A New Method for Estimating the Distribution of Scan Statistics for a Two-Dimensional Poisson Process

A method for estimating the distribution of scan statistics with high precisìon was introduced in Haiman (2000). Using that method sharp bounds for the errors were also established. This paper is concerned with the application of the method in Haiman (2000) to a two-dimensional Poisson process. The method involves the estimation by simulation of the conditional (fixed number of points) distribution of scan statistics for the particular rectangle sets of size 2 × 2, 2 × 3, 3 × 3, where the unit is the (1 × 1) dimension of the squared scanning window. In order to perform these particular estimations, we develop and test a perfect simulation algorithm. We then perform several numerical applications and compare our results with results obtained by other authors.     

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.     

Core-level electronic properties of nanostructured NiO coatings

Nanostructured NiO films with different thicknesses were grown on nanoporous alumina membrane substrates by reactive evaporation of Ni in an oxygen atmosphere. The reactive deposition process was assisted by a low energy oxygen ion-beam in order to increase the NiO input into the pores. Surface morphology and structure of the films were analyzed by SEM and XPS. SEM observations reveal a well adhered film of NiO on the substrate. This film appears to be uniform and presents a rather irregular nanostructured morphology, built of NiO clusters with sizes ranging between 5 and 30 nm. The core-level electronic properties of this nanostructured NiO film result to be similar to those of an ultrathin film about one monolayer thick. This behaviour can be explained by the large surface to volume ratio of both systems.     

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.     

Syntheses, structures and intermolecular interactions of tetraorganoammonium, -phosphonium and -stibonium dimethyl- and diphenyltetrahaloantimonates

The syntheses and spectroscopic (NMR, MS) investigations of the antimonates [Ph₄P]⁺[Me₂SbCl₄]⁻ (1), [Me₄Sb]⁺[Me₂SbCl₄]⁻ (2), [Et₄N]⁺[Ph₂SbCl₄]⁻ (3), [Bu₄N]⁺[Ph₂SbCl₄]⁻ (4), [Me₄Sb]⁺[Ph₂SbCl₄]⁻ (5), [Et₃MeSb]⁺[Ph₂SbCl₄]⁻ (6), [Et₄N]⁺[Ph₂SbF₄]⁻ (7) and [Et₄N]⁺[Ph₂SbBr₄]⁻ (8) are reported. Halogen scrambling reactions of Et₄NBr or Ph₄EBr (E = P, Sb) with R₂SbCl₃ (R = Me, Ph) produce mixtures of compounds from which crystals of [Et₄N]⁺[Ph₂SbBr_1.24Cl_2.76]⁻ (9), [Et₄N]⁺[Ph₂SbBr_2.92Cl_1.08]⁻ (10) or [Ph₄Sb]⁺[Me₂SbCl₄]⁻ (11) were isolated. The crystal and molecular structures of 1 and 3-11 are reported.