k holomorphic functions are a type of generation of holomorphic functions.In this paper,a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in C^(2).The e...k holomorphic functions are a type of generation of holomorphic functions.In this paper,a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in C^(2).The existence of the solution for the problem is studied in detail with the help of the boundary properties of Cauchy type singular integral operators with a k holomorphic kernel.Furthermore,the integral representation for the solution is obtained.展开更多
Extension of classical Mandelbrojt’s criterion for normality to several complex variables is given. Some inequalities for holomorphic functions which omit values 0 and 1 are obtained.
In this paper three Banach spaces A(ф),A(ф)and A~1(ф)of functions holomor- phic in the unit ball B of ■~n are defined.We exhibit bounded projections from C(B)onto A(ф),from L~1(B)onto A~1(ф),and from L~∞(B)onto...In this paper three Banach spaces A(ф),A(ф)and A~1(ф)of functions holomor- phic in the unit ball B of ■~n are defined.We exhibit bounded projections from C(B)onto A(ф),from L~1(B)onto A~1(ф),and from L~∞(B)onto A(ф).Using these projections,we show that A(ф)~*≌A~1(ф)and A~1(ф)~*≌A(ф).展开更多
This paper deals with two topics mentioned in the title. First, it is proved that function f in L^P（ Da） can be decomposed into a sum g ＋ h, where Da is an angular domain in the complex plane, g and h are the non-t...This paper deals with two topics mentioned in the title. First, it is proved that function f in L^P（ Da） can be decomposed into a sum g ＋ h, where Da is an angular domain in the complex plane, g and h are the non-tangential limits of functions in H^P（Da） and H^P（aD^c） in the sense of LP（Da）, respectively. Second, the sufficient and necessary conditions between boundary values of holomorphic functions and distributions in n-dimensional complex space are obtained.展开更多
Let Ω be a domain in C^(n) and let Y be a function space on Ω.If a∈Ω and g∈Y with g(a)=0,do there exist functions f_(1),f_(2),…,f_(n)∈Y such that g(z)=∑_(l=1)^(n)(z_(l)−a_(l))f_(l)(z)for all z=(z_(1),z_(2),…,...Let Ω be a domain in C^(n) and let Y be a function space on Ω.If a∈Ω and g∈Y with g(a)=0,do there exist functions f_(1),f_(2),…,f_(n)∈Y such that g(z)=∑_(l=1)^(n)(z_(l)−a_(l))f_(l)(z)for all z=(z_(1),z_(2),…,z_(n))∈Ω?This is Gleason’s problem.In this paper,we prove that Gleason’s problem is solvable on the boundary general function space F^(p,q,s)(B)in the unit ball B of C^(n).展开更多
First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmoment...First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmomentum-momentum noncommuting, namely, by using a generalized Bopp’s shift method we construct the Wignerfunction for the Klein-Gordan Landau problem both on a noncommutative space (NCS) and a noncommutative phasespace (NCPS).展开更多
The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi-Laplace equations of the first kind as well as of the sec...The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi-Laplace equations of the first kind as well as of the second.展开更多
Solution of the Riemann boundary value problem with square roots(1.1)for analytic functions proposed in[1]is reconsidered,which was solved under certain assumptions on the branch points appeared.Here the work is conti...Solution of the Riemann boundary value problem with square roots(1.1)for analytic functions proposed in[1]is reconsidered,which was solved under certain assumptions on the branch points appeared.Here the work is continued without these assumptions and the problem is solved in the general case.展开更多
The generalized Riemann boundary value problem for analytic functions is considered, where the unknown function may have branch points of the second order. Under certain assumptions, its general solution as well as th...The generalized Riemann boundary value problem for analytic functions is considered, where the unknown function may have branch points of the second order. Under certain assumptions, its general solution as well as the condition of solvability is obtained when the solution is required to be of finite order at infinity.展开更多
The solution of the non-homogeneous Riemann boundary value problem with radicals (1. 2) together with its condition of solvability is obtained for arbitrary positive integersp andq, which generalizes the results for t...The solution of the non-homogeneous Riemann boundary value problem with radicals (1. 2) together with its condition of solvability is obtained for arbitrary positive integersp andq, which generalizes the results for the casep=q=2.展开更多
The homogeneous quadratic riemann boundary value problem(1)with H?lder continuous coefficients for the normal case was considered by the author in 1997.But the solutions obtained there are incomplete.Here its general ...The homogeneous quadratic riemann boundary value problem(1)with H?lder continuous coefficients for the normal case was considered by the author in 1997.But the solutions obtained there are incomplete.Here its general method of solution is obtained.展开更多
A major challenge of any optimization problem is to find the global optimum solution. In a multi-dimensional solution space which is highly non-linear, often the optimization algorithm gets trapped around some local o...A major challenge of any optimization problem is to find the global optimum solution. In a multi-dimensional solution space which is highly non-linear, often the optimization algorithm gets trapped around some local optima. Optimal Identification of unknown groundwater pollution sources poses similar challenges. Optimization based methodology is often applied to identify the unknown source characteristics such as location and flux release history over time, in a polluted aquifer. Optimization based models for identification of these characteristics of unknown ground-water pollution sources rely on comparing the simulated effects of candidate solutions to the observed effects in terms of pollutant concentration at specified sparse spatiotemporal locations. The optimization model minimizes the difference between the observed pollutant concentration measurements and simulated pollutant concentration measurements. This essentially constitutes the objective function of the optimization model. However, the mathematical formulation of the objective function can significantly affect the accuracy of the results by altering the response contour of the solution space. In this study, two separate mathematical formulations of the objective function are compared for accuracy, by incorporating different scenarios of unknown groundwater pollution source identification problem. Simulated Annealing (SA) is used as the solution algorithm for the optimization model. Different mathematical formulations of the objective function for minimizing the difference between the observed and simulated pollutant concentration measurements show different levels of accuracy in source identification results. These evaluation results demonstrate the impact of objective function formulation on the optimal identification, and provide a basis for choosing an appropriate mathematical formulation for unknown pollution source identification in contaminated aquifers.展开更多
We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator fun...We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator function.The N´ed´elec edge elements are employed to discretize the operators,where the divergence free condition for the electric field is realized by a mixed form using a Lagrange multiplier.The convergence of the eigenvalues is proved using the abstract approximation theory for holomorphic operator functions with the regular approximation of the edge elements.The spectral indicator method is then applied to compute the discrete eigenvalues.Numerical examples are presented demonstrating the effectiveness of the proposed method.展开更多
In this paper,the authors employ the splitting method to address support vector machine within a reproducing kernel Banach space framework,where a lower semi-continuous loss function is utilized.They translate support...In this paper,the authors employ the splitting method to address support vector machine within a reproducing kernel Banach space framework,where a lower semi-continuous loss function is utilized.They translate support vector machine in reproducing kernel Banach space with such a loss function to a finite-dimensional tensor optimization problem and propose a splitting method based on the alternating direction method of mul-tipliers.Leveraging Kurdyka-Lojasiewicz property of the augmented Lagrangian function,the authors demonstrate that the sequence derived from this splitting method is globally convergent to a stationary point if the loss function is lower semi-continuous and subana-lytic.Through several numerical examples,they illustrate the effectiveness of the proposed splitting algorithm.展开更多
基金the NSF of China(11571089,11871191)the NSF of Henan Province(222300420397)+1 种基金the NSF of Hebei Province(A2022208007)the Key Foundation of Hebei Normal University(L2018Z01)。
文摘k holomorphic functions are a type of generation of holomorphic functions.In this paper,a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in C^(2).The existence of the solution for the problem is studied in detail with the help of the boundary properties of Cauchy type singular integral operators with a k holomorphic kernel.Furthermore,the integral representation for the solution is obtained.
文摘Extension of classical Mandelbrojt’s criterion for normality to several complex variables is given. Some inequalities for holomorphic functions which omit values 0 and 1 are obtained.
基金Supported in part by the National Natural Science Foundation of China.
文摘In this paper three Banach spaces A(ф),A(ф)and A~1(ф)of functions holomor- phic in the unit ball B of ■~n are defined.We exhibit bounded projections from C(B)onto A(ф),from L~1(B)onto A~1(ф),and from L~∞(B)onto A(ф).Using these projections,we show that A(ф)~*≌A~1(ф)and A~1(ф)~*≌A(ф).
基金supported by the National Natural Science Foundation of China(No.11271045)the Higher School Doctoral Foundation of China(No.20100003110004)
文摘This paper deals with two topics mentioned in the title. First, it is proved that function f in L^P（ Da） can be decomposed into a sum g ＋ h, where Da is an angular domain in the complex plane, g and h are the non-tangential limits of functions in H^P（Da） and H^P（aD^c） in the sense of LP（Da）, respectively. Second, the sufficient and necessary conditions between boundary values of holomorphic functions and distributions in n-dimensional complex space are obtained.
基金supported by the National Natural Science Foundation of China(11942109)the Natural Science Foundation of Hunan Province(2022JJ30369).
文摘Let Ω be a domain in C^(n) and let Y be a function space on Ω.If a∈Ω and g∈Y with g(a)=0,do there exist functions f_(1),f_(2),…,f_(n)∈Y such that g(z)=∑_(l=1)^(n)(z_(l)−a_(l))f_(l)(z)for all z=(z_(1),z_(2),…,z_(n))∈Ω?This is Gleason’s problem.In this paper,we prove that Gleason’s problem is solvable on the boundary general function space F^(p,q,s)(B)in the unit ball B of C^(n).
基金Supported by the National Natural Science Foundation of China under Grant Nos.10965006 and 10875035
文摘First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmomentum-momentum noncommuting, namely, by using a generalized Bopp’s shift method we construct the Wignerfunction for the Klein-Gordan Landau problem both on a noncommutative space (NCS) and a noncommutative phasespace (NCPS).
基金theResearchFoundationofEducationalCommitteeofYunnanProvince China
文摘The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi-Laplace equations of the first kind as well as of the second.
文摘Solution of the Riemann boundary value problem with square roots(1.1)for analytic functions proposed in[1]is reconsidered,which was solved under certain assumptions on the branch points appeared.Here the work is continued without these assumptions and the problem is solved in the general case.
基金Supported by the National Natural Science Foundation of China !(No.19871064)
文摘The generalized Riemann boundary value problem for analytic functions is considered, where the unknown function may have branch points of the second order. Under certain assumptions, its general solution as well as the condition of solvability is obtained when the solution is required to be of finite order at infinity.
文摘The solution of the non-homogeneous Riemann boundary value problem with radicals (1. 2) together with its condition of solvability is obtained for arbitrary positive integersp andq, which generalizes the results for the casep=q=2.
基金Supported by the National Natural Science Foun dation of China(19871064)
文摘The homogeneous quadratic riemann boundary value problem(1)with H?lder continuous coefficients for the normal case was considered by the author in 1997.But the solutions obtained there are incomplete.Here its general method of solution is obtained.
文摘A major challenge of any optimization problem is to find the global optimum solution. In a multi-dimensional solution space which is highly non-linear, often the optimization algorithm gets trapped around some local optima. Optimal Identification of unknown groundwater pollution sources poses similar challenges. Optimization based methodology is often applied to identify the unknown source characteristics such as location and flux release history over time, in a polluted aquifer. Optimization based models for identification of these characteristics of unknown ground-water pollution sources rely on comparing the simulated effects of candidate solutions to the observed effects in terms of pollutant concentration at specified sparse spatiotemporal locations. The optimization model minimizes the difference between the observed pollutant concentration measurements and simulated pollutant concentration measurements. This essentially constitutes the objective function of the optimization model. However, the mathematical formulation of the objective function can significantly affect the accuracy of the results by altering the response contour of the solution space. In this study, two separate mathematical formulations of the objective function are compared for accuracy, by incorporating different scenarios of unknown groundwater pollution source identification problem. Simulated Annealing (SA) is used as the solution algorithm for the optimization model. Different mathematical formulations of the objective function for minimizing the difference between the observed and simulated pollutant concentration measurements show different levels of accuracy in source identification results. These evaluation results demonstrate the impact of objective function formulation on the optimal identification, and provide a basis for choosing an appropriate mathematical formulation for unknown pollution source identification in contaminated aquifers.
基金China Postdoctoral Science Foundation Grant 2019M650460the NSF grant DMS-2011148.The research of J.Sun is supported partially by the Simons Foundation Grant 711922.
文摘We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator function.The N´ed´elec edge elements are employed to discretize the operators,where the divergence free condition for the electric field is realized by a mixed form using a Lagrange multiplier.The convergence of the eigenvalues is proved using the abstract approximation theory for holomorphic operator functions with the regular approximation of the edge elements.The spectral indicator method is then applied to compute the discrete eigenvalues.Numerical examples are presented demonstrating the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(Nos.12026602,12071157,12271108)the Natural Science Foundation of Guangdong Provience(No.2024A1515012288)+1 种基金the Science and Technology Commission of Shanghai Municipality(No.23JC1400501)the Ministry of Science and Technology of China(No.G2023132005L).
文摘In this paper,the authors employ the splitting method to address support vector machine within a reproducing kernel Banach space framework,where a lower semi-continuous loss function is utilized.They translate support vector machine in reproducing kernel Banach space with such a loss function to a finite-dimensional tensor optimization problem and propose a splitting method based on the alternating direction method of mul-tipliers.Leveraging Kurdyka-Lojasiewicz property of the augmented Lagrangian function,the authors demonstrate that the sequence derived from this splitting method is globally convergent to a stationary point if the loss function is lower semi-continuous and subana-lytic.Through several numerical examples,they illustrate the effectiveness of the proposed splitting algorithm.
