关于Fejer点上的一种复有理型插值的一致逼近阶

设D是一个Jordan,Г为其边界，并设Г满足Aльпер条件。本文得到了一种基于Fejer点的有理型插值算子对于f(z)∈C（Г）的一致逼近阶。     

以幂零李代数R_n为幂零根基的可解李代数(英文)

In this paper we explicitly determine automorphism group of filiform Lie algebra Rn to find the indecomposable solvable Lie algebras with filiform Lie algebra Rn nilradicals.We also prove that the indecomposable solvable Lie algebras with filiform Rn nilradicals is complete.     

Banach代数上的高阶Jordan-triple导子系的广义Hyers-Ulam-Rassias稳定性

针对Banach代数上的高阶Jordan—triple导子系,基于与函数方程有关的广义的Hyers—Ulam-Rassias稳定性的原理．采用线性算子论的方法,结合广义的Jensen等式,证明了Banach代数上与高阶导子系有关的函数方程具有广义的Hyers—Ulam-Rassias稳定性．证明结果表明该方法实用性强,...     

外加电场对光折变高阶响应影响的微扰分析

应用微扰展开法了“跳跃模型”给出了空间电荷场前三阶分量随时间，外加电场等变化的解析表达式，同时讨论了外加电场对各阶空间电荷场建立的影响，当扩散与外加电场可比拟时，外加电场对空间电荷场的影响不大，随着空间电荷场阶数的提高，其达到最大饱和值所需的外加电磁越小，在外加电场作用下，空间电荷场各阶分量随时间呈振荡衰减，直到达到饱和，外加是场越大，振荡越强烈，周期越短，在考虑高阶分量的贡献后，空间电荷场的振荡     

A characterization of generalized derivations of JSL algebras

Let AlgL be a J-subspace lattice algebra on a Banach space X and M be an operator in AlgL. We prove that if δ : AlgL → B(X) is a linear mapping satisfying δ(AB) = δ(A)B + Aδ(B)for all A, B ∈ AlgL with AMB = 0, then δ is a generalized derivation. This result can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.     

Convergence analysis for second‐order accurate schemes for the periodic nonlocal Allen‐Cahn and Cahn‐Hilliard equations

In this paper, we provide a detailed convergence analysis for fully discrete second‐order (in both time and space) numerical schemes for nonlocal Allen‐Cahn and nonlocal Cahn‐Hilliard equations. The unconditional unique solvability and energy stability ensures ? ⁴ stability. The convergence analysis for the nonlocal Allen‐Cahn equation follows the standard procedure of consistency and stability estimate for the numerical error function. For the nonlocal Cahn‐Hilliard equation, because of the complicated form of the nonlinear term, a careful expansion of its discrete gradient is undertaken, and an H ^?1 inner‐product estimate of this nonlinear numerical error is derived to establish convergence. In addition, an a priori bound of the numerical solution at the discrete level is needed in the error estimate. Such a bound can be obtained by performing a higher order consistency analysis by using asymptotic expansions for the numerical solution. Following the technique originally proposed by Strang (eg, 1964), instead of the standard comparison between the exact and numerical solutions, an error estimate between the numerical solution and the constructed approximate solution yields an O (s ³+h ⁴) convergence in norm, in which s and h denote the time step and spatial mesh sizes, respectively. This in turn leads to the necessary bound under a standard constraint s ≤C h . Here, we also prove convergence of the scheme in the maximum norm under the same constraint.     

Generalized skew derivations on triangular algebras determined by action on zero products

For a triangular algebra 𝒜 and an automorphism σ of 𝒜, we describe linear maps F,G:𝒜→𝒜 satisfying F(x)y+σ(x)G(y) = 0 whenever x,y∈𝒜 are such that xy = 0. In particular, when 𝒜 is a zero product determined triangular algebra, maps F and G satisfying the above condition are generalized skew derivations of the form F(x) = F(1)x+D(x) and G(x) = σ(x)G(1)+D(x) for all x∈𝒜, where D:𝒜→𝒜 is a skew derivation. When 𝒜 is not zero product determined, we show that there are also nonstandard solutions for maps F and G.     

Nonlinear Maps Preserving the Jordan Triple *-Product on Factor von Neumann Algebras

Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.     

Jordan generalized derivations on triangular algebras

Let 𝒜 be a unital algebra and let ? be a unitary 𝒜-bimodule. We consider Jordan generalized derivations mapping from 𝒜 into ?. Our results on unitary algebras are applied to triangular algebras. In particular, we prove that any Jordan generalized derivation of a triangular algebra is a generalized derivation.