Abelian varieties over finitely generated fields and the conjecture of Geyer and Jarden on torsion

In this paper we prove the Geyer‐Jarden conjecture on the torsion part of the Mordell‐Weil group for a large class of abelian varieties defined over finitely generated fields of arbitrary characteristic. The class consists of all abelian varieties with big monodromy, i.e., such that the image of Galois representation on ?‐torsion points, for almost all primes ?, contains the full symplectic group.     

New Poincaré-type inequalities

We present some Poincaré-type inequalities for quadratic matrix fields with applications e.g. in gradient plasticity or fluid dynamics. In particular, applications to the pseudostress–velocity formulation of the stationary Stokes problem and to infinitesimal gradient plasticity are discussed.     

Null Controllability for the Dissipative Semilinear Heat Equation

We consider the exact null controllability problem for the semi- linear heat equation with dissipative nonlinearity in a bounded domain of Rⁿ . The main result of the article asserts that if the nonlinearity is even mildly superlinear, then global null controllability in an arbitrarily short time fails; instead we provide sharp estimates for the controllability time in terms of the size of the initial data.     

The graphs with all but two eigenvalues equal to $$$$ or 0

We determine all graphs for which the adjacency matrix has at most two eigenvalues (multiplicities included) not equal to \(-2\), or 0, and determine which of these graphs are determined by their adjacency spectrum.     

Nuclear moments of neutron deficient iridium isotopes from laser spectroscopy

Laser spectroscopy measurements have been performed on neutron deficient iridium isotopes. The hyperfine structure and isotope shift of the optical Ir I transition 5d⁷6s^{2 4}F_9/2 → 5d⁷6s6p ⁶F_11/2 at 351.5 nm have been studied for the ^182–189Ir, and ^191,193Ir isotopes. The nuclear magnetic and quadrupole moments were obtained from the HFS measurements and the changes of the mean square charge radii from the IS measurements. A large mean square charge radius change between ¹⁸⁷Ir and ¹⁸⁶Ir and between and has been observed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermally‐activated post‐growth dewetting of fullerene C60 on mica

Understanding and controlling the growth and stability of molecular thin films on solid surfaces is necessary to develop nanomaterials with well‐defined physical properties. As a prominent model system in organic electronics, we investigate the post‐growth dewetting kinetics of the fullerene C₆₀ on mica with real‐time and in situ X‐ray scattering. After layer‐by‐layer growth of C₆₀, we find a thermally‐activated post‐growth dewetting, where the smooth C₆₀‐layer breaks up into islands. This clearly shows that growth is kinetically limited before the system moves over an activation barrier into an energetically favored configuration. From the temperature‐dependent dewetting kinetics we find an effective activation barrier of 0.33 eV, which describes both the temperature‐dependent macroscopic changes in the surface morphology and the microscopic processes of inter‐ and intralayer diffusion during dewetting.