Spin-orbit coupling(SOC)plays a vital role in determining the ground state and forming novel electronic states of matter where heavy elements are involved.Here,the prototypical perovskite iridate oxide SrIrO_(3)is inv...Spin-orbit coupling(SOC)plays a vital role in determining the ground state and forming novel electronic states of matter where heavy elements are involved.Here,the prototypical perovskite iridate oxide SrIrO_(3)is investigated to gain more insights into the SOC effect in the modification of electronic structure and corresponding magnetic and electrical properties.The high pressure metastable orthorhombic SrIrO_(3)is successfully stabilized by physical and chemical pressures,in which the chemical pressure is induced by Ru doping in Ir site and Mg substitution of Sr position.Detailed structural,magnetic,electrical characterizations and density functional theory(DFT)calculations reveal that the substitution of Ru for Ir renders an enhanced metallic characteristic,while the introduction of Mg into Sr site results in an insulating state with 10.1%negative magnetoresistance at 10 K under 7 T.Theoretical calculations indicate that Ru doping can weaken the SOC effect,leading to the decrease of orbital energy difference between J_(1/2)and J_(3/2),which is favorable for electron transport.On the contrary,Mg doping can enhance the SOC effect,inducing a metal-insulator-transition(MIT).The electronic phase transition is further revealed by DFT calculations,confirming that the strong SOC and electron-electron interactions can lead to the emergence of insulating state.These findings underline the intricate correlations between lattice degrees of freedom and SOC in determining the ground state,which effectively stimulate the physical pressure between like structures by chemical compression.展开更多
Interlayer exchange coupling(IEC)plays a critical role in spin-orbit torque(SOT)switching in synthetic magnets.This work establishes a fundamental correlation between IEC and SOT dynamics within Co/Pt-based synthetic ...Interlayer exchange coupling(IEC)plays a critical role in spin-orbit torque(SOT)switching in synthetic magnets.This work establishes a fundamental correlation between IEC and SOT dynamics within Co/Pt-based synthetic antiferromagnets and synthetic ferromagnets.The antiferromagnetic and ferromagnetic coupling states are precisely engineered through Ruderman-Kittel-Kasuya-Yosida(RKKY)interactions by modulating the Ir spacer thickness.Experimental results reveal that the critical switching current density exhibits a strong positive correlation with the IEC strength,regardless of the coupling type.A comprehensive theoretical framework based on the Landau-Lifshitz-Gilbert equation elucidates how IEC contributes to the effective energy barrier that must be overcome during SOT-induced magnetization switching.Significantly,the antiferromagnetically coupled samples demonstrate enhanced SOT efficiency,with the spin Hall angle being directly proportional to the antiferromagnetic exchange coupling field.These insights establish a coherent physical paradigm for understanding IEC-dependent SOT dynamics and provide strategic design principles for the development of energy-efficient next-generation spintronic devices.展开更多
We study the trimer state in a three-body system,where two of the atoms are subject to Rashba-type spin-orbit coupling and spin-dependent loss while interacting spin-selectively with the third atom.The short-time cond...We study the trimer state in a three-body system,where two of the atoms are subject to Rashba-type spin-orbit coupling and spin-dependent loss while interacting spin-selectively with the third atom.The short-time conditional dynamics of the three-body system is effectively governed by a non-Hermitian Hamiltonian with an imaginary Zeeman field.Remarkably,the interplay of non-Hermitian single particle dispersion and the spin-selective interaction results in a Borromean state and an enlarged trimer phase.The stability of trimer state can be reflected by the imaginary part of trimer energy and the momentum distribution of trimer wave function.We also show the phase diagram of the three-body system under both real and imaginary Zeeman fields.Our results illustrate the interesting consequence of non-Hermitian spectral symmetry on the few-body level,which may be readily observable in current cold-atom experiments.展开更多
Spin-orbit interaction(SOI)can be introduced by the proximity effect to modulate the electronic properties of graphene-based heterostructures.In this work,we stack trilayer WSe_(2) on Bernal tetralayer graphene to inv...Spin-orbit interaction(SOI)can be introduced by the proximity effect to modulate the electronic properties of graphene-based heterostructures.In this work,we stack trilayer WSe_(2) on Bernal tetralayer graphene to investigate the influence of SOI on the anomalous Hall effect(AHE).In this structurally asymmetric device,by comparing the magnitude of AHE at positive and negative displacement fields,we find that AHE is strongly enhanced by bringing electrons in proximity to the WSe_(2) layer.Meanwhile,the enhanced AHE signal persists up to 80 K,providing important routes for topological device applications at high temperatures.展开更多
We consider matter-wave solitons in spin-orbit coupled Bose-Einstein condensates embedded in an optical lattice and study the dynamics of the soliton within the framework of Gross-Pitaevskii equations.We express spin ...We consider matter-wave solitons in spin-orbit coupled Bose-Einstein condensates embedded in an optical lattice and study the dynamics of the soliton within the framework of Gross-Pitaevskii equations.We express spin components of the soliton pair in terms of nonlinear Bloch equations and investigate the effective spin dynamics.It is seen that the effective magnetic field that appears in the Bloch equation is affected by optical lattices,and thus the optical lattice influences the precessional frequency of the spin components.We make use of numerical approaches to investigate the dynamical behavior of density profiles and center-of-mass of the soliton pair in the presence of the optical lattice.It is shown that the spin density is periodically varying due to flipping of spinors between the two states.The amplitude of spin-flipping oscillation increases with lattice strength.We find that the system can also exhibit interesting nonlinear behavior for chosen values of parameters.We present a fixed point analysis to study the effects of optical lattices on the nonlinear dynamics of the spin components.It is seen that the optical lattice can act as a control parameter to change the dynamical behavior of the spin components from periodic to chaotic.展开更多
The eigenvalue problem of the Hamiltonian operator associated with plane elasticity problems is investigated.The eigenfunctions of the operator are directly solved with mixed boundary conditions for the displacement a...The eigenvalue problem of the Hamiltonian operator associated with plane elasticity problems is investigated.The eigenfunctions of the operator are directly solved with mixed boundary conditions for the displacement and stress in a rectangular region.The completeness of the eigenfunctions is then proved,providing the feasibility of using separation of variables to solve the problems.A general solution is obtained with the symplectic eigenfunction expansion theorem.展开更多
This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite...This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner.展开更多
The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified...The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for a separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained. Finally, a numerical test is analysed to show the correctness of the results.展开更多
The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eige...The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.展开更多
We introduce a decimation scheme of constructing renormalized Hamiltonian flows,which is useful in the study of properties of energy eigenfunctions,such as localization,as well as in approximate calculation of eigenen...We introduce a decimation scheme of constructing renormalized Hamiltonian flows,which is useful in the study of properties of energy eigenfunctions,such as localization,as well as in approximate calculation of eigenenergies.The method is based on a generalized Brillouin-Wigner perturbation theory.Each flow is specific for a given energy and,at each step of the flow,a finite subspace of the Hilbert space is decimated in order to obtain a renormalized Hamiltonian for the next step.Eigenenergies of the original Hamiltonian appear as unstable fixed points of renormalized flows.Numerical illustration of the method is given in the Wigner-band random-matrix model.展开更多
In this work we describe the algorithms to construct the skeletons, simplified 1D representations for a 3D surface depicted by a mesh of points, given the respective eigenfunctions of the Discrete Laplace-Beltrami Ope...In this work we describe the algorithms to construct the skeletons, simplified 1D representations for a 3D surface depicted by a mesh of points, given the respective eigenfunctions of the Discrete Laplace-Beltrami Operator (LBO). These functions are isometry invariant, so they are independent of the object’s representation including parameterization, spatial position and orientation. Several works have shown that these eigenfunctions provide topological and geometrical information of the surfaces of interest [1] [2]. We propose to make use of that information for the construction of a set of skeletons, associated to each eigenfunction, which can be used as a fingerprint for the surface of interest. The main goal is to develop a classification system based on these skeletons, instead of the surfaces, for the analysis of medical images, for instance.展开更多
This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial diffe...This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.展开更多
The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonia...The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method.展开更多
In this paper, the squared eigenfunction symmetries for the BTL and CTL hierarchies are expficitly constructed with the suitable modification of the ones for the TL hierarchy, by considering the BTL and GTL constraint...In this paper, the squared eigenfunction symmetries for the BTL and CTL hierarchies are expficitly constructed with the suitable modification of the ones for the TL hierarchy, by considering the BTL and GTL constraints. Also the connections with the corresponding additional symmetries are investigated： the squared eigenfunction symmetry generated by the wave function can be viewed as the generating function for the additional symmetries.展开更多
We consider the following eigenvalue problem: [GRAPHICS] Where f(x, t) is a continuous function with critical growth. We prove the existence of nontrivial solutions.
A new and simple method is developed to establish the pseudo orthogonal properties (POP) of the eigenfunction expansion form (EEF) of crack-tip stress complex potential functions for cracked anisotropic an...A new and simple method is developed to establish the pseudo orthogonal properties (POP) of the eigenfunction expansion form (EEF) of crack-tip stress complex potential functions for cracked anisotropic and piezoelectric materials, respectively. Di?erent from previous research, the complex argument separation technique is not required so that cumbersome manipulations are avoided. Moreover, it is shown, di?erent from the previous research too, that the orthogonal properties of the material characteristic matrices A and B are no longer necessary in obtaining the POP of EEF in cracked piezoelectric materials. Of the greatest signi?cance is that the method presented in this paper can be widely extended to treat many kinds of problems concerning path- independent integrals with multi-variables.展开更多
The eigenvalue problem for the Hamiltonian operator associated with the mathematical model for the deflection of a thin elastic plate is investigated.First,the problem for a rectangular plate with simply supported edg...The eigenvalue problem for the Hamiltonian operator associated with the mathematical model for the deflection of a thin elastic plate is investigated.First,the problem for a rectangular plate with simply supported edges is solved directly.Then,the completeness of the eigenfunctions is proved,thereby demonstrating the feasibility of using separation of variables to solve the problem. Finally,the general solution is obtained by using the proved expansion theorem.展开更多
The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow ...The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow field for slip flow differs much from that of no-slip flow. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip.展开更多
In this paper a method of eigenfunction expansion associated with 2nd order differential equation is developed by using the concept of theory of distribution. An application of the method to the infinite long antenna ...In this paper a method of eigenfunction expansion associated with 2nd order differential equation is developed by using the concept of theory of distribution. An application of the method to the infinite long antenna is described in detail.展开更多
Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their an...Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.展开更多
基金supported by the National Natural Science Foundation of China(NSFC,No.22090041)the Guangdong Basic and Applied Basic Research Foundation(No.2022B1515120014)。
文摘Spin-orbit coupling(SOC)plays a vital role in determining the ground state and forming novel electronic states of matter where heavy elements are involved.Here,the prototypical perovskite iridate oxide SrIrO_(3)is investigated to gain more insights into the SOC effect in the modification of electronic structure and corresponding magnetic and electrical properties.The high pressure metastable orthorhombic SrIrO_(3)is successfully stabilized by physical and chemical pressures,in which the chemical pressure is induced by Ru doping in Ir site and Mg substitution of Sr position.Detailed structural,magnetic,electrical characterizations and density functional theory(DFT)calculations reveal that the substitution of Ru for Ir renders an enhanced metallic characteristic,while the introduction of Mg into Sr site results in an insulating state with 10.1%negative magnetoresistance at 10 K under 7 T.Theoretical calculations indicate that Ru doping can weaken the SOC effect,leading to the decrease of orbital energy difference between J_(1/2)and J_(3/2),which is favorable for electron transport.On the contrary,Mg doping can enhance the SOC effect,inducing a metal-insulator-transition(MIT).The electronic phase transition is further revealed by DFT calculations,confirming that the strong SOC and electron-electron interactions can lead to the emergence of insulating state.These findings underline the intricate correlations between lattice degrees of freedom and SOC in determining the ground state,which effectively stimulate the physical pressure between like structures by chemical compression.
基金Project supported by the“Pioneer”and“Leading Goose”R&D Program of Zhejiang Province(Grant No.2022C01053)the Key Research and Development Program of Zhejiang Province(Grant No.2021C01039)+1 种基金the National Natural Science Foundation of China(Grant No.62293493)the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ21A050001)。
文摘Interlayer exchange coupling(IEC)plays a critical role in spin-orbit torque(SOT)switching in synthetic magnets.This work establishes a fundamental correlation between IEC and SOT dynamics within Co/Pt-based synthetic antiferromagnets and synthetic ferromagnets.The antiferromagnetic and ferromagnetic coupling states are precisely engineered through Ruderman-Kittel-Kasuya-Yosida(RKKY)interactions by modulating the Ir spacer thickness.Experimental results reveal that the critical switching current density exhibits a strong positive correlation with the IEC strength,regardless of the coupling type.A comprehensive theoretical framework based on the Landau-Lifshitz-Gilbert equation elucidates how IEC contributes to the effective energy barrier that must be overcome during SOT-induced magnetization switching.Significantly,the antiferromagnetically coupled samples demonstrate enhanced SOT efficiency,with the spin Hall angle being directly proportional to the antiferromagnetic exchange coupling field.These insights establish a coherent physical paradigm for understanding IEC-dependent SOT dynamics and provide strategic design principles for the development of energy-efficient next-generation spintronic devices.
基金supported by the National Natural Science Foundation of China(Grant No.11974331)。
文摘We study the trimer state in a three-body system,where two of the atoms are subject to Rashba-type spin-orbit coupling and spin-dependent loss while interacting spin-selectively with the third atom.The short-time conditional dynamics of the three-body system is effectively governed by a non-Hermitian Hamiltonian with an imaginary Zeeman field.Remarkably,the interplay of non-Hermitian single particle dispersion and the spin-selective interaction results in a Borromean state and an enlarged trimer phase.The stability of trimer state can be reflected by the imaginary part of trimer energy and the momentum distribution of trimer wave function.We also show the phase diagram of the three-body system under both real and imaginary Zeeman fields.Our results illustrate the interesting consequence of non-Hermitian spectral symmetry on the few-body level,which may be readily observable in current cold-atom experiments.
基金Project supported by the National Key R&D Program of China(Grant Nos.2021YFA1400100 and 2024YFA1409700)the National Natural Science Foudation of China(Grant Nos.12374168 and T2325026)。
文摘Spin-orbit interaction(SOI)can be introduced by the proximity effect to modulate the electronic properties of graphene-based heterostructures.In this work,we stack trilayer WSe_(2) on Bernal tetralayer graphene to investigate the influence of SOI on the anomalous Hall effect(AHE).In this structurally asymmetric device,by comparing the magnitude of AHE at positive and negative displacement fields,we find that AHE is strongly enhanced by bringing electrons in proximity to the WSe_(2) layer.Meanwhile,the enhanced AHE signal persists up to 80 K,providing important routes for topological device applications at high temperatures.
文摘We consider matter-wave solitons in spin-orbit coupled Bose-Einstein condensates embedded in an optical lattice and study the dynamics of the soliton within the framework of Gross-Pitaevskii equations.We express spin components of the soliton pair in terms of nonlinear Bloch equations and investigate the effective spin dynamics.It is seen that the effective magnetic field that appears in the Bloch equation is affected by optical lattices,and thus the optical lattice influences the precessional frequency of the spin components.We make use of numerical approaches to investigate the dynamical behavior of density profiles and center-of-mass of the soliton pair in the presence of the optical lattice.It is shown that the spin density is periodically varying due to flipping of spinors between the two states.The amplitude of spin-flipping oscillation increases with lattice strength.We find that the system can also exhibit interesting nonlinear behavior for chosen values of parameters.We present a fixed point analysis to study the effects of optical lattices on the nonlinear dynamics of the spin components.It is seen that the optical lattice can act as a control parameter to change the dynamical behavior of the spin components from periodic to chaotic.
基金supported by the National Natural Science Foundation of China(No.10962004)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20070126002)the Natural Science Foundation of Inner Mongolia of China(No.20080404MS0104)
文摘The eigenvalue problem of the Hamiltonian operator associated with plane elasticity problems is investigated.The eigenfunctions of the operator are directly solved with mixed boundary conditions for the displacement and stress in a rectangular region.The completeness of the eigenfunctions is then proved,providing the feasibility of using separation of variables to solve the problems.A general solution is obtained with the symplectic eigenfunction expansion theorem.
基金supported by the National Natural Science Foundation of China(Grant No 10562002)the Natural Science Foundation of Inner Mongolia,China(Grants No 200508010103 and 200711020106)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No 20070126002)
文摘This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner.
基金supported by the National Natural Science Foundation of China (Grant No. 10962004)the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 20080404MS0104)
文摘The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for a separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained. Finally, a numerical test is analysed to show the correctness of the results.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10875018 and 10773002)
文摘The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11275179,11535011,and 11775210
文摘We introduce a decimation scheme of constructing renormalized Hamiltonian flows,which is useful in the study of properties of energy eigenfunctions,such as localization,as well as in approximate calculation of eigenenergies.The method is based on a generalized Brillouin-Wigner perturbation theory.Each flow is specific for a given energy and,at each step of the flow,a finite subspace of the Hilbert space is decimated in order to obtain a renormalized Hamiltonian for the next step.Eigenenergies of the original Hamiltonian appear as unstable fixed points of renormalized flows.Numerical illustration of the method is given in the Wigner-band random-matrix model.
文摘In this work we describe the algorithms to construct the skeletons, simplified 1D representations for a 3D surface depicted by a mesh of points, given the respective eigenfunctions of the Discrete Laplace-Beltrami Operator (LBO). These functions are isometry invariant, so they are independent of the object’s representation including parameterization, spatial position and orientation. Several works have shown that these eigenfunctions provide topological and geometrical information of the surfaces of interest [1] [2]. We propose to make use of that information for the construction of a set of skeletons, associated to each eigenfunction, which can be used as a fingerprint for the surface of interest. The main goal is to develop a classification system based on these skeletons, instead of the surfaces, for the analysis of medical images, for instance.
基金Project supported by the National Natural Science Foundation of China (No. 10962004)the Special-ized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)+1 种基金the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010)the Natural Science Foundation of Inner Mongolia (No. 2009BS0101)
文摘This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.
基金Supported by the National Natural Science Foundation of China under Grant No.10962004the Natural Science Foundation of Inner Mongolia under Grant No.2009BS0101+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20070126002the Cultivation of Innovative Talent of "211 Project"of Inner Mongolia University
文摘The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method.
基金Supported by National Natural Science Foundation of China under Grant No. 11226196the Fundamental Research Funds for the Central Universities under Grant No. 2012QNA45
文摘In this paper, the squared eigenfunction symmetries for the BTL and CTL hierarchies are expficitly constructed with the suitable modification of the ones for the TL hierarchy, by considering the BTL and GTL constraints. Also the connections with the corresponding additional symmetries are investigated： the squared eigenfunction symmetry generated by the wave function can be viewed as the generating function for the additional symmetries.
文摘We consider the following eigenvalue problem: [GRAPHICS] Where f(x, t) is a continuous function with critical growth. We prove the existence of nontrivial solutions.
基金Project supported by the Natural Science Foundation of Shaanxi Province (No.2002A18) and the Doctorate Foundation of Xi’an Jiao-Tong University.
文摘A new and simple method is developed to establish the pseudo orthogonal properties (POP) of the eigenfunction expansion form (EEF) of crack-tip stress complex potential functions for cracked anisotropic and piezoelectric materials, respectively. Di?erent from previous research, the complex argument separation technique is not required so that cumbersome manipulations are avoided. Moreover, it is shown, di?erent from the previous research too, that the orthogonal properties of the material characteristic matrices A and B are no longer necessary in obtaining the POP of EEF in cracked piezoelectric materials. Of the greatest signi?cance is that the method presented in this paper can be widely extended to treat many kinds of problems concerning path- independent integrals with multi-variables.
基金supported by the National Natural Science Foundation of China(Grant No.10962004)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20070126002)+1 种基金the Natural Science Foundation of Inner Mongolia(Grant No. 20080404MS0104)the Research Foundation for Talented Scholars of Inner Mongolia University(Grant No. 207066)
文摘The eigenvalue problem for the Hamiltonian operator associated with the mathematical model for the deflection of a thin elastic plate is investigated.First,the problem for a rectangular plate with simply supported edges is solved directly.Then,the completeness of the eigenfunctions is proved,thereby demonstrating the feasibility of using separation of variables to solve the problem. Finally,the general solution is obtained by using the proved expansion theorem.
文摘The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow field for slip flow differs much from that of no-slip flow. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip.
文摘In this paper a method of eigenfunction expansion associated with 2nd order differential equation is developed by using the concept of theory of distribution. An application of the method to the infinite long antenna is described in detail.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10875018 and 10773002)
文摘Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.
