Showing papers in "Chinese Annals of Mathematics in 2010"
Journal Article•
TL;DR: In this article, the structures of (n+1)-dimensional n-Lie algebras over an algebraically closed field of characteristic 2 are studied and the classification of(n+ 1)-dimensional (n-Lie) algesbras is provided and the solvability and nilpotency are described.
Abstract: The structures of(n+1)-dimensional n-Lie algebras over an algebraically closed field of characteristic 2 are studied.The classification of(n+1)-dimensional n-Lie algebras is provided and the solvability and nilpotency are described.The concrete expressions of derivations and derivation algebras of(n+1)-dimensional n-Lie algebras are also given.
64 citations
Journal Article•
TL;DR: For the fully nonlinear uniformly elliptic equations, it is well known that the solutions are of C~(2,α) if the nonlinear operators are convex(or concave) as mentioned in this paper.
Abstract: For the fully nonlinear uniformly elliptic equations,it is well-known that the solutions are of C~(2,α) if the nonlinear operators are convex(or concave).By weakening this hypothesis to that the nonlinear operators are of local C~(1, β) almost everywhere for 0 β1, the C~(2,α) regularity of the solutions is still shown in this paper.To prove the conclusion,a kind of iteration method is designed where the Holder continuity is measured by L~p norms.
26 citations
Journal Article•
TL;DR: In this paper, a modification of the Roper-Suffridge extension operator on the unit ball given by F(z)=(f(z_1)+f′(z-1)P(z)-0),[f′ (z_ 1)]~(1/m)z_0)′, where f is a normalized biholomorphic function on D and P is a homogeneous polynomial of degree m and z_0=(z_2,…,z_n).
Abstract: Let m∈N and m≥2.The authors study a modification of the Roper-Suffridge extension operator on the unit ball given by F(z)=(f(z_1)+f′(z_1)P(z_0),[f′(z_1)]~(1/m)z_0)′, where f is a normalized biholomorphic function on the unit disc D,P:C~(n-1)→C is a homogeneous polynomial of degree m and z_0=(z_2,…,z_n).This operator was first introduced by Muir when m=2.In case P≡0 and m=2,the operator reduces to the well-known Roper-Suffridge extension operator.In this paper,some conditions for‖P‖are found under which the operator preserves almost starlike mappings of orderαand starlike mappings of orderα,respectively.The results generalize many recently new results,and the method is easier to handle.In particular,when f(z_1)=z_1 and m=n=2,this operator is of the classical form F(z)=(z_1+az_2~2,z_2)′which is important to construct some concrete examples in geometric function theory of several complex variables.
13 citations
Journal Article•
TL;DR: In this article, a concrete reduced form for parameterized delay differential systems with triple zero singularity is obtained by using center manifold reduction and normal form calculation, and an example is presented to illustrate the results.
Abstract: The paper is devoted to the determination of triple-zero singularity and the generalized eigenspace associated with zero eigenvalues in R~n.A concrete reduced form for parameterized delay differential systems is obtained by using center manifold reduction and normal form calculation.The results given in[A note on the triple zero linear degeneracy: Normal forms,dynamical and bifurcation behaviour of an unfolding.Int J Bifur and Chaos, 2002,12:2799-2820]are employed to analyze the bifurcation behavior of the parameterized delay differential system with triple-zero singularity in detail and an example is presented to illustrate the results.
9 citations
Journal Article•
TL;DR: In this paper, the authors studied the restricted representations of the general linear Lie superalgebras gl(m| n), and took the connection into account with rational representations of corresponding algebraic supergroup GL(m | n).
Abstract: Let k be an algebraically closed field of characteristic p2.In this paper,the authors study the restricted representations of the general linear Lie superalgebras gl(m| n), and take the connection into account with rational representations of the corresponding algebraic supergroup GL(m | n).The main results include(1) The iso-classes of restricted irreducible modules for gl(m | n) are easily parameterized.Some of those modules are just Kac-modules,for judgement of which a necessary and sufficient condition is given, parallel to the case in the field of complex number;(2) The restricted projective modules of gl(m | n)-module can be lifted to a rational GL(m | n)-module when m■n(modp) and p≥2h - 2(h = max{m,n}).Furthermore,such projective modules have Z-filtrations, i.e.,each subquotient of such a filtration is isomorphic to some"baby Verma modules"; (3) A reciprocity formula for the rth Frobenius kernels G_r of G is obtained,which reflects the relation between the multiplicities in such a filtration of the projective cover of simple G_r-modules and the composite numbers of baby Verma modules.
5 citations
Journal Article•
TL;DR: In this article, the coefficients of planar bounded harmonic mappings are sharply estimated and a better estimate of Bloch constants for such bounded-harmonic mappings has been obtained.
Abstract: The coefficients of planar bounded harmonic mappings are sharply estimated and a better estimate of Bloch constants for such bounded harmonic mappings is obtained.As an application,the analogous estimate of Bloch constants for planar biharmonic mappings is also obtained.The results improve the ones made by Grigoryan,Huang,Abdulhadi etc.
5 citations
Journal Article•
TL;DR: In this article, the boundary value problem of a class of singularly perturbed asymptotic solutions for higher order semilinear elliptic equations with two parameters is considered.
Abstract: The boundary value problem of a class of singularly perturbed asymptotic solutions for higher order semilinear elliptic equations with two parameters is considered.Under some suitable conditions,a formal asymptotic expansion of the solution is constructed.By using the fixed theorem,the existence and asymptotic behavior of the solution are studied.
4 citations
Journal Article•
TL;DR: In this paper, the necessary and sufficient conditions for locally univalent harmonic mappings in the unit disk with linearly connected image domains to be harmonic quasiconformal mappings were studied.
Abstract: The author studies the necessary and sufficient conditions for locally univalent harmonic mappings in the unit disk with linearly connected image domains to be harmonic quasiconformal mappings,and determines the parameter domain for a class of univalent harmonic mappings in the unit disk having the univalent harmonic stability property.The results improve and generalize the one made by Chuaqui and Hernandez.
4 citations
Journal Article•
TL;DR: In this article, the authors presented the nth power Δ~n(G) of the augmentation ideal Δ(G), and described the structure of the augmented quotient group Q_n (G) =Δ~ n(G)/Δ(n+1)(G) for dihedral group G = D_(2~t_r)(t≥2,r odd)
Abstract: The authors present the nth powerΔ~n(G) of the augmentation idealΔ(G) and describe the structure of the augmentation quotient group Q_n(G) =Δ~n(G)/Δ~(n+1)(G) for dihedral group G = D_(2~t_r)(t≥2,r odd)It is also obtained that Q_n(D_(2~t_)r)≌Z_2~((s(n))),where s(n) = 2n for 1≤n≤t,and s(n) = 2t + 1 for n≥t + 1
3 citations
Journal Article•
TL;DR: In this paper, it was shown that if the universal covering of N admits a nonnegative strictly convex function with polynomial growth, then there are no nontrivial quasi-harmonic spheres from R~3 to N.
Abstract: It is proved that if the universal covering of N admits a nonnegative strictly convex function with polynomial growth,then there are no nontrivial quasi-harmonic spheres from R~3 to NThe authors also generalize the famous Eells-Sampson's theorem when dim M=3
3 citations
Journal Article•
TL;DR: In this article, a characterization of additive Jordan derivations at zero between factor von Neumann algebras and C~*-algesias is given, with mild assumptions on the center of the algebra.
Abstract: Let A be a unital ring(or algebra) containing a nontrivial idempotent P andδ:A→A be an additive(or a linear) map.δis Jordan derivable at zero ifδ(A)B+Aδ(B)+δ(B)A+Bδ(A)=0 for every A,B∈A with AB+BA=0.Under some mild assumptions on A,the authors show that ifδ(I) belongs to the center of A,thenδis Jordan derivable at zero if and only if there exists an additive Jordan derivationτsuch thatδ(A)=τ(A)+δ(I) A for all A∈A.As its application,a characterization of additive maps Jordan derivable at zero between factor von Neumann algebras is given.The linear bounded maps Jordan derivable at zero between general von Neumann algebras and C~*-algebras are also characterized.
Journal Article•
TL;DR: In this paper, the authors considered the viscous problems of BSCB equation and modified BSCB system for image inpainting, and obtained the existence and uniqueness of global smooth solutions of the VB equation by using semigroup theory.
Abstract: The authors consider the viscous problems of BSCB equation and modified BSCB system for image inpainting.They obtain the existence and uniqueness of global smooth solutions of the viscous BSCB equation by using semigroup theory.In addition,they employ the method of vanishing viscosity to get that the solution of viscous modified BSCB system tends to the solution of Modified BSCB system as the viscosity coefficient v→0.
Journal Article•
TL;DR: The absorbing boundary condition as discussed by the authors is a necessary and sufficient condition for the perfectly matched layers of the Maxwell equations, which can be used to verify the models in the literature and design some new models.
Abstract: The author proves a necessary and sufficient condition for the perfectly matched layers of the Maxwell equations.The core of the condition is the absorbing boundary condition.This criterion can be used to verify the models in the literature and design some new models.Finally some examples are shown.
Journal Article•
TL;DR: It is shown that the two codes corresponding two different polygons may have the same parameters and the result that these new codes are the best at some finite field is also shown.
Abstract: The authors expand the results of JHansen and give two new Toric surface codes,calculate the dimension of the code by using the methods of cohomology and estimate the minimum distance relying on the intersection theoryThe main purpose of the present paper is to show that the two codes corresponding two different polygons may have the same parametersAt last,the result that these new codes are the best at some finite field is also shown
Journal Article•
TL;DR: In this paper, the authors considered the problem of optimal switching combined with discretionary stopping in finite horizon and characterized the optimal value and strategy of switching and stopping in terms of the solution of multi-dimensional reflected backward stochastic differential equation (RBSDE) with hybrid barriers.
Abstract: This paper deals with a problem of optimal switching combined with discretionary stopping in finite horizon.It is an optimal control problem combining features of both stochastic impulse control and optimal stopping.The optimal value and strategy of switching and stopping are characterized in terms of the solution of multi-dimensional reflected backward stochastic differential equation(RBSDE,for short) with hybrid barriers. Then a more general RBSDE is considered and the existence and uniqueness of the solution of that equation are proven.
Journal Article•
TL;DR: The second isomorphism theorem of triangulated categories has been proved in this article, where it is shown that a recollement of a triangulation can induce a recollection of quotient categories naturally.
Abstract: The author proves that a recollement of triangulated categories can induce a recollement of quotient categories naturally.In particular,the second isomorphism theorem of triangulated category,which is just like that of group,is obtained,i.e.,if U is a localizing (resp.colocalizing) subcategory of D and V is a full triangulated subcategory of U,then U/V is a localizing(resp.colocalizing) subcategory of D/V.Moreover,there is a triangulated equivalence(D/V)/(U/V)≌D/U.For the case of recollement of abelian categories,there are some analogous results.
Journal Article•
TL;DR: In this paper, the structure of the even part η of the Hamiltonian superalgebra over a field of prime characteristic was studied and the derivations from η into ■ were derived.
Abstract: The authors study the structure of the even part η of the finite-dimensional Hamiltonian superalgebra over a field of prime characteristicFirst they give a maximal ideal J of η and show that the derivations from η into ■ can be obtained by the derivations from J into ■,where ■ is the even part of the generalized Witt superalgebraThen they give the generating set of the ideal J and define three series of outer derivations from η into ■By using the results above,the derivations vanishing on the non-positive Z-components of η are computedFinally the odd Z-homogeneous derivations and negative Z-homogeneous derivations from η into ■ are determined
Journal Article•
TL;DR: In this paper, the option pricing problem when the underlying risky assets are driven by stochastic exponential of Markov switching Levy process is considered, and the pricing result can be justified by the minimal entropy martingale measure(MEMM).
Abstract: The option pricing problem when the underlying risky assets are driven by stochastic exponential of Markov switching Levy process is considered.That is,the market interest rate,the volatility of the underlying risky assets and the N-state compensator, depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process.The market described by the stochastic exponential of Markov switching Levy process is incomplete in general.Hence,the martingale measure is not unique.The authors adopt a regime switching Esscher transform to determine an equivalent martingale pricing measure.The pricing result can be justified by the minimal entropy martingale measure(MEMM).
Journal Article•
TL;DR: In this article, the smooth radial basis functions in a larger native space generated by a less smooth kernel are used to approximate functions from the larger local space on the unit sphere, and the error bound between the best approximant and the target function is established.
Abstract: The authors embed the smooth radial basis functions in a larger native space generated by a less smooth kernel,and use them,in L~p metric,to approximate functions from the larger native space on the unit sphereAs a result,the L~p error bound between the best approximant and the target function is established
Journal Article•
TL;DR: In this article, the commutativity of Toeplitz operators on the Dirichlet space D~2 with symbols in Ω was studied, which generalizes the case of bounded harmonic symbols and gives a new case for commutative which is different from that of the classical spaces such as the Hardy space or Bergman space.
Abstract: This paper deals with the commutativity of Toeplitz operators on the Dirichlet space D~2 with symbols inΩ,which generalizes the case of bounded harmonic symbols and gives a new case for commutativity which is different from that of the classical spaces such as the Hardy space or Bergman space.Also,it gives the necessary and sufficient conditions for Toeplitz operator on the Dirichlet space D~2 with symbol in L_θ~(∞,1) commuting with that with the radial or quasihomogeneous symbol.The results obtained are quite different from the case on the Hardy space or Bergman space or Dirichlet space D.