Hankel convolution operators on entire functions and distributions

In this paper we study the Hankel convolution operators on the space of even and entire functions and on Schwartz distribution spaces. We characterize the Hankel convolution operators as those ones that commute with Hankel translations and with a Bessel operator. Also we prove that the Hankel convolution operators are hypercyclic and chaotic on the spaces under consideration.     

The rank of Hankel operators on harmonic Bergman spaces

We show that on the harmonic Bergman spaces, the Hankel operators with nonconstant harmonic symbol cannot be of finite rank.

     

Zeta regularized determinants for conic manifolds

We study (relative) zeta regularized determinants of Laplace type operators on compact conic manifolds. We establish gluing formulae for relative zeta regularized determinants. For arbitrary self-adjoint extensions of the Laplace-Beltrami operator, we express the relative ζ-determinants for these as a ratio of the determinants of certain finite matrices. For the self-adjoint extensions corresponding to Dirichlet and Neumann conditions, the formula is particularly simple and elegant.     

On multiple integrals of special form

Multiple integrals generalizing the iterated kernels of integral operators are expressed as single integrals in the case of a special representation of the kernel (this is our theorem). Besides integral equations, Markov processes involve these integrals as well. As a consequence of the theorem, we obtain transition probability densities of certain Markov processes. As an illustration, we consider nine examples.     

Application of the finite Hankel transform to a diffusion problem without azimuthal symmetry

The problem treated in this paper concerns calculating the evolution of the pressure in a single-phase, slightly compressible fluid in a porous medium consisting of communicating layers. The fluid is produced through a point sink located on the side of an otherwise sealed cylindrical wellbore. This location of the sink causes the flow around the wellbore to be azimuthally asymmetric.The problem is solved through successive application of Laplace, finite Fourier and finite Hankel transforms. Although apparently straightforward, this approach leads to serious numerical difficulties. The published form of the inversion formula for the finite Hankel transform leads to inaccurate computation for the higher azimuthal modes even with 128 bit arithmetic. An alternative form is developed which enables accurate evaluation of the solution with the more practical 64 bit arithmetic. The technique for two-layer solution presented here can be directly extended to a problem with a larger number of communicating layers. This is the first instance of successful application of the finite Hankel transform to an azimuthally asymmetric diffusion problem.     

Asymptotic expansions of integrals of two Bessel functions via the generalized hypergeometric and Meijer functions

Asymptotic expansions of certain finite and infinite integrals involving products of two Bessel functions of the first kind are obtained by using the generalized hypergeometric and Meijer functions. The Bessel functions involved are of arbitrary (generally different) orders, but of the same argument containing a parameter which tends to infinity. These types of integrals arise in various contexts, including wave scattering and crystallography, and are of general mathematical interest being related to the Riemann—Liouville and Hankel integrals. The results complete the asymptotic expansions derived previously by two different methods — a straightforward approach and the Mellin-transform technique. These asymptotic expansions supply practical algorithms for computing the integrals. The leading terms explicitly provide valuable analytical insight into the high-frequency behavior of the solutions to the wave-scattering problems.     

加权Bergman空间上小Hankel算子的Schatten类

讨论了 C\+n 中有界对称域的加权Bergman空间上符号属于 L\+2\-a(Ω, dV\-λ) 的小Hankel算子, 利用符号 Φ 的某种积分变换,给出了小Hankel算子 h\-Φ 属于Schatten理想 S\-p 的特征.     

中国上市公司资本结构影响因素之实证研究

资本结构不仅是财务理论研究中的热点及难点,也日益成为公司理财决策的关键问题.本文从影响因素角度对资本结构进行实证研究.文中以深沪两市部分非金融类上市公司为样本,利用本世纪最初三年的企业财务数据,选取可能影响企业资本结构的多个指标为解释变量,利用单因素方差分析、主成分分析、逐步回归分析找出了主要影响因素及其影响方式,试图为国内上市公司资本结构决定因素提供最新实证研究证据,并为企业财务决策提供支持.     

球上加权Bergman空间上的Schatten类Hankel算子

本文给出了超球上加权Ｂｅｒｇｍａｎ空间上Ｈａｎｋｅｌ算子属于Ｓｃｈａｔｔｅｎｐ－类（２≤ｐ＜＋∞）的一个充要条件，推广了文［１０］中的主要结果。     

Molecular determinants in the bioactivation of the dopaminergic neurotoxin N-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP)

Summary Nineteen analogs of the dopaminergic neurotoxin N-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) have been used as probes to study the structural parameters that influence MAO-catalyzed oxidation. In this study, the efficiency of enzyme-catalyzed substrate oxidation was found to be unrelated to parameters such as the ionization potential, dipole moment, net atomic charge at C5 and the dihedral angle between the phenyl ring and the tetrahydropyridine moiety. Conformational analysis revealed that substitution at the C2 position of MPTP yields atropisomers. It is suggested that one of these atropisomers would be either inactive or substantially less active than the other. Therefore, the relative oxidative efficiency and toxicity of these compounds reported earlier may have been significantly underestimated. Based on the conformational analysis and other data, a rudimentary model of the MAO substrate site has been developed which partially explains the substrate specificities of MAO A and MAO B.Each substrate binding site can be divided into two regions, (a) an amine-binding pocket (for the tetrahydropyridine moiety), and (b) a bulky substituent region (for the phenyl group and its substituents). The length of the substrate binding site (measured along the long axis of MPTP) is approximately 8.5 Å, and the width of the amine-binding pocket is approximately 2.5 Å (from C3 to C5). The bulky substituent region contains a central area for binding the phenyl group of MPTP. This central area is flanked by two hydrophobic pockets, P2 and P3. In MAO A, the pocket P2-A is oriented 45–135° relative to the plane of the tetrahydropyridine moiety, with a radius of 3.1 Å from C2 of the phenyl ring. The radius of a similar but smaller pocket, P2-B, in MAO B, is approximately 2.7 Å. In MAO B, the pocket P3-B (radius 2.36 Å from C3) is larger than a similar pocket P3-A (radius 1.70 Å from C3) in MAO A. The foregoing characterization suggests that differences in the size and topography of both of the substituent pockets play an important role in determining the substrate specificities of these two isozymes.