--- 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).
We combine standard arguments to give a shorter proof of Ellentuck's Theorem.
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.
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.
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
It is shown that submultiplicative inequalities for spectral radii often imply supermultiplicative inequalities, and vice versa.
We give a short proof of Wojdyslawski's famous theorem.
This paper gives explicit evaluations for a Ramanujan-Selberg continued fraction in terms of class invariants and singular moduli.
We prove that every finitely generated group acts effectively on the universal Menger curve.
We calculate the automorphism groups of several Kummer surfaces associated with the product of two elliptic curves. We give their generators explicitly.
converges to a period two solution.
In this note we prove that the generalized SRB measure of an Axiom A basic set is stable under random diffeomorphisms type perturbations.
We present simple proofs of transience/recurrence for certain card shuffling models, that is, random walks on the infinite symmetric group.
In these notes we explore the fine structure of recurrence for semigroup actions, using the algebraic structure of compactifications of the acting semigroup.
The Gauss linear system on the theta divisor of the Jacobian of a nonhyperelliptic curve has two striking properties:
1) the branch divisor of the Gauss map on the theta divisor is dual to the canonical model of the curve;
2) those divisors in the Gauss system parametrized by the canonical curve are reducible.
In contrast, Beauville and Debarre prove on a general Prym theta divisor of dimension all Gauss divisors are irreducible and normal. One is led to ask whether properties 1) and 2) may characterize the Gauss system of the theta divisor of a Jacobian. Since for a Prym theta divisor, the most distinguished curve in the Gauss system is the Prym canonical curve, the natural analog of the canonical curve for a Jacobian, in the present paper we analyze whether the analogs of properties 1) or 2) can ever hold for the Prym canonical curve. We note that both those properties would imply that the general Prym canonical Gauss divisor would be nonnormal. Then we find an explicit geometric model for the Prym canonical Gauss divisors and prove the following results using Beauville's singularities criterion for special subvarieties of Prym varieties:
Theorem. For all smooth doubly covered nonhyperelliptic curves of genus , the general Prym canonical Gauss divisor is normal and irreducible.
Corollary. For all smooth doubly covered nonhyperelliptic curves of genus , the Prym canonical curve is not dual to the branch divisor of the Gauss map.
We prove an endpoint Strichartz estimate for radial solutions of the two-dimensional Schrödinger equation:
A bounded operator between Hilbert spaces has an adjoint if and only if the image of the unit ball is located.
We explain the existence of open sets of complex quasi-modes in terms of Hörmander's commutator condition.
It is characterized when a bilateral operator weighted shift is a Cowen-Douglas operator.
We study and classify all torsion-free genus zero congruence subgroups of the modular group.