The structure and distances in Yule recursive trees

Based on uniform recursive trees, we introduce random trees with the factor of time, which are named Yule recursive trees. The structure and the distance between the vertices in Yule recursive trees are investigated in this paper. For arbitrary time t > 0, we first give the probability that a Yule recursive tree Y_t is isomorphic to a given rooted tree γ; and then prove that the asymptotic distribution of ζ_t,m, the number of the branches of size m, is the Poisson distribution with parameter λ = 1/m. Finally, two types of distance between vertices in Yule recursive trees are studied, and some limit theorems for them are established.© 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

一种构造正交小波基的新方法

本文给出了构造正交小波基的一种新的方法,主要是通过改造钟形函数来构造有具体表达式的小波母函数,在光滑性,局部性等性质上优于一般的构造方法,其收敛于零的阶数可达到O(|t|~(-N)),N≥4。而且更进一步在S空间上构造出收敛更快的小波母函数。     

Infrared spectroscopy of racemic and enantiomeric forms of atenolol

The molecular structure of conformational isomorphs given by X-ray diffraction for racemic and enantiomeric atenolol were optimized at the HF/6-31G* level of theory and the infrared spectra of the structure were calculated. These spectra are used to characterize the differences between the various atenolol conformers. The spectra of the (R,S)- and S-atenolol solid forms were recorded and the bands corresponding to the functional groups identified with the aid of the calculated spectra, fitting analysis, temperature effect and H/D isotopic exchange. Particular attention was paid to the stretch vibration modes of the functional groups present in the atenolol.     

Study of isomorphism in fluorine-containing antimony(III) complexes

The mutual influence of the atoms on the composition of solid fluorine-containing antimony(iii) complexes formed in aqueous solutions in the (MF) _x −(M′F) _n−x −SbF₃ (M, M′=Na, K, Rb, Cs, and NH₄;n=1, 2;x=0 to 2), (KNO₂) _n −(KY) _n −SbF₃ (Y=F, Cl, SO₄;n=0.5, 1), and K₂SbF₅−K₂SbCl₅ systems was investigated by elemental, X-ray, and thermogravimetric analyses and by IR and^121,123Sb NQR spectroscopy. The isomorphism conditions for fluorine-containing antimony(iii) compounds resulting in the formation of complexes NaM′SbF₅·1.5H₂O (M′=K and Rb), K₂SbF₅·1.5H₂O, NaCs₃Sb₄F₁₆·H₂O, KsbF₃Cl, K₂SbF₂Cl₃ with constant compositions, continuous M _x M′_2−x SbF₅ (0<x<2) and limited M _x M′_1−x SbF₄ (0.25<x<0.75; M, M′=K, Rb, Cs, and NH₄) solid solutions or LiF+MSbF₄ (M=Na, K, Rb, and Cs), M₂SbF₅+Cs₂SbF₅ (M=Na and K) and MSbF₄+NaSbF₄ (M=Rb and NH₄) mechanical mixtures were determined. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 103–108, January, 1999.     

Antisymmetry and stability of aqueous systems. III. Conformations of the hexagonal rings

The antisymmetry of proton configurations was studied for the hexagonal water rings with different conformations. The change in the direction of all hydrogen bonds was used as an additional symmetry operation. The ring configuration energies were calculated using the intermolecular interaction potentials. For different ring conformations, the relationships between antisymmetry and energy were analyzed and compared.     

纳米晶粒取向连生与枝蔓晶的形成

本文研究了在水热条件下ZnO、BaTiO3、La2/3TiO3和Fe2O3纳米晶粒的取向连生和枝蔓晶的形成。用负离子配位多面体生长基元理论模型讨论了纳米晶粒的取向连生和晶粒相连的枝蔓晶，其枝蔓晶的形成与通常枝蔓晶的形成机理是一致的，都是沿着晶体中负离子配位多面体相互联结的稳定方向，为晶体生长速率最快方向，其分布的对称性与晶体结构的对称性是对应一致的。     

von Neumann代数中套子代数上的Lie同构

本文给出因子von Neumann代数中的幂等算子在广义Lie积下的一个刻画; 得到因子von Neumann代数中套子代数的幂等算子在Lie积下的一个特征．作为应用, 研究了因子von Neumann代数中套子代数上的Lie同构,并证明因子von Neumann 代数中套子代数之间的Lie同构,要么是同构与广义迹之和,要么是负反同构与广义迹之和．     

Isomorphisms of fiber spaces over Teichmüller spaces

We will be mainly concerned with some important fiber spaces over Teichmuller spaces, including the Bers fiber space and Teichmuller curve, establishing an isomorphism theorem between "punctured" Teichmuller curves and determining the biholomorphic isomorphisms of these fiber spaces.     

Rolling of a non-homogeneous ball over a sphere without slipping and twisting

Consider the problem of rolling a dynamically asymmetric balanced ball (the Chaplygin ball) over a sphere. Suppose that the contact point has zero velocity and the projection of the angular velocity to the normal vector of the sphere equals zero. This model of rolling differs from the classical one. It can be realized, in some approximation, if the ball is rubber coated and the sphere is absolutely rough. Recently, J. Koiller and K. Ehlers pointed out the measure and the Hamiltonian structure for this problem. Using this structure we construct an isomorphism between this problem and the problem of the motion of a point on a sphere in some potential field. The integrable cases are found.