Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivati...Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.展开更多
Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some ...In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.展开更多
In this paper, we explicitly determine the maximal torus of the derivation algebra of a Qn filiform Lie algebra. Using the root space decomposition of DerQn, we prove that the derivation algebra of a Qn filiform Lie a...In this paper, we explicitly determine the maximal torus of the derivation algebra of a Qn filiform Lie algebra. Using the root space decomposition of DerQn, we prove that the derivation algebra of a Qn filiform Lie algebra is complete.展开更多
In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to inv...In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.展开更多
In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen...In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.展开更多
For the potential vorticity （PV） invariant, there is a PV-based complete-form vorticity equation, which we use heuris- tically in the present paper to answer the following question： for the Ertel-Rossby invariant ...For the potential vorticity （PV） invariant, there is a PV-based complete-form vorticity equation, which we use heuris- tically in the present paper to answer the following question： for the Ertel-Rossby invariant （ERI）, is there a corresponding vorticity tendency equation？ Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors＇ influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.展开更多
We propose a versatile electrostatic trap scheme using several charged spherical electrodes and a bias electric held.We hrst give the two-ball scheme and derive the analytical solution of the electric held.In order to...We propose a versatile electrostatic trap scheme using several charged spherical electrodes and a bias electric held.We hrst give the two-ball scheme and derive the analytical solution of the electric held.In order to make a comparison,we also give the numerical solution calculated by the hnite element software（Ansoft Maxwell）.Considering the loading of cold polar molecules into the trap,we give the three-ball scheme.We hrst give the analytical and numerical solutions of the distribution of the electric held.Then we simulate the dynamic process of the loading and trapping cold molecules using the classical Monte Carlo method.We analyze the influence of the velocity of the incident molecular beam and the loading time on the loading efficiency.After that,we give the temperature of the trapped cold molecules.Our study shows that the loading efficiency can reach 82%,and the corresponding temperature of the trapped molecules is about 24.6 mK.At last,we show that the single well divides into two ones by increasing the bias electric held or decreasing the voltages applied to the spherical electrodes.展开更多
We present a method for derivation of the density matrix of an arbitrary multi-mode continuous variable Gaussian entangled state from its phase space representation.An explicit computer algorithm is given to reconstru...We present a method for derivation of the density matrix of an arbitrary multi-mode continuous variable Gaussian entangled state from its phase space representation.An explicit computer algorithm is given to reconstruct the density matrix from Gaussian covariance matrix and quadrature average values.As an example,we apply our method to the derivation of three-mode symmetric continuous variable entangled state.Our method can be used to analyze the entanglement and correlation in continuous variable quantum network with multi-mode quantum entanglement states.展开更多
Let A be a unital algebra and M be a unital .A-bimodule. A linear map δ ： A →M is said to be Jordan derivable at a nontrivial idempotent P ∈A if δ（A） o B ＋ A o δ（B） =δ（A o B） for any A,B ∈ .4 with A o B...Let A be a unital algebra and M be a unital .A-bimodule. A linear map δ ： A →M is said to be Jordan derivable at a nontrivial idempotent P ∈A if δ（A） o B ＋ A o δ（B） =δ（A o B） for any A,B ∈ .4 with A o B = P, here A o B = AB ＋ BA is the usual Jordan product. In this article, we show that if ,A = AlgAN is a Hilbert space nest Mgebra and M = B（H）, or A =M= B（X）, then, a linear mapδ： A→M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P∈ B（X） if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.展开更多
Correction to:J.For.Res.https://doi.org/10.1007/s11676-020-01191-x In the Original publication of the article,the authors found an error in the text“We recommend CLef of 5 and 12 mmol m−2 POD1 for broadleaved species...Correction to:J.For.Res.https://doi.org/10.1007/s11676-020-01191-x In the Original publication of the article,the authors found an error in the text“We recommend CLef of 5 and 12 mmol m−2 POD1 for broadleaved species and conifers,respectively”under the section abstract and conclusion.展开更多
The real time thermal propagator with 2×2 matrix structure is derived in the functional formalism of the field theory inη-ξspacetime.It is emphasized that the trouble-shooting factorization of generating functi...The real time thermal propagator with 2×2 matrix structure is derived in the functional formalism of the field theory inη-ξspacetime.It is emphasized that the trouble-shooting factorization of generating functional in the time-path method can be avoided in this derivation.展开更多
In this letter,a new derivation of Keldysh's formula is presented and a brief discussion about the comparison between the new derivation and the original one is given.
Taking advantage of the calculation based on the original fundamental ideas of Aharonov and Bohm(AB)on the one hand,and making some necessary revisions on the other hand,this paper rederives the famous AB scattering c...Taking advantage of the calculation based on the original fundamental ideas of Aharonov and Bohm(AB)on the one hand,and making some necessary revisions on the other hand,this paper rederives the famous AB scattering cross section from the known propagator by the path integral method.展开更多
Using fixed point methods, we prove the Hyers–Ulam–Rassias stability and superstability of Jordan homomorphisms （Jordan ＊-homomorphisms）, and Jordan derivations （Jordan ＊-derivations） on Banach algebras （C＊-...Using fixed point methods, we prove the Hyers–Ulam–Rassias stability and superstability of Jordan homomorphisms （Jordan ＊-homomorphisms）, and Jordan derivations （Jordan ＊-derivations） on Banach algebras （C＊-algebras） for the generalized Jensen–type functional equationwhere r is a fixed positive real number in （1, ∞）.展开更多
Dark solitons are common topological excitations in a wide array of nonlinear waves.The dark soliton excitation energy is crucial for exploring dark soliton dynamics and is necessarily calculated in a renormalized for...Dark solitons are common topological excitations in a wide array of nonlinear waves.The dark soliton excitation energy is crucial for exploring dark soliton dynamics and is necessarily calculated in a renormalized form due to its existence on a finite background.Despite its tremendous importance and success,the renormalized energy form was at first only suggested with no detailed derivation,and was then"derived"in the grand canonical ensemble.We revisit this fundamental problem and provide an alternative and intuitive derivation of the energy form from the fundamental Held energy by utilizing a limiting procedure that conserves number of particles.Our derivation yields the same result,thus putting the dark soliton energy form on a solid basis.展开更多
A simple derivation of the field theory of Ising quantum chain shows that the Ising model is equivalent to the free Majorana real spinor field.At the critical point,the field equation is conformally covariant.
The well-known tower theorem of groups （resp. Lie algebras） shows that the tower of automorphism groups （resp. derivation algebras） of a finite group （resp. a finite dimensional Lie algebra） with trivial center ...The well-known tower theorem of groups （resp. Lie algebras） shows that the tower of automorphism groups （resp. derivation algebras） of a finite group （resp. a finite dimensional Lie algebra） with trivial center terminates after finitely many steps. We generalize these results for Lie rings, and present some necessary and sufficient conditions for Lie rings to be complete.展开更多
Based on crystallographic theory, there are 63 kinds of polytypes of 13H long-period stacking order （LPSO） structure, 126 kinds of polytypes of 14H LPSO structure, 120 kinds of polytypes of 39R LPSO structure, and 2...Based on crystallographic theory, there are 63 kinds of polytypes of 13H long-period stacking order （LPSO） structure, 126 kinds of polytypes of 14H LPSO structure, 120 kinds of polytypes of 39R LPSO structure, and 223 kinds of polytypes of 42R LPSO structure in a hexagonal close-packed （HCP） system, and their stacking sequences and space groups have been derived in detail. The result provides a theoretical explanation for the various polytypes of the LPSO structure.展开更多
Let R be a prime ring with characteristic di erent from two,d a derivation of R,L a noncentral Lie ideal of R,and a2R.In the present paper it is showed that if a(d(u^m)±u^m)^n for all u∈L,where m;n are xed posit...Let R be a prime ring with characteristic di erent from two,d a derivation of R,L a noncentral Lie ideal of R,and a2R.In the present paper it is showed that if a(d(u^m)±u^m)^n for all u∈L,where m;n are xed positive integers,then a=0 unless R satis es s4,the standard polynomial identity in four variables.展开更多
基金supported by the National Natural Science Foundation of China(11101084,11071040)the Fujian Province Nature Science Foundation of China(2013J01005)
文摘Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.
文摘Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
基金National Natural Science Foundation of China(10271076)
文摘In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.
文摘In this paper, we explicitly determine the maximal torus of the derivation algebra of a Qn filiform Lie algebra. Using the root space decomposition of DerQn, we prove that the derivation algebra of a Qn filiform Lie algebra is complete.
基金supported by the Daejin University grants in 2010
文摘In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.
文摘In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.
基金supported by the National Basic Research Program of China(Grant No.2013CB430105)the Key Research Program of the Chinese Academy of Sciences(Grant No.KZZD-EW-05-01)+2 种基金the National Natural Science Foundation of China(Grant Nos.41375054 and 41375052)the Special Scientific Research Fund of the Meteorological Public Welfare of the Ministry of Sciences and Technology,China(Grant No.GYHY201406003)the Opening Foundation of the State Key Laboratory of Severe Weather,Chinese Academy of Meteorological Sciences(Grant No.2012LASW-B02)
文摘For the potential vorticity （PV） invariant, there is a PV-based complete-form vorticity equation, which we use heuris- tically in the present paper to answer the following question： for the Ertel-Rossby invariant （ERI）, is there a corresponding vorticity tendency equation？ Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors＇ influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.
基金Project supported by the National Nature Science Foundation of China(Grant No.11504318)
文摘We propose a versatile electrostatic trap scheme using several charged spherical electrodes and a bias electric held.We hrst give the two-ball scheme and derive the analytical solution of the electric held.In order to make a comparison,we also give the numerical solution calculated by the hnite element software（Ansoft Maxwell）.Considering the loading of cold polar molecules into the trap,we give the three-ball scheme.We hrst give the analytical and numerical solutions of the distribution of the electric held.Then we simulate the dynamic process of the loading and trapping cold molecules using the classical Monte Carlo method.We analyze the influence of the velocity of the incident molecular beam and the loading time on the loading efficiency.After that,we give the temperature of the trapped cold molecules.Our study shows that the loading efficiency can reach 82%,and the corresponding temperature of the trapped molecules is about 24.6 mK.At last,we show that the single well divides into two ones by increasing the bias electric held or decreasing the voltages applied to the spherical electrodes.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11574400 and 11204379the Beijing Institute of Technology Research Fund Program for Young Scholarsthe NSFC-ICTP Proposal under Grant No 11981240356
文摘We present a method for derivation of the density matrix of an arbitrary multi-mode continuous variable Gaussian entangled state from its phase space representation.An explicit computer algorithm is given to reconstruct the density matrix from Gaussian covariance matrix and quadrature average values.As an example,we apply our method to the derivation of three-mode symmetric continuous variable entangled state.Our method can be used to analyze the entanglement and correlation in continuous variable quantum network with multi-mode quantum entanglement states.
基金Supported by National Natural Foundation of China(11001194)Provincial International Cooperation Project of Shanxi(2014081027-2)
文摘Let A be a unital algebra and M be a unital .A-bimodule. A linear map δ ： A →M is said to be Jordan derivable at a nontrivial idempotent P ∈A if δ（A） o B ＋ A o δ（B） =δ（A o B） for any A,B ∈ .4 with A o B = P, here A o B = AB ＋ BA is the usual Jordan product. In this article, we show that if ,A = AlgAN is a Hilbert space nest Mgebra and M = B（H）, or A =M= B（X）, then, a linear mapδ： A→M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P∈ B（X） if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.
文摘Correction to:J.For.Res.https://doi.org/10.1007/s11676-020-01191-x In the Original publication of the article,the authors found an error in the text“We recommend CLef of 5 and 12 mmol m−2 POD1 for broadleaved species and conifers,respectively”under the section abstract and conclusion.
基金Supported by the National Natural Science Foundation of China under Grant No.19475005.
文摘The real time thermal propagator with 2×2 matrix structure is derived in the functional formalism of the field theory inη-ξspacetime.It is emphasized that the trouble-shooting factorization of generating functional in the time-path method can be avoided in this derivation.
基金supported by National Science Fonndation of China.
文摘In this letter,a new derivation of Keldysh's formula is presented and a brief discussion about the comparison between the new derivation and the original one is given.
基金Supported by the National Natural Foundation of China and Beijing Municipal Natural Sciences Foundation.
文摘Taking advantage of the calculation based on the original fundamental ideas of Aharonov and Bohm(AB)on the one hand,and making some necessary revisions on the other hand,this paper rederives the famous AB scattering cross section from the known propagator by the path integral method.
文摘Using fixed point methods, we prove the Hyers–Ulam–Rassias stability and superstability of Jordan homomorphisms （Jordan ＊-homomorphisms）, and Jordan derivations （Jordan ＊-derivations） on Banach algebras （C＊-algebras） for the generalized Jensen–type functional equationwhere r is a fixed positive real number in （1, ∞）.
基金National Natural Science Foundation of China(Grant No.11775176)Basic Research Program of Natural Science of Shaanxi Province,China(Grant No.2018KJXX-094)+2 种基金Key Innovative Research Team of Quantum Many-Body Theory and Quantum Control in Shaanxi Province,China(Grant No.2017KCT-12)Major Basic Research Program of Natural Science of Shaanxi Province,China(Grant No.2017ZDJC-32)Fundamental Research Funds for the Central Universities of China。
文摘Dark solitons are common topological excitations in a wide array of nonlinear waves.The dark soliton excitation energy is crucial for exploring dark soliton dynamics and is necessarily calculated in a renormalized form due to its existence on a finite background.Despite its tremendous importance and success,the renormalized energy form was at first only suggested with no detailed derivation,and was then"derived"in the grand canonical ensemble.We revisit this fundamental problem and provide an alternative and intuitive derivation of the energy form from the fundamental Held energy by utilizing a limiting procedure that conserves number of particles.Our derivation yields the same result,thus putting the dark soliton energy form on a solid basis.
文摘A simple derivation of the field theory of Ising quantum chain shows that the Ising model is equivalent to the free Majorana real spinor field.At the critical point,the field equation is conformally covariant.
基金supported in part by NSFC (10371032)Doctoral Foundation of Ministry of Education(20050512002)+1 种基金Youth Foundation of Tianyuan(10726020)Youth Foundation of Hubei Provincial Department of Education(Q20081008)
文摘The well-known tower theorem of groups （resp. Lie algebras） shows that the tower of automorphism groups （resp. derivation algebras） of a finite group （resp. a finite dimensional Lie algebra） with trivial center terminates after finitely many steps. We generalize these results for Lie rings, and present some necessary and sufficient conditions for Lie rings to be complete.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51371130,51171130,and 51271134)the Fundamental Research Funds for the Central Universities,Chinathe Open Research Fund of Science and Technology on High Strength Structural Materials Laboratory,Central South University,China
文摘Based on crystallographic theory, there are 63 kinds of polytypes of 13H long-period stacking order （LPSO） structure, 126 kinds of polytypes of 14H LPSO structure, 120 kinds of polytypes of 39R LPSO structure, and 223 kinds of polytypes of 42R LPSO structure in a hexagonal close-packed （HCP） system, and their stacking sequences and space groups have been derived in detail. The result provides a theoretical explanation for the various polytypes of the LPSO structure.
基金Supported by Anhui Natural Science Foundation(1808085MA141908085MA03)the Key University Science Research Project of Anhui Province(KJ2018A0433).
文摘Let R be a prime ring with characteristic di erent from two,d a derivation of R,L a noncentral Lie ideal of R,and a2R.In the present paper it is showed that if a(d(u^m)±u^m)^n for all u∈L,where m;n are xed positive integers,then a=0 unless R satis es s4,the standard polynomial identity in four variables.
