A New Relaxation Space for Obstacles

The space of obstacles (i.e. p-quasi upper semicontinuous functions) is endowed with a distance which is topologically equivalent to the -convergence. We find the metric completion of this space and we give some application for minimization problems of cost functionals depending on obstacles via their level sets. An element of the completion is a decreasing and _p -continuous on the left mapping Rt _t , where _t are positive Borel measures vanishing on sets of zero p-capacity.     

Thermal stability of alkoxy monolayers grafted on Si(1 1 1)

Direct grafting of organic monolayers on Si is of prime interest in order to give specific properties to a silicon surface. However, for microelectronics applications, this possibility is hampered by the limited stability of the grafted layers. It has been previously established that alkyl layers attached to Si surfaces through Si-C bonds become unstable at 250-300 °C, by desorption of alkenes. Changing the nature of the bonding to the surface might allow one to circumvent this desorption pathway and increase the layer stability. In our work, decanol and decyl aldehyde are reacted with the Si(1 1 1)-H surface at ∼100 °C during 20 h in order to obtain alkoxy monolayers. FTIR measurements performed in ATR geometry show that the grafted molecule surface coverage is on the order of 33% after reaction with decanol and 50% after reaction with decyl aldehyde. Characterization by AFM essentially reveals that the morphology of the grafted surfaces is unaffected as compared to that of Si-H surfaces. However, the edges of the terraces at alcohol-grafted surfaces exhibit some pitting, probably due to the presence of water in the grafting liquid. Thermal stability studies show that alkoxy chains progressively disappear from the Si surface between 200 and 400 °C. From the CH₂/CH₃ ratio in the CH region (2760-3070 cm⁻¹), it appears that the chains undergo progressive dissociation by C-C bond breaking before their complete disappearance from the surface. Therefore, the thermal behaviour of alkoxy monolayers appears quite distinct from that of alkyl monolayers that tend to leave the surface in a much narrower temperature range (250-350 °C), essentially via breaking of the Si-C bonds.     

Stanley depth of multigraded modules

The Stanley's Conjecture on Cohen–Macaulay multigraded modules is studied especially in dimension 2. In codimension 2 similar results were obtained by Herzog, Soleyman-Jahan and Yassemi. As a consequence of our results Stanley's Conjecture holds in 5 variables.     

Mineralization of biomimetically carboxymethylated collagen fibrils in a model dual membrane diffusion system

In the present work, we show for the first time, that N^?-carboxymethyllysine is the major product of the in vitro non-enzymatic glycation reaction between fibrillar collagen and glucuronic acid. Dual diffusion membrane system was effectively used for oriented crystal growth of octacalcium phosphate/hydroxyapatite on the biomimetically carboxymethylated collagen fibrils. We hypothesize that the function of biomimetically carboxymethylated collagen is to increase the local concentration of corresponding ions in such a way that a critical nucleus of ions can be formed, leading to the formation of the mineral under specific micro-environment conditions achieved by using diffusion membrane system.     

Finite filtrations of modules and shellable multicomplexes

We introduce pretty clean modules, extending the notion of clean modules by Dress, and show that pretty clean modules are sequentially Cohen–Macaulay. We also extend a theorem of Dress on shellable simplicial complexes to multicomplexes.     

Bessel sequences of exponentials on fractal measures

Jorgensen and Pedersen have proven that a certain fractal measure ν has no infinite set of complex exponentials which form an orthonormal set in L²(ν). We prove that any fractal measure μ obtained from an affine iterated function system possesses a sequence of complex exponentials which forms a Riesz basic sequence, or more generally a Bessel sequence, in L²(μ) such that the frequencies have positive Beurling dimension.