Structure of Shocks in Burgers Turbulence with Lévy Noise Initial Data

We study the structure of the shocks for the inviscid Burgers equation in dimension 1 when the initial velocity is given by Lévy noise, or equivalently when the initial potential is a two-sided Lévy process ψ ₀. When ψ ₀ is abrupt in the sense of Vigon or has bounded variation with lim?sup_|h|↓0 h ^?2 ψ ₀(h)=∞, we prove that the set of points with zero velocity is regenerative, and that in the latter case this set is equal to the set of Lagrangian regular points, which is non-empty. When ψ ₀ is abrupt we show that the shock structure is discrete. When ψ ₀ is eroded we show that there are no rarefaction intervals.     

Synchronization learning of coupled chaotic maps

We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization. Numerical calculations reveal a sharp transition between regimes of unsuccessful and successful learning as the algorithm stiffness grows. In the regime of successful learning, an optimal value of the stiffness is found for which the learning time is minimal.     

An innovative method for measuring hydrogen and deuterium: Chemical reaction interface mass spectrometry with nitrogen reactant gas

A new method for measuring deuterium isotopic enrichment with CRIMS (chemical reaction interface mass spectrometry) is described. Using nitrogen as the reactant gas in a chemical reaction interface generates molecular hydrogen that provides the H2 and HD from which the deuterium content can be analyzed with a benchtop quadrupole mass spectrometer. Samples of deuterated leucine in unlabeled leucine were used as the primary test species. Detection of deuterium enrichment was accurate, precise, and linear. We used this scheme to evaluate the results of a process to acetylate lysine residues in a peptide-neurotensin. With separation on a C18 column, we found a 61% yield of the desired monoethylated product that had a D/H ratio very close to the theoretical one. Isotope ratio monitoring for deuterated species will be important in metabolism studies where CRIMS generates a comprehensive and quantitative view of products of deuterated precursors. Where concerns about metabolic isotope effects of deuterium are absent, the use of deuterium will enable these studies to be performed with simpler syntheses and at less cost than if using 13C or 15N.     

Homoconjugated ketones with extended unsaturation: Wavelength-selective,regioselective, diastereoselective,and enantiospecific photochemical transformations of methyl 7-oxospiro[5.5]undeca-1,3-and -2,4,-diene-2-carboxylate

The title molecules were shown to photorearrange with remarkable selectivity. Wavelength variation steers the rearrangement modes, of which the [1,2]-acyl shift was found to be largely regioselective, diastereoselective, and enantiospecific. Chemical intercorrelation of products and mechanistic studies were carried out all along. The potential significance of these photochemical processes in selective synthetic schemes is discussed.     

Oligomerization of 1,2‐Ethanedithiol: An Expedient Approach to Oligothiaethylenethioglycols

Reactions of ethylenedithioglycol (ETG) with Na₂CO₃, K₂CO₃, and Cs₂CO₃ provided the oligothiaethylenethioglycols (nETG): di‐ (DETG), tri‐ (TrETG), tetra‐ (TETG), and pentathiaethylenethioglycol (PETG), along with higher polymers. The most efficient carbonate was K₂CO₃ and reactions using DETG and TrETG as starting materials—or their mixtures—were also found to afford similar species. This largely unknown oligomerization process was thoroughly explored and potential pathways were put forward. A convenient conversion of ETG to laboratory quantities of the otherwise scarce and/or expensive DETG, TrETG, TETG, and PETG oligomers, in organic or aqueous media was achieved. Notably, this straightforward reaction takes place without the addition of expensive or toxic metal catalysts and with pure water as the solvent, thereby highlighting its potential as a green chemical reaction. Moreover, the process opens up new approaches to dynamic combinatorial libraries (DCLs) of oligomers and macrocycles with manifolded nETG [(SCH₂CH₂)_nS] bridges.     

Application of a capillary gas chromatographic-selected-ion recording mass spectrometric technique to the analysis of diethylstilbestrol and its phosphorylated precursors in plasma and tissues

A method for the analysis of diethylstilbestrol (DES) which is suitable for pharmacokinetic studies has been developed using capillary gas chromatographic (GC) separation and detection with selected-ion mass spectrometry (MS). This technique has been applied to a variety of samples including human plasma samples and extracts of animal tissues including prostate and liver. To investigate the pharmacokinetics of stilphostrol (diethylstilbestrol diphosphate) we have modified the GC-MS method in two ways. One modification involves a dual assay for DES; the first a direct assay, and the second after hydrolysis of a sample with alkaline phosphatase. The difference in these values is the amount of phosphorylated DES present. The other modification separates stilphostrol and DES using a reversed-phase, ion-paired high-performance liquid chromatographic method followed by alkaline phosphatase hydrolysis followed by the GC-MS method. The details of these three methods are described and some representative data are shown.     

Selective detection of sulfur-containing compounds by gas chromatography/chemical reaction interface mass spectrometry

Addition of a reactant gas to a low pressure microwave-induced plasma creates a reaction interface in which complex molecules are converted into small polyatomic neutral species. For a given reactant gas the array of these small molecules reflect s the elemental composition of the original analyte. In this study HCI has been found highly effective as a reactant gas for selective detection of sulfur-eontaining compounds using capillary gas chromatography/ chernical reaction interface mass spectrometry. Detection limits as low as 30 pg of a sulfur-containing compound and a dynamic range of two orders of magnitude were achieved.