Geometric Generalizations in Kresin–Maz’ya Sharp Real-Part Theorems

In the present article we present some geometric generalizations of the estimates from Chapters 5,6,7 of the monograph [7]. Received: July 24, 2007. Revised: October 27, 2007.     

Weak Barriers in Nonlinear Potential Theory

We characterize regular boundary points for p-harmonic functions using weak barriers. We use this to obtain some consequences on boundary regularity. The results also hold for -harmonic functions under the usual assumptions on , and for Cheeger p-harmonic functions in metric spaces.      

Pseudofree -actions on surfaces

In this paper, we give a weak classification of locally linear pseudofree actions of the cyclic group of order on a surface, and prove the existence of such an action which cannot be realized as a smooth action on the standard smooth surface.

     

On characterization and perturbation of local -semigroups

Let be a -group with generator , and let be a local -semigroup commuting with . Then the operators , , form a local -semigroup. It is proved that if is injective and is the generator of , then is closable and is the generator of . Also proved are a characterization theorem for local -semigroups with not necessarily injective and a theorem about solvability of the abstract inhomogeneous Cauchy problem:

     

The universal central extension of the three-point loop algebra

We consider the three-point loop algebra,

where denotes a field of characteristic 0 and is an indeterminate. The universal central extension of was determined by Bremner. In this note, we give a presentation for via generators and relations, which highlights a certain symmetry over the alternating group . To obtain our presentation of , we use the realization of as the tetrahedron Lie algebra.

     

Perturbations and Weyl's theorem

A Banach space operator is completely hereditarily normaloid, , if either every part, and (also) for every invertible part , of is normaloid or if for every complex number every part of is normaloid. Sufficient conditions for the perturbation of by an algebraic operator to satisfy Weyl's theorem are proved. Our sufficient conditions lead us to the conclusion that the conjugate operator satisfies -Weyl's theorem.

     

The Noether map II

Let be a faithful representation of a finite group . In this paper we proceed with the study of the image of the associated Noether map

In our 2005 paper it has been shown that the Noether map is surjective if is a projective -module. This paper deals with the converse. The converse is in general not true: we illustrate this with an example. However, for -groups (where is the characteristic of the ground field ) as well as for permutation representations of any group the surjectivity of the Noether map implies the projectivity of .

     

Régularisation et $ \bar \partial_b $ homotopie sur les variétés CR

We give a regularization and ‐homotopy formula on CR generic manifolds. As a consequence we obtain some isomorphism theorems between cohomological groups. This work generalizes Chirka results given on complex manifolds.     

Two lower order nonconforming rectangular elements for the Reissner-Mindlin plate

In this paper, we propose two lower order nonconforming rectangular elements for the Reissner-Mindlin plate. The first one uses the conforming bilinear element to approximate both components of the rotation, and the modified nonconforming rotated element to approximate the displacement, whereas the second one uses the modified nonconforming rotated element to approximate both the rotation and the displacement. Both elements employ a projection operator to overcome the shear force locking. We prove that both methods converge at optimal rates uniformly in the plate thickness in both the - and -norms, and consequently they are locking free.

     

Unprovability of sharp versions of Friedman's sine-principle

For every and every function of one argument, we introduce the statement : ``for all , there is such that for any set of rational numbers, there is of size such that for any two -element subsets and in , we have

We prove that for and any function eventually dominated by , the principle is not provable in . In particular, the statement is not provable in Peano Arithmetic. In dimension 2, the result is: does not prove , where and is the inverse of the Ackermann function.