LaF分子基态X~1Σ~ 分析势能函数计算

用原子分子反应静力学原理导出LaF分子可能的电子状态和离解极限。在相对论有效核芯势RECP(RelativisticEffectiveCorePotential)近似下 ,用密度泛函理论中的B3LYP方法优化了LaF分子单、三重态平衡几何结构 ,计算了基态X1Σ 的振动基频和离解能。在计算出来的一系列单点势能基础上 ,用非线性最小二乘方法拟合出基态Murrell Sorbie势能曲线 ,得到分析势能函数 ,由此计算出相应光谱常数ωe、Be、αe、ωeχe的理论值并和实验测量的振转光谱比较 ,结果非常吻合。另外还比较了用两种不同有效势得到的分析势能函数和光谱参数 ,以能量一致相对论有效势ECEP(EnergyCosistentRelativisticEffectivePotential)得到的结果最好。     

Hermite Interpolation of Data Sets by Minimal Spline Spaces

Hermite interpolation of 2n + k data by spline spaces of order k with n variable knots counting multiplicities is studied. A characterization of the minimal spline spaces which admit a solution of the interpolation problem is obtained. A sufficient condition on uniqueness of interpolating spline functions is given.     

Fixed point theorems in metric spaces

In this paper, we establish two general theorems for equivalence between the Meir–Keeler type contractive conditions and the contractive definitions involving gauge functions. One of these theorems is an extension of a recent result of Lim (On characterization of Meir–Keeler contractive maps, Nonlinear Anal. 46 (2001) 113–120).     

Almost automorphic solutions for semilinear boundary differential equations

In this work, we use the extrapolation methods to study the existence and uniqueness of almost automorphic solutions to the semilinear boundary differential equation

where generates a hyperbolic -semigroup on a Banach space and are almost automorphic functions which take values in and a ``boundary space' , respectively. These equations are an abstract formulation of partial differential equations with semilinear terms at the boundary, such as population equations, retarded differential equations and boundary control systems. An application to retarded differential equations is given.

     

The Rate of Approximation by Rational Bernstein Functions in Terms of Second Order Moduli of Continuity

The aim of this note is to study the impact of the weight numbers in two concrete cases on the rate of approximation by rational Bernstein functions. The approximation is measured in terms of second order moduli of continuity. We consider also the case of rational Bernstein curves and the role of the weights to modify the shape of the curves.     

Generalized vector variational-like inequalities and vector optimization in Asplund spaces

Some properties of pseudoinvex functions, defined by means of limiting subdifferential, are obtained. Furthermore, the equivalence between vector variational-like inequalities involving limiting subdifferential and vector optimization problems are studied under pseudoinvexity condition.     

Lyapunov conditions for Super Poincaré inequalities

We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincaré inequality (for instance logarithmic Sobolev or F-Sobolev). The case of Poincaré and weak Poincaré inequalities was studied in [D. Bakry, P. Cattiaux, A. Guillin, Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré, J. Funct. Anal. 254 (3) (2008) 727-759. Available on Mathematics arXiv:math.PR/0703355, 2007]. This approach allows us to recover and extend in a unified way some known criteria in the euclidean case (Bakry and Emery, Wang, Kusuoka and Stroock, …).     

On three-term recurrence and Christoffel–Darboux identity for orthogonal rational functions on the real line

First, we give an algebraic proof to the Christoffel–Darboux identity of formal orthogonal rational functions on the real line by exposing some underlying algebraic properties. This proof does not involve the three-term recurrence relationship. Besides, it is shown that if a family of rational functions satisfies the Christoffel–Darboux relation, then it also admits a three-term recurrence relationship. Thus, the equivalence between both relations is revealed.