Bott's vanishing theorem for regular Lie algebroids

Differential geometry has discovered many objects which determine Lie algebroids playing a role analogous to that of Lie algebras for Lie groups. For example:

--- differential groupoids,

--- principal bundles,

--- vector bundles,

--- actions of Lie groups on manifolds,

--- transversally complete foliations,

--- nonclosed Lie subgroups,

--- Poisson manifolds,

--- some complete closed pseudogroups.

We carry over the idea of Bott's Vanishing Theorem to regular Lie algebroids (using the Chern-Weil homomorphism of transitive Lie algebroids investigated by the author) and, next, apply it to new situations which are not described by the classical version, for example, to the theory of transversally complete foliations and nonclosed Lie subgroups in order to obtain some topological obstructions for the existence of involutive distributions and Lie subalgebras of some types (respectively).

     

Orbifolds and analytic torsions

In this paper, we calculate the behavior of the Quillen metric by orbifold immersions. We thus extend a formula of Bismut-Lebeau to the orbifold case.

R´ESUMÉ. Dans cet article, on calcule le comportement de métrique de Quillen par immersions d'orbifold. On étend ainsi une formule de Bismut-Lebeau au cas d'orbifold.

     

Strichartz estimates for the Schrödinger equation with radial data

We prove an endpoint Strichartz estimate for radial solutions of the two-dimensional Schrödinger equation:

     

On the resolution of relative Thue equations

An efficient algorithm is given for the resolution of relative Thue equations. The essential improvement is the application of an appropriate version of Wildanger's enumeration procedure based on the ellipsoid method of Fincke and Pohst.

Recently relative Thue equations have gained an important application, e.g., in computing power integral bases in algebraic number fields. The presented methods can surely be used to speed up those algorithms.

The method is illustrated by numerical examples.

     

Abelian categories, almost split sequences, and comodules

The following are equivalent for a skeletally small abelian Hom-finite category over a field with enough injectives and each simple object being an epimorphic image of a projective object of finite length.

(a) Each indecomposable injective has a simple subobject.

(b) The category is equivalent to the category of socle-finitely copresented right comodules over a right semiperfect and right cocoherent coalgebra such that each simple right comodule is socle-finitely copresented.

(c) The category has left almost split sequences.

     

On the oscillation and periodic character of a third order rational difference equation

We prove that every positive solution of the following difference equation:

converges to a period two solution.

     

Extender-based Radin forcing

We define extender sequences, generalizing measure sequences of Radin forcing.

Using the extender sequences, we show how to combine the Gitik-Magidor forcing for adding many Prikry sequences with Radin forcing.

We show that this forcing satisfies a Prikry-like condition, destroys no cardinals, and has a kind of properness.

Depending on the large cardinals we start with, this forcing can blow the power of a cardinal together with changing its cofinality to a prescribed value. It can even blow the power of a cardinal while keeping it regular or measurable.

     

Explicit upper bounds for exponential sums over primes

We give explicit upper bounds for linear trigonometric sums over primes.

     

Solution of a functional equation arising in an axiomatization of the utility of binary gambles

For a new axiomatization, with fewer and weaker assumptions, of binary rank-dependent expected utility of gambles the solution of the functional equation

is needed under some monotonicity and surjectivity conditions. We furnish the general such solution and also the solutions under weaker suppositions. In the course of the solution we also determine all sign preserving solutions of the related general equation

     

A short proof of Ellentuck's Theorem

We combine standard arguments to give a shorter proof of Ellentuck's Theorem.

     

Good ideals in Gorenstein local rings obtained by idealization

The structure of certain equimultiple good ideals in Gorenstein local rings obtained by idealization is explored.

     

A short proof that hyperspaces of Peano continua are absolute retracts

We give a short proof of Wojdyslawski's famous theorem.

     

Error analysis for the computation of zeros of regular Coulomb wave function and its first derivative

In 1975 one of the coauthors, Ikebe, showed that the problem of computing the zeros of the regular Coulomb wave functions and their derivatives may be reformulated as the eigenvalue problem for infinite matrices. Approximation by truncation is justified but no error estimates are given there.

The class of eigenvalue problems studied there turns out to be subsumed in a more general problem studied by Ikebe et al. in 1993, where an extremely accurate asymptotic error estimate is shown.

In this paper, we apply this error formula to the former case to obtain error formulas in a closed, explicit form.

     

Characteristic classes for complex bundles with trivial real reduction

This note concerns itself with a theory of characteristic classes for those complex bundles whose real reductions are trivial.

     

Finite representability of operators in the sense of Bellenot

We present several new results about the notion of finite representability of operators introduced by Bellenot.

     

Central extensions and generalized plus-constructions

We describe the effect of homological plus-constructions on the homotopy groups of Eilenberg-MacLane spaces in terms of universal central extensions.

     

Cardinal elementary extensions

We determine the consistency strength of some model theoretic extension properties for cardinals.

     

Actions of finitely generated groups on the universal Menger curve

We prove that every finitely generated group acts effectively on the universal Menger curve.

     

A note on duality between measure and category

We show that there is no Erdös-Sierpinski mapping preserving addition.

     

Classification of torsion-free genus zero congruence groups

We study and classify all torsion-free genus zero congruence subgroups of the modular group.