On the Existence of Strong Solutions to a Coupled Fluid-Structure Evolution Problem

We consider here a model of fluid-structure evolution problem which, in particular, has been largely studied from the numerical point of view. We prove the existence of a strong solution to this problem.     

Modularity in the lattice of Σ-permutable subgroups

For a Hall system of a finite solvable group G, it is known that the set of -permutable subgroups is a sublattice of the subgroup lattice of G. We investigate the class SPM of groups in which the lattice is modular. We prove that if is modular, then U V for all (an evidently stronger condition). Both of these phenomena—the modularity of and whether two -permutable subgroups U and V permute with each other—are shown to be determined locally, by what happens at each prime. The class SPM is shown to be quotient closed, but not direct product or subgroup closed.This revised electronic version of the Abstract includes the formulas that were missing in the previous electronic version published online in September 2004.     

Congruence-preserving functions on Stone and Kleene algebras

We investigate local polynomial functions on Stone algebras and on Kleene algebras. We find a generating set for the clone of all local polynomial functions. We also represent local polynomial functions on a given algebra by polynomial functions of some canonical extension of this algebra.     

A relation between the zeros of an <Emphasis Type="Italic">L</Emphasis>-function belonging to the Selberg class and the zeros of an associated <Emphasis Type="Italic">L</Emphasis>-function twisted by a Dirichlet character

Let F (s) be a function belonging to the Selberg class. For a primitive Dirichlet character , we can define the -twist F(s) of F (s). If F(s) also belongs to the Selberg class and satisfies some other conditions then there is a relation between the zeros of F (s) and the zeros F(s). Further we give an operator theoretic interpretation of this relation according to A. Connes study.Received: 5 January 2004     

On the connectedness of self-affine attractors

Let T = T(A, D) be a self-affine attractor in defined by an integral expanding matrix A and a digit set D. In the first part of this paper, in connection with canonical number systems, we study connectedness of T when D corresponds to the set of consecutive integers . It is shown that in and , for any integral expanding matrix A, T(A, D) is connected. In the second part, we study connectedness of Pisot dual tiles, which play an important role in the study of -expansions, substitutions and symbolic dynamical systems. It is shown that each tile of the dual tiling generated by a Pisot unit of degree 3 is arcwise connected. This is naturally expected since the digit set consists of consecutive integers as above. However surprisingly, we found families of disconnected Pisot dual tiles of degree 4. We even give a simple necessary and sufficient condition of connectedness of the Pisot dual tiles of degree 4. Detailed proofs will be given in [4]. Received: 2 March 2003     

On the structure of rings which are sums of two subrings

We study the structure of rings that are sums of two subrings one of which is nil and the other reduced. Our main results concern the problem whether in this situation the nil subring must be an ideal.Received: 13 July 2001     

Many triangulated 3-spheres

We construct combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2^{O(n log n)} combinatorial types of simplicial 4-polytopes, this proves that asymptotically there are far more combinatorial types of triangulated 3-spheres than of simplicial 4-polytopes on n vertices. This complements results of Kalai (1988), who had proved a similar statement about d-spheres and (d+1)-polytopes for fixed d4.Mathematics Subject Classification (1991): 52B11, 52B70, 57Q15Supported by the Deutsche Forschungsgemeinschaft within the European graduate program Combinatorics, Geometry, and Computation (GRK 588/1) and an MSRI post-doctoral fellowship.Partially supported by Deutsche Forschungs-Gemeinschaft (DFG), via the DFG Research Center Mathematics in the Key Technologies (FZT86), the Research Group Algorithms, Structure, Randomness (Project ZI 475/3), and a Leibniz grant (ZI 475/4).     

Space-time decay of Navier–Stokes flows invariant under rotations

We show that the solutions to the non-stationary Navier–Stokes equations in (d=2,3) which are left invariant under the action of discrete subgroups of the orthogonal group O(d) decay much faster as than in generic case and we compute, for each subgroup, the precise decay rates in space-time of the velocity field.     

Automorphisms of <Emphasis Type="Italic">F</Emphasis><Subscript>4</Subscript> quadrangles

The goal of this article is to show that the automorphism group of a Moufang quadrangle of type F₄ is, up to field automorphisms, generated by the root groups. Mathematics Subject Classification (2000):51E12, 15A63, 20E42The author is a Research Assistant of the Fund for Scientific Research - Flanders (Belgium) (F.W.O.-Vlaanderen).     

The hypertree poset and the ℓ<Superscript>2</Superscript>-Betti numbers of the motion group of the trivial link

We give explicit formulae for the Euler characteristic and ²-cohomology of the group of motions of the trivial link, or isomorphically the group of free group automorphisms that send each standard generator to a conjugate of itself. The method is primarily combinatorial and ultimately relies on a computation of the Möbius function for the poset of labelled hypertrees.Partially supported by NSF grant no. DMS-0101506Partially supported by an AMS Centennial Research Fellowship