Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C~n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Given a principal value convolution on the Heisenberg group Hn = Cn×R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.     

Donaldson–Friedman construction and deformations of a triple of compact complex spaces,II

In a previous paper of the same title the author gave a generalization of the constrution of Donaldson–Friedman, to prove the existence of twistor spaces of n CP ² with a special kind of divisors. In the present paper, we consider its equivariant version. When n = 3, this gives another proof of the existence of degenerate double solid with C *–action, and we show that the branch quartic surface is birational to an elliptic ruled surface. In case n ≥ 4, this yields new Moishezon twistor spaces with C *–action, which is shown to be the most degenerate ones among twistor spaces studied by Campana and Kreußler.     

On a Generalized Cochrane Sum and Its Hybrid Mean Value Formula

The main purpose of this paper is to use a mean value theorem of Dirichlet L-functions to study the asymptotic property of a hybrid mean value of a generalized Cochrane sum, and give an interesting mean value formula.2000 Mathematics Subject Classification: Primary—11F20; Secondary—11F99     

Concerning the multiplicators of Fourier series in the trigonometric system

In this paper we prove theorems on multiplicators of Fourier series inL _p, where the conditions depend on a parameterp. An example illustrating the importance of these conditions is constructed. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 235–247, February, 1998.     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

用三个关系式与Mathematica软件求第二类自然数幂和公式

首先介绍三个第二类自然数幂和关系式并对其中的两式给出证明,接着利用这些关系式与数学软件M athem atica4.0,给出求解第二类自然数幂和公式的若干机械计算方法.     

On the multidimensional distribution of the subset sum generator of pseudorandom numbers

We show that for a random choice of the parameters, the subset sum pseudorandom number generator produces a sequence of uniformly and independently distributed pseudorandom numbers. The result can be useful for both cryptographic and quasi-Monte Carlo applications and relies on bounds of exponential sums.

     

On an approach to the study of the Jaynes–Cummings sum in quantum optics

A new approach to the study of the Jaynes–Cummings sum, which determines the atomic inversion in quantum model of a single two-level atom interacting with a single mode of the quantized radiation field, based on the number theory theorems on approximation of trigonometric sums is presented.      

非因子化方法研究D~+→ ■~0K~+衰变(英文)

在领头阶和αs 修正阶 ,用QCD因子化方法 ,并对它的软胶子效应用光锥QCD求和规则分析D+ → K0 K+ 衰变过程 ,我们分析发现朴素因子化方法的结果远离实验结果 ,QCD因子化方法结果靠近实验结果 ,但是 ,在QCD因子化方法中 ,若考虑软胶子效应 ,其结果与实验结果相一致 .另外 ,计算发现 ,软胶子效应在该衰变道中有相当大的贡献 ,因此不能被忽略     

L p -dual Quermassintegral sums

In this paper, we first introduce a concept of L _p -dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L _p -dual Quermassintegral sums. Moreover, by using Lutwak’s width-integral of index i, we establish the L _p -Brunn-Minkowski inequality for the polar mixed projection bodies. As applications, we prove some interrelated results. This work was partially supported by the National Natural Science Foundation of China (Grant No. 10271071), Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605065) and Foundation of the Education Department of Zhejiang Province of China (Grant No. 20050392)