Sous ellipticite dans le cadre du calcul S(m,g)

Abstract

We study the regularity of the free boundary in the two membranes problem. We prove that around any point the free boundary is either a C ^{1, α} surface or a cusp, as in the obstacle problem. We also prove C ^{1, 1} regularity for the pair of functions solving the problem.     

Transsynaptic transport of wheat germ agglutinin expressed in a subset of type II taste cells of transgenic mice

Background

Neurogenesis continues to occur throughout life but dramatically decreases with increasing age. This decrease is mostly related to a decline in proliferative activity as a result of an impoverishment of the microenvironment of the aged brain, including a reduction in trophic factors and increased inflammation.

Results

We determined that human umbilical cord blood mononuclear cells (UCBMC) given peripherally, by an intravenous injection, could rejuvenate the proliferative activity of the aged neural stem/progenitor cells. This increase in proliferation lasted for at least 15 days after the delivery of the UCBMC. Along with the increase in proliferation following UCBMC treatment, an increase in neurogenesis was also found in the aged animals. The increase in neurogenesis as a result of UCBMC treatment seemed to be due to a decrease in inflammation, as a decrease in the number of activated microglia was found and this decrease correlated with the increase in neurogenesis.

Conclusion

The results demonstrate that a single intravenous injection of UCBMC in aged rats can significantly improve the microenvironment of the aged hippocampus and rejuvenate the aged neural stem/progenitor cells. Our results raise the possibility of a peripherally administered cell therapy as an effective approach to improve the microenvironment of the aged brain.     

Highly Robust but Surface‐Active: An N‐Heterocyclic Carbene‐Stabilized Au25 Nanocluster

Surface organic ligands play a critical role in stabilizing atomically precise metal nanoclusters in solutions. However, it is still challenging to prepare highly robust ligated metal nanoclusters that are surface‐active for liquid‐phase catalysis without any pre‐treatment. Now, an N‐heterocyclic carbene‐stabilized Au₂₅ nanocluster with high thermal and air stabilities is presented as a homogenous catalyst for cycloisomerization of alkynyl amines to indoles. The nanocluster, characterized as [Au₂₅(ⁱPr₂‐bimy)₁₀Br₇]²⁺ (ⁱPr₂‐bimy=1,3‐diisopropylbenzimidazolin‐2‐ylidene) ( 1 ), was synthesized by direct reduction of AuSMe₂Cl and ⁱPr₂‐bimyAuBr with NaBH₄ in one pot. X‐ray crystallization analysis revealed that the cluster comprises two centered Au₁₃ icosahedra sharing a vertex. Cluster 1 is highly stable and can survive in solution at 80 °C for 12 h, which is superior to Au₂₅ nanoclusters passivated with phosphines or thiols. DFT computations reveal the origins of both electronic and thermal stability of 1 and point to the probable catalytic sites. This work provides new insights into the bonding capability of N‐heterocyclic carbene to Au in a cluster, and offers an opportunity to probe the catalytic mechanism at the atomic level.     

Self-passivating edge reconstructions of graphene

Planar reconstruction patterns at the zigzag and armchair edges of graphene were investigated with density-functional theory. It was unexpectedly found that the zigzag edge is metastable and a planar reconstruction spontaneously takes place at room temperature. The reconstruction changes electronic structure and self-passivates the edge with respect to adsorption of atomic hydrogen from a molecular atmosphere.     

A Confined <Emphasis Type="Italic">N</Emphasis>-Dimensional Harmonic Oscillator

We compute the energy eigenvalues for the N-dimensional harmonic oscillator confined in an impenetrable spherical cavity. The results show their dependence on the size of the cavity and the space dimension N. The obtained results are compared with those for the free N-dimensional harmonic oscillator, and as a result, the notion of fractional dimensions is pointed out. Finally, we examine the correlation between eigenenergies for confined oscillators in different dimensions.     

X-ray diffraction and Mössbauer spectroscopy of high energy ball-milled α-Fe2O3/TiO2 composite powders

α–Fe₂O₃/TiO₂ Composite powders have been prepared by high energy ball-milling for different times. The composites were studied using Mössbauer Spectroscopy (MS) and X-ray diffraction (XRD). The patterns of XRD show broadening in the diffraction peaks, indicating a decrease in the particle size of the composites with milling time. Also, the XRD patterns show an evolving new structural phase correlated with an evolving Titanium ferrite species with milling time. Mössbauer Spectroscopy shows the evolving titanium ferrite species characterized by a quadrupole doublet at the expense of the α–Fe₂O₃ represented by the magnetic sextet. The doublet corresponding to the Ti-ferrite phase dominates the Mössbauer spectra at long milling time (greater than 100 h of milling).     

Application of a novel nano-immobilization of ionic liquid on an MCM-41 system for trimethylsilylation of alcohols and phenols with hexamethyldisilazane

Research on Chemical Intermediates - 3-[(3-(Trisilyloxy)propyl)chloride]-1-methylimidazolium tribromide ionic liquid supported on MCM-41 [nano-MCM-41@(CH2)3-1-methylimidazole]Br3 as a novel...