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
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.
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
In this paper, we introduce some new subclasses of meromorphically uniformly reciprocal starlike functions associated with the generalized Dziok-Srivastava operator and its corresponding integral operator defined by s...In this paper, we introduce some new subclasses of meromorphically uniformly reciprocal starlike functions associated with the generalized Dziok-Srivastava operator and its corresponding integral operator defined by subordination. We obtain the inclusion relation, sufficient conditions and raajorization property of the class. Moreover, we point out some new and interesting corollaries of our main result. These results generalize some known results.展开更多
In this paper, a kind of new definitions of singular integral operators in the weighted L-2 space with the generalized Jacobi weights are given, then the boundedness in the weighted L-2 space, the relationships betwee...In this paper, a kind of new definitions of singular integral operators in the weighted L-2 space with the generalized Jacobi weights are given, then the boundedness in the weighted L-2 space, the relationships between these operators and the classic singular integral operators are proved. For the convenience in the later use, similar results in the L-2 space with Jacobi weights are given.展开更多
In this paper,we study the generalized complete(p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters,and establish the monotonicity,generali...In this paper,we study the generalized complete(p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters,and establish the monotonicity,generalized convexity and concavity of these functions.In particular,some Turán type inequalities are given.Finally,we also show some new series representations of these functions by applying Alzer and Richard's methods.展开更多
In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space whic...In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.展开更多
In this paper, we prove the uniqueness of generalized solution defined by Lebesgue-Stieltjes integral for the Cauchy problem of transportation equations. Our results are based on the discussions for linear system with...In this paper, we prove the uniqueness of generalized solution defined by Lebesgue-Stieltjes integral for the Cauchy problem of transportation equations. Our results are based on the discussions for linear system with discontinuous coefficient.展开更多
This paper presents a Poisson theory of the generalized Birkhoff equations, including the algebraic structure of the equations, the sufficient and necessary condition on the integral and the conditions under which a n...This paper presents a Poisson theory of the generalized Birkhoff equations, including the algebraic structure of the equations, the sufficient and necessary condition on the integral and the conditions under which a new integral can be deduced by a known integral as well as the form of the new integral.展开更多
The purpose of this paper is to give the extensions of some identities involving generalized Fibonacci and Lucas numbers with binomial coefficients.These results generalize the identities by Gulec,Taskara and Uslu in ...The purpose of this paper is to give the extensions of some identities involving generalized Fibonacci and Lucas numbers with binomial coefficients.These results generalize the identities by Gulec,Taskara and Uslu in Appl.Math.Lett.23(2010)68-72 and Appl.Math.Comput.220(2013)482-486.展开更多
In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentiall...In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.展开更多
In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some e...In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.展开更多
The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by em- ploying two-photon interference in Feynman＇s path integral theory. It is concluded that whether the sec...The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by em- ploying two-photon interference in Feynman＇s path integral theory. It is concluded that whether the second-order temporal interference pattern can or cannot be retrieved via two-photon coincidence counting rate is dependent on the resolution time of the detection system and the frequency difference between these two lasers. Two identical and tunable single-mode continuous-wave diode lasers are employed to verify the predictions. These studies are helpful to understand the physics of two-photon interference with photons of different spectra.展开更多
A new entangled state ｜η 0） is proposed by the technique of integral within an ordered product. A generalized Hadamaxd transformation is derived by virtue of η; θ）, which plays a role of Hadamard transformation ...A new entangled state ｜η 0） is proposed by the technique of integral within an ordered product. A generalized Hadamaxd transformation is derived by virtue of η; θ）, which plays a role of Hadamard transformation for （a1 sinθ - a2 cosθ） and （a1 cosθ ＋ a2 sin θ）.展开更多
This paper discusses a class of forced second-order half-linear differential equations. By using the generalized Riccati technique and the averaging technique, some new interval oscillation criteria are obtained.
With the aid of Lenard recursion equations, an integrable hierarchy of nonlinear evolution equations associated with a 2 × 2 matrix spectral problem is proposed, in which the first nontrivial member in the positi...With the aid of Lenard recursion equations, an integrable hierarchy of nonlinear evolution equations associated with a 2 × 2 matrix spectral problem is proposed, in which the first nontrivial member in the positive flows can be reduced to a new generalization of the Wadati–Konno–Ichikawa(WKI) equation. Further, a new generalization of the Fokas–Lenells(FL) equation is derived from the negative flows. Resorting to these two Lax pairs and Riccati-type equations, the infinite conservation laws of these two corresponding equations are obtained.展开更多
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.
基金Supported by the National Natural Science Foundation of China(11561001)Supported by the Natural Science Foundation of Inner Mongolia Province(2014MS0101)Supported by the Higher School Foundation of Inner Mongolia Province(2015NJZY240)
文摘In this paper, we introduce some new subclasses of meromorphically uniformly reciprocal starlike functions associated with the generalized Dziok-Srivastava operator and its corresponding integral operator defined by subordination. We obtain the inclusion relation, sufficient conditions and raajorization property of the class. Moreover, we point out some new and interesting corollaries of our main result. These results generalize some known results.
基金Supported by the Foundation of TY of China(10126028)
文摘In this paper, a kind of new definitions of singular integral operators in the weighted L-2 space with the generalized Jacobi weights are given, then the boundedness in the weighted L-2 space, the relationships between these operators and the classic singular integral operators are proved. For the convenience in the later use, similar results in the L-2 space with Jacobi weights are given.
基金supported by the Natural Science Foundation of Shandong Province (ZR2019QA003 and ZR2018MF023)by the National Natural Science Foundation of China (11601036)by the Major Project of Binzhou University (2020ZD02)
文摘In this paper,we study the generalized complete(p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters,and establish the monotonicity,generalized convexity and concavity of these functions.In particular,some Turán type inequalities are given.Finally,we also show some new series representations of these functions by applying Alzer and Richard's methods.
文摘In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.
文摘In this paper, we prove the uniqueness of generalized solution defined by Lebesgue-Stieltjes integral for the Cauchy problem of transportation equations. Our results are based on the discussions for linear system with discontinuous coefficient.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)
文摘This paper presents a Poisson theory of the generalized Birkhoff equations, including the algebraic structure of the equations, the sufficient and necessary condition on the integral and the conditions under which a new integral can be deduced by a known integral as well as the form of the new integral.
基金Supported by the Youth Backbone Teacher Foundation of Henan's University(Grant No.2016GGJS-117)Supported by the National Natural Science Foundation of China(Grant No.11871258)。
文摘The purpose of this paper is to give the extensions of some identities involving generalized Fibonacci and Lucas numbers with binomial coefficients.These results generalize the identities by Gulec,Taskara and Uslu in Appl.Math.Lett.23(2010)68-72 and Appl.Math.Comput.220(2013)482-486.
基金This project is supported by the National Science Foundation of China.
文摘In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.
基金supported by the Research Foundation of Education Bureau of Hubei Province,China (Grant No Z200612001)the Natural Science Foundation of Yangtze University (Grant No 20061222)
文摘In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.
基金Project supported by the National Natural Science Foundation of China(Grant No.11404255)the Doctor Foundation of Education Ministry of China(Grant No.20130201120013)
文摘The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by em- ploying two-photon interference in Feynman＇s path integral theory. It is concluded that whether the second-order temporal interference pattern can or cannot be retrieved via two-photon coincidence counting rate is dependent on the resolution time of the detection system and the frequency difference between these two lasers. Two identical and tunable single-mode continuous-wave diode lasers are employed to verify the predictions. These studies are helpful to understand the physics of two-photon interference with photons of different spectra.
基金Project supported by the National Natural Science Foundation of China(Grant No.10574060)the Natural Science Foundation of Shandong Province of China(Grant No.Y2008A16)+1 种基金the University Experimental Technology Foundation of Shandong Province,China(Grant No.S04W138)the Natural Science Foundation of Heze University of Shandong Province,China(GrantNos.XY07WL01 and XY08WL03)
文摘A new entangled state ｜η 0） is proposed by the technique of integral within an ordered product. A generalized Hadamaxd transformation is derived by virtue of η; θ）, which plays a role of Hadamard transformation for （a1 sinθ - a2 cosθ） and （a1 cosθ ＋ a2 sin θ）.
文摘This paper discusses a class of forced second-order half-linear differential equations. By using the generalized Riccati technique and the averaging technique, some new interval oscillation criteria are obtained.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11971441,11871440,and 11931017)Key Scientific Research Projects of Colleges and Universities in Henan Province,China(Grant No.20A110006).
文摘With the aid of Lenard recursion equations, an integrable hierarchy of nonlinear evolution equations associated with a 2 × 2 matrix spectral problem is proposed, in which the first nontrivial member in the positive flows can be reduced to a new generalization of the Wadati–Konno–Ichikawa(WKI) equation. Further, a new generalization of the Fokas–Lenells(FL) equation is derived from the negative flows. Resorting to these two Lax pairs and Riccati-type equations, the infinite conservation laws of these two corresponding equations are obtained.
