Q_k(x)与F_k(x)的渐近公式

设ｎ，ｋ为自然数，Ｇ（ｎ）阶群中的同构类数，Ｆｋ（ｘ）与Ｑｋ（ｘ）分别表示不超过ｘ的自然数中使Ｇ（ｎ）＝ｋ的自然数、无平方因子自然数的个数．本文的目的是用Ｂｒｕｎ筛法证明Ｑｋ（ｘ）的条件渐近公式并对Ｆｋ（ｘ）的渐近性质做出了推测．     

Oriented Cohomology Theories of Algebraic Varieties

This article contains proofs of the results announced by Panin and Smirnov (http://www. math.uiuc.edu/k-theory/0459/2000) in the part concerning general properties of oriented cohomology theories of algebraic varieties. It is constructed one-to-one correspondences between orientations, Chern structures and Thom structures on a given ring cohomology theory. The theory is illustrated by motivic cohomology, algebraic K-theory, algebraic cobordism theory and by other examples.     

Additive Jordan isomorphisms of nest algebras on normed spaces

Let X be a real or complex Banach space. Let and be two nest algebras on X. Suppose that φ is an additive bijective mapping from onto such that φ(A²)=φ(A)² for every . Then φ is either a ring isomorphism or a ring anti-isomorphism. Moreover, if X is a real space or an infinite dimensional complex space, then there exists a continuous (conjugate) linear bijective mapping T such that either φ(A)=TAT⁻¹ for every or φ(A)=TA∗T−1 for every .     

交换群层的正合序列与同态定理

在交换群层（简称层）中给出了层的单（满）同态核与上核的泛性定理及正合交换图的一系列结论,进而证明了交换群层的同态（同构）定理。     

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．     

Additive maps preserving the ascent and descent of operators

Let and be the algebras of all bounded linear operators on infinite dimensional complex Banach spaces X and Y, respectively. We characterize additive maps from onto preserving different quantities such as the nullity, the defect, the ascent, and the descent of operators.     

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.     

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.     

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.