This paper presents a novel active disturbance rejection control(ADRC)scheme based on a cascade connection of generalized proportional integral observers(GPIOs)with internal models designed to estimate both polynomial...This paper presents a novel active disturbance rejection control(ADRC)scheme based on a cascade connection of generalized proportional integral observers(GPIOs)with internal models designed to estimate both polynomial and resonant disturbances.In this estimator structure,referred to as Cascade GPIO(CGPIO),the total disturbance sensitivity is the product of the sensitivities at each cascade level.This approach improves system performance against both periodic and non-periodic disturbances and enhances robustness under frequency variations in harmonic components.Additionally,the decoupled nature of the estimator reduces the order of the GPIOs,thereby simplifying tuning and limiting observer gains.The proposed control scheme is supported by a frequency-domain analysis and is experimentally validated in the current control of a grid-connected converter subject to control gain uncertainties,harmonic distortion,frequency deviations,and measurement noise.Experimental results demonstrate that the CGPIO-based ADRC outperforms benchmark solutions,including proportional-integral(PI)and proportional-resonant(PR)controllers.展开更多
We presents a generalized(2+1)-dimensional Sharma-Tasso-Olver-Burgers(STOB)equation,unifying dissipative and dispersive wave dynamics.By introducing an auxiliary potential𝑦as a new space variable and employing...We presents a generalized(2+1)-dimensional Sharma-Tasso-Olver-Burgers(STOB)equation,unifying dissipative and dispersive wave dynamics.By introducing an auxiliary potential𝑦as a new space variable and employing a simpler deformation algorithm,we deform the(1+1)-dimensional STOB model to higher dimensions.The resulting equation is proven Lax-integrable via introducing strong and weak Lax pairs.Traveling wave solutions of the(2+1)-dimensional STOB equation are derived through an ordinary differential equation reduction,with implicit solutions obtained for a special case.Crucially,we demonstrate that the system admits dispersionless decompositions into two types:Case 1 yields non-traveling twisted kink and bell solitons,while Case 2 involves complex implicit functions governed by cubic-algebraic constraints.Numerical visualizations reveal novel anisotropic soliton structures,and the decomposition methodology is shown to generalize broadly to other higher dimensional dispersionless decomposition solvable integrable systems.展开更多
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
The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid i...The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.展开更多
Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2...Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.展开更多
We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
This paper studies a type of integral and reduction of the generalized Birkhoffian system. An existent condition and the form of the integral are obtained. By using the integral, the dimension of the system can be red...This paper studies a type of integral and reduction of the generalized Birkhoffian system. An existent condition and the form of the integral are obtained. By using the integral, the dimension of the system can be reduced two degrees. An example is given to illustrate the application of the results.展开更多
Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable coup...Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.展开更多
In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff...In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results.展开更多
Two kinds of integrals of generalized Hamilton systems with additional terms are discussed. One kind is the integral deduced by Poisson method; the other is Hojman integral obtained by Lie symmetry.
In this paper, we will establish the boundedness of the commutator generated by fractional integral operator and RBMO（μ） function on generalized Morrey space in the non-homogeneous space.
A new isospectral problem is firstly presented, then we derive integrable system of soliton hierarchy. Also we obtain new integrable couplings of the generalized Kaup-Newell soliton equations hierarchy and its Hamilto...A new isospectral problem is firstly presented, then we derive integrable system of soliton hierarchy. Also we obtain new integrable couplings of the generalized Kaup-Newell soliton equations hierarchy and its Hamiltonian structures by using Tu scheme and the quadratic-form identity. The method can be generalized to other soliton hierarchy.展开更多
Two efficient recursive algorithms epsilon_algorithm and eta_algorithm are introduced to compute the generalized inverse function_valued Padé approximants. The approximants were used to accelerate the convergenc...Two efficient recursive algorithms epsilon_algorithm and eta_algorithm are introduced to compute the generalized inverse function_valued Padé approximants. The approximants were used to accelerate the convergence of the power series with function_valued coefficients and to estimate characteristic value of the integral equations. Famous Wynn identities of the Pad approximants is also established by means of the connection of two algorithms.展开更多
The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are g...The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.展开更多
In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscil...In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.展开更多
By means of singularity structure analysis, the integrability of a generalized fifth-order KdV equation is investigated. It is proven that this equation passes the Painleve test for integrability only for three distin...By means of singularity structure analysis, the integrability of a generalized fifth-order KdV equation is investigated. It is proven that this equation passes the Painleve test for integrability only for three distinct cases. Moreover, the multi- soliton solutions are presented for this equation under three sets of integrable conditions. Finally, by selecting appropriate parameters, we analyze the evolution of two solitons, which is especially interesting as it may describe the overtaking and the head-on collisions of solitary waves of different shapes and different types.展开更多
Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds, the fractional integral operators with rough kernels and fractional maximal operators with rough ke...Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds, the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases, we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control, then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces.展开更多
In this paper, we study the boundedness of higher order commutators of gen- eralized fractional integral operators on weighted Lp spaces and Herz-type Hardy spaces.
After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions f...After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions for the following singular integral equation展开更多
We obtain weak type （1, q） inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the str...We obtain weak type （1, q） inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the strong type inequalities in [13, 14, 15].展开更多
文摘This paper presents a novel active disturbance rejection control(ADRC)scheme based on a cascade connection of generalized proportional integral observers(GPIOs)with internal models designed to estimate both polynomial and resonant disturbances.In this estimator structure,referred to as Cascade GPIO(CGPIO),the total disturbance sensitivity is the product of the sensitivities at each cascade level.This approach improves system performance against both periodic and non-periodic disturbances and enhances robustness under frequency variations in harmonic components.Additionally,the decoupled nature of the estimator reduces the order of the GPIOs,thereby simplifying tuning and limiting observer gains.The proposed control scheme is supported by a frequency-domain analysis and is experimentally validated in the current control of a grid-connected converter subject to control gain uncertainties,harmonic distortion,frequency deviations,and measurement noise.Experimental results demonstrate that the CGPIO-based ADRC outperforms benchmark solutions,including proportional-integral(PI)and proportional-resonant(PR)controllers.
基金supported by the National Natural Science Foundations of China(Grant Nos.12235007,12375003,and 11975131).
文摘We presents a generalized(2+1)-dimensional Sharma-Tasso-Olver-Burgers(STOB)equation,unifying dissipative and dispersive wave dynamics.By introducing an auxiliary potential𝑦as a new space variable and employing a simpler deformation algorithm,we deform the(1+1)-dimensional STOB model to higher dimensions.The resulting equation is proven Lax-integrable via introducing strong and weak Lax pairs.Traveling wave solutions of the(2+1)-dimensional STOB equation are derived through an ordinary differential equation reduction,with implicit solutions obtained for a special case.Crucially,we demonstrate that the system admits dispersionless decompositions into two types:Case 1 yields non-traveling twisted kink and bell solitons,while Case 2 involves complex implicit functions governed by cubic-algebraic constraints.Numerical visualizations reveal novel anisotropic soliton structures,and the decomposition methodology is shown to generalize broadly to other higher dimensional dispersionless decomposition solvable integrable systems.
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.
文摘The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.
基金Supported by National 973 Project(G.19990751)the SEDF of China(20040027001)
文摘Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.
基金supported by the Natural Science Foundation of China(11701176,61673169,11301127,11626101,11601485)the Science and Technology Research Program of Zhejiang Educational Committee(Y201635325)
文摘We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10772025, 10932002, and 10972031)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics
文摘This paper studies a type of integral and reduction of the generalized Birkhoffian system. An existent condition and the form of the integral are obtained. By using the integral, the dimension of the system can be reduced two degrees. An example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China(1127100861072147+1 种基金11071159)the First-Class Discipline of Universities in Shanghai and the Shanghai University Leading Academic Discipline Project(A13-0101-12-004)
文摘Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.
基金supported by National Natural Science Foundation of China under Grant No. 10572021
文摘In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation （Grant No 10272021） and Doctoral Programme Foundation of Institute of Higher Education of China （Grant No 20040007022）.
文摘Two kinds of integrals of generalized Hamilton systems with additional terms are discussed. One kind is the integral deduced by Poisson method; the other is Hojman integral obtained by Lie symmetry.
基金Supported by the NSF of Education Committee of Anhui Province (KJ2011A138)
文摘In this paper, we will establish the boundedness of the commutator generated by fractional integral operator and RBMO（μ） function on generalized Morrey space in the non-homogeneous space.
基金Supported by the Natural Science Foundation of China under Grant Nos. 61072147, 11071159, and 10971031by the Natural Science Foundation of Shanghai and Zhejiang Province under Grant Nos. 09ZR1410800 and Y6100791+1 种基金the Shanghai Shuguang Tracking Project under Grant No. 08GG01the Shanghai Leading Academic Discipline Project under Grant No. J50101
文摘A new isospectral problem is firstly presented, then we derive integrable system of soliton hierarchy. Also we obtain new integrable couplings of the generalized Kaup-Newell soliton equations hierarchy and its Hamiltonian structures by using Tu scheme and the quadratic-form identity. The method can be generalized to other soliton hierarchy.
文摘Two efficient recursive algorithms epsilon_algorithm and eta_algorithm are introduced to compute the generalized inverse function_valued Padé approximants. The approximants were used to accelerate the convergence of the power series with function_valued coefficients and to estimate characteristic value of the integral equations. Famous Wynn identities of the Pad approximants is also established by means of the connection of two algorithms.
基金The project supported by the Natural Science Foundation of Heilongjiang Province of China under Grant No. 9507
文摘The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.
文摘In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11201290 and 71103118)
文摘By means of singularity structure analysis, the integrability of a generalized fifth-order KdV equation is investigated. It is proven that this equation passes the Painleve test for integrability only for three distinct cases. Moreover, the multi- soliton solutions are presented for this equation under three sets of integrable conditions. Finally, by selecting appropriate parameters, we analyze the evolution of two solitons, which is especially interesting as it may describe the overtaking and the head-on collisions of solitary waves of different shapes and different types.
文摘Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds, the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases, we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control, then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces.
基金Supported by the NSF of China (10371087)NSF of Anhui Province (07021019)+2 种基金Education Committee ofAnhui Province (KJ2007A009Kj2008B244)the Grant for Younth of Anhui Normal University (2009xqn58)
文摘In this paper, we study the boundedness of higher order commutators of gen- eralized fractional integral operators on weighted Lp spaces and Herz-type Hardy spaces.
基金Supported by the National Natural Science Foundation of China( No.2 0 1980 6 33)
文摘After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions for the following singular integral equation
基金Supported by Fundamental Research Program 2011-2012
文摘We obtain weak type （1, q） inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the strong type inequalities in [13, 14, 15].
