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科学通报 1989年第1期34卷 76-76页

作者：张根凯复旦大学数学研究所上海

记B=B为C中的开单位球,dm为B上的Lebesgue测度。记L=L（B）为Bergman空间。令P为L（B,dm）到L上的正交投影。对f∈H（B）,定义Hankel算

关键词：算子泛函分析 Hankel Bergman

Interaction due to various sources in saturated porous media with incompressible fluid

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Journal of Central South University 2016年第5期23卷 1232-1242页

作者： Rajneesh Kumar Ibrahim A.Abbas Department of Mathematics Kurukshetra University Department of Mathematics Faculty of Science and Arts-KhulaisUniversity of Jeddah Nonlinear Analysis and Applied Mathematics Research Group (NAAM) Department of MathematicsKing Abdulaziz University Department of Mathematics Faculty of ScienceSohag University

The disturbance due to mechanical and thermal sources in saturated porous media with incompressible fluid for two-dimensional axi-symmetric problem is investigated.The Laplace and Hankel transforms techniques are used to investigate the problem.The concentrated source and source over circular region have been taken to show the utility of the approach.The transformed components of displacement,stress and pore pressure are obtained.Numerical inversion techniques are used to obtain the resulting quantities in the physical domain and the effect of porosity is shown on the resulting quantities.All the field quantities are found to be sensitive towards the porosity parameters.It is observed that porosity parameters have both increasing and decreasing effect on the numerical values of the physical quantities.Also the values of the physical quantities are affected by the different boundaries.A special case of interest is also deduced.

关键词：不可压缩流体饱和多孔介质相互作用种源多孔介质力学 Hankel 轴对称问题物理量

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A new C~*-algebra and its essential commutant

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Chinese Science Bulletin 1999年第3期44卷 204-207页

作者： Jinshan Liu Yunxin Zhang Kunyu Guo Fudan Univ Inst Math Shanghai 200433 Peoples R China

A new C~* -algebra E+E_* is established. It contains the large Hankel algebra N^G produced by all Toeplitz operators and Hankel operators. It is the proper algebra of B (H^2) and its essential commutant is obtained, which is generated by those Toeplitz operators that have symmetric continuous function symbols and compact operators.

关键词： essential commutant Toeplitz operator Hankel operator.

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Operators on the orthogonal complement of the Dirichlet space (Ⅱ)

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Science China Mathematics 2011年第9期54卷 2005-2012页

作者： YU Tao Department of Mathematics Zhejiang Normal University Jinhua 321004 China

In this paper we first prove that a dual Hankel operator R φ on the orthogonal complement of the Dirichlet space is compact for φ∈ W 1,∞(D),and then that a semicommutator of two Toeplitz operators on the Dirichlet space or two dual Toeplitz operators on the orthogonal complement of the Dirichlet space in Sobolev space is compact.We also prove that a dual Hankel operator R φ with φ∈ W 1,∞(D) is of finite rank if and only if B φ is orthogonal to the Dirichlet space for some finite Blaschke product B,and give a sufficient and necessary condition for the semicommutator of two dual Toeplitz operators to be of finite rank.

关键词： Dirichlet空间正交补 Toeplitz算子运算符 Sobolev空间 Hankel 充分必要条件证明

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实用软包装加工常见问题及解决办法集锦

全球软包装工业 2009年第2期 82-91页

Q PVC压延法包装薄膜的配方是什么？A 德国Hankel公司的无毒食品用PVC包装压延法透明薄膜配方如下：

关键词：包装加工 Hankel 包装薄膜压延法 PVC 膜配方食品用

Bergman空间上的Hankel算子、函数空间和Schatten类

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科学通报 1988年第21期33卷 1677-1677页

作者：张根凯复旦大学数学研究所上海

记B~n为C~n中的单位球,dm为B~n上的Lebesgue测度,m(B~n)=1。令H(B~n)为B~n上解析函数全体,L~2(B~n)为Bergman空间,P为L~2(B~n,dm)到L~2(B~n)上的正交投影。对f∈H(B~n),定义Hankel算子R如下:

关键词： Bergman Hankel Schatten 算子泛函分析

Identification of Forerunners and Transmission of Energy to Tsunami Waves Generated by Instanteneous Ground Motion on a Non-Uniformly Sloping Beach

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International Journal of Geosciences 2013年第2期4卷 454-460页

作者： Arghya Bandyopadhyay Department of Mathematics Khalisani College Chandannagar India

The problem of generation and propagation of tsunami waves is mainly focused on plane beach, there are very few analytical works where wave generation is considered on non-uniformly sloping beach and as a result those works might have failed to capture important facts which are influenced by bottom-slope of the beach. Some researchers provided solution to the forced long linear waves but on a beach with uniform slope while the importance of including variable bottom topography is mentioned by few researchers but they also stayed away from considering continuous variability of the ocean bed as they were studying runup problem. This paper analyzes tsunami waves which are generated by instantaneous bottom dislocation on a ocean floor with variable slope of the form y=-qxr, q > 0, r > 0. Attempts are made to find analytical solution of the problem and along the way tsunami forerunners are identified while investigating the short time wave behavior, not found even with constant slope beaches. In our study a rather significant phenomenon with regard to energy transmission to the waves at steady-state are observed with some notable features.

关键词： Tsunami Waves Shallow Water Equations Hankel Transform Hankel Functions Asymptotic Expansion

On the Build-Up Factor from the Multi-Group Neutron Diffusion Equation with Cylindrical Symmetry

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World Journal of Nuclear Science and Technology 2013年第1期3卷 1-5页

作者： Julio Cesar Lombaldo Fernandes Marco Túllio Vilhena Bardo Ernst Bodmann Volnei Borges DepartmentofAppliedMath Universidade Federal do Rio Grande do Sul Porto Alegre Brazil

We consider the time dependent neutron diffusion equation for one energy group in cylinder coordinates, assuming translational symmetry along the cylinder axis. This problem for a specific energy group is solved analytically applying the Hankel transform in the radial coordinate r. Our special interest rests in the build-up factor for a time dependent linear neutron source aligned with the cylinder axis, which in the limit of zero decay constant reproduces also the static case. The new approach to solve the diffusion equation by integral transform technique is presented and results for several parameter sets and truncation in the solution for the flux and build-up factor are shown and found to be compatible to those of literature [1,2].

关键词： Build-Up Factor Cylindrical Geometry Hankel Transform

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强夯动力Biot方程的理论研究

强夯动力Biot方程的理论研究

Effects of Residual Stress on the Hydro-Elastic Vibration of Circular Diaphragm

第九届全国结构工程学术会议

作者：许金余张鲁渝梅平空军工程大学工程学院空军第一工程总队工程科

本文考虑了强夯中孔隙水的紊流特性,建立了动力Biot固结基本方程。从基本方程的laplace变换式出发,通过关于径向坐标的Hankel变换,得到固结问题基本量之间的传递矩阵,同时在考虑夯钟自重的基础上,导出了强夯的边界接触应力与沉降在变换... 详细信息

本文考虑了强夯中孔隙水的紊流特性,建立了动力Biot固结基本方程。从基本方程的laplace变换式出发,通过关于径向坐标的Hankel变换,得到固结问题基本量之间的传递矩阵,同时在考虑夯钟自重的基础上,导出了强夯的边界接触应力与沉降在变换域中的解析式。利用传递矩阵,边界条件及Hankel、Laplace逆变换可求出任意深度Z处的状态向量与时程的关系。

关键词： Biot动力方程 Laplace Hankel 成层弹性地基传递矩阵法

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World Journal of Mechanics 2012年第6期2卷 361-368页

作者： Junfeng Zhao Song Yu Department of Engineering Mechanics Shandong University Jinan China

The effects of residual stress on the hydro-elastic vibration of circular diaphragm are theoretically investigated by using the added mass approach. The Kirchhoff theory of plates is used to model the elastic thin circular diaphragm on an aperture of an infinite rigid wall and in contact with a fluid on one side. The fluid is assumed to be incompressible and inviscid and the velocity potential is used to describe its irrotational motion. A non-dimensional tension parameter is defined, and the effects of the tension parameter on the frequency parameters and mode shapes of the diaphragm in the air are presented. The Hankel transform is applied to solve the fluid-diaphragm coupled system;boundary conditions are expressed by integral equations. Finally, the effects of residual stress on the non-dimensional added virtual mass incremental (NAVMI) factors of the diaphragm contact with a fluid on one side are investigated. It is found that the effects of the residual stress cannot be neglected when the edges of the circular diaphragm are clamped. The effects of residual stress for NAVMI factors can be increases 11% when the non-dimensional tension parameter is 1000.

关键词： Circular Diaphragm Residual Stress Hankel Transform Frequency Parameter Mode Shape NAVMI