In this paper the author proves that the commutator of the Marcinkiewicz integral operator with rough variable kernel is bounded from the homogeneous Sobolev space Lγ^2（R^n） to the Lebesgue space L^2（R^n）, which ...In this paper the author proves that the commutator of the Marcinkiewicz integral operator with rough variable kernel is bounded from the homogeneous Sobolev space Lγ^2（R^n） to the Lebesgue space L^2（R^n）, which is a substantial improvement and extension of some known results.展开更多
The iterated spherical average∆(A1)^(N)is an important operator in harmonic analysis,and has very important applications in approximation theory and probability theory,where∆is the Laplacian,A_(1)is the unit spherical...The iterated spherical average∆(A1)^(N)is an important operator in harmonic analysis,and has very important applications in approximation theory and probability theory,where∆is the Laplacian,A_(1)is the unit spherical average and(A1)^(N)is its iteration.In this paper,we mainly study the sufficient and necessary conditions for the boundedness of this operator in Besov-Lipschitz space,and prove the boundedness of the operator in Triebel-Lizorkin space.Moreover,we use above conclusions to improve the existing results of the boundedness of this operator in L^(p)space.展开更多
A 2.45 GHz electron cyclotron resonance intense proton source and a low energy beam transport line with dual-Glaser lens were designed and fabricated by Institute of Modern Physics for a compact pulsed hadron source a...A 2.45 GHz electron cyclotron resonance intense proton source and a low energy beam transport line with dual-Glaser lens were designed and fabricated by Institute of Modern Physics for a compact pulsed hadron source at Tsinghua. The intense proton beams extracted from the ion source are transported through the transport line to match the downstream radio frequency quadrupole accelerator. Particle-in-cell code BEAMPATH was used to carry out the beam transport simulations and optimize the magnetic field structures of the transport line. Emittance growth due to space charge and spherical aberrations of the Glaser lens were studied in both theory and simulation. The results show that narrow beam has smaller aberrations and better beam quality through the transport line. To better match the radio frequency quadrupole accelerator, a shorter transport line is desired with sufficient space charge neutralization.展开更多
In this paper,by using the theory and method of distance geometry,we study the geometric inequality of a n-dimensional simplex in the spherical space and establish two geometric inequalities involving the edge-length ...In this paper,by using the theory and method of distance geometry,we study the geometric inequality of a n-dimensional simplex in the spherical space and establish two geometric inequalities involving the edge-length and volume of one simplex and the volume,height and(n-1)-dimensional volume of the side of another simplex in the n-dimensional spherical space.They are the extensions of the results [10] in the n-dimensional Euclidean geometry to the n-dimensional spherical space.展开更多
基金NSF of China(Grant Nos.10571015 and 10826046)SRFDP of China(Grant No.20050027025)
文摘In this paper the author proves that the commutator of the Marcinkiewicz integral operator with rough variable kernel is bounded from the homogeneous Sobolev space Lγ^2（R^n） to the Lebesgue space L^2（R^n）, which is a substantial improvement and extension of some known results.
文摘The iterated spherical average∆(A1)^(N)is an important operator in harmonic analysis,and has very important applications in approximation theory and probability theory,where∆is the Laplacian,A_(1)is the unit spherical average and(A1)^(N)is its iteration.In this paper,we mainly study the sufficient and necessary conditions for the boundedness of this operator in Besov-Lipschitz space,and prove the boundedness of the operator in Triebel-Lizorkin space.Moreover,we use above conclusions to improve the existing results of the boundedness of this operator in L^(p)space.
基金Supported by the Compact Pulsed Hadron Source (CPHS) project at Tsinghua UniversityNational Nature Science foundation of China (11027508)
文摘A 2.45 GHz electron cyclotron resonance intense proton source and a low energy beam transport line with dual-Glaser lens were designed and fabricated by Institute of Modern Physics for a compact pulsed hadron source at Tsinghua. The intense proton beams extracted from the ion source are transported through the transport line to match the downstream radio frequency quadrupole accelerator. Particle-in-cell code BEAMPATH was used to carry out the beam transport simulations and optimize the magnetic field structures of the transport line. Emittance growth due to space charge and spherical aberrations of the Glaser lens were studied in both theory and simulation. The results show that narrow beam has smaller aberrations and better beam quality through the transport line. To better match the radio frequency quadrupole accelerator, a shorter transport line is desired with sufficient space charge neutralization.
文摘In this paper,by using the theory and method of distance geometry,we study the geometric inequality of a n-dimensional simplex in the spherical space and establish two geometric inequalities involving the edge-length and volume of one simplex and the volume,height and(n-1)-dimensional volume of the side of another simplex in the n-dimensional spherical space.They are the extensions of the results [10] in the n-dimensional Euclidean geometry to the n-dimensional spherical space.
基金Supported in part by the State Maintenance Program for Young Russian Scientists and the Leading Scientific Schools of the Russian Federation(NSh-921.2012.1)
