A simple proof of the Grobman–Hartman theorem for nonuniformly hyperbolic flows

We give a simple and direct proof of the Grobman–Hartman theorem for nonautonomous differential equations obtained from perturbing a nonuniform exponential dichotomy. In particular, we do not need to pass through discrete time and obtain the result as a consequence of a corresponding result for maps. To the best of our knowledge, this is the first direct approach for nonuniform exponential dichotomies. We also show that the conjugacies are continuous in time and Hölder continuous in space. In addition, we describe the dependence of the conjugacies on the perturbation, and we obtain a reversibility result for the conjugacies of reversible differential equations. We emphasize that the additional work required to consider nonuniform exponential dichotomies is substantial.     

Structural insights for the design of new PPARgamma partial agonists with high binding affinity and low transactivation activity

Peroxisome Proliferator-Activated Receptor γ (PPARγ) full agonists are molecules with powerful insulin-sensitizing action that are used as antidiabetic drugs. Unfortunately, these compounds also present various side effects. Recent results suggest that effective PPARγ agonists should show a low transactivation activity but a high binding affinity to inhibit phosphorylation at Ser273. We use several structure activity relationship studies of synthetic PPARγ agonists to explore the different binding features of full and partial PPARγ agonists with the aim of differentiating the features needed for binding and those needed for the transactivation activity of PPARγ. Our results suggest that effective partial agonists should have a hydrophobic moiety and an acceptor site with an appropriate conformation to interact with arm II and establish a hydrogen bond with Ser342 or an equivalent residue at arm III. Despite the fact that interactions with arm I increase the binding affinity, this region should be avoided in order to not increase the transactivation activity of potential PPARγ partial agonists.     

Local analytic first integrals of planar analytic differential systems

We study the existence of local analytic first integrals of a class of analytic differential systems in the plane, obtained from the Chua?s system studied in L.O. Chua (1992, 1995), N.V. Kuznetsov et al. (2011), G.A. Leonov et al. (2012) , ,  and . The method used can be applied to other analytic differential systems.     

Production of Upsilon(1S) mesons from chi(b) decays in p&pmacr; collisions at sqrt

We have reconstructed the radiative decays chi(b)(1P)-->Upsilon(1S)gamma and chi(b)(2P)-->Upsilon(1S)gamma in p&pmacr; collisions at sqrt[s] = 1.8 TeV, and measured the fraction of Upsilon(1S) mesons that originate from these decays. For Upsilon(1S) mesons with p(Upsilon)(T)>8.0 GeV/c, the fractions that come from chi(b)(1P) and chi(b)(2P) decays are [27.1+/-6.9(stat)+/-4. 4(syst)]% and [10.5+/-4.4(stat)+/-1.4(syst)]%, respectively. We have derived the fraction of directly produced Upsilon(1S) mesons to be [50.9+/-8.2(stat)+/-9.0(syst)]%.     

Center manifolds for infinite delay

We obtain a C¹ center manifold theorem for perturbations of delay difference equations in Banach spaces with infinite delay. Our results extend in several directions the existing center manifold theorems. Besides considering infinite delay equations, we consider perturbations of nonuniform exponential trichotomies and generalized trichotomies that may exhibit stable, unstable and central behaviors with respect to arbitrary asymptotic rates ecρ(n) for some diverging sequence ρ(n). This includes as a very special case the usual exponential behavior with ρ(n)=n.     

Diffusive motion in a model for particle hopping

The diffusive motion of adsorbates on crystal planes is studied by means of a lattice gas model with stochastic dynamics, in the disordered phase and at half coverage. The diffusion coefficient and the time-correlation functions measured in field-emission experiments are calculated. These correlation functions are shown to have the proper hydrodynamic power law decay at long times. It is pointed out that if experiments are done at times before the onset of the hydrodynamic regime the value of the diffusion coefficient obtained will be too small. Our results show also that correlations among the adsorbed particles persist for times longer than predicted by a hydrodynamical approximation.     

Limits on light gravitino production and new processes with large missing transverse energy in p&pmacr; collisions at sqrt

Events collected by the Collider Detector at Fermilab (CDF) with an energetic jet plus large missing transverse energy can be used to search for physics beyond the standard model. We see no deviations from the expected backgrounds and set upper limits on the production of new processes. We consider in addition the production of light gravitinos and set a limit at 95% confidence level on the breaking scale sqrt[F]>/=217 GeV, which excludes gravitino masses smaller than 1.1x10(-5) eV/c(2).