In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness...In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness, give the definitions of k-poles, isolated and essential singular points and removable singularity, discuss some properties, and further obtain the residue theorems.展开更多
By evaluating a contour integral with the Cauchy residue theorem, we prove a general summation formula on trigonometric sum, which contains several interesting trigonometric identities as special cases.
This paper proposes a residue theorem based soft sliding mode control strategy for a permanent magnet synchronous generator(PMSG)based wind power generation system(WPGS),to achieve the maximum energy conversion and im...This paper proposes a residue theorem based soft sliding mode control strategy for a permanent magnet synchronous generator(PMSG)based wind power generation system(WPGS),to achieve the maximum energy conversion and improved in the system dynamic performance.The main idea is to set a soft dynamic boundary for the controlled variables around a reference point.Thus the controlled variables would lie on a point inside the boundary.The convergence of the operating point is ensured by following the Forward Euler method.The proposed control has been verified via simulation and experiments,compared with conventional sliding mode control(SMC)and proportional integral(PI)control.展开更多
This paper presents the contour integral method for solving the linear constant coefficient ordinary differential equations in complex plane,and obtains the uniform expressions of the general solutions.Firstly,by usin...This paper presents the contour integral method for solving the linear constant coefficient ordinary differential equations in complex plane,and obtains the uniform expressions of the general solutions.Firstly,by using Residue Theorem,the general form of the contour integral representation for the homogeneous complex differential equation is obtained,which can be degenerated to classical results in real line.As for inhomogeneous complex differential equations with constant coefficients,we construct the integral expression of the particular solution for any continuous forcing term,and give rigorous proof via Residue Theorem.Thus the general solutions of inhomogeneous complex differential equations are also given.The main purpose of this paper is to give a foundation for a complete theory of linear complex differential equations with constant coefficients by a contour integral method.The results can not only solve the inhomogeneous complex differential equation well,but also explain the forms that are difficult to be understood in the classical solutions.展开更多
基金Supported by the National Natural Science Foundation of China (10471107)the Specialized Research Fund for the Doctoral Program of Higher Education of China (20060486001)
文摘In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness, give the definitions of k-poles, isolated and essential singular points and removable singularity, discuss some properties, and further obtain the residue theorems.
文摘By evaluating a contour integral with the Cauchy residue theorem, we prove a general summation formula on trigonometric sum, which contains several interesting trigonometric identities as special cases.
基金This study has been funded by the Royal Commission for Jubail and Yanbu,Saudi Arabia and the University of Liverpool,UK.
文摘This paper proposes a residue theorem based soft sliding mode control strategy for a permanent magnet synchronous generator(PMSG)based wind power generation system(WPGS),to achieve the maximum energy conversion and improved in the system dynamic performance.The main idea is to set a soft dynamic boundary for the controlled variables around a reference point.Thus the controlled variables would lie on a point inside the boundary.The convergence of the operating point is ensured by following the Forward Euler method.The proposed control has been verified via simulation and experiments,compared with conventional sliding mode control(SMC)and proportional integral(PI)control.
基金Supported by the National Natural Science Foundation of China(11561055)the Natural Science Foundation of Ningxia(2018AAC03057)。
文摘This paper presents the contour integral method for solving the linear constant coefficient ordinary differential equations in complex plane,and obtains the uniform expressions of the general solutions.Firstly,by using Residue Theorem,the general form of the contour integral representation for the homogeneous complex differential equation is obtained,which can be degenerated to classical results in real line.As for inhomogeneous complex differential equations with constant coefficients,we construct the integral expression of the particular solution for any continuous forcing term,and give rigorous proof via Residue Theorem.Thus the general solutions of inhomogeneous complex differential equations are also given.The main purpose of this paper is to give a foundation for a complete theory of linear complex differential equations with constant coefficients by a contour integral method.The results can not only solve the inhomogeneous complex differential equation well,but also explain the forms that are difficult to be understood in the classical solutions.
