For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving function...For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving functions in the class T(α,β). And we estimate the bounds of coefficients and solve Fekete-Szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or bi-univalent functions.展开更多
In this article,the refined Schwarz-Pick estimates for positive real part holomorphic functions p(x)=p(0)+Σ_(m=k)^(∞)D^(M)p(0)(x^(m))/m!:G→Care given,where k is a positive integer,and G is a balanced domain in comp...In this article,the refined Schwarz-Pick estimates for positive real part holomorphic functions p(x)=p(0)+Σ_(m=k)^(∞)D^(M)p(0)(x^(m))/m!:G→Care given,where k is a positive integer,and G is a balanced domain in complex Banach spaces.In particular,the results of first order Fréchet derivative for the above functions and higher order Frechet derivatives for positive real part holomorphic functions p(x)=p(0)+Σ_(s=1)^(∞)D^(sk)p(0)(x^(sk))/(sk)!:G→Care sharp for G=B,where B is the unit ball of complex Banach spaces or the unit ball of complex Hilbert spaces.Their results reduce to the classical result in one complex variable,and generalize some known results in several complex variables.展开更多
AC impedance spectroscopy in pure room temperature ionic liquids （RTILs） and RTIL-water mixture was measured at the temperature of range from 30 ℃ down to -30 ℃. The cations of RTILs are N,N-diethyl-N-methyl-N-（2...AC impedance spectroscopy in pure room temperature ionic liquids （RTILs） and RTIL-water mixture was measured at the temperature of range from 30 ℃ down to -30 ℃. The cations of RTILs are N,N-diethyl-N-methyl-N-（2-methoxyethyl） ammonium （[DEME]）, 1-ethyl-3-methylimidazolium （[C2mim]） and l-butyl-3-methylimidazolium （[Camim]）, the anions are tetrafluoroborate （[BF4]） and bis（trifluoromethanesulfonyl）imide （[TFSI]）. In all pure RTILs, there are two kinds of local minima in real part of the AC impedance Zreal. By adding water to [DEME][BF4] （0 mol% 〈 x 〈 94 mol%） at room temperature, the local minimum value at higher frequency decreased remarkably at the fixed frequency with increasing water concentration. Above 94 mol% H20, a quite different profile of the AC impedance spectroscopy was obtained. In addition to Zreal. temperature dependence of an imaginary part of the impedance Zimag had an isosbestic point below 94 mol%. The isosbestic point disappeared above 94 mol%. The isosbestic point in Zing reveals an interaction between [DEME][BFa] and H2O.展开更多
We give an explicit proof of equivalence of the two-point function to one-loop order in the two formalisms of thermal theory based on the expressions in the real-time formalism and indicate that the key point of comp...We give an explicit proof of equivalence of the two-point function to one-loop order in the two formalisms of thermal theory based on the expressions in the real-time formalism and indicate that the key point of completing the proof is to separate carefully the imaginary part of the zero-temperature loop integral from relevant expressions and this fact will certainly be very useful for examination of the equivalent problem of two formalisms of thermal field theory in other theories, including the one of the propagators for scalar bound states in an NJL model.展开更多
基金supported by Kyungsung University Re-search Grants in 2013.
文摘For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving functions in the class T(α,β). And we estimate the bounds of coefficients and solve Fekete-Szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or bi-univalent functions.
基金supported by the National Natural Science Foundation of China(Nos.11871257,12071130)。
文摘In this article,the refined Schwarz-Pick estimates for positive real part holomorphic functions p(x)=p(0)+Σ_(m=k)^(∞)D^(M)p(0)(x^(m))/m!:G→Care given,where k is a positive integer,and G is a balanced domain in complex Banach spaces.In particular,the results of first order Fréchet derivative for the above functions and higher order Frechet derivatives for positive real part holomorphic functions p(x)=p(0)+Σ_(s=1)^(∞)D^(sk)p(0)(x^(sk))/(sk)!:G→Care sharp for G=B,where B is the unit ball of complex Banach spaces or the unit ball of complex Hilbert spaces.Their results reduce to the classical result in one complex variable,and generalize some known results in several complex variables.
文摘AC impedance spectroscopy in pure room temperature ionic liquids （RTILs） and RTIL-water mixture was measured at the temperature of range from 30 ℃ down to -30 ℃. The cations of RTILs are N,N-diethyl-N-methyl-N-（2-methoxyethyl） ammonium （[DEME]）, 1-ethyl-3-methylimidazolium （[C2mim]） and l-butyl-3-methylimidazolium （[Camim]）, the anions are tetrafluoroborate （[BF4]） and bis（trifluoromethanesulfonyl）imide （[TFSI]）. In all pure RTILs, there are two kinds of local minima in real part of the AC impedance Zreal. By adding water to [DEME][BF4] （0 mol% 〈 x 〈 94 mol%） at room temperature, the local minimum value at higher frequency decreased remarkably at the fixed frequency with increasing water concentration. Above 94 mol% H20, a quite different profile of the AC impedance spectroscopy was obtained. In addition to Zreal. temperature dependence of an imaginary part of the impedance Zimag had an isosbestic point below 94 mol%. The isosbestic point disappeared above 94 mol%. The isosbestic point in Zing reveals an interaction between [DEME][BFa] and H2O.
文摘We give an explicit proof of equivalence of the two-point function to one-loop order in the two formalisms of thermal theory based on the expressions in the real-time formalism and indicate that the key point of completing the proof is to separate carefully the imaginary part of the zero-temperature loop integral from relevant expressions and this fact will certainly be very useful for examination of the equivalent problem of two formalisms of thermal field theory in other theories, including the one of the propagators for scalar bound states in an NJL model.
