This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, d...This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, distributional chaotic of type k ( k∈{ 1,2,2 1 2 ,3 } ), and ( 0,1 ) -distribution.展开更多
The Jaynes-Cummings model is solved with the raising and lowering(shift) operators using the matrix-diagonalizing technique. Bell nonlocality is also found to be present ubiquitously in the excitation states of the ...The Jaynes-Cummings model is solved with the raising and lowering(shift) operators using the matrix-diagonalizing technique. Bell nonlocality is also found to be present ubiquitously in the excitation states of the model.展开更多
In this paper, we establish sufficient conditions on weights which ensurethat high-order Riesz-Bessel transformations generated by the generalized shift operator actboundedly from one weighted L_p-space into another.
The reseearch on the relation between weighted shift operators on Hilbert spaces and other important class of operators attracted the attention of some mathematicians. For example, the relation between weighted shift ...The reseearch on the relation between weighted shift operators on Hilbert spaces and other important class of operators attracted the attention of some mathematicians. For example, the relation between weighted shift operators and subnormal operators has been thoroughly studied by J. Stampfli, R. Gellar and D. A. Herrero, etc. (see reference [1]) But the decomposability of weighted shift operators has not yet attracted enough attention up to now. We made initial research展开更多
Based on the rotation transformation in phase space and the technique of integration within an ordered product of operators, the coherent state representation of the multimode phase shifting operator and one of its ne...Based on the rotation transformation in phase space and the technique of integration within an ordered product of operators, the coherent state representation of the multimode phase shifting operator and one of its new applications in quantum mechanics are given. It is proved that the coherent state is a natural language for describing the phase shifting operator or multimode phase shifting operator. The multimode phase shifting operator is also a useful tool to solve the dynamic problems of the mnltimode coordinate-momentum coupled harmonic oscillators. The exact energy spectra and eigenstates of such multimode coupled harmonic oscillators can be easily obtained by using the rnultimode phase shifting operator.展开更多
In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we prop...In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources.展开更多
In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holde...In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.展开更多
In this paper. we stady the nonwandering operator, which is a linear operator with chaos character and is in intnite dimensionol linear space. We give the hypercyclic bacomposition on the compact set of nonwandering o...In this paper. we stady the nonwandering operator, which is a linear operator with chaos character and is in intnite dimensionol linear space. We give the hypercyclic bacomposition on the compact set of nonwandering operators.展开更多
A necessary and sufficient condition for the generalized shift operator T = S-k - (a(1)((1)), a(2)((1)),...) x e(1) - ... -(a(1)((j)), a(2)((j)),...) x e(j) (j greater than or equal to k) on l(1) to be power bounded i...A necessary and sufficient condition for the generalized shift operator T = S-k - (a(1)((1)), a(2)((1)),...) x e(1) - ... -(a(1)((j)), a(2)((j)),...) x e(j) (j greater than or equal to k) on l(1) to be power bounded is obtained. Moreover,this note points out that the power bounded operator T = S - (1, 1,...) x c(1) can shift a basis of [e(j+1) - e(j)](j = 1)(infinity), and this basis is not equivalent to {T(n)e(1)} (infinity)(n=0).展开更多
This paper proceeds the papers [3] [4], we make use of the idea of the variable ,number operators and some concepts and conclusions of the shifting operators serieswith variable coefficients in the operational field o...This paper proceeds the papers [3] [4], we make use of the idea of the variable ,number operators and some concepts and conclusions of the shifting operators serieswith variable coefficients in the operational field of Mikusinski, it is devoted to thesolution of the general three-order linear difference equation with variable,coefficients,and it is also devoted to the better solution .formula for the some special three-orderlinear difference equations with variable coefficients, in addition, we try to provide theidea and method for realizing solution of the more than three-order linear differenceequation with variable coefficients.展开更多
In order to improve the efficiency of gear shifter testing,a kind of shift robot with a special pas-sive joint is proposed to complete the human-like shifting operation automatically.The shift robot is mainly composed...In order to improve the efficiency of gear shifter testing,a kind of shift robot with a special pas-sive joint is proposed to complete the human-like shifting operation automatically.The shift robot is mainly composed of two prismatic pairs,a cylindrical pair and a passive joint.The two prismatic pairs act as actuators of the mechanism to complete a part of the shifting operation,and then the shift lever can be pulled into the accurate gear position by the shift torque of the gear shifter.However,the shifting lever may skip the target gear position into the next gear position.In order to solve the gear-skip phenomenon,a limit block is applied to the passive joint.Then,the shifting processes are simulated through the dynamic model of the shift robot.The optimal position of the limit block is de-termined based on its dynamic characteristics.展开更多
The transmission coefficients of electromagnetic (EM) waves due to a superconductor-dielectric superlattice are numerically calculated. Shift operator finite difference time domain (SO-FDTD) method is used in the ...The transmission coefficients of electromagnetic (EM) waves due to a superconductor-dielectric superlattice are numerically calculated. Shift operator finite difference time domain (SO-FDTD) method is used in the analysis. By using the SO-FDTD method, the transmission spectrum is obtained and its characteristics are investigated for different thicknesses of superconductor layers and dielectric layers, from which a stop band starting from zero frequency can be apparently observed. The relation between this low-frequency stop band and relative temperature, and also the London penetration depth at a superconductor temperature of zero degree are discussed, separately. The low-frequency stop band properties of superconductor-dielectric superlattice thus are well disclosed.展开更多
For an operator weighted shift S,the essential spectrum σ_e(S) and the indices associated with holes in σ_e(S) are described.Moreover,Banach reducibility of S is investigated and a condition for S~* to be a Cowen-Do...For an operator weighted shift S,the essential spectrum σ_e(S) and the indices associated with holes in σ_e(S) are described.Moreover,Banach reducibility of S is investigated and a condition for S~* to be a Cowen-Douglas operator is characterized.展开更多
Abstract Let H be a complex seperable Hilbert space and ^(Jt^) denote the collection of bounded linear operators on H. For an operator in L(H), rad{A}' denotes the Jacobson radical of the commutant of A. This pap...Abstract Let H be a complex seperable Hilbert space and ^(Jt^) denote the collection of bounded linear operators on H. For an operator in L(H), rad{A}' denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}'/rad{A}'. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant is commutative.展开更多
In this paper, we investigate the value distribution of the difference counterpart △f(z)- af(z)^n of f′(z)- af(z)^n and obtain an almost direct difference analogue of result of Hayman.
High order discretization schemes playmore important role in fractional operators than classical ones.This is because usually for classical derivatives the stencil for high order discretization schemes is wider than l...High order discretization schemes playmore important role in fractional operators than classical ones.This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones;but for fractional operators the stencils for high order schemes and low order ones are the same.Then using high order schemes to solve fractional equations leads to almost the same computational cost with first order schemes but the accuracy is greatly improved.Using the fractional linear multistep methods,Lubich obtains the n-th order(n≤6)approximations of the a-th derivative(a>0)or integral(a<0)[Lubich,SIAM J.Math.Anal.,17,704-719,1986],because of the stability issue the obtained scheme can not be directly applied to the space fractional operator with a∈(1,2)for time dependent problem.By weighting and shifting Lubich’s 2nd order discretization scheme,in[Chen&Deng,SINUM,arXiv:1304.7425]we derive a series of effective high order discretizations for space fractional derivative,called WSLD operators there.As the sequel of the previous work,we further provide new high order schemes for space fractional derivatives by weighting and shifting Lubich’s 3rd and 4th order discretizations.In particular,we prove that the obtained 4th order approximations are effective for space fractional derivatives.And the corresponding schemes are used to solve the space fractional diffusion equation with variable coefficients.展开更多
This paper focuses on the finite dimensional irreducible representations of Lie superalgebra D(2,1;α).We explicitly construct the finite dimensional representations of the superalgebra D(2,1;α)by using the shift ope...This paper focuses on the finite dimensional irreducible representations of Lie superalgebra D(2,1;α).We explicitly construct the finite dimensional representations of the superalgebra D(2,1;α)by using the shift operator and differential operator representations.Unlike ordinary Lie algebra representation,there are typical and atypical representations for most superalgebras.Therefore,its typical and atypical representation conditions are also given.Our results are expected to be useful for the construction of primary fields of the corresponding current superalgebra of D(2,1;α).展开更多
Let f(z)beanon-constantmeromorphicfunctionoffiniteorder,c∈C\{0}andk∈N.Suppose f(z)and f(k)(z+c)share1CM(IM),f(z)and f(z+c)share∞CM.If N(r,0;f)=S(r,f)(N(r,0;f(z))+N(r,0;f(k)(z+c))=S(r,f)),then either f(z)≡f(k)(z+c)...Let f(z)beanon-constantmeromorphicfunctionoffiniteorder,c∈C\{0}andk∈N.Suppose f(z)and f(k)(z+c)share1CM(IM),f(z)and f(z+c)share∞CM.If N(r,0;f)=S(r,f)(N(r,0;f(z))+N(r,0;f(k)(z+c))=S(r,f)),then either f(z)≡f(k)(z+c)or f(z)is a solution of the following equation:f((z+c)−1=a(z)(f(z)−1))f(z)+1 a(z)),and N(r,0;f(z)+1 a(z))=S(r,f)(f′(z+c)−1=a(z)(f(z)−1)(f(z)+1 a(z)))where a(z)(≡−1,0,∞)(a(z)(≡0,∞))is a meromorphic function satisfying T(r,a)=S(r,f).Also we exhibit some examples to show that the conditions of our results are the best possible.展开更多
We work with the abstract K and J interpolation method generated by a sequence lattice Г. We investigate the deviation of an interpolated operator from a given operator ideal by establishing formulae for the ideal me...We work with the abstract K and J interpolation method generated by a sequence lattice Г. We investigate the deviation of an interpolated operator from a given operator ideal by establishing formulae for the ideal measure of the interpolated operator in terms of the ideal measures of restrictions of the operator. Formulae are given in terms of the norms of the shift operators on Г.展开更多
文摘This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, distributional chaotic of type k ( k∈{ 1,2,2 1 2 ,3 } ), and ( 0,1 ) -distribution.
基金Supported by the National Natural Science Foundations of China under Grant Nos 11475089,11675119 and 11575125
文摘The Jaynes-Cummings model is solved with the raising and lowering(shift) operators using the matrix-diagonalizing technique. Bell nonlocality is also found to be present ubiquitously in the excitation states of the model.
文摘In this paper, we establish sufficient conditions on weights which ensurethat high-order Riesz-Bessel transformations generated by the generalized shift operator actboundedly from one weighted L_p-space into another.
文摘The reseearch on the relation between weighted shift operators on Hilbert spaces and other important class of operators attracted the attention of some mathematicians. For example, the relation between weighted shift operators and subnormal operators has been thoroughly studied by J. Stampfli, R. Gellar and D. A. Herrero, etc. (see reference [1]) But the decomposability of weighted shift operators has not yet attracted enough attention up to now. We made initial research
基金Project supported by the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A16)the Natural Science Foundation of Heze University of Shandong Province, China (Grant No. XY09WL01)
文摘Based on the rotation transformation in phase space and the technique of integration within an ordered product of operators, the coherent state representation of the multimode phase shifting operator and one of its new applications in quantum mechanics are given. It is proved that the coherent state is a natural language for describing the phase shifting operator or multimode phase shifting operator. The multimode phase shifting operator is also a useful tool to solve the dynamic problems of the mnltimode coordinate-momentum coupled harmonic oscillators. The exact energy spectra and eigenstates of such multimode coupled harmonic oscillators can be easily obtained by using the rnultimode phase shifting operator.
文摘In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources.
文摘In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.
文摘In this paper. we stady the nonwandering operator, which is a linear operator with chaos character and is in intnite dimensionol linear space. We give the hypercyclic bacomposition on the compact set of nonwandering operators.
基金the Education DepartmentFoundation of Henan province.
文摘A necessary and sufficient condition for the generalized shift operator T = S-k - (a(1)((1)), a(2)((1)),...) x e(1) - ... -(a(1)((j)), a(2)((j)),...) x e(j) (j greater than or equal to k) on l(1) to be power bounded is obtained. Moreover,this note points out that the power bounded operator T = S - (1, 1,...) x c(1) can shift a basis of [e(j+1) - e(j)](j = 1)(infinity), and this basis is not equivalent to {T(n)e(1)} (infinity)(n=0).
文摘This paper proceeds the papers [3] [4], we make use of the idea of the variable ,number operators and some concepts and conclusions of the shifting operators serieswith variable coefficients in the operational field of Mikusinski, it is devoted to thesolution of the general three-order linear difference equation with variable,coefficients,and it is also devoted to the better solution .formula for the some special three-orderlinear difference equations with variable coefficients, in addition, we try to provide theidea and method for realizing solution of the more than three-order linear differenceequation with variable coefficients.
基金Supported by the National Natural Science Foundation of China(No.51975008)the Beijing Municipal Natural Science Foundation(No.3192002).
文摘In order to improve the efficiency of gear shifter testing,a kind of shift robot with a special pas-sive joint is proposed to complete the human-like shifting operation automatically.The shift robot is mainly composed of two prismatic pairs,a cylindrical pair and a passive joint.The two prismatic pairs act as actuators of the mechanism to complete a part of the shifting operation,and then the shift lever can be pulled into the accurate gear position by the shift torque of the gear shifter.However,the shifting lever may skip the target gear position into the next gear position.In order to solve the gear-skip phenomenon,a limit block is applied to the passive joint.Then,the shifting processes are simulated through the dynamic model of the shift robot.The optimal position of the limit block is de-termined based on its dynamic characteristics.
基金Project supported partly by the Open Research Program in State Key Laboratory of Millimeter Waves of China(Grant No.K200802)partly by the National Natural Science Foundation of China(Grant No.60971122)
文摘The transmission coefficients of electromagnetic (EM) waves due to a superconductor-dielectric superlattice are numerically calculated. Shift operator finite difference time domain (SO-FDTD) method is used in the analysis. By using the SO-FDTD method, the transmission spectrum is obtained and its characteristics are investigated for different thicknesses of superconductor layers and dielectric layers, from which a stop band starting from zero frequency can be apparently observed. The relation between this low-frequency stop band and relative temperature, and also the London penetration depth at a superconductor temperature of zero degree are discussed, separately. The low-frequency stop band properties of superconductor-dielectric superlattice thus are well disclosed.
基金Supported by MCME.Doctoral Foundation of the Ministry of Education and Science Foundation of Liaoning University
文摘For an operator weighted shift S,the essential spectrum σ_e(S) and the indices associated with holes in σ_e(S) are described.Moreover,Banach reducibility of S is investigated and a condition for S~* to be a Cowen-Douglas operator is characterized.
文摘Abstract Let H be a complex seperable Hilbert space and ^(Jt^) denote the collection of bounded linear operators on H. For an operator in L(H), rad{A}' denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}'/rad{A}'. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant is commutative.
基金supported by the National Natural Science Foundation of China(11171119)
文摘In this paper, we investigate the value distribution of the difference counterpart △f(z)- af(z)^n of f′(z)- af(z)^n and obtain an almost direct difference analogue of result of Hayman.
基金supported by the National Natural Science Foundation of China under Grant No.11271173,the Fundamental Research Funds for the Central Universities under Grant No.lzujbky-2014-228,and the Program for New Century Excellent Talents in University under Grant No.NCET-09-0438.
文摘High order discretization schemes playmore important role in fractional operators than classical ones.This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones;but for fractional operators the stencils for high order schemes and low order ones are the same.Then using high order schemes to solve fractional equations leads to almost the same computational cost with first order schemes but the accuracy is greatly improved.Using the fractional linear multistep methods,Lubich obtains the n-th order(n≤6)approximations of the a-th derivative(a>0)or integral(a<0)[Lubich,SIAM J.Math.Anal.,17,704-719,1986],because of the stability issue the obtained scheme can not be directly applied to the space fractional operator with a∈(1,2)for time dependent problem.By weighting and shifting Lubich’s 2nd order discretization scheme,in[Chen&Deng,SINUM,arXiv:1304.7425]we derive a series of effective high order discretizations for space fractional derivative,called WSLD operators there.As the sequel of the previous work,we further provide new high order schemes for space fractional derivatives by weighting and shifting Lubich’s 3rd and 4th order discretizations.In particular,we prove that the obtained 4th order approximations are effective for space fractional derivatives.And the corresponding schemes are used to solve the space fractional diffusion equation with variable coefficients.
基金financial support from the National Natural Science Foundation of China(Grant No.11405051)supported by the Australian Research Council Discovery Project DP190101529supported by NSFC Grant 11775299。
文摘This paper focuses on the finite dimensional irreducible representations of Lie superalgebra D(2,1;α).We explicitly construct the finite dimensional representations of the superalgebra D(2,1;α)by using the shift operator and differential operator representations.Unlike ordinary Lie algebra representation,there are typical and atypical representations for most superalgebras.Therefore,its typical and atypical representation conditions are also given.Our results are expected to be useful for the construction of primary fields of the corresponding current superalgebra of D(2,1;α).
文摘Let f(z)beanon-constantmeromorphicfunctionoffiniteorder,c∈C\{0}andk∈N.Suppose f(z)and f(k)(z+c)share1CM(IM),f(z)and f(z+c)share∞CM.If N(r,0;f)=S(r,f)(N(r,0;f(z))+N(r,0;f(k)(z+c))=S(r,f)),then either f(z)≡f(k)(z+c)or f(z)is a solution of the following equation:f((z+c)−1=a(z)(f(z)−1))f(z)+1 a(z)),and N(r,0;f(z)+1 a(z))=S(r,f)(f′(z+c)−1=a(z)(f(z)−1)(f(z)+1 a(z)))where a(z)(≡−1,0,∞)(a(z)(≡0,∞))is a meromorphic function satisfying T(r,a)=S(r,f).Also we exhibit some examples to show that the conditions of our results are the best possible.
基金The authors have been supported in part by the Spanish Ministerio de Educación y Ciencia(MTM2004-01888)
文摘We work with the abstract K and J interpolation method generated by a sequence lattice Г. We investigate the deviation of an interpolated operator from a given operator ideal by establishing formulae for the ideal measure of the interpolated operator in terms of the ideal measures of restrictions of the operator. Formulae are given in terms of the norms of the shift operators on Г.