In deformation quantization, static Wigner functions obey functional ,-genvalue equation, which is equivalent to time-independent Schrodinger equation in Hilbert space operator formalism of quantum mechanics. This equ...In deformation quantization, static Wigner functions obey functional ,-genvalue equation, which is equivalent to time-independent Schrodinger equation in Hilbert space operator formalism of quantum mechanics. This equivalence is proved mostly for Hamiltonian with form H^ = （1/2）p^2 ＋ V（x^） [D. Fairlie, Proc. Camb. Phil. Soc. 60 （1964） 581]. In this note we generalize this proof to a very general Hamiltonian H^（x^,p^） and give examples to support it.展开更多
In this note,we discuss some properties of reflexive algebras on a Hilbert space with invariant subspace lattices as realizations of the pentagon and the double triangle and give some results concerning hyperreflexivi...In this note,we discuss some properties of reflexive algebras on a Hilbert space with invariant subspace lattices as realizations of the pentagon and the double triangle and give some results concerning hyperreflexivity,automorphism and finite rank operators.展开更多
In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B＇ in separable complex Hilbert spaces H and H＇, respectively. It is found that if the ...In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B＇ in separable complex Hilbert spaces H and H＇, respectively. It is found that if the mapping f ∈ C^1＋α at z0 ∈ B with f（zo） = wo ∈ OB＇, then the Fr＆het derivative operator Df（z0） maps the tangent space Tz0（ B^n） to Tw0（ B＇）, the holomorphic tangent space Tz0^（1,0） to Tw0（1,0）（ B＇）,respectively.展开更多
. Let S = k[x1,..., xn] be a non-standard polynomial ring over a field k and let M be a finitely generated graded S-module. In this paper, we investigate the behaviour of Hilbert function of M and its relations with l.... Let S = k[x1,..., xn] be a non-standard polynomial ring over a field k and let M be a finitely generated graded S-module. In this paper, we investigate the behaviour of Hilbert function of M and its relations with lattice point counting. More precisely, by using combinatorial tools, we prove that there exists a polytope such that the image of Hilbert function in some degree is equal to the number of lattice points of this polytope.展开更多
This paper introduces a three-step iteration for finding a common element of the set of fixedpoints of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone map...This paper introduces a three-step iteration for finding a common element of the set of fixedpoints of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping by viscosity approximation methods in a Hilbert space.The authors showthat the iterative sequence converges strongly to a common element of the two sets,which solves somevariational inequality.Subsequently,the authors consider the problem of finding a common fixed pointof a nonexpansive mapping and a strictly pseudo-contractive mapping and the problem of finding acommon element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping.The results obtained in this paper extend and improve the correspondingresults announced by Nakajo,Takahashi,and Toyoda.展开更多
基金Supported by the National Natural Science Foundation of China(11071109,11401296)the Jiangsu Provincial Natural Science Foundation of China(BK20141008)the Natural Science Fund for Colleges and Universities in Jiangsu Province(14KJB110007)
基金supported by National Natural Science Foundation of China under Grant No.10675106
文摘In deformation quantization, static Wigner functions obey functional ,-genvalue equation, which is equivalent to time-independent Schrodinger equation in Hilbert space operator formalism of quantum mechanics. This equivalence is proved mostly for Hamiltonian with form H^ = （1/2）p^2 ＋ V（x^） [D. Fairlie, Proc. Camb. Phil. Soc. 60 （1964） 581]. In this note we generalize this proof to a very general Hamiltonian H^（x^,p^） and give examples to support it.
文摘In this note,we discuss some properties of reflexive algebras on a Hilbert space with invariant subspace lattices as realizations of the pentagon and the double triangle and give some results concerning hyperreflexivity,automorphism and finite rank operators.
基金supported by the National Natural Science Foundation of China(Nos.11671361,11571256)the Zhejiang Provincial Natural Science Foundation of China(No.LY14A010008)
文摘In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B＇ in separable complex Hilbert spaces H and H＇, respectively. It is found that if the mapping f ∈ C^1＋α at z0 ∈ B with f（zo） = wo ∈ OB＇, then the Fr＆het derivative operator Df（z0） maps the tangent space Tz0（ B^n） to Tw0（ B＇）, the holomorphic tangent space Tz0^（1,0） to Tw0（1,0）（ B＇）,respectively.
文摘. Let S = k[x1,..., xn] be a non-standard polynomial ring over a field k and let M be a finitely generated graded S-module. In this paper, we investigate the behaviour of Hilbert function of M and its relations with lattice point counting. More precisely, by using combinatorial tools, we prove that there exists a polytope such that the image of Hilbert function in some degree is equal to the number of lattice points of this polytope.
基金supported by the National Natural Science Foundation of China under Grant No. 10771050
文摘This paper introduces a three-step iteration for finding a common element of the set of fixedpoints of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping by viscosity approximation methods in a Hilbert space.The authors showthat the iterative sequence converges strongly to a common element of the two sets,which solves somevariational inequality.Subsequently,the authors consider the problem of finding a common fixed pointof a nonexpansive mapping and a strictly pseudo-contractive mapping and the problem of finding acommon element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping.The results obtained in this paper extend and improve the correspondingresults announced by Nakajo,Takahashi,and Toyoda.
