Optimal portfolio for a small investor in a market model with discontinuous prices

A consumption-investment problem is considered for a small investor in the case of a market model in which prices evolve according to a stochastic equation with a jump-process component. The techniques we use include the martingale representation theorem, Lagrange multiplier methods, and Markovian methods for the resolution of stochastic differential equations. We establish a Black-Scholes formula.     

Fonctions holomorphes bornees sur la boule unite deC n

Sans résumé     

Oblique derivative and interface problems on polygonal domains and networks

We Investigate oblique derivative problems associated to the Laplace operator on a polygon and we extend our study to "polygonal interface problems" which are an extension to networks of the prevlous ones. We focus on the non variational character of such problems. We obtain index formulae, a calculus of the dimension of the kernel, an expansion of the 'semi-variational" (or weak) solutions into regular and singular parts and formulae for the coefficients of the singularities In such expanslons.     

Electrochromatography in poly(dimethyl)siloxane microchips using organic monolithic stationary phases

This paper shows the in situ synthesis of an hexyl acrylate monolith in PDMS microfluidic devices and its subsequent use as stationary phase for electrochromatography on chip. To overcome the ability of PDMS material to absorb organic monomers, surface modification of the enclosed channels was realized by UV-mediated graft polymerization. This grafting procedure is based on the preliminary adsorption of a photoinitiator onto the PDMS surface and polymerization of charged monomers. Next, hexyl acrylate monoliths were cast in situ using photopolymerization process. The chromatographic behavior of the monolithic column was confirmed by the successful separation of derivatized catecholamines in the PDMS device using a 30 mm effective separation length (100 microm x 100 microm section). Efficiencies reached up to 200,000 plates per meter.     

Chromatographic behaviour of steroidal saponins studied by high-performance liquid chromatography-mass spectrometry

The chromatographic behaviour of steroidal saponins found in Anemarrhena asphodeloides, Asparagus officinalis, Convallaria majalis, Digitalis purpurea and Ruscus aculeatus was studied by HPLC-MS using a C-18 reversed-phase column and aqueous acetonitrile or aqueous methanol mobile phase gradients, with or without the addition of 1% acetic acid. The behaviour was compared to that of triterpene saponins found in Aesculus hippocastanum, Centella asiatica, Panax notoginseng and Potentilla tormentilla. Inclusion of methanol in the mobile phase under acidic conditions was found to cause furostanol saponins hydroxylated at C-22 to chromatograph as broad peaks, whereas the peak shapes of the spirostanol saponins and triterpene saponins studied remained acceptable. In aqueous methanol mobile phases without the addition of acid, furostanol saponins chromatographed with good peak shape, but each C-22 hydroxylated furostanol saponin was accompanied by a second chromatographic peak identified as its C-22 methyl ether. Methanolic extracts analysed in non-acidified aqueous acetonitrile mobile phases also resolved pairs of C-22 hydroxy and C-22 methoxy furostanol saponins. The C-22 methyl ether of deglucoruscoside was found to convert to deglucoruscoside during chromatography in acidified aqueous acetonitrile, or by dissolving in water. Poor chromatography of furostanol saponins in acidified aqueous methanol is due to the interconversion of the C-22 hydroxy and C-22 methoxy forms. It is recommended that initial analysis of saponins by HPLC-MS using a C-18 stationary phase is performed using acidified aqueous acetonitrile mobile phase gradients. The existence of naturally-occurring furostanol saponins methoxylated at C-22 can be investigated with aqueous acetonitrile mobile phases and avoiding methanol in the extraction solvent.     

Target analysis of primary photoprocesses involved in the oxyblepharismin-binding protein

Target analysis is performed on previously published transient absorption spectra of the 200-kDa oxyblepharismin-binding protein (OBIP) thought to trigger the photophobic response of the ciliate Blepharisma japonicum. The OBIP sample is considered as heterogeneous and made of two distinct classes of chromophore-protein complexes. A so-called nonreactive class is seen to be comparable to free oxyblepharismin in organic solution. Another, reactive, class is shown to undergo a fast picosecond photocycle involving the formation in 4 ps of an intermediate state noted Y1. The spectrum associated to Y1 bears striking similarities with that of the oxyblepharismin radical cation. This element favors the hypothesis that an excited-state intermolecular electron-transfer could be the primary step of the sensory transduction chain of B. japonicum. Proton release is also considered as a possible secondary step. These possibilities support the idea that reactive OBIP functions like an electron or proton pump. We alternatively propose a new hypothesis stating that the fast photocycle of reactive OBIP actually does not generate any photoproduct or protein change of conformation but is involved in another biological function. It would act as a kind of solar screen, providing additional protection to the light-adapted form of B. japonicum in case of excessive illumination.     

β‐Elimination of an aziridine to an allylic amine: a mechanistic study

The base‐induced rearrangement of aziridines has been examined using a combination of calculations and experiment. The calculations show that the substituent on nitrogen is a critical feature that greatly affects the favorability of both α‐deprotonation, and β‐elimination to form an allylic amine. Experiments were carried out to determine whether E2‐like rearrangement to the allylic amine with lithium diisopropyl amide (LDA) is possible. N‐tosyl aziridines were found to deprotonate on the tosyl group, preventing further reaction. A variety of N‐benzenesulfonyl aziridines having both α‐ and β‐protons decomposed when treated with LDA in either tetrahydrofuran or hexamethylphosphoramide. However, when α‐protons were not present, allylic amine was formed, presumably via β‐elimination. Copyright © 2011 John Wiley & Sons, Ltd.     

NMR parameters in alkali, alkaline earth and rare earth fluorides from first principle calculations

(19)F isotropic chemical shifts for alkali, alkaline earth and rare earth of column 3 basic fluorides are measured and the corresponding isotropic chemical shieldings are calculated using the GIPAW method. When using the PBE exchange-correlation functional for the treatment of the cationic localized empty orbitals of Ca(2+), Sc(3+) (3d) and La(3+) (4f), a correction is needed to accurately calculate (19)F chemical shieldings. We show that the correlation between experimental isotropic chemical shifts and calculated isotropic chemical shieldings established for the studied compounds allows us to predict (19)F NMR spectra of crystalline compounds with a relatively good accuracy. In addition, we experimentally determine the quadrupolar parameters of (25)Mg in MgF(2) and calculate the electric field gradients of (25)Mg in MgF(2) and (139)La in LaF(3) using both PAW and LAPW methods. The orientation of the EFG components in the crystallographic frame, provided by DFT calculations, is analysed in terms of electron densities. It is shown that consideration of the quadrupolar charge deformation is essential for the analysis of slightly distorted environments or highly irregular polyhedra.