Convergence of delay differential equations driven by fractional Brownian motion

In this note, we prove an existence and uniqueness result of solution for stochastic differential delay equations with hereditary drift driven by a fractional Brownian motion with Hurst parameter H > 1/2. Then, we show that, when the delay goes to zero, the solutions to these equations converge, almost surely and in L ^p , to the solution for the equation without delay. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann–Stieltjes integral.     

Origin of stereoinduction by chiral aminophosphane phosphinite ligands in enantioselective catalysis: asymmetric hydroformylation

The origin of stereoinduction by chiral aminophosphane phosphinite (AMPP) ligands in asymmetric hydroformylation was investigated with a theoretical approach. The roles of the stereogenic center at the aminophosphane phosphorus atom (NP*) and of the chirality of the backbone were analyzed by considering three experimentally tested cases: 1) P-stereogenic yielding high ee, 2) P-nonstereogenic yielding low ee, and 3) P-stereogenic yielding low ee. We succeeded in reproducing the experimentally observed trends for the three studied AMPP ligands. Our results indicated that alkene insertion into the rhodium-hydride bond is the selectivity-determining step, and not alkene coordination. Additional calculations on model systems revealed that the different nonbonding weak-type interactions of styrene with the substituents of the NP* stereogenic center in an axial position is responsible for stereodifferentiation. The chirality of the AMPP backbone plays a secondary role. The rationalization of the stereochemical outcome is not straightforward, because two competitive equatorial/axial reaction paths, showing opposite asymmetric induction, must be considered. Construction of stereochemical models and evaluation of stereoinduction for novel ligand systems suggested that two prerequisites are required to improve the performance of AMPP-type ligands in asymmetric hydroformylation: 1) combination of stereorecognition and stereohindrance by substituents at the NP* atom, and 2) more rigid backbones.     

Analysis of pesticides and metabolites in Spanish surface waters by isotope dilution gas chromatography/mass spectrometry with previous automated solid-phase extraction Estimation of the uncertainty of the analytical results

A method based on isotope dilution gas chromatography/mass spectrometry (GC/MS) with automated solid-phase extraction (SPE) is described for the analysis of 32 pesticides and metabolites in surface waters. This approach consist in the use of nine isotopically labelled representative pesticides as internal standards, which allows high accuracy (trueness and precision) and sensitivity for most analysed compounds, as it is required for isotope dilution-based methods. Uncertainties associated with pesticide determination in real samples were estimated using quality assurance/quality control (QA/QC) data. For most pesticides expanded uncertainty was below 40%, according to the commonly established requirements for analytical results. Ninety three Spanish surface waters collected in June-July and September-November 2004 were analysed. Concentration and occurrence of pesticides were evaluated. These parameters were higher in the summer than in the autumn period. In summer four pesticides were found in more than 50% of the analysed samples and four compounds were detected above the concentration level of 1 microg/l (atrazine, terbutylazine, 3,4-dichloroaniline and fenitrothion), while in autumn percentage of detection was below 50% for all pesticides and only one compound (terbutylazine) exceeded 1 microg/l.     

Alternative syntheses of the new D2d symmetric tetramethyl tricyclo- [3.3.0.0(3,7)]octane-1,3,5,7-tetracarboxylate

Two alternative syntheses of the new D2d symmetric tetramethyl tricyclo[3.3.0.0(3,7)]octane-1,3,5,7-tetracarboxylate from the known dimethyl 3,7-dioxo-cis-bicyclo[3.3.0]octane-1,5-dicarboxylate and 1,5-(2,2'-biphenylene)-cis-bicyclo[3.3.0]octane-3,7-dione are described.     

Structural dimorphism of N-(3-hydroxysalicylidene)-2,4,6-trimethylaniline

The title compound N-(3-hydroxysalicylidene)-2,4,6-trimethylaniline exhibits dimorphism. The structure of (I) is orthorhombic Pbca with a = 22.222(3), b = 16.200(2), c = 7.596(2) Å, V = 2735(1) ų, and Z = 8. The structure of (II) is monoclinic P2₁/c with a = 11.734(1), b = 15.734(1), c = 7.432(2) Å, = 100.97(1)°, V = 1347.0(5)ų, and Z = 4. The two structures are analyzed in relation with the possibility of an equilibrium between two tautomeric phenol and quinone forms by rapid hydrogen transfer. The molecules associated by intermolecular hydrogen bonds form centrosymmetric dimers. The compounds are thermochromic. The results are compared with the photochromic analog N-(hydroxysalicylidene)-2,4,6-trimethylaniline (compound III) and with the thermochromic one N-(5-hydroxysalicylidene)-2,4,6-trimethylaniline (compound IV). It is concluded that the 3-hydroxyl substituent of the salicylidene moiety enables the intermolecular hydrogen transfer from oxygen to nitrogen.     

Convex decomposition of games and axiomatizations of the core and the D-core

This paper provides an axiomatic framework to compare the D-core (the set of undominated imputations) and the core of a cooperative game with transferable utility. Theorem 1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity. Moreover, these axioms also characterize the core on the domain of convex games, totally balanced games, balanced games, and superadditive games.