaneously applied,the mechanical force can reduce the coercive electric field because both the piezoelectricity from the homogeneous strain and the flexoelectricity from strain gradient contribute to the internal electric field in the film.The mechanically switched domains exhibit a slightly lower surface potential when compared with that exhibited by the electrically switched domains due to no charge injection in the mechanical method.Furthermore,both the mechanically and electrically switched domains exhibit a tunneling electroresistance in the BFO ferroelectric tunnel junction.     

CaPtAs: A new noncentrosymmetric superconductor

We report the discovery of a new noncentrosymmetric superconductor CaPtAs.It crystallizes in a tetragonal structure(space group I41md,No.109),featuring three dimensional honeycomb networks of Pt-As and a much elongated c-axis(a=b=4.18?,and c=43.70?).The superconductivity of CaPtAs with Tc=1.47 K was characterized by means of electrical resistivity,specific heat,and ac magnetic susceptibility.The electronic specific heat Ce(T)/T shows evidence for a deviation from the behavior of a conventional BCS superconductor,and can be reasonably fitted by a p-wave model.The upper critical fieldμ0Hc2 of CaPtAs exhibits a moderate anisotropy,with an in-plane value of around 204 mT and an out-of-plane value of 148 mT.Density functional theory calculations indicate that the Pt-5 d and As-4 p orbitals mainly contribute to the density of states near the Fermi level,showing that the Pt-As honeycomb networks may significantly influence the superconducting properties.     

一种脉冲强电流条件下导线电阻测量方法

在超强激光辐照电容线圈靶产生强磁场实验中,在约50 ps时,线圈电流达到20 kA以上。通过该实验结果与磁场产生理论模型对比,可得出该导线电阻值比常温直流电阻高出3个量级。对导线材料电阻率与趋肤效应的分析结果表明,该电阻值在量级上是合理的。获得超快脉冲强电流条件下的导线电阻值,有助于更深入理解线圈靶产生强磁场过程。     

快凝Pd82Si18合金原子团簇的演化特性及遗传机制

采用分子动力学(MD)模拟计算,对Pd82Si18合金快凝过程中基本原子团簇的遗传特性、演化趋势和结构稳定性进行了研究.团簇类型指数法(CTIM)分析表明:非晶固体中Si原子为中心的(102/14418/1551)双帽阿基米德反棱柱(BSAP)团簇数目占据优势.快凝过程中,BSAP结构团簇具有最大的遗传分数,并且其他以Si原子为中心的Kasper团簇大多都会向BSAP结构团簇转变.通过对Si原子为中心的Kasper基本团簇电子性质第一性原理计算发现,体系中BSAP团簇的结合能最低,结构稳定性较高,与分子动力学计算结果一致.     

Harmonically pump a femtosecond optical parametric oscillator to 1.13 GHz by a femtosecond 515 nm laser

We demonstrate a harmonically pumped femtosecond optical parametric oscillator(OPO)laser using a frequency-doubled mode-locked Yb:KGW laser at a repetition rate of 75.5 MHz as the pump laser.Based on a bismuth borate nonlinear crystal,repetition rates up to 1.13 GHz are realized,which is 15 times that of the pump laser.The signal wavelength is tunable from 700 nm to 887 nm.The maximum power of the signal is 207 m W at the central wavelength of 750 nm and the shortest pulse duration is 117 fs at 780 nm.The beam quality(M^2 factor)in the horizontal and vertical directions of the output beam are 1.077 and 1.141,respectively.