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
This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of th...This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).展开更多
In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size condi...In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction. The main results essentially improve and extend certain previous results.展开更多
In the article,we prove that the inequalities H_(p)(K(r);E(r))>π/2;L_(q)(K(r);E(r))>π/2 hold for all r 2(0;1)if and only if p≥3=4 and q≥3=4,where Hp(a;b)and Lq(a;b)are respectively the p-th power-type Heroni...In the article,we prove that the inequalities H_(p)(K(r);E(r))>π/2;L_(q)(K(r);E(r))>π/2 hold for all r 2(0;1)if and only if p≥3=4 and q≥3=4,where Hp(a;b)and Lq(a;b)are respectively the p-th power-type Heronian mean and q-th Lehmer mean of a and b,and K(r)and E(r)are respectively the complete elliptic integrals of the first and second kinds.展开更多
In this paper, the authors give a different and more precise analysis of the stability of the classical Gauss-Laguerre quadrature rule for the Cauchy P.V. integrals on the half line. Moreover, in order to obtain this ...In this paper, the authors give a different and more precise analysis of the stability of the classical Gauss-Laguerre quadrature rule for the Cauchy P.V. integrals on the half line. Moreover, in order to obtain this result they give some new estimates for the distance of the zeros of the Laguerre polynomials that can be useful also in other contests.展开更多
在我国“双碳”背景下,建立综合能源系统(integrated energy system,IES)已经成为实现“碳达峰”、“碳中和”目标,加快能源结构转型的重要举措,而综合需求响应(integrated demand response,IDR)是综合能源系统减少碳排放、缓解供需双...在我国“双碳”背景下,建立综合能源系统(integrated energy system,IES)已经成为实现“碳达峰”、“碳中和”目标,加快能源结构转型的重要举措,而综合需求响应(integrated demand response,IDR)是综合能源系统减少碳排放、缓解供需双侧不平衡的有效途径。然而,现有关于IDR的研究大多仅考虑其经济效益,未考虑其环境效益,忽略了需求侧用户对不同时段激励价格的比价行为以及不同用户的差异化响应特性。该文提出了基于碳排放因子的IDR碳排放折算模型,并将碳排放成本加入综合能源系统服务商(integrated energy system provider,IESP)的目标函数中;通过建立激励交叉弹性耦合矩阵对用户的比价行为进行了有效建模以提升模型的精确性;同时计及用户的差异化响应特性,通过制定差异化的激励策略以充分挖掘用户的响应潜力。所提模型被建立为一个IESP-用户双层优化模型,并将该模型转化为了一个单层的凸优化模型以实现高效地求解。最后通过仿真算例验证了模型的有效性,不仅减少了碳排放量,同时降低了IESP的响应成本并提升了用户的舒适度,实现了多方共赢。展开更多
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.
文摘This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).
基金Supported by the National Natural Science Foundation of China(12071437)the Natural Science Foundation of Zhejiang Province,China(LQ22A010018)。
文摘In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction. The main results essentially improve and extend certain previous results.
基金Supported by the National Natural Science Foundation of China(11971142)the Natural Science Foundation of Zhejiang Province(LY19A010012)。
文摘In the article,we prove that the inequalities H_(p)(K(r);E(r))>π/2;L_(q)(K(r);E(r))>π/2 hold for all r 2(0;1)if and only if p≥3=4 and q≥3=4,where Hp(a;b)and Lq(a;b)are respectively the p-th power-type Heronian mean and q-th Lehmer mean of a and b,and K(r)and E(r)are respectively the complete elliptic integrals of the first and second kinds.
文摘In this paper, the authors give a different and more precise analysis of the stability of the classical Gauss-Laguerre quadrature rule for the Cauchy P.V. integrals on the half line. Moreover, in order to obtain this result they give some new estimates for the distance of the zeros of the Laguerre polynomials that can be useful also in other contests.
文摘在我国“双碳”背景下,建立综合能源系统(integrated energy system,IES)已经成为实现“碳达峰”、“碳中和”目标,加快能源结构转型的重要举措,而综合需求响应(integrated demand response,IDR)是综合能源系统减少碳排放、缓解供需双侧不平衡的有效途径。然而,现有关于IDR的研究大多仅考虑其经济效益,未考虑其环境效益,忽略了需求侧用户对不同时段激励价格的比价行为以及不同用户的差异化响应特性。该文提出了基于碳排放因子的IDR碳排放折算模型,并将碳排放成本加入综合能源系统服务商(integrated energy system provider,IESP)的目标函数中;通过建立激励交叉弹性耦合矩阵对用户的比价行为进行了有效建模以提升模型的精确性;同时计及用户的差异化响应特性,通过制定差异化的激励策略以充分挖掘用户的响应潜力。所提模型被建立为一个IESP-用户双层优化模型,并将该模型转化为了一个单层的凸优化模型以实现高效地求解。最后通过仿真算例验证了模型的有效性,不仅减少了碳排放量,同时降低了IESP的响应成本并提升了用户的舒适度,实现了多方共赢。
