Schro¨dinger方程双线性元的超收敛分析和外推

研究了Schro¨dinger方程双线性有限元逼近。利用导数转移技巧和该单元的高精度结果,得到了H 1模意义下O（h2）阶的超逼近性质。同时利用插值后处理技术,给出了H 1模意义下整体超收敛结果。近一步地,通过构造一个新的外推格式,导出了比传统有限元误差高两阶的O（h3）阶的外推解。     

Adaptive fuzzy controller for a class of strict-feedback nonaffine nonlinear systems

A robust adaptive fuzzy control scheme is presented for a class of strict-feedback nonaffine nonlinear systems with modeling uncertainties and external disturbances by using a backstepping approach.Fuzzy logic systems are employed to approximate the unknown parts of the desired virtual controls,and the approximation errors of fuzzy systems are only required to be norm-bounded.The function tanh(·) is introduced to avoid problems associated with sgn(·).The tracking error is guaranteed to be uniformly ultimately bounded with the aid of an additional adaptive compensation term.Chua’s circuit system and R o¨ssler system are presented to illustrate the feasibility and effectiveness of the proposed control technique.     

Schrdinger方程的一个显格式

本文构造了一个解ＳｃｈｒＯ¨ｄｉｎｇｅｒ方程的三层显式差分格式,格式绝对稳定,截断误差为Ｏ（τ２＋ｈ２）．     

一类 Dirac 算子特征值的渐近式

主要研究势函数为分段光滑的 Dirac 微分算子特征值的渐近性，给出其特征值阶为 O（1／n2）型渐近估计式。     

一类解析函数的Fekete-Szeg(o)问题

引入一个新的函数类B（λ,α,β）,讨论了它的Fekete-Szeg（o）不等式,获得了准确的结果.所得结论推广了已有的相关结果.     

Anick分解和量子群U_q(sl_2)的一些同调性质

利用Grbner-Shirshov基和Anick方法,构造了量子包络代数Uq(sl2)的Anick分解。作为一个应用,还讨论了Uq(sl2)的一些同调性质和Poincaré级数。     

关于对称共轭点的亚纯双向单叶倒星象函数类的系数估计

在单复变函数几何理论的研究中,构造函数类及研究它的几何性质是重要的研究课题.而在几何性质的研究中,对于系数的估计具有重要的作用.国内外许多学者对于单叶函数类和多叶函数类都进行了较为深入的研究.而对于亚纯函数类尤其是倒结构的亚纯函数类的研究却很少.引入了一类关于对称共轭点的亚纯双向单叶倒星象函数类,得到了该函数类的积分表达式和系数估计.特别地,得到了Fekete-Szeg问题的精确估计.     

Neutron diffraction studies on ‘‘simple’’ iron oxides under pressure： Fe3O4, a-Fe2O3, and FeO

Fe3O4（magnetite）, a-Fe2O3（hematite）, and Fe O（wu¨ stite） are the three major iron oxides and some of the most fundamental solids in nature. Interest in these systems is due to their abundance as minerals in the Earth and other telluric planets as well as their interesting electronic and magnetic properties which have been studied for decades. In this article, we review high-pressure studies on these three systems using neutron powder diffraction in the0–14 GPa range with a particular focus on the behavior of magnetism under pressure. Unpublished data on the pressure dependence of the Ne′el temperature in Fe O are presented. This review will give at the same time an introduction into technical aspects and illustrate the potential of high-pressure neutron scattering in the future.     

关于一类解析函数的Fekete-Szego不等式

引进了一个新的解析函数类L（λ,α,σ,β）,并用复分析的初等方法讨论了该函数类的Fekete-Szeg不等式,得到了准确值,从而推出了一些相关结果.     

一类扩展的Bazilevic函数的Fekete-Szego不等式

引进了一类扩展的Bazilevic函数Lα（β,σ）,并讨论了该函数类的Fekete-Szego不等式,得到了准确值.从而推出了一些有趣的结果.