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
By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian （or spherical） mapping, a series of invariants or geometric conser...By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian （or spherical） mapping, a series of invariants or geometric conservation quantities under Gaussian （or spherical） mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed展开更多
In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular...In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green＇s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.展开更多
In this paper we study the problem of generation of surface waves produced due to a） rolling of the plate and b） presence of a line source in front of a fixed vertical plate. The amplitudes of radiated waves at larg...In this paper we study the problem of generation of surface waves produced due to a） rolling of the plate and b） presence of a line source in front of a fixed vertical plate. The amplitudes of radiated waves at large distance from the plate, in both cases, are obtained by a suitable application of Green＇s integral theorem. These are then studied graphically for various values of the ice cover parameter.展开更多
The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of...The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green＇s integral theorem in terms of difference of potential functicns across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.展开更多
Following the spirit of thermo field dynamics initiated by Takahashi and Umezawa, we employ the technique of integration within an ordered product of operators to derive the thermal vacuum state （TVS） for the Hamilt...Following the spirit of thermo field dynamics initiated by Takahashi and Umezawa, we employ the technique of integration within an ordered product of operators to derive the thermal vacuum state （TVS） for the Hamiltonian H of the two-coupled-oscillator model. The ensemble averages of the system are derived conveniently by using the TVS. In addition, the entropy for this system is discussed based on the relation between the generalized Hellmann-Feynman theorem and the entroy variation in the context of the TVS.展开更多
A new gradient operator was derived in recent studies of topological structures and shape transi- tions in biomembranes. Because this operator has widespread potential uses in mechanics, physics, and biology, the oper...A new gradient operator was derived in recent studies of topological structures and shape transi- tions in biomembranes. Because this operator has widespread potential uses in mechanics, physics, and biology, the operator’s general mathematical characteristics should be investigated. This paper explores the integral characteristics of the operator. The second divergence and the differential properties of the operator are used to demonstrate new integral transformations for vector and scalar fields on curved surfaces, such as the second divergence theorem, the second gradient theorem, the second curl theorem, and the second circulation theorem. These new theorems provide a mathematical basis for the use of this operator in many disciplines.展开更多
To make the geometrical basis for soft matters with curved surfaces such as biomembranes as simple as possible, a symmetrical analytical system was developed in conventional differential geometry. The conventional sec...To make the geometrical basis for soft matters with curved surfaces such as biomembranes as simple as possible, a symmetrical analytical system was developed in conventional differential geometry. The conventional second fundamental tensor is replaced by the so-called conjugate fundamental tensor. Because the differential properties of the conjugate fundamental tensor and the first fundamental tensor are symmetrical, the symmetrical analytical system including the symmetrical differential operators, symmetrical differential characteristics, and symmetrical integral theorems for tensor fields defined on curved surfaces can be constructed. From the symmetrical analytical system, the symmetrical integral theorems for mean curvature and Gauss curvature, with which the symmetrical Minkowski integral formulas are easily deduced just as special cases, can be derived. The applications of this symmetrical analytical system to biology not only display its simplicity and beauty, but also show its powers in depicting the symmetrical patterns of networks of biomembrane nanotubes. All these symmetrical patterns in soft matters should be just the reasonable and natural results of the symmetrical analytical system.展开更多
Based on the second gradient operator and corresponding integral theorems such as the second divergence theorem, the second gradient theorem, the second curl theorem, and the second circulation theorem on curved surfa...Based on the second gradient operator and corresponding integral theorems such as the second divergence theorem, the second gradient theorem, the second curl theorem, and the second circulation theorem on curved surfaces, a few new scalar differential operators are defined and a series of integral transformations are derived. Interesting transformations between the average curvature and the Gauss cur- vature are presented. Various conserved integrals related to the Gauss curvature and the second fundamental tensor are disclosed. The important applications of the results in disciplines such as the geometry, physics, mechanics, and biology are briefly discussed.展开更多
Let （Ω,∑,μ） be a complete probability space and let X be a Banach space. We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a n...Let （Ω,∑,μ） be a complete probability space and let X be a Banach space. We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a new convergence theorem. We Mso obtain a Vituli type Z-convergence theorem for Pettis integrals where Z is an ideal on N. Keywords Convergence theorems for integrals, Pettis integral, scalar equi-convergence in measure, Z-convergence展开更多
This paper analyzes the geometric quantities that remain unchanged during parallel mapping （i.e., mapping from a reference curved surface to a parallel surface with identical normal direction）. The second gradient o...This paper analyzes the geometric quantities that remain unchanged during parallel mapping （i.e., mapping from a reference curved surface to a parallel surface with identical normal direction）. The second gradient operator, the second class of integral theorems, the Gauss-curvature-based integral theorems, and the core property of parallel mapping are used to derive a series of parallel mapping invariants or geometrically conserved quantities. These include not only local mapping invariants but also global mapping invafiants found to exist both in a curved surface and along curves on the curved surface. The parallel mapping invariants are used to identify important transformations between the reference surface and parallel surfaces. These mapping invariants and transformations have potential applications in geometry, physics, biomechanics, and mechanics in which various dynamic processes occur along or between parallel surfaces.展开更多
This paper deals with the analytic Feynman integral of functionals on a Wiener space. First the authors establish the existence of the analytic Feynman integrals of functionals in a Banach algebra S_α. The authors th...This paper deals with the analytic Feynman integral of functionals on a Wiener space. First the authors establish the existence of the analytic Feynman integrals of functionals in a Banach algebra S_α. The authors then obtain a formula for the first variation of integrals. Finally, various analytic Feynman integration formulas involving the first variation are established.展开更多
基金Supported by the National Natural Science Foundation of China(11871191)the Science Foundation of Hebei Province(A2023205006,A2019106037)+2 种基金the Key Development Foundation of Hebei Normal University in2024(L2024ZD08)the Graduate Student Innovation Project Fund of Hebei Province(CXZZBS2022066)the Key Foundation of Hebei Normal University(L2018Z01)。
文摘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.
基金Project supported by the National Natural Science Foundation of China (No.10572076)
文摘By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian （or spherical） mapping, a series of invariants or geometric conservation quantities under Gaussian （or spherical） mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed
基金Partially Supported by the Department of Science and Technology Through a Research Grant to RG(No.SR/FTP/MS-020/2010)
文摘In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green＇s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.
基金Supported by the Department of Science and Technology,Government of India for their financial support of this work through the SERC Fast Track Scheme for Young Scientist(No.SR/FTP/MS-037/2011)
文摘In this paper we study the problem of generation of surface waves produced due to a） rolling of the plate and b） presence of a line source in front of a fixed vertical plate. The amplitudes of radiated waves at large distance from the plate, in both cases, are obtained by a suitable application of Green＇s integral theorem. These are then studied graphically for various values of the ice cover parameter.
基金supported by the Department of Science and Technology of New Delhi (No.SR/SY/MS:521/08)
文摘The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green＇s integral theorem in terms of difference of potential functicns across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11264018)the Natural Science Foundation of Jiangxi Province, China (Grant Nos. 20132BAB212006, 20114BAB202004, and 2009GZW0006)+1 种基金the Research Foundation of the Education Department of Jiangxi Province, China (Grant No. GJJ12171)the Open Foundation of the Key Laboratory of Optoelectronic and Telecommunication of Jiangxi Province, China (Grant No. 2013004)
文摘Following the spirit of thermo field dynamics initiated by Takahashi and Umezawa, we employ the technique of integration within an ordered product of operators to derive the thermal vacuum state （TVS） for the Hamiltonian H of the two-coupled-oscillator model. The ensemble averages of the system are derived conveniently by using the TVS. In addition, the entropy for this system is discussed based on the relation between the generalized Hellmann-Feynman theorem and the entroy variation in the context of the TVS.
文摘A new gradient operator was derived in recent studies of topological structures and shape transi- tions in biomembranes. Because this operator has widespread potential uses in mechanics, physics, and biology, the operator’s general mathematical characteristics should be investigated. This paper explores the integral characteristics of the operator. The second divergence and the differential properties of the operator are used to demonstrate new integral transformations for vector and scalar fields on curved surfaces, such as the second divergence theorem, the second gradient theorem, the second curl theorem, and the second circulation theorem. These new theorems provide a mathematical basis for the use of this operator in many disciplines.
基金the National Natural Science Foundation of China (No.10572076)
文摘To make the geometrical basis for soft matters with curved surfaces such as biomembranes as simple as possible, a symmetrical analytical system was developed in conventional differential geometry. The conventional second fundamental tensor is replaced by the so-called conjugate fundamental tensor. Because the differential properties of the conjugate fundamental tensor and the first fundamental tensor are symmetrical, the symmetrical analytical system including the symmetrical differential operators, symmetrical differential characteristics, and symmetrical integral theorems for tensor fields defined on curved surfaces can be constructed. From the symmetrical analytical system, the symmetrical integral theorems for mean curvature and Gauss curvature, with which the symmetrical Minkowski integral formulas are easily deduced just as special cases, can be derived. The applications of this symmetrical analytical system to biology not only display its simplicity and beauty, but also show its powers in depicting the symmetrical patterns of networks of biomembrane nanotubes. All these symmetrical patterns in soft matters should be just the reasonable and natural results of the symmetrical analytical system.
文摘Based on the second gradient operator and corresponding integral theorems such as the second divergence theorem, the second gradient theorem, the second curl theorem, and the second circulation theorem on curved surfaces, a few new scalar differential operators are defined and a series of integral transformations are derived. Interesting transformations between the average curvature and the Gauss cur- vature are presented. Various conserved integrals related to the Gauss curvature and the second fundamental tensor are disclosed. The important applications of the results in disciplines such as the geometry, physics, mechanics, and biology are briefly discussed.
基金Supported by the Polish Ministry of Science and Higher Education(Grant Nos.N N201 414939 for M.Balcerzak,N N201 416139 for K.Musial)
文摘Let （Ω,∑,μ） be a complete probability space and let X be a Banach space. We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a new convergence theorem. We Mso obtain a Vituli type Z-convergence theorem for Pettis integrals where Z is an ideal on N. Keywords Convergence theorems for integrals, Pettis integral, scalar equi-convergence in measure, Z-convergence
基金Supported by the National Natural Science Foundation of China(Nos.10572076 and 10872114)the Natural Science Foundation of Jiangsu Province,China (No.BK2008370)
文摘This paper analyzes the geometric quantities that remain unchanged during parallel mapping （i.e., mapping from a reference curved surface to a parallel surface with identical normal direction）. The second gradient operator, the second class of integral theorems, the Gauss-curvature-based integral theorems, and the core property of parallel mapping are used to derive a series of parallel mapping invariants or geometrically conserved quantities. These include not only local mapping invariants but also global mapping invafiants found to exist both in a curved surface and along curves on the curved surface. The parallel mapping invariants are used to identify important transformations between the reference surface and parallel surfaces. These mapping invariants and transformations have potential applications in geometry, physics, biomechanics, and mechanics in which various dynamic processes occur along or between parallel surfaces.
基金supported by the research fund of Dankook University in 2015
文摘This paper deals with the analytic Feynman integral of functionals on a Wiener space. First the authors establish the existence of the analytic Feynman integrals of functionals in a Banach algebra S_α. The authors then obtain a formula for the first variation of integrals. Finally, various analytic Feynman integration formulas involving the first variation are established.
