Here some properties on filters of double MS-algebras are descripted. We show that,for a normal filter F of a double MS-algebra (L;0, + )(x,y) ∈θ(F) (a,b ∈ F) (x ∧α)∨b+= (y ∧ a)∨ b+.
Let A and B be two regular multiplier Hopf algebras.First,the notion of diagonal crossed product B#A of multiplier Hopf algebras is constructed using the bimodule algebra,which is a generalization of the diagonal cros...Let A and B be two regular multiplier Hopf algebras.First,the notion of diagonal crossed product B#A of multiplier Hopf algebras is constructed using the bimodule algebra,which is a generalization of the diagonal crossed product in the sense of Hopf algebras.The result that the product in B#A is non-degenerate is given.Next,the definition of the comultiplicationΔ#on B#A is introduced,which is composed of the multiplierΔB(b)on B⊗B and the multiplierΔA(a)on A⊗A,and the elementΔ#(b⊗a)is a two-side multiplier of B#A⊗B#A,for any b∈B and a∈A.Then,a sufficient condition for B#A to be a regular multiplier Hopf algebra is described.In particular,Delvaux's main theorem in the case of smash products is generalized.Finally,these integrals on a diagonal crossed product of multiplier Hopf algebras are considered.展开更多
An anharmonic oscillator algebra model is used to study the collinear collisions of two diatomic molecules. The transition probability for vibration-vibration energy transfer is presented. For an application of the me...An anharmonic oscillator algebra model is used to study the collinear collisions of two diatomic molecules. The transition probability for vibration-vibration energy transfer is presented. For an application of the method, we talk about the collision of N2＋CO, N2＋O2, and N2＋N2. Through long time averaging, the transition probability changes to the function of total energy of the system. Comparing the results with the quantum results, we can see that the dynamical Lie algebraic method is useful for describing the anharmonie diatomic molecular collision.展开更多
Two-photon fluorescence dyes have shown promising applications in biomedical imaging.However,the substitution site effect on geometric structures and photophysical properties of fluorescence dyes is rarely illustrated...Two-photon fluorescence dyes have shown promising applications in biomedical imaging.However,the substitution site effect on geometric structures and photophysical properties of fluorescence dyes is rarely illustrated in detail.In this work,a series of new lipid droplets detection dyes are designed and studied,molecular optical properties and non-radiative transitions are analyzed.The intramolecular weak interaction and electron-hole analysis reveal its inner mechanisms.All dyes are proven to possess excellent photophysical properties with high fluorescence quantum efficiency and large stokes shift as well as remarkable two-photon absorption cross section.Our work reasonably elucidates the experimental measurements and the effects of substitution site on two-photon absorption and excited states properties of lipid droplets detection NAPBr dyes are highlighted,which could provide a theoretical perspective for designing efficient organic dyes for lipid droplets detection in biology and medicine fields.展开更多
Let A be a reflexive algebra in reflexive Banach space X such that both O+ ≠O and X_ ≠ X in LatA, then the set of all derivations of A into B(X) is topologically algebraically bireflexive.
In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its...In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A_(g,n)(M) and intertwining operators. Especially, bimodule A _(g,n)-1T(M) is a natural quotient of A_(g,n)(M) and there is a linear isomorphism between the space IM^k M Mjof intertwining operators and the space of homomorphisms HomA_(g,n)(V)(A_(g,n)(M) A_(g,n)(V)M^j(s), M^k(t)) for s, t ≤ n, M^j, M^k are g-twisted V modules, if V is g-rational.展开更多
As a critical component of alkaline fuel cells, anion exchange membranes determine the energy efficiency, output power density and the long term stability. Recently, the anion exchange membranes with gemini-cation sid...As a critical component of alkaline fuel cells, anion exchange membranes determine the energy efficiency, output power density and the long term stability. Recently, the anion exchange membranes with gemini-cation side chains exhibit superior ion conductivity due to their good nanophase separation. However, the costly and complicated synthesis limits their scaling up and commercialization. To address this problem, a convenient synthetic procedure under mild conditions is well developed. A tertiary amine precursor is introduced onto the polymer by the nucleophilic substitution reaction to avoid the conventional chloro/bromo-methylation. Followed by a simple Menshutkin reaction with 6- bromo-N,N,N-trimethylhexan-1-am inium bromide, the polym er electrolytes are obtained in a high yield. The resulting anion exchange membranes with high conductivity, good fuel cell performance and restricted swelling suggest the potential for the application in fuel cell devices.展开更多
A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational iden...A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.展开更多
文摘Here some properties on filters of double MS-algebras are descripted. We show that,for a normal filter F of a double MS-algebra (L;0, + )(x,y) ∈θ(F) (a,b ∈ F) (x ∧α)∨b+= (y ∧ a)∨ b+.
基金The National Natural Science Foundation of China(No.11371088,11571173,11871144)the Natural Science Foundation of Jiangsu Province(No.BK20171348)。
文摘Let A and B be two regular multiplier Hopf algebras.First,the notion of diagonal crossed product B#A of multiplier Hopf algebras is constructed using the bimodule algebra,which is a generalization of the diagonal crossed product in the sense of Hopf algebras.The result that the product in B#A is non-degenerate is given.Next,the definition of the comultiplicationΔ#on B#A is introduced,which is composed of the multiplierΔB(b)on B⊗B and the multiplierΔA(a)on A⊗A,and the elementΔ#(b⊗a)is a two-side multiplier of B#A⊗B#A,for any b∈B and a∈A.Then,a sufficient condition for B#A to be a regular multiplier Hopf algebra is described.In particular,Delvaux's main theorem in the case of smash products is generalized.Finally,these integrals on a diagonal crossed product of multiplier Hopf algebras are considered.
基金Supported by the National Science Foundation of China under Grant No. 20173013Partial Financial Supports from the Science Foundation of Shandong Province under Grant No. Y2008C102the Foundation of Taishan Meidical College under Grant No. TSB016
文摘An anharmonic oscillator algebra model is used to study the collinear collisions of two diatomic molecules. The transition probability for vibration-vibration energy transfer is presented. For an application of the method, we talk about the collision of N2＋CO, N2＋O2, and N2＋N2. Through long time averaging, the transition probability changes to the function of total energy of the system. Comparing the results with the quantum results, we can see that the dynamical Lie algebraic method is useful for describing the anharmonie diatomic molecular collision.
基金This work was supported by the National Natural Science Foundation of China(No.11804196 and No.11904210)the Project funded by China Postdoctoral Science Foundation(No.2018M642689)the Open Fund of Guangdong Provincial Key Laboratory of Luminescence from Molecular Aggregates,(South China University of Technology)(No.2019B030301003).
文摘Two-photon fluorescence dyes have shown promising applications in biomedical imaging.However,the substitution site effect on geometric structures and photophysical properties of fluorescence dyes is rarely illustrated in detail.In this work,a series of new lipid droplets detection dyes are designed and studied,molecular optical properties and non-radiative transitions are analyzed.The intramolecular weak interaction and electron-hole analysis reveal its inner mechanisms.All dyes are proven to possess excellent photophysical properties with high fluorescence quantum efficiency and large stokes shift as well as remarkable two-photon absorption cross section.Our work reasonably elucidates the experimental measurements and the effects of substitution site on two-photon absorption and excited states properties of lipid droplets detection NAPBr dyes are highlighted,which could provide a theoretical perspective for designing efficient organic dyes for lipid droplets detection in biology and medicine fields.
文摘Let A be a reflexive algebra in reflexive Banach space X such that both O+ ≠O and X_ ≠ X in LatA, then the set of all derivations of A into B(X) is topologically algebraically bireflexive.
基金supported by National Natural Science Foundation of China(Grant Nos.11101269 and 11431010)
文摘In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A_(g,n)(M) and intertwining operators. Especially, bimodule A _(g,n)-1T(M) is a natural quotient of A_(g,n)(M) and there is a linear isomorphism between the space IM^k M Mjof intertwining operators and the space of homomorphisms HomA_(g,n)(V)(A_(g,n)(M) A_(g,n)(V)M^j(s), M^k(t)) for s, t ≤ n, M^j, M^k are g-twisted V modules, if V is g-rational.
基金supported by the National Natural Science Foundation of China (21720102003, 91534203 and 21522607)the Fundamental Research Funds for the Central Universities (WK2060190072 and WK2340000066)
文摘As a critical component of alkaline fuel cells, anion exchange membranes determine the energy efficiency, output power density and the long term stability. Recently, the anion exchange membranes with gemini-cation side chains exhibit superior ion conductivity due to their good nanophase separation. However, the costly and complicated synthesis limits their scaling up and commercialization. To address this problem, a convenient synthetic procedure under mild conditions is well developed. A tertiary amine precursor is introduced onto the polymer by the nucleophilic substitution reaction to avoid the conventional chloro/bromo-methylation. Followed by a simple Menshutkin reaction with 6- bromo-N,N,N-trimethylhexan-1-am inium bromide, the polym er electrolytes are obtained in a high yield. The resulting anion exchange membranes with high conductivity, good fuel cell performance and restricted swelling suggest the potential for the application in fuel cell devices.
基金Project supported by the State Administration of Foreign Experts Affairs of Chinathe National Natural Science Foundation of China (Nos.10971136,10831003,61072147,11071159)+3 种基金the Chunhui Plan of the Ministry of Education of Chinathe Innovation Project of Zhejiang Province (No.T200905)the Natural Science Foundation of Shanghai (No.09ZR1410800)the Shanghai Leading Academic Discipline Project (No.J50101)
文摘A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.
