We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Rie...We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter＇s theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson＇s theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson＇s theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres.展开更多
Converging spherical and cylindrical elastic-plastic waves in an isotropic work-hardening medium is investigated on the basis of a finite difference method. The small amplitude pressure is applied instantaneously and ...Converging spherical and cylindrical elastic-plastic waves in an isotropic work-hardening medium is investigated on the basis of a finite difference method. The small amplitude pressure is applied instantaneously and maintained on the outer surface of a spherical or a cylindrical medium. It is found that for undercritical loading, the induced wave structure is an elastic front followed in turn by an expanding plastic region and an expanding elastic region. For supercritical loading, the elastic front is followed in turn by an expanding plastic region, a narrowing elastic region and an expanding plastic region. After yielding is initiated, the strength of the elastic front is constant and equal to the critical loading pressure. The motion of the continuous elastic-plastic interface is discussed in detail. Spatial distributions of pressure near the axis show the strength of the converging wave is nearly doubled in the reflecting stage.展开更多
This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of tho...This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of those on the circle.展开更多
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the researc...As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.展开更多
We consider the VEM system in the context of spherical symmetry and we try to establish a global static solutions with isotropic pressure that approaches Minkowski spacetime at infinity and have a regular center. To b...We consider the VEM system in the context of spherical symmetry and we try to establish a global static solutions with isotropic pressure that approaches Minkowski spacetime at infinity and have a regular center. To be in accordance with numerical investigation we take here low charge particles.展开更多
In this article,some basic and important properties of spherically convex functions,such as the Lipschitz-continuity,are investigated.It is shown that,under a weaker condition,every family of spherically convex functi...In this article,some basic and important properties of spherically convex functions,such as the Lipschitz-continuity,are investigated.It is shown that,under a weaker condition,every family of spherically convex functions is equi-Lipschitzian on each closed spherically convex subset contained in the relative interior of their common domain,and from which a powerful result is derived:the pointwise convergence of a sequence of spherically convex functions implies its uniform convergence on each closed spherically convex subset contained in the relative interior of their common domain.展开更多
Given a continuous boundary value on the boundary of a ＂simply closed surface＂ as that encloses the whole Earth, a regular harmonic fictitious field V＊（P） in the domain outside an inner sphere Ki that lies inside...Given a continuous boundary value on the boundary of a ＂simply closed surface＂ as that encloses the whole Earth, a regular harmonic fictitious field V＊（P） in the domain outside an inner sphere Ki that lies inside the Earth could be determined, and it is proved that V＊（P） coincides with the Earth＇s real field V（P） in the whole domain outside the Earth. Since in the domain outside the inner sphere Ki and the fictitious regular harmonic function V＊（P） could be expressed as a uniformly convergent spherical harmonic series, it is concluded that the Earth＇s potential field could be expressed as a uniformly convergent spherical harmonic expansion series in the whole domain outside the Earth.展开更多
Consideration is given to results of experimental and theoretical investigations how alpha-epsilon phase transition in the unalloyed iron and the 30 KhGSA steel and its absence in the austenitic 12Kh18N10T stainless s...Consideration is given to results of experimental and theoretical investigations how alpha-epsilon phase transition in the unalloyed iron and the 30 KhGSA steel and its absence in the austenitic 12Kh18N10T stainless steel influence processes under explosive deformation of spheres made of these materials.Polymorphous transition is shown to significantly effect on:amount of explosion-products energy transferred to a sphere,evolution of the converging-wave structure and its parameters,profiles of stress wave and temperature T(R,t)for some Lagrangian particles along the sphere radius,character of energy cumulation under spherical convergence of waves.展开更多
基金Sponsored by Research Grant of the University of Macao No. RG024/03-04S/QT/FST
文摘We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter＇s theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson＇s theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson＇s theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres.
文摘Converging spherical and cylindrical elastic-plastic waves in an isotropic work-hardening medium is investigated on the basis of a finite difference method. The small amplitude pressure is applied instantaneously and maintained on the outer surface of a spherical or a cylindrical medium. It is found that for undercritical loading, the induced wave structure is an elastic front followed in turn by an expanding plastic region and an expanding elastic region. For supercritical loading, the elastic front is followed in turn by an expanding plastic region, a narrowing elastic region and an expanding plastic region. After yielding is initiated, the strength of the elastic front is constant and equal to the critical loading pressure. The motion of the continuous elastic-plastic interface is discussed in detail. Spatial distributions of pressure near the axis show the strength of the converging wave is nearly doubled in the reflecting stage.
文摘This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of those on the circle.
基金Supported by the NSF of China under the Grant 10471010partially by the NSERC Canada under Grant G121211001
文摘As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.
文摘We consider the VEM system in the context of spherical symmetry and we try to establish a global static solutions with isotropic pressure that approaches Minkowski spacetime at infinity and have a regular center. To be in accordance with numerical investigation we take here low charge particles.
基金Supported by the National NSF of China(Grant Nos.12071334,11671293)。
文摘In this article,some basic and important properties of spherically convex functions,such as the Lipschitz-continuity,are investigated.It is shown that,under a weaker condition,every family of spherically convex functions is equi-Lipschitzian on each closed spherically convex subset contained in the relative interior of their common domain,and from which a powerful result is derived:the pointwise convergence of a sequence of spherically convex functions implies its uniform convergence on each closed spherically convex subset contained in the relative interior of their common domain.
基金Supported by the National Natural Science Foundation of China （No.40637034, No. 40574004）, the National 863 Program of China （No. 2006AA12Z211）. The author thanks Prof. Dr. Sjoberg for his valuable comments on the original manuscript.
文摘Given a continuous boundary value on the boundary of a ＂simply closed surface＂ as that encloses the whole Earth, a regular harmonic fictitious field V＊（P） in the domain outside an inner sphere Ki that lies inside the Earth could be determined, and it is proved that V＊（P） coincides with the Earth＇s real field V（P） in the whole domain outside the Earth. Since in the domain outside the inner sphere Ki and the fictitious regular harmonic function V＊（P） could be expressed as a uniformly convergent spherical harmonic series, it is concluded that the Earth＇s potential field could be expressed as a uniformly convergent spherical harmonic expansion series in the whole domain outside the Earth.
文摘Consideration is given to results of experimental and theoretical investigations how alpha-epsilon phase transition in the unalloyed iron and the 30 KhGSA steel and its absence in the austenitic 12Kh18N10T stainless steel influence processes under explosive deformation of spheres made of these materials.Polymorphous transition is shown to significantly effect on:amount of explosion-products energy transferred to a sphere,evolution of the converging-wave structure and its parameters,profiles of stress wave and temperature T(R,t)for some Lagrangian particles along the sphere radius,character of energy cumulation under spherical convergence of waves.
