Suppose that U is a norm closed nest algebra module. Using the characterization of rank one operators in U⊥, a complete description of the extreme points of the unit ball U1 is given.
Electronic regulation of two-dimensional(2 D)transition metal dichalcogenides(TMDCs)is a crucial step towards next-generation optoelectronics and electronics.Here,we demonstrate controllable and selective-area defect ...Electronic regulation of two-dimensional(2 D)transition metal dichalcogenides(TMDCs)is a crucial step towards next-generation optoelectronics and electronics.Here,we demonstrate controllable and selective-area defect engineering in 2D molybdenum disulfide(MoS_(2))using a focused ion beam with a low-energy gallium ion(Ga^(+))source.We find that the surface defects of MoS_(2)can be tuned by the precise control of ion energy and dose.Furthermore,the fieldeffect transistors based on the monolayer MoS_(2)show a significant threshold voltage modulation over 70 V after Ga+irradiation.First-principles calculations reveal that the Ga impurities in the monolayer MoS_(2)introduce a defect state near the Fermi level,leading to a shallow acceptor level of 0.25 eV above the valence band maximum.This defect engineering strategy enables direct writing of complex pattern at the atomic length scale in a controlled and facile manner,tailoring the electronic properties of 2D TMDCs for novel devices.展开更多
In this paper, the famous Amann three-solution theorem is generalized. Multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, ...In this paper, the famous Amann three-solution theorem is generalized. Multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least six distinct fixed points of nonlinear operators is proved. The theoretical results are then applied to nonlinear system of Hammerstein integral equations.展开更多
Insa and Pauer presented a basic theory of Grbner bases for differential operators with coefficients in a commutative ring and an improved version of this result was given by Ma et al.In this paper,we present an algor...Insa and Pauer presented a basic theory of Grbner bases for differential operators with coefficients in a commutative ring and an improved version of this result was given by Ma et al.In this paper,we present an algorithmic approach for computing Grbner bases in difference-differential modules with coefficients in a commutative ring.We combine the generalized term order method of Zhou and Winkler with SPoly method of Insa and Pauer to deal with the problem.Our result is a generalization of theories of Insa and Pauer,Ma et al.,Zhou and Winkler and includes them as special cases.展开更多
We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared ...We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared in one dimension, which results from the operation of symmetry or antisymmetry of identical particles. In two and higher dimensions, we give the energy spectrum and the analytical ground state wave [unctions and the degree of degeneracy. By comparison, we refine A vinash Khare＇s results by making some items in his article precisely.展开更多
文摘Suppose that U is a norm closed nest algebra module. Using the characterization of rank one operators in U⊥, a complete description of the extreme points of the unit ball U1 is given.
基金supported by Fujian Minjiang Distinguished Scholar Programthe Department of Science and Technology of Fujian Province(2020J01704 and 2019L3008)the Scientific Research Foundation from Jimei University(ZP2020066 and ZP2020065)。
文摘Electronic regulation of two-dimensional(2 D)transition metal dichalcogenides(TMDCs)is a crucial step towards next-generation optoelectronics and electronics.Here,we demonstrate controllable and selective-area defect engineering in 2D molybdenum disulfide(MoS_(2))using a focused ion beam with a low-energy gallium ion(Ga^(+))source.We find that the surface defects of MoS_(2)can be tuned by the precise control of ion energy and dose.Furthermore,the fieldeffect transistors based on the monolayer MoS_(2)show a significant threshold voltage modulation over 70 V after Ga+irradiation.First-principles calculations reveal that the Ga impurities in the monolayer MoS_(2)introduce a defect state near the Fermi level,leading to a shallow acceptor level of 0.25 eV above the valence band maximum.This defect engineering strategy enables direct writing of complex pattern at the atomic length scale in a controlled and facile manner,tailoring the electronic properties of 2D TMDCs for novel devices.
基金This research is supported by NSFC (10071042)NSFSP (Z2000A02).
文摘In this paper, the famous Amann three-solution theorem is generalized. Multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least six distinct fixed points of nonlinear operators is proved. The theoretical results are then applied to nonlinear system of Hammerstein integral equations.
基金supported by National Natural Science Foundation of China (Grant No.10871017)Natural Science Foundation of Beijing (Grant No. 1102026)
文摘Insa and Pauer presented a basic theory of Grbner bases for differential operators with coefficients in a commutative ring and an improved version of this result was given by Ma et al.In this paper,we present an algorithmic approach for computing Grbner bases in difference-differential modules with coefficients in a commutative ring.We combine the generalized term order method of Zhou and Winkler with SPoly method of Insa and Pauer to deal with the problem.Our result is a generalization of theories of Insa and Pauer,Ma et al.,Zhou and Winkler and includes them as special cases.
基金Supported by the National Natural Science Foundation of China under Grant No.10975125
文摘We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared in one dimension, which results from the operation of symmetry or antisymmetry of identical particles. In two and higher dimensions, we give the energy spectrum and the analytical ground state wave [unctions and the degree of degeneracy. By comparison, we refine A vinash Khare＇s results by making some items in his article precisely.
