Approximation on Nash sets with monomial singularities

This paper is devoted to the approximation of differentiable semialgebraic functions by Nash functions. Approximation by Nash functions is known for semialgebraic functions defined on an affine Nash manifold M, and here we extend it to functions defined on Nash subsets X of M whose singularities are monomial. To that end we discuss first "finiteness" and "weak normality" for such sets X. Namely, we prove that (i) X is the union of finitely many open subsets, each Nash diffeomorphic to a finite union of coordinate linear varieties of an affine space and (ii) every function on X which is Nash on every irreducible component of X extends to a Nash function on M. Then we can obtain approximation for semialgebraic functions and even for certain semialgebraic maps on Nash sets with monomial singularities. As a nice consequence we show that m-dimensional affine Nash manifolds with divisorial corners which are class k semialgebraically diffeomorphic, for k>m^2, are also Nash diffeomorphic.Comment: 39 page

Searching for Dark Matter at the LHC with a Mono-Z

We investigate a mono-Z process as a potential dark matter search strategy at the LHC. In this channel a single Z boson recoils against missing transverse momentum, attributed to dark matter particles, $\chi$, which escape the detector. This search strategy is related, and complementary to, monojet and monophoton searches. For illustrative purposes we consider the process $q\bar{q} -> \chi\chi Z$ in a toy dark matter model, where the Z boson is emitted from either the initial state quarks, or from the internal propagator. Among the signatures of this process will be a pair of muons with high pT that reconstruct to the invariant mass of the Z, and large amounts of missing transverse energy. Being a purely electroweak signal, QCD and other Standard Model backgrounds are relatively easily removed with modest selection cuts. We compare the signal to Standard Model backgrounds and demonstrate that, even for conservative cuts, there exist regions of parameter space where the signal may be clearly visible above background in future LHC data, allowing either new discovery potential or the possibility of supplementing information about the dark sector beyond that available from other observable channels.Comment: 11 pages, 13 figure

Samarium iodide-promoted asymmetric Reformatsky reaction of 3-(2-Haloacyl)-2-oxazolidinones with enals

3-(2-Haloacyl)-2-oxazolidinones were shown to react with enals in an asymmetric SmI2-promoted Reformatsky reaction to give stereochemically well-defined 3-hydroxy-4-alkenyl- and 3-hydroxy-2-methyl-4-alkenyl imides. Chirality transfer of the Evans (S)-oxazolidinone unit via a Zimmerman-Traxler-like transition state resulted in Reformatsky products with a relative syn-configuration. The absolute configuration of compounds obtained is opposite to the corresponding products obtained via aldol addition of boron enolates to enals using the same Evans oxazolidinones

The evaluation of surface diffusion coefficients of gold and platinum atoms at electrochemical interfaces from combined STM-SEM imaging and electrochemical techniques

A simple method is presented for measuring the surface diffusion coefficients of Au and Pt atoms at electrodispersed electrodes of the same metals in contact with 0.5M H2SO4. The technique is based upon the time dependence of the surface roughness factor of electrodispersed metal overlayers. The method requires a model for the surface roughness of the metal structure. The model is deduced from microscopic measurements by a STM integrated into a conventional SEM microscope. This allows the relationship between the roughness factor and the area of the surface structure to be obtained. For Au and Pt in contact with an electrolyte solution, the values of our diffusion coefficients are higher than those reported in vacuum at the same temperature.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA)Facultad de Ciencias Exacta

The evaluation of surface diffusion coefficients of gold and platinum atoms at electrochemical interfaces from combined STM-SEM imaging and electrochemical techniques

A simple method is presented for measuring the surface diffusion coefficients of Au and Pt atoms at electrodispersed electrodes of the same metals in contact with 0.5M H2SO4. The technique is based upon the time dependence of the surface roughness factor of electrodispersed metal overlayers. The method requires a model for the surface roughness of the metal structure. The model is deduced from microscopic measurements by a STM integrated into a conventional SEM microscope. This allows the relationship between the roughness factor and the area of the surface structure to be obtained. For Au and Pt in contact with an electrolyte solution, the values of our diffusion coefficients are higher than those reported in vacuum at the same temperature.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA)Facultad de Ciencias Exacta

Activation of High and Low Affinity Dopamine Receptors Generates a Closed Loop that Maintains a Conductance Ratio and its Activity Correlate

Neuromodulators alter network output and have the potential to destabilize a circuit. The mechanisms maintaining stability in the face of neuromodulation are not well described. Using the pyloric network in the crustacean stomatogastric nervous system, we show that dopamine (DA) does not simply alter circuit output, but activates a closed loop in which DA-induced alterations in circuit output consequently drive a change in an ionic conductance to preserve a conductance ratio and its activity correlate. DA acted at low affinity type 1 receptors (D1Rs) to induce an immediate modulatory decrease in the transient potassium current (I A ) of a pyloric neuron. This, in turn, advanced the activity phase of that component neuron, which disrupted its network function and thereby destabilized the circuit. DA simultaneously acted at high affinity D1Rs on the same neuron to confer activity-dependence upon the hyperpolarization activated current (I h ) such that the DA- induced changes in activity subsequently reduced I h . This DA-enabled, activity-dependent, intrinsic plasticity exactly compensated for the modulatory decrease in I A to restore the I A :I h ratio and neuronal activity phase, thereby closing an open loop created by the modulator. Activation of closed loops to preserve conductance ratios may represent a fundamental operating principle neuromodulatory systems use to ensure stability in their target networks