镍基超导母体材料EuNi_2Si_2的结构和热力学性质研究

应用Chen-Mbius晶格反演获得的原子间相互作用势,对镍基超导母体材料EuNi2Si2不同空间群的结构进行结构弛豫、切变拉伸、随机扰动和X射线衍射谱的分析.研究表明,空间群号为139结构的EuNi2Si2母体材料能量最低,结构最稳定.另外,还计算了空间群号为139稳定晶格结构的声子态密度和热力学性质.计算结果表明:对于声子态密度,原子质量较大的稀土元素Eu在低频范围内贡献最大,随着频率的升高,原子质量较小的元素Si的贡献越来越突出;对于比热容和振动熵,在低温区元素Eu和Ni的贡献较大,随着温度的升高,元素Si的贡献越来越突出.     

M(o)bius inversion of convolution-type series and cylindrical functions

系统讨论了柱函数与虚宗量柱函数中卷积型级数的M(o)bius反演问题,包括它们的加法公式与倍乘公式的反演问题.得到了许多有意思的新结果.     

卷积型级数的Mbius反演与柱函数

系统讨论了柱函数与虚宗量柱函数中卷积型级数的Mbius反演问题,包括它们的加法公式与倍乘公式的反演问题.得到了许多有意思的新结果.     

P-反演半群的P-次直积

本文研究了P-反演半群的P-次直积和E-囿P-反演盖.利用P-反演半群的P-次直积的结构,引入了P-反演半群的E-囿P-反演盖概念,并刻画了它们的结构.最后,讨论了P-反演半群到给定群上的囿P-次同态,推广了文献[9]中的一些结果到P-反演半群上.     

组模偏正则化及其应用

本文研究组模下偏正则最小化问题,证明了解的存在性,稀疏性.研究了零空间性质对最优解的刻画.仔细探讨了解的一种单调性,并应用这种单调性说明最优化问题的求解可以分解到各组中.最后给出了一个所证定理在地震反演的应用.     

带根单行平面地图的计数

提供了根点为一个奇点的带根单行平面地图以其边数、根点次和非根奇点次为参数的生成函数所满足的一些函数方程,并且导出了这些函数的显式,它们有两个是无和式.     

ON THE ORDER OF SUMMABILITY OF THE FOURIER INVERSION FORMULA

In this article we show that the order of the point value, in the sense of Lojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesaro summable to the distributional point value of order k＋1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesaro summable of order k, then the distribution is the （k ＋ 1）-th derivative of a locally integrable function, and the distribution has a distributional point value of order k ＋ 2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems.     

声波方程系数逆演问题的非线性积分方程及时卷特征迭代法(TCC)

本文将一维、二维和三维声波方程系数逆演问题转化为非线性积分方程。在一维情形,非线性积分方程是第二类的,在二维和三维情形,非线性积分方程是有趣的积分几何问题,并考虑求解上述积分方程的迭代法。本文所讨论的非线性积分方程及相应的迭代解法,对于声波方程系数逆演问题的理论及数值方法研究及在科学与工程中的应用有重要作用。     

Uniqueness of Inversion Problems Described by First—Kind Integral Equations

We propose a general method to prove the uniqueness of the inversion problems described by first-kind integral equations.The method depends on the analytical properties of the Fourier transform of the integral kernel and the finiteness of the total states (or probability,if normalized),the integration of the “local” density of states,which is a rather moderate condition and satisfied by many inversion problems arising from physics and engineering.