The study of stratospheric airships has become the focus in many countries in recent years,because of its potential applications in many fields.Lightweight and high strength envelopes are the keys to the design of str...The study of stratospheric airships has become the focus in many countries in recent years,because of its potential applications in many fields.Lightweight and high strength envelopes are the keys to the design of stratospheric airships,as it directly determines the endurance flight performance and loading deformation characteristics of the airship.A typical envelope of any stratospheric airship is a coated-fabric material which is composed of a fiber layer and several functional membrane layers.According to composite structure,nonlinearity and viscoelasticity are the two main characteristics of such envelope.Based on the analysis on the interaction between the different components in the micro-mechanical model of the coated-fabric,several invariant values reflecting the characteristics of the envelope material are obtained according to invariant theory.Furthermore,the constitutive equation that describes the viscoelasticity of the envelope material is derived.The constitutive equation can represent both the individual roles of the warp and weft fibers,and their further coupled interactions.The theoretical computation results were verified by off-axial tension tests.The results can help gain a deeper understanding of the mechanical mechanism and provide a reference for structural design of envelope material.展开更多
After the birth of quantum mechanics, the notion in physics that the frequency of light is the only factor that determines the energy of a single photon has played a fundamental role. However, under the assumption tha...After the birth of quantum mechanics, the notion in physics that the frequency of light is the only factor that determines the energy of a single photon has played a fundamental role. However, under the assumption that the theory of Lewis-Riesenfeld invariants is applicable in quantum optics, it is shown in the present work that this widely accepted notion is valid only for light described by a time-independent Hamiltonian, i.e., for light in media satisfying the conditions, ε(t) = ε(0), u(t) = u(0), and σ(t) = 0 simultaneously. The use of the Lewis Riesenfeld invariant operator method in quantum optics leads to a marvelous result: the energy of a single photon propagating through time-varying linear media exhibits nontrivial time dependence without a change of frequency.展开更多
A novel La Shalle's invariant set theory (LSIST) based adaptive asymptotic synchronization (LSISAAS) method is proposed to asymptotically synchronize Duffing system with unknown parameters which also are consider...A novel La Shalle's invariant set theory (LSIST) based adaptive asymptotic synchronization (LSISAAS) method is proposed to asymptotically synchronize Duffing system with unknown parameters which also are considered as system states. The LSISASS strategy depends on the only information, i.e. one state of the master system. According to the LSIST, the LSISASS method can asymptotically synchronize fully the states of the master system and the unknown system parameters as well. Simulation results also validate that the LSISAAS approach can obtain asymptotic synchronization.展开更多
We investigate the block basis for modular coinvariants of finite pseudo-reflection groups.We are particularly interested in the case of a subgroup G of the parabolic subgroups of GLn(q)which generalizes the Weyl grou...We investigate the block basis for modular coinvariants of finite pseudo-reflection groups.We are particularly interested in the case of a subgroup G of the parabolic subgroups of GLn(q)which generalizes the Weyl groups of restricted Cartan typeLiealgebra.展开更多
The relationship between quantum mechanics and classical mechanics is investigated by taking a Gaussian-type wave packet as a solution of the Schr o¨dinger equation for the Caldirola–Kanai oscillator driven by a...The relationship between quantum mechanics and classical mechanics is investigated by taking a Gaussian-type wave packet as a solution of the Schr o¨dinger equation for the Caldirola–Kanai oscillator driven by a sinusoidal force. For this time-dependent system, quantum properties are studied by using the invariant theory of Lewis and Riesenfeld. In particular,we analyze time behaviors of quantum expectation values of position and momentum variables and compare them to those of the counterpart classical ones. Based on this, we check whether the Ehrenfest theorem which was originally developed in static quantum systems can be extended to such time-varying systems without problems.展开更多
In this paper, we describe the variety defined by the twisted transfer ideal. It turns out that this variety is nothing but the union of reflecting hyperplanes and the fixed subspaces of the elements of order p in G.
Let K be a compact group.For a symplectic quotient M_(λ) of a compact Hamiltonian Kahler K-manifold,we show that the induced complex structure on M_(λ) is locally invariant when the parameter λ varies in Lie(K)^(*)...Let K be a compact group.For a symplectic quotient M_(λ) of a compact Hamiltonian Kahler K-manifold,we show that the induced complex structure on M_(λ) is locally invariant when the parameter λ varies in Lie(K)^(*).To prove such a result,we take two di erent approaches:(i)use the complex geometry properties of the symplectic implosion construction;(ii)investigate the variation of geometric invariant theory(GIT)quotients.展开更多
基金supported by the China Postdoctoral Science Foundation under Grant No.2016M600891。
文摘The study of stratospheric airships has become the focus in many countries in recent years,because of its potential applications in many fields.Lightweight and high strength envelopes are the keys to the design of stratospheric airships,as it directly determines the endurance flight performance and loading deformation characteristics of the airship.A typical envelope of any stratospheric airship is a coated-fabric material which is composed of a fiber layer and several functional membrane layers.According to composite structure,nonlinearity and viscoelasticity are the two main characteristics of such envelope.Based on the analysis on the interaction between the different components in the micro-mechanical model of the coated-fabric,several invariant values reflecting the characteristics of the envelope material are obtained according to invariant theory.Furthermore,the constitutive equation that describes the viscoelasticity of the envelope material is derived.The constitutive equation can represent both the individual roles of the warp and weft fibers,and their further coupled interactions.The theoretical computation results were verified by off-axial tension tests.The results can help gain a deeper understanding of the mechanical mechanism and provide a reference for structural design of envelope material.
基金supported by National Research Foundation of Korea Grant funded by the Korean Government (No. 2009-0077951)
文摘After the birth of quantum mechanics, the notion in physics that the frequency of light is the only factor that determines the energy of a single photon has played a fundamental role. However, under the assumption that the theory of Lewis-Riesenfeld invariants is applicable in quantum optics, it is shown in the present work that this widely accepted notion is valid only for light described by a time-independent Hamiltonian, i.e., for light in media satisfying the conditions, ε(t) = ε(0), u(t) = u(0), and σ(t) = 0 simultaneously. The use of the Lewis Riesenfeld invariant operator method in quantum optics leads to a marvelous result: the energy of a single photon propagating through time-varying linear media exhibits nontrivial time dependence without a change of frequency.
文摘A novel La Shalle's invariant set theory (LSIST) based adaptive asymptotic synchronization (LSISAAS) method is proposed to asymptotically synchronize Duffing system with unknown parameters which also are considered as system states. The LSISASS strategy depends on the only information, i.e. one state of the master system. According to the LSIST, the LSISASS method can asymptotically synchronize fully the states of the master system and the unknown system parameters as well. Simulation results also validate that the LSISAAS approach can obtain asymptotic synchronization.
基金supported by NSFC(No.12101544)Fundamental Research Funds of Yunnan Province(No.202301AT070415).
文摘We investigate the block basis for modular coinvariants of finite pseudo-reflection groups.We are particularly interested in the case of a subgroup G of the parabolic subgroups of GLn(q)which generalizes the Weyl groups of restricted Cartan typeLiealgebra.
基金supported by Fund from the Algerian Ministry of Higher Education and Scientific Research(Grant No.CNEPRU/D01220120010)the Basic Science Research Program of the year 2015 through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(Grant No.NRF-2013R1A1A2062907)
文摘The relationship between quantum mechanics and classical mechanics is investigated by taking a Gaussian-type wave packet as a solution of the Schr o¨dinger equation for the Caldirola–Kanai oscillator driven by a sinusoidal force. For this time-dependent system, quantum properties are studied by using the invariant theory of Lewis and Riesenfeld. In particular,we analyze time behaviors of quantum expectation values of position and momentum variables and compare them to those of the counterpart classical ones. Based on this, we check whether the Ehrenfest theorem which was originally developed in static quantum systems can be extended to such time-varying systems without problems.
文摘In this paper, we describe the variety defined by the twisted transfer ideal. It turns out that this variety is nothing but the union of reflecting hyperplanes and the fixed subspaces of the elements of order p in G.
基金supported by China Postdoctoral Science Foundation(Grant No.BX201700008).
文摘Let K be a compact group.For a symplectic quotient M_(λ) of a compact Hamiltonian Kahler K-manifold,we show that the induced complex structure on M_(λ) is locally invariant when the parameter λ varies in Lie(K)^(*).To prove such a result,we take two di erent approaches:(i)use the complex geometry properties of the symplectic implosion construction;(ii)investigate the variation of geometric invariant theory(GIT)quotients.