This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space p^N（C） with truncated multiplicities, and our results improve some earlier work.
The purpose of this article is to deal with uniqueness problem with truncated multiplicities for meromorphic mappings in several complex variables. We obtain a degeneracy theorem of meromorphic mappings without taking...The purpose of this article is to deal with uniqueness problem with truncated multiplicities for meromorphic mappings in several complex variables. We obtain a degeneracy theorem of meromorphic mappings without taking account of multiplicities of order 〉 k in counting functions and a uniqueness theorem for meromorphic mappings sharing 2n ＋ 2（n ≥ 2） hyperplanes in general position, which improve and extend some earlier work.展开更多
In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three multiplicities of an eigenvalue of the l...In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three multiplicities of an eigenvalue of the linear differential operator are given, and a fundamental fact that the algebraic, geometric and analytic multiplicities for any eigenvalue of self-adjoint differential operators are equal is proven.展开更多
In the framework of the Color Glass Condensate, the pseudo-rapidity distributions of charged hadrons in pp and pA collisions at the LHC are studied with the UGD function from the GBW model. With a X2 analysis of the C...In the framework of the Color Glass Condensate, the pseudo-rapidity distributions of charged hadrons in pp and pA collisions at the LHC are studied with the UGD function from the GBW model. With a X2 analysis of the CMS data in pp collisions at √s=0.9, 2.36, 7 TeV, the normalization factor is obtained and the theoretical results are in good agreement with the experimental data. Then, considering the influence of nucleon hard partons transverse distribution on the number of participants in pA collisions by using a Glauber Monte Carlo method, we also give the predictive results for the multiplicity distributions in pPb collisions at √s=4.4 TeV.展开更多
Let Δυ be the unit ball in ?υ with center 0 (the origin of υ) and let F:Δυ→?υbe a holomorphic map withF(0) = 0. This paper is to study the fixed point multiplicities at the origin 0 of the iteratesF i =F°...Let Δυ be the unit ball in ?υ with center 0 (the origin of υ) and let F:Δυ→?υbe a holomorphic map withF(0) = 0. This paper is to study the fixed point multiplicities at the origin 0 of the iteratesF i =F°?°F (i times),i = 1,2,.... This problem is easy when υ = 1, but it is very complicated when υ > 1. We will study this problem generally.展开更多
We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the ...We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to this counting function will be given in terms of the degree of the hypersurface, the dimension of the singular locus, the upper bounds of height, and the degree of the field of definition.展开更多
Let A∈N,B∈Z with gcd(A,B)=1,B{-1,0,1}. For the binary recurrence (Lucas sequence) of the form u 0=0, u 1=1, u n+2 =Au n+1 +Bu n, let N 1(A,B,k) be the number of the terms n of |u n|=k, where k∈N. In this paper, usi...Let A∈N,B∈Z with gcd(A,B)=1,B{-1,0,1}. For the binary recurrence (Lucas sequence) of the form u 0=0, u 1=1, u n+2 =Au n+1 +Bu n, let N 1(A,B,k) be the number of the terms n of |u n|=k, where k∈N. In this paper, using a new result of Bilu, Hanrot and Voutier on primitive divisors, we proved that N 1(A,B,k)≤1 except N 1(1,-2,1)=5[n=1,2,3,5,13], N 1(1,-3,1)=3, N 1(1,-5,1)=3,N 1(1,B,1)=2(B{-2,-3,-5}), N 1(12,-55,1)=2, N 1(12,-377,1)=2, N 1(A,B,1)=2(A 2+B=±1, A>1), N 1(1,-2,3)=2, N 1(A,B,A)=2(A 2+2B=±1,A>1. For Lehmer sequence, we got a similar result. In addition, we also obtained some applications of the above results to some Diophantime equations.展开更多
Using the techniques proposed in [3], we prove that two nonconstant meromorphic functions f and g on C must be linked by a quasi-Mbius transformation if they share some pairs of small functions with more precise trunc...Using the techniques proposed in [3], we prove that two nonconstant meromorphic functions f and g on C must be linked by a quasi-Mbius transformation if they share some pairs of small functions with more precise truncated multiplicities, which improve and extend the results of Duc Quang Si.展开更多
Experiments at the Large Hadron Collider(LHC)have measured multiplicity distributions in p+p and p+Pb collisions at a new domain of collision energy.Based on considering an energy-dependent broadening of the nucleon&#...Experiments at the Large Hadron Collider(LHC)have measured multiplicity distributions in p+p and p+Pb collisions at a new domain of collision energy.Based on considering an energy-dependent broadening of the nucleon's density distribution,charged hadron multiplicities are studied with the phenomenological saturation model and the evolution equation dependent saturation model.By assuming the saturation scale has a small dependence on the 3-dimensional root mean square(rms)radius at different energy,the theoretical results are in good agreement with the experimental data from CMS and ALICE collaboration.The predictive results in p+p collisions at s^(1/2)=14 TeV of the LHC are also given.展开更多
基金supported in part by the National Natural Science Foundation of China(10971156,11271291)
文摘This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space p^N（C） with truncated multiplicities, and our results improve some earlier work.
基金Supported by National Natural Science Foundation of China(Grant Nos.11401291 and 11461042)
文摘The purpose of this article is to deal with uniqueness problem with truncated multiplicities for meromorphic mappings in several complex variables. We obtain a degeneracy theorem of meromorphic mappings without taking account of multiplicities of order 〉 k in counting functions and a uniqueness theorem for meromorphic mappings sharing 2n ＋ 2（n ≥ 2） hyperplanes in general position, which improve and extend some earlier work.
文摘In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three multiplicities of an eigenvalue of the linear differential operator are given, and a fundamental fact that the algebraic, geometric and analytic multiplicities for any eigenvalue of self-adjoint differential operators are equal is proven.
基金Supported by Natural Science Foundation of Hebei Province (A2012210043)National Natural Science Foundation of China (11247322/A050306)
文摘In the framework of the Color Glass Condensate, the pseudo-rapidity distributions of charged hadrons in pp and pA collisions at the LHC are studied with the UGD function from the GBW model. With a X2 analysis of the CMS data in pp collisions at √s=0.9, 2.36, 7 TeV, the normalization factor is obtained and the theoretical results are in good agreement with the experimental data. Then, considering the influence of nucleon hard partons transverse distribution on the number of participants in pA collisions by using a Glauber Monte Carlo method, we also give the predictive results for the multiplicity distributions in pPb collisions at √s=4.4 TeV.
文摘Let Δυ be the unit ball in ?υ with center 0 (the origin of υ) and let F:Δυ→?υbe a holomorphic map withF(0) = 0. This paper is to study the fixed point multiplicities at the origin 0 of the iteratesF i =F°?°F (i times),i = 1,2,.... This problem is easy when υ = 1, but it is very complicated when υ > 1. We will study this problem generally.
文摘We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to this counting function will be given in terms of the degree of the hypersurface, the dimension of the singular locus, the upper bounds of height, and the degree of the field of definition.
文摘Let A∈N,B∈Z with gcd(A,B)=1,B{-1,0,1}. For the binary recurrence (Lucas sequence) of the form u 0=0, u 1=1, u n+2 =Au n+1 +Bu n, let N 1(A,B,k) be the number of the terms n of |u n|=k, where k∈N. In this paper, using a new result of Bilu, Hanrot and Voutier on primitive divisors, we proved that N 1(A,B,k)≤1 except N 1(1,-2,1)=5[n=1,2,3,5,13], N 1(1,-3,1)=3, N 1(1,-5,1)=3,N 1(1,B,1)=2(B{-2,-3,-5}), N 1(12,-55,1)=2, N 1(12,-377,1)=2, N 1(A,B,1)=2(A 2+B=±1, A>1), N 1(1,-2,3)=2, N 1(A,B,A)=2(A 2+2B=±1,A>1. For Lehmer sequence, we got a similar result. In addition, we also obtained some applications of the above results to some Diophantime equations.
基金supported by the NSFC(11401291,11101201)the NSF of Jiangxi(2012 2BAB211001)NSF of ED of Jiangxi(GJJ13077)
文摘Using the techniques proposed in [3], we prove that two nonconstant meromorphic functions f and g on C must be linked by a quasi-Mbius transformation if they share some pairs of small functions with more precise truncated multiplicities, which improve and extend the results of Duc Quang Si.
基金Supported by National Natural Science Foundation of China(No.11247322/A050306)Natural Science Foundation of Hebei Province(No.A2012210043)
文摘Experiments at the Large Hadron Collider(LHC)have measured multiplicity distributions in p+p and p+Pb collisions at a new domain of collision energy.Based on considering an energy-dependent broadening of the nucleon's density distribution,charged hadron multiplicities are studied with the phenomenological saturation model and the evolution equation dependent saturation model.By assuming the saturation scale has a small dependence on the 3-dimensional root mean square(rms)radius at different energy,the theoretical results are in good agreement with the experimental data from CMS and ALICE collaboration.The predictive results in p+p collisions at s^(1/2)=14 TeV of the LHC are also given.
