Shooting Methods for Numerical Solution of Nonlinear Stochastic Boundary-Value Problems

Abstract

In the present investigation, shooting methods are described for numerically solving nonlinear stochastic boundary-value problems. These stochastic shooting methods are analogous to standard shooting methods for numerical solution of ordinary deterministic boundary-value problems. It is shown that the shooting methods provide accurate approximations. An error analysis is performed and computational simulations are described.     

Kinetics and mechanisms of gas‐phase elimination of 2,2‐diethoxyethyl amine and 2,2‐diethoxy‐N,N‐diethylethanamine

The gas‐phase elimination kinetics of 2,2‐diethoxyethyl amine and 2,2‐diethoxy‐N,N‐diethylethanamine (320–380 °C; 40–150 Torr) in a seasoned reaction vessel are homogeneous, unimolecular and obey a first‐order rate law. These elimination processes involve two parallel reactions. The first gives ethanol and the corresponding 2‐ethoxyethenamine. The latter compound further decomposes to ethylene, CO and the corresponding amine. The second parallel reaction produce ethane and the corresponding ethyl ester of an α‐amino acid. The following Arrhenius expressions are given as: For 2,2‐diethoxyethyl amine For 2,2‐diethoxy‐N,N‐diethylethanamine Comparative kinetic and thermodynamic parameters of the overall, the parallel and the consecutive reactions lead to consider two types of mechanisms in terms of a concerted polar cyclic transition state structures. Copyright © 2008 John Wiley & Sons, Ltd.     

Antidiarrhoeic effect and dereplication of the aqueous extract of Annona crassiflora (Annonaceae)

We investigated the antidiarrhoeic effect of the aqueous extract of Annona crassiflora leaves (AEAC). The AEAC decreased the diarrhoeic stools and enteropooling induced by castor oil, without altering total faecal output; moreover, the distance travelled by charcoal meal in the intestine was increased. Twenty-eight compounds were identified by LC-DAD-MS in the AEAC, including flavonoids, alkaloids and proanthocyanidins. In addition, two oligomeric series of condensed tannins of up to nine flavan-3-ol units were characterised by MALDI-MS. These data suggest that the antidiarrhoeic effect of the AEAC is related to its ability to inhibit intestinal secretion and/or to increase intestinal absorption. Moreover, the prokinetic effect of AEAC, together with its inhibitory effect on enteropooling induced by castor oil, explains why this extract decreased diarrhoeic faeces without altering the total faecal output. All these effects are in agreement with the pharmacological activity reported in the literature for many of the secondary metabolites identified.     

Collection of NMR Scalar and Residual Dipolar Couplings Using a Single Experiment

A new DMSO‐compatible aligning gel based on cross‐linked poly(2‐hydroxylethyl methacrylate) (poly‐HEMA) has been developed. Due to a significant difference in bulk magnetic susceptibility between the DMSO inside and outside the gel, it is possible to simultaneously collect isotropic and anisotropic NMR data, such as residual dipolar couplings (RDC), in the same NMR tube. RDC‐assisted structural analysis of menthol and the alkaloid retrorsine is reported as proof of concept.     

Resonance Assisted Chalcogen Bonding as a New Synthon in the Design of Dyes

Intramolecular chalcogen bonding in arylhydrazones of sulfamethizole is strengthened by conjugation in the π-system of a noncovalent five-membered ring. The S⋅⋅⋅O distance in the sulfamethizole moiety of these compounds ranges from 2.698(3) to 2.806(15) Å, which indicates its strong dependence on the attached arylhydrazone fragments. Information on the nature of the intramolecular chalcogen bond was afforded by DFT calculations.     

Diffusion of magnetic field lines in a confined RFP plasma

Summary  A volume-preserving symplectic map is proposed to describe the magnetic field lines when the Taylor equilibriumis perturbed in a generic way. The standard scenario is observed by varying the perturbation strength, but the statistical properties in the chaotic regions are not simple due to the presence of boundaries and remnants of invariant structures. Simpler models of volume-preserving maps are proposed. The slowly modulated standard map captures the basic topological and statistical features. The diffusion is analytically described for large perturbations (above the break-up of the last KAM torus) in terms of correlation functions and for small perturbations using the adiabatic theory, provided that the modulation is sufficiently slow.     

Water-soluble and stable dinitrogen phosphine complexes trans-[ReCl(N2)(PTA-H)n(PTA)4-n]n+ (n = 0-4), the first with 1,3,5-triaza-7-phosphaadamantane

The first dinitrogen complexes with the hydrosoluble PTA ligand, or its protonated form PTA-H, trans-[ReCl(N2)(PTA-H)n(PTA)(4-n)]n+ (n = 0-4), are prepared, shown to be soluble and stable in water, interconvertible by stepwise protonation/deprotonation and to form, upon N2 loss, the corresponding penta-coordinate compounds. Dinitrogen displacement by CO affords trans-[ReCl(CO)(PTA)4].     

The condensation of salicylaldehydes and malononitrile revisited: synthesis of new dimeric chromene derivatives

The reaction of salicylic aldehydes with malononitrile was reinvestigated, and the reaction pathway was followed by 1H NMR spectroscopy. A delicate control of the experimental conditions allowed the synthesis of 2-imino-2H-chromene-3-carbonitriles 1, (2-amino-3-cyano-4H-chromen-4-yl)malononitriles 2, 4-amino-5-imino-2,7-dimethoxy-5H-chromeno[3,4-c]pyridine-1-carbonitrile 12, and (4,5-diamino-1-cyano-1,10b-dihydro-2H-chromeno[3,4-c]pyridin-2-ylidene)malononitrile 13. Two novel 2-iminochromene dimers, with structures 8 and 9, were isolated and fully characterized. The activity of compound 8a on Aspergillus spp. growth and on ochratoxin A production was evaluated. The results of the bioassays indicate that compound 8a, applied at concentrations of 2 mM, totally inhibited the growth of the fungi tested. Ochratoxin A production by Aspergillus alliaceus was reduced by about 93% with a 200 microM solution of this compound. A moderate inhibitory effect was observed for the analogous structure 8b, and no inhibition was registered for compounds 2 and 1, used as synthetic precursors of the dimeric species 8.