This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters.The boson-fermion correspondence for these symmetric ...This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters.The boson-fermion correspondence for these symmetric functions have been presented.In virtue of quantum fields,we derive a series of infinite order nonlinear integrable equations,namely,universal character hierarchy,symplectic KP hierarchy and symplectic universal character hierarchy,respectively.In addition,the solutions of these integrable systems have been discussed.展开更多
This work shows that each kind of Chebyshev polynomials may be calculated from a symbolic formula similar to the Lucas formula for Bernoulli polynomials. It exposes also a new approach for obtaining generating functio...This work shows that each kind of Chebyshev polynomials may be calculated from a symbolic formula similar to the Lucas formula for Bernoulli polynomials. It exposes also a new approach for obtaining generating functions of them by operator calculus built from the derivative and the positional operators.展开更多
For the sequences satisfying the recurrence relation of the second order,the generating functions for the products of the powers of these sequences are established.This study was from Carlita and Riordan who began a s...For the sequences satisfying the recurrence relation of the second order,the generating functions for the products of the powers of these sequences are established.This study was from Carlita and Riordan who began a study on closed form of generating functions for powers of second-order recurrence sequences.This investigation was completed by Stnica.Inspired by the recent work of Istva＇n about the non-closed generating functions of the products of the powers of the second-order sequences,the authors give several extensions of Istva＇n＇s results in this paper.展开更多
In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditio...In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.展开更多
In [2-4], symplectic schemes of arbitrary order are constructed by generating functions. However the construction of generating functions is dependent on the chosen coordinates. One would like to know that under what ...In [2-4], symplectic schemes of arbitrary order are constructed by generating functions. However the construction of generating functions is dependent on the chosen coordinates. One would like to know that under what circumstance the construction of generating functions will be independent of the coordinates. The generating functions are deeply associated with the conservation laws, so it is important to study their properties and computations. This paper will begin with the study of Darboux transformation, then in section 2, a normalization Darboux transformation will be defined naturally. Every symplectic scheme which is constructed from Darboux transformation and compatible with the Hamiltonian equation will satisfy this normalization condition. In section 3, we will study transformation properties of generator maps and generating functions. Section 4 will be devoted to the study of the relationship between the invariance of generating functions and the generator maps. In section 5, formal symplectic erengy of symplectic schemes are presented.展开更多
For a nonlinear finite time optimal control problem,a systematic numerical algorithm to solve the Hamilton-Jacobi equation for a generating function is proposed in this paper.This algorithm allows one to obtain the Ta...For a nonlinear finite time optimal control problem,a systematic numerical algorithm to solve the Hamilton-Jacobi equation for a generating function is proposed in this paper.This algorithm allows one to obtain the Taylor series expansion of the generating function up to any prescribed order by solving a sequence of first order ordinary differential equations recursively.Furthermore,the coefficients of the Taylor series expansion of the generating function can be computed exactly under a certain technical condition.Once a generating function is found,it can be used to generate a family of optimal control for different boundary conditions.Since the generating function is computed off-line,the on-demand computational effort for different boundary conditions decreases a lot compared with the conventional method.It is useful to online optimal trajectory generation problems.Numerical examples illustrate the effectiveness of the proposed algorithm.展开更多
Describes the representation of moment generating function for the S-lambda type random variables. Higher order asymptotic formula for generalized Feller operators; Regular n-r order moment for the random variables.
The classical Levy-Meixner polynomials are distinguished through the special forms of their generating functions. In fact, they are completely determined by 4 parameters： c1, c2,γ and β. In this paper, for-1 〈q〈 ...The classical Levy-Meixner polynomials are distinguished through the special forms of their generating functions. In fact, they are completely determined by 4 parameters： c1, c2,γ and β. In this paper, for-1 〈q〈 1, we obtain a unified explicit form of q-deformed Levy-Meixner polynomials and their generating functions in term of c1, c2, γand β, which is shown to be a reasonable interpolation between classical case （q=1） and fermionic case （q=-1）.In particular, when q=0 it＇s also compatible with the free case.展开更多
In this paper, we consider the numerical inversion of a variety of generating functions （GFs） that arise in the area of engineering and non-engineering fields. Three classes of GFs are taken into account in a compre...In this paper, we consider the numerical inversion of a variety of generating functions （GFs） that arise in the area of engineering and non-engineering fields. Three classes of GFs are taken into account in a comprehensive manner： classes of probability generating functions （PGFs） that are given in rational and non-rational forms, and a class of GFs that are not PGFs. Among others, those PGFs that are not explicitly given but contain a number of unknowns are largely considered as they are often encountered in many interesting applied problems. For the numerical inversion of GFs, we use the methods of the discrete （fast） Fourier transform and the Taylor series expansion. Through these methods, we show that it is remarkably easy to obtain the desired sequence to any given accuracy, so long as enough numerical precision is used in computations. Since high precision is readily available in current software packages and programming languages, one can now lift, with little effort, the so-called Laplacian curtain that veils the sequence of interest. To demonstrate, we take a series of representative examples： the PGF of the number of customers in the discrete-time Geo^X/Geo/c queue, the same in the continuous-time M^X/D/c queue, and the GFs arising in the discrete-time renewal process.展开更多
In this paper,we obtain some new results on bilateral generating functions of the modified Laguerre polynomials.We also get generating function relations between the modified Laguerre polynomials and the generalized L...In this paper,we obtain some new results on bilateral generating functions of the modified Laguerre polynomials.We also get generating function relations between the modified Laguerre polynomials and the generalized Lauricella functions.Some special cases and important applications are also discussed.展开更多
The classical phase field model has wide applications for brittle materials,but nonlinearity and inelasticity are found in its stress-strain curve.The degradation function in the classical phase field model makes it a...The classical phase field model has wide applications for brittle materials,but nonlinearity and inelasticity are found in its stress-strain curve.The degradation function in the classical phase field model makes it a linear formulation of phase field and computationally attractive,but stiffness reduction happens even at low strain.In this paper,generalized polynomial degradation functions are investigated to solve this problem.The first derivative of degradation function at zero phase is added as an extra constraint,which renders higher-order polynomial degradation function and nonlinear formulation of phase field.Compared with other degradation functions(like algebraic fraction function,exponential function,and trigonometric function),this polynomial degradation function enables phase in[0,1](should still avoid the first derivative of degradation function at zero phase to be 0),so there is noconvergence problem.The good and meaningful finding is that,under the same fracture strength,the proposed phase field model has a larger length scale,which means larger element size and better computational efficiency.This proposed phase field model is implemented in LS-DYNA user-defined element and user-defined material and solved by the Newton-Raphson method.A tensile test shows that the first derivative of degradation function at zero phase does impact stress-strain curve.Mode I,mode II,and mixed-mode examples show the feasibility of the proposed phase field model in simulating brittle fracture.展开更多
A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fra...A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fractional inequalities involving generalized midpoint type,trapezoid type and Simpson type are derived as consequences.Furthermore,as some applications,special means inequalities and numerical quadratures for local fractional integrals are discussed.展开更多
We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functi...We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functions are derived.Furthermore,we introduce two integrable systems known as the generalized UC(GUC)hierarchy and the generalized Btype UC(GBUC)hierarchy satisfied by the generalized universal character and the generalized B-type universal character,respectively.Based on infinite sequences of complex numbers,we further establish the multiparameter generalized universal character and the multiparameter generalized B-type universal character,which have been proved to be solutions of the GUC hierarchy and the GBUC hierarchy,respectively.展开更多
New renewable energy exploitation technologies in offshore structures are vital for future energy production systems.Offshore hybrid wind-wave power generation(HWWPG)systems face increased component failure rates beca...New renewable energy exploitation technologies in offshore structures are vital for future energy production systems.Offshore hybrid wind-wave power generation(HWWPG)systems face increased component failure rates because of harsh weather,significantly affecting the maintenance procedures and reliability.Different types of failure rates of the wind turbine(WT)and wave energy converter(WEC),e.g.,the degradation and failure rates during regular wind speed fluctuation,the degradation and failure rates during intense wind speed fluctuation are considered.By incorporating both WT and WEC,the HWWPG system is designed to enhance the overall amount of electrical energy produced by the system over a given period under varying weather conditions.The universal generating function technique is used to calculate the HWWPG system dependability measures in a structured and efficient manner.This research highlights that intense weather conditions increase the failure rates of both WT and WEC,resulting in higher maintenance costs and more frequent downtimes,thus impacting the HWWPG system’s reliability.Although the HWWPG system can meet the energy demands in the presence of high failure rates,the reliance of the hybrid system on both WT and WEC helps maintain a relatively stable demand satisfaction during periods of high energy demand despite adverse weather conditions.To confirm the added value and applicability of the developed model,a case study of an offshore hybrid platform is conducted.The findings underscore the system’s robustness in maintaining energy production under varied weather conditions,though higher failure rates and maintenance costs arise in intense scenarios.展开更多
The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicat...The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.展开更多
Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej＋ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f sati...Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej＋ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f satisfies the equation Lf=0,where ……qi 〉0, i =-, 1, - ……, n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in Rn＋1 will be investigated.展开更多
In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel function...In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z（Bκ＋1^c f（z））′= κBκ^c f（z）-（κ- 1）Bκ＋1^c f（z）,where b, c, p ∈ C and κ = p ＋（b ＋ 1）/2 ∈ C ／ Z0^-（Z0^-= {0,-1,-2, … }）. The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out.展开更多
We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m（x）,∞∑n=0sntm/n!m!H2n,2m（x,y）,and ∞∑n=0sntm/n!m!H2n＋l,2m＋k（x,y）.We employ the operator Herm...We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m（x）,∞∑n=0sntm/n!m!H2n,2m（x,y）,and ∞∑n=0sntm/n!m!H2n＋l,2m＋k（x,y）.We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.展开更多
By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials wh...By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.展开更多
By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are prese...By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are presented.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11965014 and 12061051)the National Science Foundation of Qinghai Province,China(Grant No.2021-ZJ-708)。
文摘This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters.The boson-fermion correspondence for these symmetric functions have been presented.In virtue of quantum fields,we derive a series of infinite order nonlinear integrable equations,namely,universal character hierarchy,symplectic KP hierarchy and symplectic universal character hierarchy,respectively.In addition,the solutions of these integrable systems have been discussed.
文摘This work shows that each kind of Chebyshev polynomials may be calculated from a symbolic formula similar to the Lucas formula for Bernoulli polynomials. It exposes also a new approach for obtaining generating functions of them by operator calculus built from the derivative and the positional operators.
基金Project supported by the Shanghai Leading Academic Discipline Project (Grant No.S30104)
文摘For the sequences satisfying the recurrence relation of the second order,the generating functions for the products of the powers of these sequences are established.This study was from Carlita and Riordan who began a study on closed form of generating functions for powers of second-order recurrence sequences.This investigation was completed by Stnica.Inspired by the recent work of Istva＇n about the non-closed generating functions of the products of the powers of the second-order sequences,the authors give several extensions of Istva＇n＇s results in this paper.
基金supported by the National Natural Science Foundation of China(12171373)Chen's work also supported by the Fundamental Research Funds for the Central Universities of China(GK202207018).
文摘In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.
文摘In [2-4], symplectic schemes of arbitrary order are constructed by generating functions. However the construction of generating functions is dependent on the chosen coordinates. One would like to know that under what circumstance the construction of generating functions will be independent of the coordinates. The generating functions are deeply associated with the conservation laws, so it is important to study their properties and computations. This paper will begin with the study of Darboux transformation, then in section 2, a normalization Darboux transformation will be defined naturally. Every symplectic scheme which is constructed from Darboux transformation and compatible with the Hamiltonian equation will satisfy this normalization condition. In section 3, we will study transformation properties of generator maps and generating functions. Section 4 will be devoted to the study of the relationship between the invariance of generating functions and the generator maps. In section 5, formal symplectic erengy of symplectic schemes are presented.
基金supported by“the Fundamental Research Funds for the Central Universities”under Grant No.HIT.NSRIF.201620。
文摘For a nonlinear finite time optimal control problem,a systematic numerical algorithm to solve the Hamilton-Jacobi equation for a generating function is proposed in this paper.This algorithm allows one to obtain the Taylor series expansion of the generating function up to any prescribed order by solving a sequence of first order ordinary differential equations recursively.Furthermore,the coefficients of the Taylor series expansion of the generating function can be computed exactly under a certain technical condition.Once a generating function is found,it can be used to generate a family of optimal control for different boundary conditions.Since the generating function is computed off-line,the on-demand computational effort for different boundary conditions decreases a lot compared with the conventional method.It is useful to online optimal trajectory generation problems.Numerical examples illustrate the effectiveness of the proposed algorithm.
基金the Natural Science Foundation of Hubei Province.
文摘Describes the representation of moment generating function for the S-lambda type random variables. Higher order asymptotic formula for generalized Feller operators; Regular n-r order moment for the random variables.
基金Project Nos.10571065 and 10401011 supported by NSFC
文摘The classical Levy-Meixner polynomials are distinguished through the special forms of their generating functions. In fact, they are completely determined by 4 parameters： c1, c2,γ and β. In this paper, for-1 〈q〈 1, we obtain a unified explicit form of q-deformed Levy-Meixner polynomials and their generating functions in term of c1, c2, γand β, which is shown to be a reasonable interpolation between classical case （q=1） and fermionic case （q=-1）.In particular, when q=0 it＇s also compatible with the free case.
基金support provided by the Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston where he held a Visiting Research Fellowship under NSERC Grant
文摘In this paper, we consider the numerical inversion of a variety of generating functions （GFs） that arise in the area of engineering and non-engineering fields. Three classes of GFs are taken into account in a comprehensive manner： classes of probability generating functions （PGFs） that are given in rational and non-rational forms, and a class of GFs that are not PGFs. Among others, those PGFs that are not explicitly given but contain a number of unknowns are largely considered as they are often encountered in many interesting applied problems. For the numerical inversion of GFs, we use the methods of the discrete （fast） Fourier transform and the Taylor series expansion. Through these methods, we show that it is remarkably easy to obtain the desired sequence to any given accuracy, so long as enough numerical precision is used in computations. Since high precision is readily available in current software packages and programming languages, one can now lift, with little effort, the so-called Laplacian curtain that veils the sequence of interest. To demonstrate, we take a series of representative examples： the PGF of the number of customers in the discrete-time Geo^X/Geo/c queue, the same in the continuous-time M^X/D/c queue, and the GFs arising in the discrete-time renewal process.
文摘In this paper,we obtain some new results on bilateral generating functions of the modified Laguerre polynomials.We also get generating function relations between the modified Laguerre polynomials and the generalized Lauricella functions.Some special cases and important applications are also discussed.
文摘The classical phase field model has wide applications for brittle materials,but nonlinearity and inelasticity are found in its stress-strain curve.The degradation function in the classical phase field model makes it a linear formulation of phase field and computationally attractive,but stiffness reduction happens even at low strain.In this paper,generalized polynomial degradation functions are investigated to solve this problem.The first derivative of degradation function at zero phase is added as an extra constraint,which renders higher-order polynomial degradation function and nonlinear formulation of phase field.Compared with other degradation functions(like algebraic fraction function,exponential function,and trigonometric function),this polynomial degradation function enables phase in[0,1](should still avoid the first derivative of degradation function at zero phase to be 0),so there is noconvergence problem.The good and meaningful finding is that,under the same fracture strength,the proposed phase field model has a larger length scale,which means larger element size and better computational efficiency.This proposed phase field model is implemented in LS-DYNA user-defined element and user-defined material and solved by the Newton-Raphson method.A tensile test shows that the first derivative of degradation function at zero phase does impact stress-strain curve.Mode I,mode II,and mixed-mode examples show the feasibility of the proposed phase field model in simulating brittle fracture.
基金Supported by the National Natural Science Foundation of China(Grant No.11801342)the Natural Science Foundation of Shaanxi Province(Grant No.2023-JC-YB-043).
文摘A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fractional inequalities involving generalized midpoint type,trapezoid type and Simpson type are derived as consequences.Furthermore,as some applications,special means inequalities and numerical quadratures for local fractional integrals are discussed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12461048 and 12061051)the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant No.2023MS01003)+2 种基金the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(Grant No.NJYT23096)the financial support from the Program of China Scholarships Council(Grant No.202306810054)for one year study at the University of Leedsthe support of Professor Ke Wu and Professor Weizhong Zhao at Capital Normal University,China。
文摘We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functions are derived.Furthermore,we introduce two integrable systems known as the generalized UC(GUC)hierarchy and the generalized Btype UC(GBUC)hierarchy satisfied by the generalized universal character and the generalized B-type universal character,respectively.Based on infinite sequences of complex numbers,we further establish the multiparameter generalized universal character and the multiparameter generalized B-type universal character,which have been proved to be solutions of the GUC hierarchy and the GBUC hierarchy,respectively.
文摘New renewable energy exploitation technologies in offshore structures are vital for future energy production systems.Offshore hybrid wind-wave power generation(HWWPG)systems face increased component failure rates because of harsh weather,significantly affecting the maintenance procedures and reliability.Different types of failure rates of the wind turbine(WT)and wave energy converter(WEC),e.g.,the degradation and failure rates during regular wind speed fluctuation,the degradation and failure rates during intense wind speed fluctuation are considered.By incorporating both WT and WEC,the HWWPG system is designed to enhance the overall amount of electrical energy produced by the system over a given period under varying weather conditions.The universal generating function technique is used to calculate the HWWPG system dependability measures in a structured and efficient manner.This research highlights that intense weather conditions increase the failure rates of both WT and WEC,resulting in higher maintenance costs and more frequent downtimes,thus impacting the HWWPG system’s reliability.Although the HWWPG system can meet the energy demands in the presence of high failure rates,the reliance of the hybrid system on both WT and WEC helps maintain a relatively stable demand satisfaction during periods of high energy demand despite adverse weather conditions.To confirm the added value and applicability of the developed model,a case study of an offshore hybrid platform is conducted.The findings underscore the system’s robustness in maintaining energy production under varied weather conditions,though higher failure rates and maintenance costs arise in intense scenarios.
文摘The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.
基金supported by NNSF of China (11171260)RFDP of Higher Education of China (20100141110054)Scientific Research Fund of Leshan Normal University (Z1265)
文摘Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej＋ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f satisfies the equation Lf=0,where ……qi 〉0, i =-, 1, - ……, n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in Rn＋1 will be investigated.
基金partly supported by the Natural Science Foundation of China(11271045)the Higher School Doctoral Foundation of China(20100003110004)+2 种基金the Natural Science Foundation of Inner Mongolia of China(2010MS0117)athe Higher School Foundation of Inner Mongolia of China(NJZY13298)the Commission for the Scientific Research Projects of Kafkas Univertsity(2012-FEF-30)
文摘In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z（Bκ＋1^c f（z））′= κBκ^c f（z）-（κ- 1）Bκ＋1^c f（z）,where b, c, p ∈ C and κ = p ＋（b ＋ 1）/2 ∈ C ／ Z0^-（Z0^-= {0,-1,-2, … }）. The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out.
基金Project supported by the National Natural Science Foundation of China(Grnat No.11175113)the Fundamental Research Funds for the Central Universities of China(Grant No.WK2060140013)
文摘We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m（x）,∞∑n=0sntm/n!m!H2n,2m（x,y）,and ∞∑n=0sntm/n!m!H2n＋l,2m＋k（x,y）.We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.
基金supported by the National Natural Science Foundation of China(Grant No.11175113)the Fundamental Research Funds for the Central Universities of China(Grant No.WK2060140013)
文摘By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.
基金supported by the National Natural Science Foundation of China(Grant No.11175113)the Fundamental Research Funds for the Central Universities of China(Grant No.WK2060140013)the Natural Science Foundation of Jiangsu Higher Education Institution of China(Grant No.14KJD140001)
文摘By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are presented.
