Critical Points and Error Rank in Best H 2 Matrix Rational Approximation of Fixed McMillan Degree

This paper deals with best rational approximation of prescribed McMillan degree to matrix-valued functions in the real Hardy space of the complement of the unit disk endowed with the Frobenius L ₂ -norm. We describe the topological structure of the set of approximants in terms of inner-unstable factorizations. This allows us to establish a two-sided tangential interpolation equation for the critical points of the criterion, and to prove that the rank of the error F-H is at most k-n when F is rational of degree k , and H is critical of degree n . In the particular case where k=n , it follows that H=F is the unique critical point, and this entails a local uniqueness result when approximating near-rational functions. January 23, 1996. Date revised: September 16, 1996.     

原子质心运动与暗态原子

本文利用高阶量子绝热近似方法讨论了量子微腔驻波场中三能级暗态原子与光场相互作用中原子质心运动对电子,光场系统动力学的影响。文章分析了绝热近似成立的条件以及非绝热因子对动力学演化的影响。文中还计算了原子在腔中的非绝热跃迁几率及各部分能量分布的平均值。     

强电,磁场中的原子

简要地叙述了强电场和强磁场中的原子物理问题的研究进展，着重介绍了原子电场电离的实验结果和理论分析，对称性对磁场中原子行为的影响，以及与经典混沌和量子谱相关的共振现象。     

Dynamical spin susceptibility of the d–p model in the over doping region

Dynamical spin susceptibility χ^s(q,ω) of the d–p model in the over doping region is investigated by using the auxiliary boson technique. It includes higher order terms of the 1/N-expansion within the random phase approximation (RPA) of the local vertex, where frequency dependence of the quasi-particle interaction is taken into account. The incommensurate spin fluctuation is obtained due to the nesting effect in the low energy region (ωω^*), whereas the commensurate one in the high energy region (ωω^*), the characteristic energy ω^* is estimated to be about 30 meV. Both of the spin–lattice relaxation rate 1/T₁ and the spin–spin relaxation rate 1/T_g monotonically increase as T decreases, while the spin Knight shift K is almost independent of T.     

运用有限振荡核方法提高正线性算子的逼近阶

为改造正线性算子以提高其逼近阶，本文利用有限振荡核方法，从常见的Ｆｅｊｅｒ算子出发，构造出一种莼性多项式算子Ｌｎ＾（ｍ）（ｆ；ｘ），称Ｆ－Ｂ算子，它的表达式具有良好的递推性能；通过对其收敛性和饱和性的讨论，证得Ｆ－Ｂ算子对充分光滑函数的逼近阶可达Ｏ（１／ｎ＾２ｍ＋１），优于Ｂｕｔｚｅｒ与Ｓｔａｒｋ的结果（Ｏ（１／ｎ＾４）），并包含Ｂａｓｋａｋｏｖ的结果（Ｏ（１／ｎ＾３）与Ｏ（１／ｎ＾５））为其特例     

Navier-Stokes方程对称破坏分歧点的谱Galerkin逼近[英文]

本文研究了Navier-Stokes方程对称破坏分歧点的谱Galerkin逼近问题，构造了定常Navier-Stokes方程对称破坏分歧点扩充系统及其谱Galerkin逼近扩充系统，证明了谱Galerkin逼扩充系统解的存在性和收敛性，从而给出了Navier-Stokes方程对称破坏分歧点的谱Galerkin逼近，并给出了逼近的误差估计。     

Predicting the Capillary Imbibition of Porous Rocks from Microstructure

The kinetics of capillary imbibition into porous rocks is studied experimentally and theoretically. The Washburn law is modified by introducing various corrections relating to the microstructure of the rocks, such as tortuosity, pore shape (obtained experimentally), and applying the effective medium approximation (EMA) in order to calculate the effective radius that defines the hydraulic conductance and the topology of the capillary imbibition. The application of the EMA shows that capillary imbibition is mainly produced in 1-D, and the pore structure is constituted by different pore throats in series, linked by chamber pores. The capillary process has been discussed as a function of their petrography and pore structure. Our study of the Washburn equation and the addition of correction factors for the pore structure allows a very accurate prediction of the weight rate.     

Limit laws for the number of near maxima via the Poisson approximation

Given a sequence of i.i.d. random variables, new proofs are given for limit theorems for the number of observations near the maximum up to time n, as n → ∞. The proofs rely on a Poisson approximation to conditioned binomial laws, and they reveal the origin in the limit laws of mixing with respect to extreme value laws. For the case of attraction to the Fréchet law, the effects of relaxing a technical condition are examined. The results are set in the broader context of counting observations near upper order statistics. This involves little extra effort.     

Nonlinear elastic waves in a monatomic chain with nonlinear interaction

1　ＩＮＴＲＯＤＵＣＴＩＯＮＢｅｃａｕｓｅｓｏｍｅｉｍｐｏｒｔａｎｔ ｐｒｏｐｅｒｔｉｅｓｏｆｃｒｙｓｔａｌ(ｓｕｃｈａｓｓｐｅｃｉｆｉｃｈｅａｔａｔｈｉｇｈｔｅｍｐｅｒａｔｕｒｅ ,ｍｅｌｔｉｎｇ ,ｔｈｅｒｍａｌｅｘｐａｎｓｉｏｎ ,ｔｅｍｐｅｒａｔｕｒｅｄｅ     

Approximation to the Sobolev classesW q r of functions of several variables by bilinear forms inL p for 2≤q≤p≤∞

We study the approximation of functions of several variables by bilinear forms that are the pairwise products of functions of fewer variables. The order of approximation of Sobolev classesW _q ^r by bilinear forms inL _p for 2≤q≤p≤∞ is found. Translated by N. K. Kulman Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 18–34, July, 1997.