Characterizations of ( m,n )-Jordan Derivations and ( m,n )-Jordan Derivable Mappings on Some Algebras

Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n = 0. An additive mapping δ from R into M is called an(m, n)-Jordan derivation if(m +n)δ(A~2) = 2 mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every(m, n)-Jordan derivation with m = n from a C*-algebra into its Banach bimodule is zero. An additive mappingδ from R into M is called a(m, n)-Jordan derivable mapping at W in R if(m + n)δ(AB + BA) =2mδ(A)B + 2 mδ(B)A + 2 nAδ(B) + 2 nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left(right) separating set generated algebraically by all idempotents in A, then every(m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital(A, B)-bimodule and U = [A M N B] is a generalized matrix algebra, then every(m, n)-Jordan derivable mapping at zero from U into itself is equal to zero.     

A note on envelopes of homotopies

In this article, we deal with the notion of the envelopes of homotopies which is the generalized version of functional envelopes in discrete dynamical systems. We prove the stability for envelopes of homotopies in complete normed algebra and we get the stabilities of the derivation and the extended derivation for the notion in the spaces.     

Several Jordan-algebraic aspects of optimization†

We describe some concepts from the theory of Euclidean Jordan algebras and their use in optimization theory. This includes: primal-dual algorithms, optimality conditions, convexity of spectral functions, proof of some inequalities and a Jordan-algebraic version of Horn–Schur theorem     

Determination of sulfonamide residues in cultured sea cucumber by pre-column derivatization capillary electrophoresis with fluorescence detection

A simple and mild method for the separation of sulfonamide residues based on a condensation reaction with O-phthalaldehyde solution (OPA) as labeling reagent with capillary electrophoresis has been developed. A 58.5 cm × 50 μm i.d. (50 cm effective length) untreated fused-silica capillary was used. To optimize the separation conditions, the background electrolyte concentration, pH, column temperature, voltage and other factors were evaluated. The optimal separation conditions were as follows: 20 mmol L^?1 borate buffer; pH 9.1; column temperature 20 °C; separation voltage 18 kV, pressure 50 mbar and injection time 8 s. Under the optimal conditions, 10 kinds of sulfonamide derivatives could be well-separated within 8 min, and the linear ranges were 0.35–100 μg kg^?1. The detection limit (at a signal-to-noise ratio of 3) was in the range of 0.12–0.25 μg kg^?1, and the quantification limit (at a signal-to-noise ratio of 10) was in the range of 0.35–0.70 μg kg^?1. The sulfonamide residues from cultured sea cucumber samples were determined under the optimal conditions with satisfactory results.     

算子代数上2-局部Lie三重导子的结构

设X是维数大于2的Banach空间,映射δ:B(X)→B(X)是2-局部Lie三重导子,则对所有A∈B(X)有δ(A)=[A,T]+ψ(A),这里T∈B(X),ψ是从B(X)到FI的齐次映射且满足对所有A,B∈B(X)有ψ(A+B)=ψ(A),其中B是交换子的和.     

Jordan–Cattaneo waves: Analogues of compressible flow

We review work of Jordan on a hyperbolic variant of the Fisher–KPP equation, where a shock solution is found and the amplitude is calculated exactly. The Jordan procedure is extended to a hyperbolic variant of the Chafee–Infante equation. Extension of Jordan’s ideas to a model for traffic flow are also mentioned. We also examine a diffusive susceptible–infected (SI) model, and generalizations of diffusive Lotka–Volterra equations, including a Lotka–Volterra–Bass competition model with diffusion. For all cases we show how a Jordan–Cattaneo wave may be analysed and we indicate how to find the wavespeeds and the amplitudes. Finally we present details of a fully nonlinear analysis of acceleration waves in a Cattaneo–Christov poroacoustic model.     

对甲氧基苯磺酰氯柱前衍生测定尿中游离羟脯氨酸与脯氨酸

以对甲氧基苯磺酰氯为衍生试剂,建立了分离测定人尿中游离羟脯氨酸和脯氨酸的高效液相色谱方法。考察了衍生温度、衍生缓冲液pH值、衍生时间、衍生剂用量对衍生反应的影响以及流动相组成、流动相缓冲液浓度、pH值和柱温对分离的影响。在优化条件下,羟脯氨酸和脯氨酸分别在5～100μmol/L和5～250μmol/L范围内呈良好线性,相关系数分别为0.999 4、0.999 5,检出限(S/N=3)分别为0.50 nmol/L和0.20 nmol/L,回收率(n=5)分别为95%～99%和96%～102%,相对标准偏差分别为2.1%～4.3%和2.0%～4.8%。该方法可用于人尿中游离羟脯氨酸和脯氨酸的定性定量分析。     

THE EIGENVALUE PERTURBATION BOUND FOR ARBITRARY MATRICES

In this paper we present some new absolute and relative perturbation bounds for theeigenvalue for arbitrary matrices, which improves some recent results. The eigenvalueinclusion region is also discussed.     

4维幂零李代数的导子与triple导子

利用导子和triple导子的定义,刻画了特征不等于2的代数闭域上4维幂零李代数的导子和triple导子.