Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation

Let H be a Tonelli Hamiltonian defined on the cotangent bundle of a compact and connected manifold and let u be a semi-concave function defined on M. If E (u) is the set of all the super-differentials of u and (\phi t) the Hamiltonian flow of H, we prove that for t > 0 small enough, \phi-t (E (u)) is an exact Lagrangian Lipschitz graph. This provides a geometric interpretation/explanation of a regularization tool that was introduced by P.~Bernard to prove the existence of C 1,1 subsolutions

Footprints in the sky: using student track logs from a "bird's eye view" virtual field trip to enhance learning

Research into virtual field trips (VFTs) started in the 1990s but, only recently, the maturing technology of devices and networks has made them viable options for educational settings. By considering an experiment, the learning benefits of logging the movement of students within a VFT are shown. The data are visualized by two techniques: “animated path maps” are dynamic animations of students' movement in a VFT; “paint spray maps” show where students concentrated their visual attention and are static. A technique for producing these visualizations is described and the educational use of tracking data in VFTs is critically discussed

Algebraic lattice constellations: bounds on performance

In this work, we give a bound on performance of any full-diversity lattice constellation constructed from algebraic number fields. We show that most of the already available constructions are almost optimal in the sense that any further improvement of the minimum product distance would lead to a negligible coding gain. Furthermore, we discuss constructions, minimum product distance, and bounds for full-diversity complex rotated Z[i]/sup n/-lattices for any dimension n, which avoid the need of component interleaving

Renal colic in a dialysis patient: a case of renal stone disease

Renal colic in a dialysis patient: a case of renal stone diseas

Displacement energy of unit disk cotangent bundles

We give an upper bound of a Hamiltonian displacement energy of a unit disk cotangent bundle $D^*M$ in a cotangent bundle $T^*M$, when the base manifold $M$ is an open Riemannian manifold. Our main result is that the displacement energy is not greater than $C r(M)$, where $r(M)$ is the inner radius of $M$, and $C$ is a dimensional constant. As an immediate application, we study symplectic embedding problems of unit disk cotangent bundles. Moreover, combined with results in symplectic geometry, our main result shows the existence of short periodic billiard trajectories and short geodesic loops.Comment: Title slightly changed. Close to the version published online in Math Zei

A variational principle for actions on symmetric symplectic spaces

We present a definition of generating functions of canonical relations, which are real functions on symmetric symplectic spaces, discussing some conditions for the presence of caustics. We show how the actions compose by a neat geometrical formula and are connected to the hamiltonians via a geometrically simple variational principle which determines the classical trajectories, discussing the temporal evolution of such ``extended hamiltonians'' in terms of Hamilton-Jacobi-type equations. Simplest spaces are treated explicitly.Comment: 28 pages. Edited english translation of first author's PhD thesis (2000

Evaluation of European Land Data Assimilation System (ELDAS) products using in site observations

Three land-surface models with land-data assimilation scheme (DA) were evaluated for one growing season using in situ observations obtained across Europe. To avoid drifts in the land-surface state in the models, soil moisture corrections are derived from errors in screen-level atmospheric quantities. With the in situ data it is assessed whether these land-surface schemes produce adequate results regarding the annual range of the soil water content, the monthly mean soil moisture content in the root zone and evaporative fraction (the ratio of evapotranspiration to energy available at the surface). DA considerably reduced bias in net precipitation, while slightly reducing RMSE as well. Evaporative fraction was improved in dry conditions but was hardly affected in moist conditions. The amplitude of soil moisture variations tended to be underestimated. The impact of improved land-surface properties like Leaf Area Index, water holding capacity and rooting depth may be as large as corrections of the DA systems. Because soil moisture memorizes errors in the hydrological cycle of the models, DA will remain necessary in forecast mode. Model improvements should be balanced against improvements of DA per se. Model bias appearing from persistent analysis increments arising from DA systems should be addressed by model improvement