The Ultrametric Space of Plane Branches

We study properties of the space of irreducible germs of plane curves (branches), seen as an ultrametric space. We provide various geometrical methods to measure the distance between two branches and to compare distances between branches, in terms of topological invariants of the singularity which comprises some of the branches. We show that, in spite of being very close to the notion of intersection multiplicity between two germs, this notion of distance behaves very differently. For instance, any value in [0, 1] ∩ ? is attained as the distance between a fixed branch and some other branch, in contrast with the fact that the semigroup of the fixed branch has gaps. We also present results that lead to interpret this distance as a sort of geometric distance between the topological equivalence or equisingularity classes of branches.     

Urine NMR Metabolomic Study on Biochemical Activities to Investigate the Effect of P. betle Extract on Obese Rats

Applied Biochemistry and Biotechnology - The present studies are to evaluate the ability of PB to induce weight loss and urine metabolite profile of Piper betle L. (PB) leaf extracts using...     

The hexagonal close-packed nickel nanocrystals prepared by fast scan voltammetry

The nickel (Ni) nanocrystals (average diameter 9.7 ± 2.3 nm) were deposited onto composite graphite electrode from a plating solution of 5.0 mM NiCl₂6H₂O and 1.0 M NH₄Cl using scan rate of 6500 mV s⁻¹. The initial potential −1.5 V and final potential −0.5 V vs. Ag/AgCl with applied time 120 s were used for the whole deposition process. The variations of applied overpotentials and deposition times have affected the characteristics of Ni nanocrystals. It was found that the structural formation of Ni nanocrystals obtained were almost pure hexagonal close-packed (hcp). This study has demonstrated that the tuning of the final size, morphology and structural formation of the Ni nanocrystal were affected by control of nucleation, growth and hydrogen evolution processes in fast scan voltammetry technique used.     

Gold nanoparticle superlattice crystallization probed in situ

The nucleation and growth of three-dimensional superlattices of gold nanoparticles has been followed directly in situ by means of small angle x-ray scattering. These assemblies spontaneously form in a dilute solution providing the particles are large enough to generate a van der Waals driven attraction sufficient to counterbalance the thermal energy. The superlattices nucleate very soon after the birth of the individual particles and their growth kinetics is slower than predicted by a mechanism of simple diffusion of the nanoparticles towards the superlattices. The superlattices are first limited in size (170 nm in diameter) and have a globular shape with a low polydispersity. They present a fcc inner structure with nanoparticles being separated by a capping agent bilayer yielding a low gold internal volume fraction (phi SL = 0.33). In a second stage, these superlattices coalesce with time.     

Some results on Riccati equations,Floquet theory and applications

In this paper, we present two new results to the classical Floquet theory, which provides the Floquet multipliers for two classes of the planar periodic system. One of these results provides the Floquet multipliers independently of the solution of system. To demonstrate the application of these analytical results, we consider a cholera epidemic model with phage dynamics and seasonality incorporated.     

Linear perturbation amplification in self-similar ablation flows of inertial confinement fusion

Exact similarity solutions for inviscid compressible ablative flows in slab symmetry with nonlinear heat conduction are proposed for studying unsteadiness and compressibility effects on the hydrodynamic stability of ablation fronts relevant to inertial confinement fusion. Both the similarity solutions and their linear perturbations are numerically computed with a dynamical multidomain Chebyshev pseudospectral method. Herewith the first analysis of laser-imprinting based on a dynamic solution is presented, showing that maximum perturbation amplification occurs for a laser-intensity modulation of zero transverse wave number, with growth dominated by the mean flow stretching.