This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weie...This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations.展开更多
Armchair carbon nanocoils (CNCs) with different geometric parameters are constructed and optimized using a tight-binding (TB) total energy model. The quantum conductance of these nanocoils is simulated employing a π-...Armchair carbon nanocoils (CNCs) with different geometric parameters are constructed and optimized using a tight-binding (TB) total energy model. The quantum conductance of these nanocoils is simulated employing a π-orbital TB model incorporated with the non-equilibrium Green's function theory. Compared with the perfect armchair carbon nanotubes (CNTs) and armchair CNTs with only Stone-Wales (SW) defects, the quantum conductance spectra of the armchair CNCs present distinct gaps around the Fermi level, which are mainly originated from the existence of sp3 carbon in the three-dimensional spiral structures. Moreover, the detailed conductance spectra of the armchair CNCs depend sensitively on their geometric parameters, such as tubular diameter and block-block distance.展开更多
We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a...We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a（r） and Ramanujan＇s cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan＇s cubic transformation.展开更多
基金supported by the Open Project of Key Laboratory of Mathematics Mechanization,CAS under Grant No.KLMM0602
文摘This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations.
基金supported by the Fundamental Research Funds for the Central Universities of China (Grant No. DUT10ZD211)the National Natural Science Foundation of China (Grant Nos. 51072027 and 40874039)
文摘Armchair carbon nanocoils (CNCs) with different geometric parameters are constructed and optimized using a tight-binding (TB) total energy model. The quantum conductance of these nanocoils is simulated employing a π-orbital TB model incorporated with the non-equilibrium Green's function theory. Compared with the perfect armchair carbon nanotubes (CNTs) and armchair CNTs with only Stone-Wales (SW) defects, the quantum conductance spectra of the armchair CNCs present distinct gaps around the Fermi level, which are mainly originated from the existence of sp3 carbon in the three-dimensional spiral structures. Moreover, the detailed conductance spectra of the armchair CNCs depend sensitively on their geometric parameters, such as tubular diameter and block-block distance.
基金supported by National Natural Science Foundation of China(Grant Nos.11371125,11171307 and 61374086)Natural Science Foundation of Zhejiang Province(Grant No.LY13A010004)+1 种基金Natural Science Foundation of Hunan Province(Grant No.12C0577)PhD Students Innovation Foundation of Hunan Province(Grant No.CX2012B153)
文摘We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a（r） and Ramanujan＇s cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan＇s cubic transformation.
