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
This paper studies the non-homogeneous generalized Riemann-Hilbert(RH)problems involving two unknown functions.Using the uniformization theorem,such problems are transformed into the case of homogeneous type.By the th...This paper studies the non-homogeneous generalized Riemann-Hilbert(RH)problems involving two unknown functions.Using the uniformization theorem,such problems are transformed into the case of homogeneous type.By the theory of classical boundary value problems,we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains,and analyze the conditions of solvability and properties of solutions in various domains.展开更多
In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green fun...In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.展开更多
A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some resul...A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.展开更多
Based on the displacement-squeezing related squeezed coherent state representation ｜z〉g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator,...Based on the displacement-squeezing related squeezed coherent state representation ｜z〉g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula （Huygens-Fresnel integration transformation describing optical diffraction）. The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz -- rz^＊ in the ｜Z〉g representation, while ｜z〉g in phase space is graphically denoted by an ellipse.展开更多
By virtue of the normal ordering of vacuum projector we directly derive some new complicated operatoridentities, regarding to the generalized Stirling number.
We have written a new equation to study the statistics of earthquake distributions. We call this equation “the generalized logistic equation”. The Gutenberg-Richter frequency-magnitude formula was derived from the s...We have written a new equation to study the statistics of earthquake distributions. We call this equation “the generalized logistic equation”. The Gutenberg-Richter frequency-magnitude formula was derived from the solution of the generalized logistic equation as an asymptotic case for the approximation of large magnitudes. To illustrate how the solution of the generalized logistic equation works, it was used to approximate the observed cumulative distribution of earthquakes in four different geological provinces: the Central Atlantic (40N - 25N, 5W - 35W), Canary Islands, Magellan Mountains (20N - 9S, 148E - 170E), and the Sea of Japan. This approximation showed an excellent correlation between the theoretical curves and observed data for earthquakes of magnitudes 1 < m < 9.展开更多
In this paper, we present an extension of the so-called classical Sherman-Morrison-Woodbury (for short SMW) formula for bounded homogeneous generalized inverse in Banach spaces. Some particular cases and applications ...In this paper, we present an extension of the so-called classical Sherman-Morrison-Woodbury (for short SMW) formula for bounded homogeneous generalized inverse in Banach spaces. Some particular cases and applications will be also considered. Our results generalize the results of many authors for finite dimensional matrices and Hilbert space operators in the literature.展开更多
In this article, we study the Lax pairs of -dimensional equation: the modified generalized dispersive long wave (MGDLW) equation. Based on the well-known binary Darboux transformation, we dig out the recursion formula...In this article, we study the Lax pairs of -dimensional equation: the modified generalized dispersive long wave (MGDLW) equation. Based on the well-known binary Darboux transformation, we dig out the recursion formulas of the first part of the Lax pairs. Then by further discussion and doing some revisional work, we make the recursion formulas fit for the second part of Lax pairs. At last, some solutions to the MGDLW equation are worked out by using the recursion formula.展开更多
In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.
We present a new generalized version of Cline's formula and Jacobson's lemma for g-Drazin inverses in a ring.These generalized results extend many known results,e.g.,Chen and Abdolyousefi[Generalized Jacobson&...We present a new generalized version of Cline's formula and Jacobson's lemma for g-Drazin inverses in a ring.These generalized results extend many known results,e.g.,Chen and Abdolyousefi[Generalized Jacobson's lemma in a Banach algebra,Comm.Algebra 49(2021)3263-3272],and Yan and Zeng[The generalized inverses of the products of two elements in a ring,Turkish J.Math.44(2020)1744-1756].展开更多
目的利用可视化文献分析方法,对AI数字人的发展脉络与研究现状进行归纳与总结,并结合现阶段数字人在数字化空间中应用情况的分析,尝试推断出未来研究与发展方向。方法应用CiteSpace软件,以中国知网和Web of Science核心数据库为基础,通...目的利用可视化文献分析方法,对AI数字人的发展脉络与研究现状进行归纳与总结,并结合现阶段数字人在数字化空间中应用情况的分析,尝试推断出未来研究与发展方向。方法应用CiteSpace软件,以中国知网和Web of Science核心数据库为基础,通过发文趋势研究、核心作者分析、聚类分析和发文机构分析等方法,探索AI数字人领域的研究热点和趋势。结果AI数字人以虚拟角色形象,通过“具象化”的方式进行互动性表现,无论对数字空间的构建,还是数字交互智能化发展均具有积极的市场前景。结论国内外对AI数字人研究呈上升趋势,作者与科研机构之间的合作不断发展紧密,研究侧重点主要包括生命政治、人工智能、人机交互、媒体融合、数字乡村建设、深度学习等,将通过发展趋势分析尝试为未来研究AI数字人多样性构建提供更多思路。展开更多
基金Supported by National Nature Science Foundation in China(12101564,11971425,11801508)Nature Science Foundation of Zhejiang province(LY22A010013)Domestic Visiting Scholar Teacher Professional Development Project(FX2021042)。
文摘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.
基金Supported by National Natural Science Foundation of China(Grant No.11971015).
文摘This paper studies the non-homogeneous generalized Riemann-Hilbert(RH)problems involving two unknown functions.Using the uniformization theorem,such problems are transformed into the case of homogeneous type.By the theory of classical boundary value problems,we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains,and analyze the conditions of solvability and properties of solutions in various domains.
文摘In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.
文摘A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10874174 and 10675108)the President Foundation of the Chinese Academy of Sciencesthe Specilized Research Fund for the Doctorial Program of the Higher Education of China (Grant No.20070358009)
文摘Based on the displacement-squeezing related squeezed coherent state representation ｜z〉g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula （Huygens-Fresnel integration transformation describing optical diffraction）. The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz -- rz^＊ in the ｜Z〉g representation, while ｜z〉g in phase space is graphically denoted by an ellipse.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10874174 and 10947017/A05 the Specialized Research Fund for the Doctorial Progress of Higher Education of China under Grant No.20070358009
文摘By virtue of the normal ordering of vacuum projector we directly derive some new complicated operatoridentities, regarding to the generalized Stirling number.
文摘We have written a new equation to study the statistics of earthquake distributions. We call this equation “the generalized logistic equation”. The Gutenberg-Richter frequency-magnitude formula was derived from the solution of the generalized logistic equation as an asymptotic case for the approximation of large magnitudes. To illustrate how the solution of the generalized logistic equation works, it was used to approximate the observed cumulative distribution of earthquakes in four different geological provinces: the Central Atlantic (40N - 25N, 5W - 35W), Canary Islands, Magellan Mountains (20N - 9S, 148E - 170E), and the Sea of Japan. This approximation showed an excellent correlation between the theoretical curves and observed data for earthquakes of magnitudes 1 < m < 9.
文摘In this paper, we present an extension of the so-called classical Sherman-Morrison-Woodbury (for short SMW) formula for bounded homogeneous generalized inverse in Banach spaces. Some particular cases and applications will be also considered. Our results generalize the results of many authors for finite dimensional matrices and Hilbert space operators in the literature.
基金The project supported by National Natural Science Foundation of China under Grant No.10101025
文摘In this article, we study the Lax pairs of -dimensional equation: the modified generalized dispersive long wave (MGDLW) equation. Based on the well-known binary Darboux transformation, we dig out the recursion formulas of the first part of the Lax pairs. Then by further discussion and doing some revisional work, we make the recursion formulas fit for the second part of Lax pairs. At last, some solutions to the MGDLW equation are worked out by using the recursion formula.
文摘In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.
基金supported by the Natural Science Foundation of Zhejiang Province,China(No.LY21A010018).
文摘We present a new generalized version of Cline's formula and Jacobson's lemma for g-Drazin inverses in a ring.These generalized results extend many known results,e.g.,Chen and Abdolyousefi[Generalized Jacobson's lemma in a Banach algebra,Comm.Algebra 49(2021)3263-3272],and Yan and Zeng[The generalized inverses of the products of two elements in a ring,Turkish J.Math.44(2020)1744-1756].
文摘目的利用可视化文献分析方法,对AI数字人的发展脉络与研究现状进行归纳与总结,并结合现阶段数字人在数字化空间中应用情况的分析,尝试推断出未来研究与发展方向。方法应用CiteSpace软件,以中国知网和Web of Science核心数据库为基础,通过发文趋势研究、核心作者分析、聚类分析和发文机构分析等方法,探索AI数字人领域的研究热点和趋势。结果AI数字人以虚拟角色形象,通过“具象化”的方式进行互动性表现,无论对数字空间的构建,还是数字交互智能化发展均具有积极的市场前景。结论国内外对AI数字人研究呈上升趋势,作者与科研机构之间的合作不断发展紧密,研究侧重点主要包括生命政治、人工智能、人机交互、媒体融合、数字乡村建设、深度学习等,将通过发展趋势分析尝试为未来研究AI数字人多样性构建提供更多思路。
