宇宙学常数疑难

当代天文学的一系列观测事实都支持应该存在一个非零的正的宇宙学常数，但是，人们发现当前宇宙学常数值太小，而且宇宙学常数即真空能量密度与现在的物质密度巧合地具有相同的量级，然而现有物理学理论还无法给出合理的解释，因此宇宙学常数问题成为物理学和天文学上最重大的疑难之一。文章综述了近年来宇宙在加速膨胀这一重大的天文发现和宇宙学常数的观测结果以及当前理论物理学在宇宙学常数问题上的一些尝试。     

Nest代数上的在零点广义可导映射

设A为B（H）的子代数,　是A到B（H）的线性映射,我们说　在0点广义可导（广义双边可导）,如果对任意的S,T∈A且ST=0（ST=0或TS=0）,有　（ST）=　（S）T+S　（T）-S　（I）T.本文主要得到如下结果:（1）有限Nest代数上的每个范数拓扑连续的在0点广义可导的线性映射是广义内导子;（2）若N是完备Nest且H_　 H,则algN上的每个范数拓扑连续的在0点广义双边可导的线性映射是广义内导子.     

Determination of the Constants of Binding of Acridine Dyes with Micelles of Sodium Dodecyl Sulfate Using the Quenching of Delayed Fluorescence by Heavy Atoms

The constants of binding dye molecules with the micelles of sodium dodecyl sulfate are determined using quenching of delayed fluorescence of acridine dyes by sodium iodide in aqueous–micellar solutions. Kinetic equations have been composed that describe the processes of deactivation of the excited states of dyes. By solving these equations at the concentration of the quencher sodium iodide corresponding to the minimum lifetime of triplet states and at the concentration of micelles corresponding to the least value of the delayed fluorescence quenching rate constants, we obtained the constants of binding dyes with micelles equal to 1.3·10⁷, 2.9·10⁷, and 3.1·10⁷ M^–1 for trypaflavine, acridine orange, and acridine yellow, respectively. We calculated the rate constants of quenching of the triplet states of the molecules of dyes by iodide ions (I ^–) that decreased in transition from trypaflavine to acridine orange and acridine yellow.     

CH3S CH2SH异化反应的理论研究

利用密度泛函理论(DFT)和从头算(ab initio)研究了CH3S←→CH2SH互异化的反应机理．采用HF、B3LYP、MP2理论水平和中等基组6-31(d)，计算了CH3S、CH2SH及其过渡态的结构参数、谐振频率、零点能(ZPF)、总能量和相对能量，并利用B3LYP／6-31(d)的方法计算了反应的内禀反应坐标(IRC)，给出了分子构型和自旋污染沿反应坐标的变化曲线，以及最小能量曲线(MEP)、绝热能量曲线．此外，利用传统过渡态理论(CTST)研究了该互异化反应的速率常数和平衡常数在200～1000K的变化．     

Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces

Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D₄,E₆,E₇,E₈). To such a diagram one can attach a group G whose generators correspond to the legs of the affinization, have orders equal to the leg lengths plus 1, and the product of the generators is 1. The group G is then a 2-dimensional crystallographic group: G=Z??Z², where ? is 2, 3, 4, and 6, respectively. In this paper, we define a flat deformation H(t,q) of the group algebra C[G] of this group, by replacing the relations saying that the generators have prescribed orders by their deformations, saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots (which are deformation parameters). The algebra H(t,q) for D₄ is the Cherednik algebra of type C^∨C₁, which was studied by Noumi, Sahi, and Stokman, and controls Askey-Wilson polynomials. We prove that H(t,q) is the universal deformation of the twisted group algebra of G, and that this deformation is compatible with certain filtrations on C[G]. We also show that if q is a root of unity, then for generic t the algebra H(t,q) is an Azumaya algebra, and its center is the function algebra on an affine del Pezzo surface. For generic q, the spherical subalgebra eH(t,q)e provides a quantization of such surfaces. We also discuss connections of H(t,q) with preprojective algebras and Painlevé VI.     

Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian

We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential (hemivariational inequality). Using the degree theory for multivalued perturbations of (S)₊-operators and the spectrum of a class of weighted eigenvalue problems for the scalar p-Laplacian, we prove the existence of at least three distinct nontrivial solutions, two of which have constant sign.     

The logarithmic norm. History and modern theory

In his 1958 thesis Stability and Error Bounds, Germund Dahlquist introduced the logarithmic norm in order to derive error bounds in initial value problems, using differential inequalities that distinguished between forward and reverse time integration. Originally defined for matrices, the logarithmic norm can be extended to bounded linear operators, but the extensions to nonlinear maps and unbounded operators have required a functional analytic redefinition of the concept.This compact survey is intended as an elementary, but broad and largely self-contained, introduction to the versatile and powerful modern theory. Its wealth of applications range from the stability theory of IVPs and BVPs, to the solvability of algebraic, nonlinear, operator, and functional equations. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65L05     

A new class of Ornstein transformations with singular spectrum

It is shown that for any family of probability measures in Ornstein type constructions, the corresponding transformation has almost surely a singular spectrum. This is a new generalization of Bourgain's theorem [J. Bourgain, On the spectral type of Ornstein class one transformations, Israel J. Math. 84 (1993) 53–63], same result is proved for Rudolph's construction [D. Rudolph, An example of a measure-preserving map with minimal self-joining and applications, J. Anal. Math. 35 (1979) 97–122].     

Generalized Solution of a Kind of Nonparametric Curvature Evolution with Boundary Condition

The existence and uniqueness of the generalized solution for a kind of nonparametric curvature flow problem are obtained. This kind of curvature flow problem describes the evolution of graphs with speed depending on the reciprocal of the Gauss curvature.     

热效应对光折变晶体两波耦合的特性影响的理论分析

用一种模型对两波耦合进行了分析，导出了强度相位的解析式，对影响两波耦合的参数进行了理论分析。分析了对ＢａＴｉＯ３光折变晶体的两波耦合的测量结果。