Multiplication operators on the Bergman space via analytic continuation

In this paper, using the group-like property of local inverses of a finite Blaschke product ?, we will show that the largest C^?-algebra in the commutant of the multiplication operator M? by ? on the Bergman space is finite dimensional, and its dimension equals the number of connected components of the Riemann surface of ?−1°? over the unit disk. If the order of the Blaschke product ? is less than or equal to eight, then every C^?-algebra contained in the commutant of M? is abelian and hence the number of minimal reducing subspaces of M? equals the number of connected components of the Riemann surface of ?−1°? over the unit disk.     

Extended Deligne–Lusztig varieties for general and special linear groups

We give a generalisation of Deligne–Lusztig varieties for general and special linear groups over finite quotients of the ring of integers in a non-archimedean local field. Previously, a generalisation was given by Lusztig by attaching certain varieties to unramified maximal tori inside Borel subgroups. In this paper we associate a family of so-called extended Deligne–Lusztig varieties to all tamely ramified maximal tori of the group.Moreover, we analyse the structure of various generalised Deligne–Lusztig varieties, and show that the “unramified” varieties, including a certain natural generalisation, do not produce all the irreducible representations in general. On the other hand, we prove results which together with some computations of Lusztig show that for SL₂(Fq???/(?²)), with odd q, the extended Deligne–Lusztig varieties do indeed afford all the irreducible representations.     

Monotonicity of solutions of Fully nonlinear uniformly elliptic equations in the half-plane

In this paper we study the monotonicity of positive (or non-negative) viscosity solutions to uniformly elliptic equations F(∇u,D²u)=f(u) in the half plane, where f is locally Lipschitz continuous (with f(0)?0) and zero Dirichlet boundary conditions are imposed. The result is obtained without assuming the u or |∇u| are bounded.     

A Reilly inequality for the first Steklov eigenvalue

Let M be a compact submanifold with boundary of a Euclidean space or a Sphere. In this paper, we derive an upper bound for the first non-zero eigenvalue p₁ of Steklov problem on M in terms of the r-th mean curvatures of its boundary ∂M. The upper bound obtained is sharp.     

A note on geodesic connectedness of Gödel type spacetimes

In this note we reduce the problem of geodesic connectedness in a wide class of Gödel type spacetimes to the search of critical points of a functional naturally involved in the study of geodesics in standard static spacetimes. Then, by using some known accurate results on the latter, we improve previous results on the former.     

On the weak topology of Banach spaces over non-archimedean fields

It is known that within metric spaces analyticity and K-analyticity are equivalent concepts. It is known also that non-separable weakly compactly generated (shortly WCG) Banach spaces over R or C provide concrete examples of weakly K-analytic spaces which are not weakly analytic. We study the case which totally differs from the above one. A general theorem is provided which shows that a Banach space E over a locally compact non-archimedean non-trivially valued field is weakly Lindelöf iff E is separable iff E is WCG iff E is weakly web-compact (in the sense of Orihuela). This provides a non-archimedean version of a remarkable Amir-Lindenstrauss theorem.     

Failure of n‐uniqueness: a family of examples

In this paper, the connections between model theory and the theory of infinite permutation groups (see 11 ) are used to study the n‐existence and the n‐uniqueness for n‐amalgamation problems of stable theories. We show that, for any n ? 2, there exists a stable theory having (k + 1)‐existence and k‐uniqueness, for every k ? n, but has neither (n + 2)‐existence nor (n + 1)‐uniqueness. In particular, this generalizes the example, for n = 2, due to Hrushovski given in 3 . © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

类铜Au50+离子电子碰撞激发特性的研究

利用全相对论扭曲波（RDW）方法,系统计算了类铜Au50+离子的外壳层电子4s激发到4l 、5l （ l= s、p、d、f,除去4s-4s ）和内壳层电子3l （l = s、p、d）激发到4l 、5l （l = s、p、d、f）的碰撞激发截面,研究了在不同入射电子能量下截面的变化规律,给出了3d-4f 和3d-5f 精细结构能级的碰撞激发截面。部分计算结果与其它理论及最新实验结果进行了比较,取得了很好的一致性。     

Solutions of the Yang–Baxter equations on quadratic Lie groups: The case of oscillator groups

A Lie group is called quadratic if it carries a bi-invariant semi-Riemannian metric. Oscillator Lie groups constitute a subclass of the class of quadratic Lie groups. In this paper, we determine the Lie bialgebra structures and the solutions of the classical Yang–Baxter equation on a generic class of oscillator Lie algebras. Moreover, we show that any solution of the generalized classical Yang–Baxter equation (resp. classical Yang–Baxter equation) on a quadratic Lie group determines a left invariant locally symmetric (resp. flat) semi-Riemannian metric on the corresponding dual Lie groups.     

Impedance spectroscopy and conductometric biosensing for probing catalase reaction with cyanide as ligand and inhibitor

In this work, a new biosensor was prepared through immobilization of bovine liver catalase in a photoreticulated poly (vinyl alcohol) membrane at the surface of a conductometric transducer. This biosensor was used to study the kinetics of catalase–H₂0₂ reaction and its inhibition by cyanide. Immobilized catalase exhibited a Michaelis–Menten behaviour at low H₂0₂ concentrations (< 100 mM) with apparent constant K_M^app = 84 ± 3 mM and maximal initial velocity V_M^app = 13.4 μS min^? 1. Inhibition by cyanide was found to be non-competitive and inhibition binding constant K_i was 13.9 ± 0.3 μM. The decrease of the biosensor response by increasing cyanide concentration was linear up to 50 μM, with a cyanide detection limit of 6 μM. In parallel, electrochemical characteristics of the catalase/PVA biomembrane and its interaction with cyanide were studied by cyclic voltammetry and impedance spectroscopy. Addition of the biomembrane onto the gold electrodes induced a significant increase of the interfacial polarization resistance R_P. On the contrary, cyanide binding resulted in a decrease of Rp proportional to KCN concentration in the 4 to 50 μM range. Inhibition coefficient I₅₀ calculated by this powerful label-free and substrate-free technique (24.3 μM) was in good agreement with that determined from the substrate-dependent conductometric biosensor (24.9 μM).