In this paper by virtue of the technique of integration within an ordered product （IWOP） of operators and the intermediate coordinate-momentum representation in quantum optics, we derive the normal ordering and anti...In this paper by virtue of the technique of integration within an ordered product （IWOP） of operators and the intermediate coordinate-momentum representation in quantum optics, we derive the normal ordering and antinormal ordering products of the operator （fQ＋gP）n when n is an arbitrary integer. These products are very useful in calculating their matrix elements and expectation values and obtaining some useful mathematical formulae. Finally, the applications of some new identities are given.展开更多
For Hermite polynomials of radial coordinate operator in three-dimensional coordinate space we derive its normal ordering expansion, which are new operator identities. This is done by virtue of the technique of integr...For Hermite polynomials of radial coordinate operator in three-dimensional coordinate space we derive its normal ordering expansion, which are new operator identities. This is done by virtue of the technique of integration within an ordered product of operators. Application of the new formulas is briefly discussed.展开更多
Generally, open string boundary conditions play a nontrivial role in string theory. For example, in the presence of an antisymmetric tensor background field, they will lead the spacetime coordinates noncommutative. In...Generally, open string boundary conditions play a nontrivial role in string theory. For example, in the presence of an antisymmetric tensor background field, they will lead the spacetime coordinates noncommutative. In this paper, we mainly discuss how to build up a generalized Dirichlet normal ordered product of open bosonic string embedding operators that satisfies both the equations of motion and the generalized Dirichlet boundary conditions at the quantum level in the presence of an antisymmetric background field, as the generalized Neumann case has already been discussed in the literature. Further, we also give a brief check of the consistency of the theory under the newly introduced normal ordering.展开更多
By virtue of the coherent state representation and the operator ordering method we find a new approach for transiting Hermite polynomials to Laguerre polynomials. We also derive the new reciprocal relation of Laguerre...By virtue of the coherent state representation and the operator ordering method we find a new approach for transiting Hermite polynomials to Laguerre polynomials. We also derive the new reciprocal relation of Laguerre polynomials ∑n=0 （-1）n （n^l）Ln （x） = x^l/n, n-O and its application in deriving the sum rule of the Wingner function of Fock states is demonstrated. Some new expansion identities about the operator Laguerre polynomial are also derived. This opens a new route of deriving mathematical polynomials formulas by virtute of the quantum mechanical representations and operator ordering technique.展开更多
By virtue of the technique of integration within an ordered product of operators we present a new approach to obtain operators' normal ordering. We first put operators into their Weyl ordering through the Weyl-Wig...By virtue of the technique of integration within an ordered product of operators we present a new approach to obtain operators' normal ordering. We first put operators into their Weyl ordering through the Weyl-Wigner quantization scheme, and then we convert the Weyl ordered operators into normal ordering by virtue of the normally ordered form of the Wigner operator.展开更多
We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by u...We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.展开更多
Using the normally ordered Gaussian form of the Wigner operator we recapitulate the quantum phase space representation, we derive a new formula for searching for the classical correspondence of quantum mechanical oper...Using the normally ordered Gaussian form of the Wigner operator we recapitulate the quantum phase space representation, we derive a new formula for searching for the classical correspondence of quantum mechanical operators; we also show that if there exists the eigenvector ｜q〉λ,v of linear combination of the coordinate and momentum operator, （λQ ＋ vP）, where λ,v are real numbers, and ｜q〉λv is complete, then the projector ｜q〉λ,vλ,v〈q｜ must be the Radon transform of Wigner operator. This approach seems concise and physical appealing.展开更多
Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical...Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical system with nilpotent linear part and Z(2)-asymmetry are computed. According to normal forms obtained, universal unfoldings for some degenerate bifurcation cases of codimension 3 and simple global characterizations, are studied.展开更多
In this paper, we establish the stochastic ordering of median from an exchangeable trivaxiate normal vector based on the strength of the correlation coefficient. Specifically, by considering two exchangeable trivariat...In this paper, we establish the stochastic ordering of median from an exchangeable trivaxiate normal vector based on the strength of the correlation coefficient. Specifically, by considering two exchangeable trivariate normal vectors with different correlation coefficients, we show that the absolute value of the median in the vector with smaller correlation coefficient is stochastically smaller than the absolute value of the median in the vector with larger correlation coefficient. We prove this result by utilizing skew-normal distributions.展开更多
In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original...In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original scale. We obtain two estimators which minimize the asymptotic mean squared error （MM） and the asymptotic bias （MB）, respectively. Both the estimators are very easy to implement, and simulation studies show that they are perform better.展开更多
In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalize...In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.展开更多
Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
In this article, the higher order asymptotic expansions of cumulative distribution function and probability density function of extremes for generalized Maxwell distribution are established under nonlinear normalizati...In this article, the higher order asymptotic expansions of cumulative distribution function and probability density function of extremes for generalized Maxwell distribution are established under nonlinear normalization. As corollaries, the convergence rates of the distribu- tion and density of maximum are obtained under nonlinear normalization.展开更多
智能软开关(soft normally open point, SNOP)凭借其灵活的功率调节能力逐渐应用于配电网中。但由于大量分布式电源(distributed generation, DG)接入,SNOP受到线路容量的限制,调节能力有限。为发挥其最大调节能力,文中提出适用于配电...智能软开关(soft normally open point, SNOP)凭借其灵活的功率调节能力逐渐应用于配电网中。但由于大量分布式电源(distributed generation, DG)接入,SNOP受到线路容量的限制,调节能力有限。为发挥其最大调节能力,文中提出适用于配电系统的SNOP对线路有功功率裕度调节灵敏度的定义,将其作为SNOP调节能力的评价指标,由此建立SNOP的选址优化模型。在此基础上,引入系统节点电压裕度以及线路功率裕度2个安全评价指标,构建以综合运行裕度最大为目标函数的配电网运行优化模型。将上述模型转化为二阶锥模型,通过MATLAB工具实现该问题的有效求解。最后,通过改进的IEEE 33节点算例对所提模型与求解方法进行验证,进一步表明了所提选址方法能够发挥SNOP的最大调节作用,优化控制策略可以实现配电网安全经济运行。展开更多
By using the parameter differential method of operators,we recast the combination function of coordinate and momentum operators into its normal and anti-normal orderings,which is more ecumenical,simpler,and neater tha...By using the parameter differential method of operators,we recast the combination function of coordinate and momentum operators into its normal and anti-normal orderings,which is more ecumenical,simpler,and neater than the existing ways.These products are very useful in obtaining some new differential relations and useful mathematical integral formulas.Further,we derive the normally ordered form of the operator(fQ+gP)^-n with n being an arbitrary positive integer by using the parameter tracing method of operators together with the intermediate coordinate-momentum representation.In addition,general mutual transformation rules of the normal and anti-normal orderings,which have good universality,are derived and hence the anti-normal ordering of(fQ+gP)^-n is also obtained.Finally,the application of some new identities is given.展开更多
该文研究了具有正二阶色散系数的四阶薛定谔方程的归一化解的存在性和渐近性.在质量超临界情形,通过引入两类局部极小化问题并且证明其等价,回避了局部化限制半径对质量的依赖性,证明了相应极小化序列的紧性,得到了方程基态解的存在性....该文研究了具有正二阶色散系数的四阶薛定谔方程的归一化解的存在性和渐近性.在质量超临界情形,通过引入两类局部极小化问题并且证明其等价,回避了局部化限制半径对质量的依赖性,证明了相应极小化序列的紧性,得到了方程基态解的存在性.进一步,借助细致的能量估计和分析,也给出了基态解和拉格朗日乘子在参数趋近于零时的渐近性质.该文去掉了文献[7](Sci China Math,2023,66:1237-1262)中的径向对称性条件,给出了比文献[8](J Differential Equations,2022,330:1-65)更简洁的证明方法.展开更多
针对高等数学课程的教学评价问题,提出了一种基于投影测度和优劣解距离法(Technique for Order Perfomance by Similarity to Ideal Solution,TOPSIS)技术的多属性决策模型。给出一种新的标准化投影测度,以度量含实数与区间的含混向量...针对高等数学课程的教学评价问题,提出了一种基于投影测度和优劣解距离法(Technique for Order Perfomance by Similarity to Ideal Solution,TOPSIS)技术的多属性决策模型。给出一种新的标准化投影测度,以度量含实数与区间的含混向量的接近程度;将标准化投影测度融入TOPSIS方法中,建立了一种改进的TOPSIS模型;将其应用于高等数学课程的教学评价实践,并通过与其他模型对比,验证了模型的可行性与有效性。展开更多
In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almos...In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in Cn is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings.展开更多
基金Project supported by the Natural Science Foundation of Shandong Province of China (Grant No Y2008A23)the Natural Science Foundation of Liaocheng University (Grant No X071049)
文摘In this paper by virtue of the technique of integration within an ordered product （IWOP） of operators and the intermediate coordinate-momentum representation in quantum optics, we derive the normal ordering and antinormal ordering products of the operator （fQ＋gP）n when n is an arbitrary integer. These products are very useful in calculating their matrix elements and expectation values and obtaining some useful mathematical formulae. Finally, the applications of some new identities are given.
基金The project supported by the President Foundation of the Chinese Academy of Sciences
文摘For Hermite polynomials of radial coordinate operator in three-dimensional coordinate space we derive its normal ordering expansion, which are new operator identities. This is done by virtue of the technique of integration within an ordered product of operators. Application of the new formulas is briefly discussed.
基金supported by National Natural Science Foundation and the Doctor Education Fund of the Ministry of Education
文摘Generally, open string boundary conditions play a nontrivial role in string theory. For example, in the presence of an antisymmetric tensor background field, they will lead the spacetime coordinates noncommutative. In this paper, we mainly discuss how to build up a generalized Dirichlet normal ordered product of open bosonic string embedding operators that satisfies both the equations of motion and the generalized Dirichlet boundary conditions at the quantum level in the presence of an antisymmetric background field, as the generalized Neumann case has already been discussed in the literature. Further, we also give a brief check of the consistency of the theory under the newly introduced normal ordering.
基金supported by the National Natural Science Foundation of China (Grant No. 10874174)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20070358009)
文摘By virtue of the coherent state representation and the operator ordering method we find a new approach for transiting Hermite polynomials to Laguerre polynomials. We also derive the new reciprocal relation of Laguerre polynomials ∑n=0 （-1）n （n^l）Ln （x） = x^l/n, n-O and its application in deriving the sum rule of the Wingner function of Fock states is demonstrated. Some new expansion identities about the operator Laguerre polynomial are also derived. This opens a new route of deriving mathematical polynomials formulas by virtute of the quantum mechanical representations and operator ordering technique.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10947017/A05)the Specialized Research Fund for the Doctorial Progress of Higher Education of China (GrantNo. 20070358009)
文摘By virtue of the technique of integration within an ordered product of operators we present a new approach to obtain operators' normal ordering. We first put operators into their Weyl ordering through the Weyl-Wigner quantization scheme, and then we convert the Weyl ordered operators into normal ordering by virtue of the normally ordered form of the Wigner operator.
基金The project supported by the President Foundation of the Chinese Academy of Sciences and National Natural Science Foundation of China under Grant No. 10475056.
文摘We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10874174 and 10775097
文摘Using the normally ordered Gaussian form of the Wigner operator we recapitulate the quantum phase space representation, we derive a new formula for searching for the classical correspondence of quantum mechanical operators; we also show that if there exists the eigenvector ｜q〉λ,v of linear combination of the coordinate and momentum operator, （λQ ＋ vP）, where λ,v are real numbers, and ｜q〉λv is complete, then the projector ｜q〉λ,vλ,v〈q｜ must be the Radon transform of Wigner operator. This approach seems concise and physical appealing.
文摘Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical system with nilpotent linear part and Z(2)-asymmetry are computed. According to normal forms obtained, universal unfoldings for some degenerate bifurcation cases of codimension 3 and simple global characterizations, are studied.
文摘In this paper, we establish the stochastic ordering of median from an exchangeable trivaxiate normal vector based on the strength of the correlation coefficient. Specifically, by considering two exchangeable trivariate normal vectors with different correlation coefficients, we show that the absolute value of the median in the vector with smaller correlation coefficient is stochastically smaller than the absolute value of the median in the vector with larger correlation coefficient. We prove this result by utilizing skew-normal distributions.
基金The NSF(11271155) of ChinaResearch Fund(20070183023) for the Doctoral Program of Higher Education
文摘In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original scale. We obtain two estimators which minimize the asymptotic mean squared error （MM） and the asymptotic bias （MB）, respectively. Both the estimators are very easy to implement, and simulation studies show that they are perform better.
基金This work was supported by National Natural Science Foundation of China(No.60710002)Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT).
文摘In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.
文摘Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
基金Supported by the Natural Science Foundation of China(61673015,61273020)the Fundamental Research Funds for the Central Universities(XDJK2015A007,SWU1809002)+3 种基金the Science Computing and Intelligent Information Processing of Guangxi Higher Education Key Laboratory(GXSCIIP201702)the Science and Technology Plan Project of Guizhou Province(LH[2015]7053,LH[2015]7055)Science and Technology Foundation of Guizhou Province(Qian Ke He Ji Chu[2016]1161)Guizhou Province Natural Science Foundation in China(Qian Jiao He KY[2016]255)
文摘In this article, the higher order asymptotic expansions of cumulative distribution function and probability density function of extremes for generalized Maxwell distribution are established under nonlinear normalization. As corollaries, the convergence rates of the distribu- tion and density of maximum are obtained under nonlinear normalization.
文摘智能软开关(soft normally open point, SNOP)凭借其灵活的功率调节能力逐渐应用于配电网中。但由于大量分布式电源(distributed generation, DG)接入,SNOP受到线路容量的限制,调节能力有限。为发挥其最大调节能力,文中提出适用于配电系统的SNOP对线路有功功率裕度调节灵敏度的定义,将其作为SNOP调节能力的评价指标,由此建立SNOP的选址优化模型。在此基础上,引入系统节点电压裕度以及线路功率裕度2个安全评价指标,构建以综合运行裕度最大为目标函数的配电网运行优化模型。将上述模型转化为二阶锥模型,通过MATLAB工具实现该问题的有效求解。最后,通过改进的IEEE 33节点算例对所提模型与求解方法进行验证,进一步表明了所提选址方法能够发挥SNOP的最大调节作用,优化控制策略可以实现配电网安全经济运行。
基金Project supported by the National Natural Science Foundation of China(Grant No.11347026)the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2016AM03 and ZR2017MA011)the Natural Science Foundation of Heze University,China(Grant Nos.XY17KJ09 and XY18PY13).
文摘By using the parameter differential method of operators,we recast the combination function of coordinate and momentum operators into its normal and anti-normal orderings,which is more ecumenical,simpler,and neater than the existing ways.These products are very useful in obtaining some new differential relations and useful mathematical integral formulas.Further,we derive the normally ordered form of the operator(fQ+gP)^-n with n being an arbitrary positive integer by using the parameter tracing method of operators together with the intermediate coordinate-momentum representation.In addition,general mutual transformation rules of the normal and anti-normal orderings,which have good universality,are derived and hence the anti-normal ordering of(fQ+gP)^-n is also obtained.Finally,the application of some new identities is given.
文摘该文研究了具有正二阶色散系数的四阶薛定谔方程的归一化解的存在性和渐近性.在质量超临界情形,通过引入两类局部极小化问题并且证明其等价,回避了局部化限制半径对质量的依赖性,证明了相应极小化序列的紧性,得到了方程基态解的存在性.进一步,借助细致的能量估计和分析,也给出了基态解和拉格朗日乘子在参数趋近于零时的渐近性质.该文去掉了文献[7](Sci China Math,2023,66:1237-1262)中的径向对称性条件,给出了比文献[8](J Differential Equations,2022,330:1-65)更简洁的证明方法.
文摘针对高等数学课程的教学评价问题,提出了一种基于投影测度和优劣解距离法(Technique for Order Perfomance by Similarity to Ideal Solution,TOPSIS)技术的多属性决策模型。给出一种新的标准化投影测度,以度量含实数与区间的含混向量的接近程度;将标准化投影测度融入TOPSIS方法中,建立了一种改进的TOPSIS模型;将其应用于高等数学课程的教学评价实践,并通过与其他模型对比,验证了模型的可行性与有效性。
基金The research was supported by the National Nat ural Science Foundation of China(10571164)Specialized Research Fund for the Doctoral Program of Higher Education(20050358052)+1 种基金Guangdong Natural Science Foundation(06301315)the Doctoral Foundation of Zhanjiang Normal University(Z0420)
文摘In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in Cn is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings.
