The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative, associative algebra A. It espec...The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative, associative algebra A. It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group, analogous to the well known relationship of Lie algebras and Lie groups.展开更多
Mutagenesis of Lactobacillus casei subsp, rhamnosus Xl-12 after low power microwave irradiation was investigated. Under a microwave power of 400 W and irradiation length of 3 min, a mutated strain W4-3-9 with high-yie...Mutagenesis of Lactobacillus casei subsp, rhamnosus Xl-12 after low power microwave irradiation was investigated. Under a microwave power of 400 W and irradiation length of 3 min, a mutated strain W4-3-9 with high-yield L-lactic acid was obtained by screening. Compared with the starting strain X1-12, the L-lactic acid production of W4-3-9 was increased by 58.0% at a concentration of 115.8 g/L. The strain maintained the capability of producing a high L-lactic acid level after 10 generations. Cell surface morphology and DNA structures of parental and mutated strains were observed by atomic force microscopy （ AFM ）. Amplified fragment length polymorphism （AFLP） analysis suggested the difference in AFLP band pattern between the mutated and non-mutated strains. Sequencing and BLAST analysis revealed that the catalytic site of lactate dehydrogenase （DHL） was changed due to the microwave induced mutation.展开更多
The paper deals with one important class of reaction-diffusion equations, u' + μ(u - uk) = 0(2 ≤ k ∈ Z+) with boundary value condition u(0) = u(π) = 0. Singularity theory based on the method of L-S (Liapunov-S...The paper deals with one important class of reaction-diffusion equations, u' + μ(u - uk) = 0(2 ≤ k ∈ Z+) with boundary value condition u(0) = u(π) = 0. Singularity theory based on the method of L-S (Liapunov-Schmidt) is applied to its bifurcation analysis. And the satisfactory results are obtained.展开更多
We completely determine the universal central extension of the generalized orthosymplectic Lie superalgebra ospm 12n（R,-） that is coordinatized by an arbitrary unital associative superalgebra （R,-） with superinvol...We completely determine the universal central extension of the generalized orthosymplectic Lie superalgebra ospm 12n（R,-） that is coordinatized by an arbitrary unital associative superalgebra （R,-） with superinvolution. As a result, an identification between the second homology group of the Lie superalgebra ospm｜2n （R,-） and the first skew-dihedral homology group of the associative superalgebra （R,-） with superin-volution is created for positive integers m and n with （m, n）≠ （1, 1） and （m, n）≠（2, 1）. The second homology groups of the Lie superalgebras ospm1｜2（R,-） and ospm｜2n （R,-） are also characterized explicitly.展开更多
The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibr...The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.展开更多
基金the China Postdoctoral Science Foundation(20060400017)
文摘The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative, associative algebra A. It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group, analogous to the well known relationship of Lie algebras and Lie groups.
基金Sponsored by the National Natural Science Foundation of China(Grant No.50778053)
文摘Mutagenesis of Lactobacillus casei subsp, rhamnosus Xl-12 after low power microwave irradiation was investigated. Under a microwave power of 400 W and irradiation length of 3 min, a mutated strain W4-3-9 with high-yield L-lactic acid was obtained by screening. Compared with the starting strain X1-12, the L-lactic acid production of W4-3-9 was increased by 58.0% at a concentration of 115.8 g/L. The strain maintained the capability of producing a high L-lactic acid level after 10 generations. Cell surface morphology and DNA structures of parental and mutated strains were observed by atomic force microscopy （ AFM ）. Amplified fragment length polymorphism （AFLP） analysis suggested the difference in AFLP band pattern between the mutated and non-mutated strains. Sequencing and BLAST analysis revealed that the catalytic site of lactate dehydrogenase （DHL） was changed due to the microwave induced mutation.
基金Supported by the National Natural Science Foundation (19971057) and by theYouth Science Foundation of Shanghai Municipal Commi
文摘The paper deals with one important class of reaction-diffusion equations, u' + μ(u - uk) = 0(2 ≤ k ∈ Z+) with boundary value condition u(0) = u(π) = 0. Singularity theory based on the method of L-S (Liapunov-Schmidt) is applied to its bifurcation analysis. And the satisfactory results are obtained.
基金supported by National Natural Science Foundation of China (Grant No. 11501213)the China Postdoctoral Science Foundation (Grant No. 2015M570705)+2 种基金the Fundamental Research Funds for the Central Universities (Grant No. 2015ZM085)the China Postdoctoral Science Foundation (Grant No. 2015M571928)the Fundamental Research Funds for the Central Universities
文摘We completely determine the universal central extension of the generalized orthosymplectic Lie superalgebra ospm 12n（R,-） that is coordinatized by an arbitrary unital associative superalgebra （R,-） with superinvolution. As a result, an identification between the second homology group of the Lie superalgebra ospm｜2n （R,-） and the first skew-dihedral homology group of the associative superalgebra （R,-） with superin-volution is created for positive integers m and n with （m, n）≠ （1, 1） and （m, n）≠（2, 1）. The second homology groups of the Lie superalgebras ospm1｜2（R,-） and ospm｜2n （R,-） are also characterized explicitly.
文摘The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.
