EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.

UNIT VECTOR FIELDS ON ANTIPODALLY PUNCTURED SPHERES: BIG INDEX, BIG VOLUME

We establish in this paper a lower bound for the volume of a unit vector field (v) over right arrow defined ou S(n) \ {+/-x}, n = 2,3. This lower bound is related to the sum of the absolute values of the indices of (v) over right arrow at x and -x.

Some classes of semisimple group (and loop) algebras over finite fields

We determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the Wedderburn decompositions have the least number of simple components We apply our work to obtain similar information about the loop algebras of mdecomposable RA loops and to produce negative answers to the isomorphism problem over various fields (C) 2010 Elsevier Inc All rights reserved

Chemical modification of a nanocrystalline TiO(2) film for efficient electric connection of glucose oxidase

A novel biosensor for glucose was prepared by adsorption of 1,1`-bis(4-carboxybenzyl)-4,4`-bipyridinium di-bromide compound (H(2)BpybcBr(2)) onto the surface of a nanocrystalline TiO(2) film deposited onto FTO glasses, which was used as a platform to assemble the enzyme glucose oxidase to the electrode surface. The H(2)BpybcBr(2)/TiO(2)/FTO modified electrode was characterized by scanning electron microscopy, X-ray fluorescence image, cyclic voltammograms and spectroelectrochemical measurements. The immobilization of GOD on functionalized TiO(2) film led to stable amperometric biosensing for glucose with a linear range from 153 mu mol L(-1) to 1.30 mmol L(-1) and a detection limit of 51 mu mol L(-1). The apparent Michaelis-Menten constant (K(m)) was estimated to be 3.76 mmol L(-1), which suggested a high enzyme-substrate affinity. The maximum electrode sensitivity was 1.25 mu A mmol L(-1). The study proved that the combination of viologen mediators with TiO(2) film retains the electrocatalytic activity of the enzyme, and also enhances the electron transfer process, and hence regenerating the enzyme in the reaction with glucose. (C) 2010 Elsevier Inc. All rights reserved.