期刊文献+
共找到1,457篇文章
< 1 2 73 >
每页显示 20 50 100
A Cauchy integral formula for(p,q)-monogenic functions withα-weight
1
作者 GAO Long DU Xiao-jing +1 位作者 LIU Yue XIE Yong-hong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第3期545-553,共9页
Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-... Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-monogenic functions withα-weight are given. 展开更多
关键词 (p q)-monogenic functions with-weight Cauchy-Pompeiu formula Cauchy integral formula Cauchy integral theorem
下载PDF
The tangential k-Cauchy-Fueter type operator and Penrose type integral formula on the generalized complex Heisenberg group
2
作者 REN Guang-zhen SHI Yun KANG Qian-qian 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第1期181-190,共10页
The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.I... The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex. 展开更多
关键词 the generalized complex Heisenberg group the tangential k-Cauchy-Fueter type operator Penrose-type integral formula
下载PDF
CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS
3
作者 曹南斌 李尊凤 +1 位作者 杨贺菊 乔玉英 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期369-385,共17页
Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quan... Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution. 展开更多
关键词 Clifford analysis Cauchy type integral Plemelj formula Holder continuous boundary value problems
下载PDF
KIRCHHOFF FORMULA WITH LINE INTEGRAL FORM AND ITS APPLICATIONS
4
作者 顾长青 徐金平 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 1999年第2期183-187,共5页
In this paper, Kirchhoff formula has been transformed from surface integral form into a line integral form. The new form of the formula can be applied to separate geometrical optical field from diffraction field, and ... In this paper, Kirchhoff formula has been transformed from surface integral form into a line integral form. The new form of the formula can be applied to separate geometrical optical field from diffraction field, and reduce the time of numerical computation greatly. Based on the new form, an analytical formula of diffraction field in the far zone has been presented for the polygonal aperture illuminated by a uniform plane wave. 展开更多
关键词 wave propagation DIFFRACTION integrals of Cauchy type Kirchhoff formula line integral
下载PDF
Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape.Part I:Theory and Integral Formulae 被引量:9
5
作者 Qin XU 高守亭 曹洁 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2011年第6期1433-1444,共12页
The non-uniqueness of solution and compatibility between the coupled boundary conditions in computing velocity potential and streamfunction from horizontal velocity in a limited domain of arbitrary shape are revisited... The non-uniqueness of solution and compatibility between the coupled boundary conditions in computing velocity potential and streamfunction from horizontal velocity in a limited domain of arbitrary shape are revisited theoretically with rigorous mathematic treatments.Classic integral formulas and their variants are used to formulate solutions for the coupled problems.In the absence of data holes,the total solution is the sum of two integral solutions.One is the internally induced solution produced purely and uniquely by the domain internal divergence and vorticity,and its two components(velocity potential and streamfunction) can be constructed by applying Green's function for Poisson equation in unbounded domain to the divergence and vorticity inside the domain.The other is the externally induced solution produced purely but non-uniquely by the domain external divergence and vorticity,and the non-uniqueness is caused by the harmonic nature of the solution and the unknown divergence and vorticity distributions outside the domain.By setting either the velocity potential(or streamfunction) component to zero,the other component of the externally induced solution can be expressed by the imaginary(or real) part of the Cauchy integral constructed using the coupled boundary conditions and solvability conditions that exclude the internally induced solution.The streamfunction(or velocity potential) for the externally induced solution can also be expressed by the boundary integral of a double-layer(or singlelayer) density function.In the presence of data holes,the total solution includes a data-hole-induced solution in addition to the above internally and externally induced solutions. 展开更多
关键词 integral formulae streamfunction velocity potential domain of arbitrary shape
下载PDF
ON QUADRATURE FORMULAE FOR SINGULAR INTEGRALS OF ARBITRARY ORDER 被引量:3
6
作者 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2004年第1期9-27,共19页
Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also gi... Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given. 展开更多
关键词 Peano derivative generalized Hermite interpolation singular integral of arbitrary order singular quadrature formula
下载PDF
Plemelj Formula for Cauchy Type Integral on Certain Distinguished Boundary in Universal Clifford Analysis 被引量:3
7
作者 XU Na DU Jinyuan 《Wuhan University Journal of Natural Sciences》 CAS 2007年第3期385-390,共6页
Under the foundation of Cauchy integral formula on certain distinguished boundary for functions with values in universal Clifford algebra, we define the Cauchy type integral with values in a universal Clifford algebra... Under the foundation of Cauchy integral formula on certain distinguished boundary for functions with values in universal Clifford algebra, we define the Cauchy type integral with values in a universal Clifford algebra, obtain its Cauchy principal value and Plemelj formula on certain distinguished boundary. 展开更多
关键词 universal Clifford analysis Cauchy type integral Plemelj formula
下载PDF
General Integral Formulasof (0, q)(q 〉 0)Differential Forms on the Analytic Varieties 被引量:3
8
作者 CHEN Shu-jin 《Chinese Quarterly Journal of Mathematics》 2017年第4期355-370,共16页
In this paper, firstly using different method and technique we derive the cor-responding integral representation formulas of (0, q)(q 〉 0) differential forms for the twotypes of the bounded domains in complex sub... In this paper, firstly using different method and technique we derive the cor-responding integral representation formulas of (0, q)(q 〉 0) differential forms for the twotypes of the bounded domains in complex submanifolds with codimension-m. Secondly weobtain the unified integral representation formulas of (0, q)(q 〉 0) differential forms for thegeneral bounded domain in complex submanifold with codimension-m, which include Hatzi-afratis formula, i.e. Koppelman type integral formula for the bounded domain with smoothboundary in analytic varieties. In particular, when m -- 0, we obtain the unified integralrepresentation formulas of (0, q)(q 〉 0) differential forms for general bounded domain in Cn,which are the generalization and the embodiment of Koppelman-Leray formula. 展开更多
关键词 Complex SUBMANIFOLD ANALYTIC VARIETIES UNIFIED formula Extension Differ-ential form integral representation
下载PDF
ORTHOGONAL POLYNOMIALS AND DETERMINANT FORMULAS OF FUNCTION-VALUED PADE-TYPE APPROXIMATION USING FOR SOLUTION OF INTEGRAL EQUATIONS 被引量:2
9
作者 顾传青 潘宝珍 吴蓓蓓 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第6期853-860,共8页
To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the s... To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given. 展开更多
关键词 generalized linear functional function-valued Padé-type approximation Fredholm integral equation orthogonal polynomial determinant formula
下载PDF
THE PERMUTATION FORMULA OF SINGULAR INTEGRALS WITH BOCHNER-MARTINELLI KERNEL ON STEIN MANIFOLDS 被引量:1
10
作者 钟同德 陈吕萍 《Acta Mathematica Scientia》 SCIE CSCD 2006年第4期679-690,共12页
Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^(1) smooth boundary on a Stein manifold. As an a... Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^(1) smooth boundary on a Stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner-Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation. 展开更多
关键词 Stein manifold singular integral with Bochner-Martinelli kernel permutation formula regularization problem
下载PDF
AN INTEGRATION BY PARTS FORMULA FOR STOCHASTIC HEAT EQUATIONS WITH FRACTIONAL NOISE
11
作者 尹修伟 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期349-362,共14页
In this paper,we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling.As an application,we also obtain the shift Harnack inequal... In this paper,we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling.As an application,we also obtain the shift Harnack inequalities. 展开更多
关键词 integration by parts formula stochastic heat equations fractional Brownian motion shift Harnack inequality coupling by change of measures
下载PDF
The Leray-Stokes Type Integral Representation Formulas on the Analytic Varieties 被引量:1
12
作者 CHEN Shu-jin 《Chinese Quarterly Journal of Mathematics》 2018年第4期395-416,共22页
The closure of the bounded domains D in Cnconsists of a chain of the slit spaces,and may be divided into two types. Based on the two types of bounded domains in C^n, firstly using different method and technique we der... The closure of the bounded domains D in Cnconsists of a chain of the slit spaces,and may be divided into two types. Based on the two types of bounded domains in C^n, firstly using different method and technique we derive the corresponding integral representation formulas of differentiable functions for complex n-m(0 ≤ m < n) dimensional analytic varieties in the two types of the bounded domains. Secondly we obtain the unified integral representation formulas of differentiable functions for complex n-m(0 ≤ m < n) dimensional analytic varieties in the general bounded domains. When functions are holomorphic, the integral formulas in this paper include formulas of Stout^([1]), Hatziafratis^([2]) and the author^([3]),and are the extension of all the integral representations for holomorphic functions in the existing papers to analytic varieties. In particular, when m = 0, firstly we gave the integral representation formulas of differentiable functions for the two types of bounded domains in C^n. Therefore they can make the concretion of Leray-Stokes formula. Secondly we obtain the unified integral representation formulas of differentiable functions for general bounded domains in C^n. So they can make the Leray-Stokes formula generalizations. 展开更多
关键词 Complex SUBMANIFOLD ANALYTIC VARIETIES Unified formula Extension DIFFERENTIABLE function integral representation
下载PDF
HURWITZ-HODGE INTEGRAL IDENTITIES FROM THE ORBIFOLD MARIO-VAFA FORMULA
13
作者 赵晨 《Acta Mathematica Scientia》 SCIE CSCD 2016年第1期139-156,共18页
In this paper, we present some polynomial identities of Hurwitz-Hodge integral. Subsequently, we present how to obtain some Hurwitz-Hodge integral identities from the polynomial identity. Lastly, we give a recursion f... In this paper, we present some polynomial identities of Hurwitz-Hodge integral. Subsequently, we present how to obtain some Hurwitz-Hodge integral identities from the polynomial identity. Lastly, we give a recursion formula for Hurwitz-Hodge integral (TbL λgλ1)ag. 展开更多
关键词 Hurwitz-Hodge integral orbifold Marifio-Vafa formula polynomial identities recursion formula
下载PDF
Numerical integral formula of two-dimension based on optimal approximation
14
作者 吴勃英 王勇 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2002年第2期217-219,共3页
There are such problems as convergence and stability of numerical calculations during multivariate interpolation. Moreover, it is very difficult to construct a overall multivariate numerical interpolation formula to e... There are such problems as convergence and stability of numerical calculations during multivariate interpolation. Moreover, it is very difficult to construct a overall multivariate numerical interpolation formula to ensure convergence for a set of irregular nodes. In this paper by means of an optimal binary interpolation formula given in a reproducing kernel space, a high precision overall two dimension numerical integral formula is established and its advantage is that it ensures the convergence for arbitrary irregular node set in the integral domain. 展开更多
关键词 OPTIMAL APPROXIMATION NUMERICAL integral formula CONVERGENCE and stability
下载PDF
COMPUTATION FORMULAS OF GENERALIZED INVERSE PAD APPROXIMANTS USING FOR SOLUTION OF INTEGRAL EQUATIONS
15
作者 GU Chuan-qing(顾传青) +1 位作者 LI Chun-jing(李春景) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第9期1057-1063,共7页
For the generalized inverse function-valued Pade approximants, its intact computation formulas are given. The explicit determinantal formulas for the denominator scalar polynomials and the numerator function-valued po... For the generalized inverse function-valued Pade approximants, its intact computation formulas are given. The explicit determinantal formulas for the denominator scalar polynomials and the numerator function-valued polynomials are first established. A useful existence condition is given by means of determinant form. 展开更多
关键词 Pade approximant determinantal formula EXISTENCE integral equation
下载PDF
Lamb's integral formulas of two-phase saturated medium for soil dynamic with drainage
16
作者 丁伯阳 党改红 袁金华 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第9期1113-1124,共12页
When dynamic force is applied to a saturated porous soil, drainage is common. In this paper, the saturated porous soil with a two-phase saturated medium is simulated, and Lamb's integral formulas with drainage and st... When dynamic force is applied to a saturated porous soil, drainage is common. In this paper, the saturated porous soil with a two-phase saturated medium is simulated, and Lamb's integral formulas with drainage and stress formulas for a two-phase saturated medium are given based on Biot's equation and Betti's theorem (the reciprocal theorem). According to the basic solution to Biot's equation, Green's function Gij and three terms of Green's function G4i, Gi4, and G44 of a two-phase saturated medium subject to a concentrated force on a spherical coordinate are presented. The displacement field with drainage, the magnitude of drainage, and the pore pressure of the center explosion source are obtained in computation. The results of the classical Sharpe's solutions and the solutions of the two-phase saturated medium that decays to a single-phase medium are compared. Good agreement is observed. 展开更多
关键词 explosive field drainage dynamic response Lamb's integral formula
下载PDF
PLEMELJ FORMULA OF CAUCHY TYPE INTEGRAL ON STEIN MANIFOLDS
17
作者 陈吕萍 林良裕 《Acta Mathematica Scientia》 SCIE CSCD 2005年第4期647-657,共11页
Let D be a bounded domain with piecewise C^(1) smooth orientable boundary on Stein manifolds, and let Φ(z) be a Cauchy type integral with Bochner-Martinelli kernel Ω(φ^V, S^-, S) and Holder continuous density... Let D be a bounded domain with piecewise C^(1) smooth orientable boundary on Stein manifolds, and let Φ(z) be a Cauchy type integral with Bochner-Martinelli kernel Ω(φ^V, S^-, S) and Holder continuous density function φ(ζ), the authors define a solid angular coefficient α(t) at the point t∈δD, prove that there exist the interior and outer limit values Φ^±(t) under the meaning of the Cauchy principal value, and obtain the more general Plemelj formula and jump formula. 展开更多
关键词 Stein manifold Cauchy type integral Plemelj formula solid angular coefficient
下载PDF
A Pfaffian Formula of the Generalized Inverse Function-Valued Padé Approximant Used in Solving Integral Equations
18
作者 李春景 顾传青 《Journal of Shanghai University(English Edition)》 CAS 2003年第4期318-321,共4页
The generalized inverse function-valued Padé approximant was defined to solve the integral equations. However, it is difficult to compute the approximants by some high-order determinant formulas. In this paper, t... The generalized inverse function-valued Padé approximant was defined to solve the integral equations. However, it is difficult to compute the approximants by some high-order determinant formulas. In this paper, to simplify computation of the function-valued Padé approximants, an efficient Pfaffian formula for the determinants was extended from the matrix form to the function-valued form. As an important application, a Pfaffian formula of [4/4] type Padé approximant was established. 展开更多
关键词 Padé approximant DETERMINANT Pfaffian formula integral equation.
下载PDF
BOUNDARY INTEGRAL FORMULA OF ELASTICPROBLEMS IN CIRCLE PLANE
19
作者 董正筑 李顺才 余德浩 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第5期604-608,共5页
By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be dire... By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be directly calculated. After the stress function is expounded to Fourier series, making use of some formulas in generalized functions to the convolutions, the boundary integral formula which does not include strongly singular integral is derived further. Then the stress function can be got simply by the integration of the values of the stress function and its derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function for the elastic problem is convenient. 展开更多
关键词 elastic problem in circle plane bi-harmonic equation stress function boundary integral formula
下载PDF
BOUNDARY INTEGRAL FORMULAS FOR ELASTIC PLANE PROBLEM OF EXTERIOR CIRCULAR DOMAIN
20
作者 董正筑 李顺才 余德浩 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第7期993-1000,共8页
After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress func... After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain. 展开更多
关键词 elastic plane problem of exterior circular domain bi-harmonic equation Fourier series stress function boundary integral formula
下载PDF
上一页 1 2 73 下一页 到第
使用帮助 返回顶部