On the Shape of the Ground State Eigenfunction for Stable Processes

We prove that the ground-state eigenfunction for symmetric stable processes of order α∈(0,2) killed upon leaving the interval (?1,1) is concave on $(-\frac{1}{2},\frac{1}{2})We prove that the ground-state eigenfunction for symmetric stable processes of order α∈(0,2) killed upon leaving the interval (−1,1) is concave on . We call this property “mid-concavity”. A similar statement holds for rectangles in ℝ^d, d>1. These result follow from similar results for finite-dimensional distributions of Brownian motion and subordination. Mathematics Subject Classification (2000) 30C45. Rodrigo Ba?uelos: R. Ba?uelos was supported in part by NSF grant # 9700585-DMS. Tadeusz Kulczycki: T. Kulczycki was supported by KBN grant 2 P03A 041 22 and RTN Harmonic Analysis and Related Problems, contract HPRN-CT-2001-00273-HARP.     

超重核的球形和变形壳结构

应用宏观 微观模型系统研究了超重核的形状和结构性质.其中,宏观能是由基于核子密度泛函的连续介质模型计算得到.计算结果很好地再现了超重核的结合能、α衰变能和寿命的实验数据.对单粒子能级的计算和分析表明超重核的壳结构是形变和同位旋相关的.位能曲面的计算结果显示,与其它区域的核相比,超重核的形状不易变化. The structure of superheavy nuclei has been studied by using the macroscopic-microscopic model. The macroscopic energy was calculated with the continuous medium model in which the energy is expressed as a functional of nucleon densities. The deformations and structures of superheavy nuclei were investigated systematically. Calculations reproduce well the available data of experimental α decay energies and half-lifes. The investigation of single-particle levels shows that the shell structure is deformed a...     

Fluorescence Quenching of 2,2″-dimethyl-p-terphenyl by Carbon Tetrachloride in Binary Mixtures

The fluorescence quenching of 2,2″-dimethyl-p-terphenyl (DMT) by carbon tetrachloride (CCl₄) was investigated in different solvent mixtures of benzene and acetonitrile at room temperature (300 K). A positive deviation from linearity was observed in the Stern-Volmer plots for all the solvent mixtures. This could be explained satisfactorily by static and dynamic quenching models. The nonlinearities in the S-V plots are interpreted in terms of ground state complex model and the sphere of action static quenching model. The results suggest that positive deviations in the S-V plot are due to the presence of both static and dynamic quenching processes. To explain that bimolecular reactions are diffusion limited, we have used finite sink approximation model. Various rate parameters for the quenching process have been determined by static and dynamic quenching models. The dynamic quenching constant depends on the solvent polarity and indicates that quenching reaction is diffusion limited.     

铁磁—反铁磁双层系统基态能

利用线性自旋波理和数值计算方法得到铁磁—反铁磁双层系统的基态能。     

MnC±(M=Fe,Co,Ni,Cu,n=1～5)团簇的密度泛函理论研究

本文用密度泛函理论系统地研究了混合团簇MnC^±（M=Fe,Co,Ni,Cu,n=1—5）的基态几何结构和电子结构．从中性团簇体系移除一个电子对基态几何结构的影响相比给中性团簇体系增加一个电子对基态几何结构所引起的影响更加明显．在相应的序列中,Cu3C^-有相对较高的稳定性,可视其结构为幻数结构．过渡金属MnC^±（TM=Fe,Co,Ni）与C^±之间的相互作用强度彼此接近,并且明显大于Cu与C^±之间的相互作用强度;金属与碳之间的相互作用强度在中性体系、带正电体系和带负电体系中由大到小依次是带正电体系→中性体系→带负电体系．根据相互作用强度模型,在带正电体系中增强的金属与碳之间的相互作用强度可能更有利于单壁碳纳米管的生长与合成．     

Classical structures in modern valence bond theory

The results of some recent ab initio valence bond calculations, in which both structure coefficients and orbital forms are optimized, are analysed. The origin of structures in which the optimum orbitals are no longer atomic in character but instead delocalized, is traced back to the presence of certain symmetries in the wavefunction. When such symmetries exist it is possible to choose alternative linear combinations of the delocalized orbitals and to rewrite the wavefunction in terms of VB structures of classical form. The advantages of the classical structures are discussed in the context of a simple example — a square planar conformation of four hydrogen atoms.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

An improved result for a class of Klein–Gordon–Maxwell system with quasicritical potential vanishing at infinity

The following kind of Klein–Gordon–Maxwell system is investigated where $\omega >0$ is a parameter, and V is vanishing potential. By using some suitable conditions on K and f, we obtain a Palais–Smale sequence by using Pohožaev equality and prove the ground-state solution for this system by employing variational methods. Our result improves the related one in the literature.     

离散固定梁方程特征函数的振荡性质及其应用

该文建立了带权函数$m:[2, N+1]_\mathbb{Z}\to (0,\infty)$的离散固定梁方程$\Delta^4 u(k-2)=\lambda m(k)u(k),\ k\in[2, N+1]_\mathbb{Z}$, $u(1)=\Delta u(1)=0=u(N+2)=\Delta u(N+2)$的特征值结构和相应特征函数的振荡性质, 其中$[2,N+1]_\mathbb{Z}=\{2,3,\cdots,N+1\}$. 作为应用,当非线性项在零点和无穷远处分别满足适当的增长性条件时, 获得了相应非线性问题结点解的全局结构.