In the article,we provide a sharp lower bound for the weighted Lehmer mean of the complete p-elliptic integrals of the first and second kinds,which is the extension of the previous results for complete p-elliptic inte...In the article,we provide a sharp lower bound for the weighted Lehmer mean of the complete p-elliptic integrals of the first and second kinds,which is the extension of the previous results for complete p-elliptic integrals.展开更多
This paper considers the following Marcinkiewicz type integrals■which can be regarded as an extension of the classical Marcinkiewicz integral po introduced by Stein in[Trans Amer Math Soc,88(1958):159-172],where Ω i...This paper considers the following Marcinkiewicz type integrals■which can be regarded as an extension of the classical Marcinkiewicz integral po introduced by Stein in[Trans Amer Math Soc,88(1958):159-172],where Ω is a homogeneous function of degree zero on R^(n)with mean value zero in the unit sphere S^(n-1),Under the assumption that Ω∈L^(∞)(S^(n-1)),the authors establish the L^(q)-estimate and weak(1,1)type estimate as well as the corresponding weighted estimates for po.s with 1<q<∞ and 0<β(q-1)n/q.Moreover,the bounds do not depend on β and the strong(q,q)type and weak(1,1)type estimates for the classical Marcinkiewicz integral po can be recovered from the above estimates of μΩ,β whenβ→0.展开更多
We derive the discontinuities of banana integrals using the dispersion relation iteratively,and find a series of identities between the parameterized discontinuities of banana integrals(p-DOBIs).Similar to elliptic in...We derive the discontinuities of banana integrals using the dispersion relation iteratively,and find a series of identities between the parameterized discontinuities of banana integrals(p-DOBIs).Similar to elliptic integrals,these identities enable the reduction of various p-DOBIs to be a linear combination of some fundamental ones.We present a practical application of p-DOBIs for deriving the Picard–Fuchs operator.Then we establish the expression of generalized dispersion relation,which enables us to obtain the dispersion relation representation of arbitrary banana integrals.Moreover,we propose a hypothesis for generalized dispersion relation and p-DOBIs,which provides a simple way to calculate the discontinuities and transform dispersion relation representation to p-DOBIs.展开更多
Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quan...Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.展开更多
This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward m...This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.展开更多
基金Supported by the National Natural Science Foundation of China(11971142)the Natural Science Foundation of Zhejiang Province(LY19A010012)the key Scientific Research Projects of Hunan Provincial Department of Education in 2021(21A0526)。
文摘In the article,we provide a sharp lower bound for the weighted Lehmer mean of the complete p-elliptic integrals of the first and second kinds,which is the extension of the previous results for complete p-elliptic integrals.
文摘This paper considers the following Marcinkiewicz type integrals■which can be regarded as an extension of the classical Marcinkiewicz integral po introduced by Stein in[Trans Amer Math Soc,88(1958):159-172],where Ω is a homogeneous function of degree zero on R^(n)with mean value zero in the unit sphere S^(n-1),Under the assumption that Ω∈L^(∞)(S^(n-1)),the authors establish the L^(q)-estimate and weak(1,1)type estimate as well as the corresponding weighted estimates for po.s with 1<q<∞ and 0<β(q-1)n/q.Moreover,the bounds do not depend on β and the strong(q,q)type and weak(1,1)type estimates for the classical Marcinkiewicz integral po can be recovered from the above estimates of μΩ,β whenβ→0.
基金supported by the National Natural Science Foundation of China(Grant No.12175318)the Natural Science Foundation of Guangdong Province of China(Grant No.2022A1515011922).
文摘We derive the discontinuities of banana integrals using the dispersion relation iteratively,and find a series of identities between the parameterized discontinuities of banana integrals(p-DOBIs).Similar to elliptic integrals,these identities enable the reduction of various p-DOBIs to be a linear combination of some fundamental ones.We present a practical application of p-DOBIs for deriving the Picard–Fuchs operator.Then we establish the expression of generalized dispersion relation,which enables us to obtain the dispersion relation representation of arbitrary banana integrals.Moreover,we propose a hypothesis for generalized dispersion relation and p-DOBIs,which provides a simple way to calculate the discontinuities and transform dispersion relation representation to p-DOBIs.
基金supported by the NSF of Hebei Province(A2022208007)the NSF of China(11571089,11871191)the NSF of Henan Province(222300420397)。
文摘Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.
文摘This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.
