Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w...Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w); |w|>1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, L n(·) means the leading coefficient of the orthonormal matrix polynomials Φ n(z;·). Finally, we deduce the asymptotic behavior of Φ n(w;)Φ n(w;Ω)* in the case when M=I.展开更多
The q-deformed entangled states are introduced by using deformation quantization methods and new normal ordering of the vacuum projection operator for q-deformed boson oscillator. In similar way, by virtue of the tech...The q-deformed entangled states are introduced by using deformation quantization methods and new normal ordering of the vacuum projection operator for q-deformed boson oscillator. In similar way, by virtue of the technique of integration within an ordered product （IWOP） of operators, the new completeness and orthogonMity relations composed of the bra and ket, which are not mutually Hermitian conjugates are obtained. Furthermore, the property of squeezing operator represented by the q-deformed entangled states is exhibited. Lastly, the nonclassical properties of the q-deformed two-mode squeezed vacuum state are studied.展开更多
The aim of this work is to find exact solutions of the Dirac equation in(1+1) space-time beyond the already known class.We consider exact spin(and pseudo-spin) symmetric Dirac equations where the scalar potential is e...The aim of this work is to find exact solutions of the Dirac equation in(1+1) space-time beyond the already known class.We consider exact spin(and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus(and minus) the vector potential.We also include pseudo-scalar potentials in the interaction.The spinor wavefunction is written as a bounded sum in a complete set of square integrable basis,which is chosen such that the matrix representation of the Dirac wave operator is tridiagonal and symmetric.This makes the matrix wave equation a symmetric three-term recursion relation for the expansion coefficients of the wavefunction.We solve the recursion relation exactly in terms of orthogonal polynomials and obtain the state functions and corresponding relativistic energy spectrum and phase shift.展开更多
Let G be a finite group and K a field of characteristic zero.It is well-known that if K is a splitting field for G,then G is abelian if and only if any irreducible representation of G has degree 1.In this paper,we gen...Let G be a finite group and K a field of characteristic zero.It is well-known that if K is a splitting field for G,then G is abelian if and only if any irreducible representation of G has degree 1.In this paper,we generalize this result to the case that K is an arbitrary field of characteristic zero（that is,K need not be a splitting field for G）,and we also obtain the orthogonality relations of irreducible K-characters of G in this case.Our results generalize some well-known theorems.展开更多
文摘Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w); |w|>1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, L n(·) means the leading coefficient of the orthonormal matrix polynomials Φ n(z;·). Finally, we deduce the asymptotic behavior of Φ n(w;)Φ n(w;Ω)* in the case when M=I.
文摘The q-deformed entangled states are introduced by using deformation quantization methods and new normal ordering of the vacuum projection operator for q-deformed boson oscillator. In similar way, by virtue of the technique of integration within an ordered product （IWOP） of operators, the new completeness and orthogonMity relations composed of the bra and ket, which are not mutually Hermitian conjugates are obtained. Furthermore, the property of squeezing operator represented by the q-deformed entangled states is exhibited. Lastly, the nonclassical properties of the q-deformed two-mode squeezed vacuum state are studied.
基金King Fahd University of Petroleum and Minerals (KFUPM) for their support under research grant RG1502the material support and encouragements of the Saudi Center for Theoretical Physics (SCTP)
文摘The aim of this work is to find exact solutions of the Dirac equation in(1+1) space-time beyond the already known class.We consider exact spin(and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus(and minus) the vector potential.We also include pseudo-scalar potentials in the interaction.The spinor wavefunction is written as a bounded sum in a complete set of square integrable basis,which is chosen such that the matrix representation of the Dirac wave operator is tridiagonal and symmetric.This makes the matrix wave equation a symmetric three-term recursion relation for the expansion coefficients of the wavefunction.We solve the recursion relation exactly in terms of orthogonal polynomials and obtain the state functions and corresponding relativistic energy spectrum and phase shift.
基金Supported by the National Natural Science Foundation of China (Grant No.10771132)the Natural Science Foundation of Shandong Province (Grant No.Y2008A03)
文摘Let G be a finite group and K a field of characteristic zero.It is well-known that if K is a splitting field for G,then G is abelian if and only if any irreducible representation of G has degree 1.In this paper,we generalize this result to the case that K is an arbitrary field of characteristic zero（that is,K need not be a splitting field for G）,and we also obtain the orthogonality relations of irreducible K-characters of G in this case.Our results generalize some well-known theorems.
