Existence of minimizers for a class of quasi-convex functionals with non-standard growth

We study the lower semicontinuity properties of non-autonomous variational integrals whose energy densities satisfy general growth conditions. We apply these results to solve Dirichlet’s boundary value problems for such functionals. Received: June 14, 2000; in final form: November 25, 2000 Published online: December 19, 2001     

Index growth of hypersurfaces with constant mean curvature

In this paper we give the precise index growth for the embedded hypersurfaces of revolution with constant mean curvature (cmc) 1 in (Delaunay unduloids). When n=3, using the asymptotics result of Korevaar, Kusner and Solomon, we derive an explicit asymptotic index growth rate for finite topology cmc 1 surfaces with properly embedded ends. Similar results are obtained for hypersurfaces with cmc bigger than 1 in hyperbolic space. Received: 6 July 2000; in final form: 10 September 2000 / Published online: 25 June 2001     

Poincaré series and monodromy of a two-dimensional quasihomogeneous hypersurface singularity

A relation is proved between the Poincaré series of the coordinate algebra of a two-dimensional quasihomogeneous isolated hypersurface singularity and the characteristic polynomial of its monodromy operator. For a Kleinian singularity not of type A _{2 n} , this amounts to the statement that the Poincaré series is the quotient of the characteristic polynomial of the Coxeter element by the characteristic polynomial of the affine Coxeter element of the corresponding root system. We show that this result also follows from the McKay correspondence. Received: Received: 25 October 2001 / Revised version: 19 November 2001     

Grothendieck space ideals and weak continuity of polynomials on locally convex spaces

We introduce the classes of locally convex spaces with the local Dunford-Pettis property and locally dual Schur spaces. We examine their properties and their relationship to other classes of locally convex spaces. In the class of locally convex spaces with the local Dunford-Pettis property all polynomials are weakly sequentially continuous whereas in the class of locally dual Schur spaces all polynomials are weakly continuous on bounded sets. Research supported by Science Foundation Ireland, Basic Research Grant 2004.     

The effect of concentrating potentials in some singularly perturbed problems

The equation with boundary Dirichlet zero data is considered in a bounded domain . Under the assumption that concentrates, as , round a manifold and that f is a superlinear function, satisfying suitable growth assumptions, the existence of multiple distinct positive solutions is proved. Received: 19 December 2000 / Accepted: 8 May 2001 / Published online: 5 September 2002     

On Some Second Order Differential Equations with Convergent Solutions

Via a special integral transformation, asymptotic integration results for ordinary differential equations are used to establish accurate asymptotic developments for radial solutions of the elliptic equation Δu + K(|x|)e ^u = 0, |x| > x ₀ > 0, in the bidimensional case.     

On some equations in prime rings

The main purpose of this paper is to prove the following result. Let R be a prime ring of characteristic different from two and let T : R → R be an additive mapping satisfying the relation T(x ³) = T(x)x ² − xT(x)x + x ² T(x) for all x ∈ R. In this case T is of the form 4T(x) = qx + xq, where q is some fixed element from the symmetric Martindale ring of quotients. This result makes it possible to solve some functional equations in prime rings with involution which are related to bicircular projections.     

Efficient separation routines for the symmetric traveling salesman problem I: general tools and comb separation

This is the first of a series of two papers dedicated to efficient separation heuristics for violated inequalities in the context of solving to optimality instances of the Traveling Salesman Problem via branch-and-cut. In this paper we give the basic ideas behind these heuristics and design heuristics for comb separation. The second paper will deal with more complex inequalities such as Clique Tree, Star or Path and Ladder inequalities and give computational results. Received: September 1999 / Accepted: August 2001?Published online February 14, 2002     

Large Sieve Inequality with Quadratic Amplitudes

In this paper, we develop a large sieve type inequality with quadratic amplitude. We use the double large sieve to establish non-trivial bounds.