The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson'...The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.展开更多
We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt d...We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.展开更多
For an entire function represented by a generalized dirichlet series, we define its maximal term, maximal modulus, order and type. We use the classical methods to study the relation between order, type and coeFFIcient...For an entire function represented by a generalized dirichlet series, we define its maximal term, maximal modulus, order and type. We use the classical methods to study the relation between order, type and coeFFIcients, exponents, which improve and generalize some results of the dirichlet series with real exponents.展开更多
For the structure system with epistemic and aleatory uncertainties,a new state dependent parameter(SDP) based method is presented for obtaining the importance measures of the epistemic uncertainties.By use of the marg...For the structure system with epistemic and aleatory uncertainties,a new state dependent parameter(SDP) based method is presented for obtaining the importance measures of the epistemic uncertainties.By use of the marginal probability density function(PDF) of the epistemic variable and the conditional PDF of the aleatory one at the fixed epistemic variable,the epistemic and aleatory uncertainties are propagated to the response of the structure firstly in the presented method.And the computational model for calculating the importance measures of the epistemic variables is established.For solving the computational model,the high efficient SDP method is applied to estimating the first order high dimensional model representation(HDMR) to obtain the importance measures.Compared with the direct Monte Carlo method,the presented method can considerably improve computational efficiency with acceptable precision.The presented method has wider applicability compared with the existing approximation method,because it is suitable not only for the linear response functions,but also for nonlinear response functions.Several examples are used to demonstrate the advantages of the presented method.展开更多
文摘The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.
文摘We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.
基金the Natural Science Youth Foundation of Jiangxi Province (No.2007GQS0159)Research Plan Program of Education Bureau of Jiangxi Province (Nos.GJJ08161 GJJ09463)
文摘For an entire function represented by a generalized dirichlet series, we define its maximal term, maximal modulus, order and type. We use the classical methods to study the relation between order, type and coeFFIcients, exponents, which improve and generalize some results of the dirichlet series with real exponents.
基金supported by the National Natural Science Foundation of China (Grant No. 51175425)the Aviation Science Foundation (Grant No.2011ZA53015)the Doctorate Foundation of Northwestern Polytechnical University (Grant No. CX201205)
文摘For the structure system with epistemic and aleatory uncertainties,a new state dependent parameter(SDP) based method is presented for obtaining the importance measures of the epistemic uncertainties.By use of the marginal probability density function(PDF) of the epistemic variable and the conditional PDF of the aleatory one at the fixed epistemic variable,the epistemic and aleatory uncertainties are propagated to the response of the structure firstly in the presented method.And the computational model for calculating the importance measures of the epistemic variables is established.For solving the computational model,the high efficient SDP method is applied to estimating the first order high dimensional model representation(HDMR) to obtain the importance measures.Compared with the direct Monte Carlo method,the presented method can considerably improve computational efficiency with acceptable precision.The presented method has wider applicability compared with the existing approximation method,because it is suitable not only for the linear response functions,but also for nonlinear response functions.Several examples are used to demonstrate the advantages of the presented method.
