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
Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were appli...Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.展开更多
In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications o...In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications of this inequality.展开更多
Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA ...Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA structure statistical mechanical model,and time complexity and precision were analyzed on the calculated results.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.
文摘Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.
基金Supported by the National Natural Science Foundation of China(10931001, 10871173)
文摘In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications of this inequality.
基金Supported by Inner Mongolia Natural Science Foundation(200711020112)Innovation Fundation of Inner Mongolia University of Science and Technology (2009NC064)~~
文摘Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA structure statistical mechanical model,and time complexity and precision were analyzed on the calculated results.
