Extensions of p-adic vector measures

For R being a separating algebra of subsets of a set X, E a complete Hausdorff non-Archimedean locally convex space and m: R → E a bounded finitely additive measure, it is shown that:

a If m is σ-additive and strongly additive, then m has a unique σ-additive extension m^σ on the σ-algebra R^σ generated by R.

b If m is strongly additive and τ-additive, then m has a unique τ-additive extension m^τ on the α-algebra R^bo of all τ_R-Borel sets, where τ_R is the topology having R as a basis.

Also, some other results concerning such measures are given.     

Adaptive finite element methods for Cahn–Hilliard equations

We develop a method for adaptive mesh refinement for steady state problems that arise in the numerical solution of Cahn–Hilliard equations with an obstacle free energy. The problem is discretized in time by the backward-Euler method and in space by linear finite elements. The adaptive mesh refinement is performed using residual based a posteriori estimates; the time step is adapted using a heuristic criterion. We describe the space–time adaptive algorithm and present numerical experiments in two and three space dimensions that demonstrate the usefulness of our approach.     

S-烷基异硫脲盐作为硫醇替代物经环氧开环反应合成β-羟基硫化物

S-烷基异硫脲盐作为一种无毒、无味、易于制备的硫醇替代物，在碱性水介质中、室温下与多种环氧化合物发生环氧开环反应，区域选择性、高收率地合成了一系列β-羟基硫化物。     

Embeddability of multiple cones

The main result of this paper is that if X is a Peano continuum such that its nth cone Cn(X) embeds into Rn+2 then X embeds into S². This solves a problem proposed by W. Rosicki.     

On Euler numbers, polynomials and related p-adic integrals

In this note we give a new proof of Witt's formula for Euler numbers, which are related to some known or new identities involving the Euler numbers. We also obtain a brief proof of a classical result on Euler numbers modulo of two due to M.A. Stern using the approach of p-adic integration, which was recently proved by G. Liu, and Z.-W. Sun. Finally some explicit formulas for Genocchi numbers are proved and applications are given.     

Strongly clean matrix rings over commutative local rings

We will completely characterize the commutative local rings for which M_n(R) is strongly clean, in terms of factorization in R[t]. We also obtain similar elementwise results which show additionally that for any monic polynomial f∈R[t], the strong cleanness of the companion matrix of f is equivalent to the strong cleanness of all matrices with characteristic polynomial f.     

Hopf structures on ambiskew polynomial rings

We derive necessary and sufficient conditions for an ambiskew polynomial ring to have a Hopf algebra structure of a certain type. This construction generalizes many known Hopf algebras, for example U(sl₂), U_q(sl₂) and the enveloping algebra of the three-dimensional Heisenberg Lie algebra. In a torsion-free case we describe the finite-dimensional simple modules, in particular their dimensions, and prove a Clebsch-Gordan decomposition theorem for the tensor product of two simple modules. We construct a Casimir type operator and prove that any finite-dimensional weight module is semisimple.     

A remark on rank varieties for a class of local algebras

We answer a question raised in [9] by showing the equality of two different definitions of rank variety for finitely generated modules over truncated polynomial algebras. We do this by establishing an isomorphism of algebras used in the two definitions of rank variety. Received: 23 April 2007     

水／离子液体两相体系中出芽短梗霉催化4-氯-乙酰乙酸乙酯不对称还原合成（S）-4-氯-3-羟基-丁酸乙酯

考察了水/离子液体两相体系中出芽短梗霉(Aureobasidium pullulansCGMCC1244)催化4-氯乙酰乙酸乙酯(COBE)不对称还原生成光学活性(S)-4-氯-3-羟基丁酸乙酯((S)-CHBE)的性能,并对反应条件如摇床转速、相体积比、温度、初始底物浓度和pH值等进行了优化.结果表明,在水/1-丁基-3-甲基咪唑六氟磷酸盐体系中,出芽短梗霉催化COBE不对称还原生成(S)-CHBE,在30℃,pH6·6,摇床转速180r/min和不对称反应8h条件下,反应物的转化率、产物ee值和浓度分别达到95·6%,98·5%和47·1g/L.在控制pH值为6·6的情况下,通过分添加底物可有效提高产物(S)-CHBE浓度至75·1g/L.