Preserving exponential mean-square stability in the simulation of hybrid stochastic differential equations

Positive results are derived concerning the long time dynamics of fixed step size numerical simulations of stochastic differential equation systems with Markovian switching. Euler–Maruyama and implicit theta-method discretisations are shown to capture exponential mean-square stability for all sufficiently small time-steps under appropriate conditions. Moreover, the decay rate, as measured by the second moment Lyapunov exponent, can be reproduced arbitrarily accurately. New finite-time convergence results are derived as an intermediate step in this analysis. We also show, however, that the mean-square A-stability of the theta method does not carry through to this switching scenario. The proof techniques are quite general and hence have the potential to be applied to other numerical methods.     

Palladium-catalyzed regioselective arylation of imidazo[1,2-b][1,2,4]triazine: synthesis of an alpha 2/3-selective GABA agonist

A convergent, practical, and efficient synthesis of 2',6-difluoro-5'-[3-(1-hydroxy-1-methylethyl)imidazo[1,2-b][1,2,4]triazin-7-yl]biphenyl-2-carbonitrile (1), an orally active GABA(A) alpha(2/3)-selective agonist, is described. The seven-step, chromatography-free synthesis was demonstrated on a multi-kilogram scale and utilized biaryl bromide 6 and imidazotriazine 22 as key intermediates. Biaryl bromide 6 was prepared via a highly selective aromatic bromination. The regioselective condensation of aminotriazine 15 with chloroacetaldehyde provided the desired imidazotriazine intermediate 22. A highly regioselective palladium-catalyzed arylation in the final step highlights the efficiency of the route.     

Parallel synthesis and in vitro activity of novel anthranilic hydroxamate-based inhibitors of the prostaglandin H2 synthase peroxidase activity

Currently available non-steroidal anti-inflammatory drugs (NSAIDs) such as aspirin are directed at the cyclooxygenase (COX) site, but not the peroxidase (POX) activity of prostaglandin H2 synthase (PGHS). They are thus unable to inhibit the free-radical induced tissue injury associated with PGHS peroxidase activity, which can occur independently of the COX site. A lead compound, anthranilic hydroxamic acid (AHA) was found to have significant PGHS-POX inhibitory activity (IC50= 72 microM). To define the critical parameters for PGHS-POX inhibition, we investigated 29 AHA derivatives, synthesised from their acid precursors, using solid phase synthesis. In vitro analysis demonstrated a ten-fold improvement in inhibition with 3,5-diiodoanthranilic hydroxamic acid (IC50= 7 microM).     

Non-exponential picosecond fluorescence decay in isolated pentafluorobenzene and hexafluorobenzene

Two-component fluorescence decay has been observed in isolated pentafluorobenzene and hexafluorobenzene excited at 266 nm. From the temperature and pressure dependence of the decay constants an attempt has been made to separate sequence congestion effects from other possible causes of non-exponential behavior.     

Chemistry of the SO Bond. 8—A stereochemical investigation of some methyl-substituted trimethylene sulphites (1,3,2-Dioxathian 2-Oxides) via 13C nuclear magnetic resonance

¹³C NMR chemical shifts for trimethylene sulphite and 35 derivatives are presented. From the magnitudes of the β shifts it has been possible to establish chemical shift additivity relationships for a series of compounds. The results are discussed in terms of probable conformations in solution.     

The preparation and tin-119 Mössbauer spectra of new adducts of the type organotetrachlorostannate(IV) base (11)

New adducts Et₄N(RSnCl₄ · L) (R butyl and phenyl; L pyridine, trimethylamine, tri-n-butylphosphine, triphenylphosphine oxide, triphenylarsine oxide, dimethylsulphoxide, dimethylformamide) have been isolated and their Mössbauer spectra studied. Definite structural assignments are made for the phosphine and phosphine oxide adducts from Mössbauer quadrupole splitting data. Comments are made on the choice of partial splitting values for phenyl and butyl groups.     

Electronic states of ketene radical cation

The doublet electronic states of ketene, and ketene-d₂, radical cations produced by photoionisation with Helα (58.4 nm) and Hellα (30.4 nm) radiation, were studied by photoelectron spectroscopy. Seven such states were found below 28 eV ionisation energy and were assigned by comparison with the ionisation energies calculated by the correlated PNO-CEPA approach. The agreement is within ≈ 0.3 eV of the experimental data. An analysis of the contributions of reorganisation and correlation effects to the calculated ionisation energies is presented. The vibrational frequencies exciteα in four of the states of ketene-d₂ and ketene are presented and discussed in view of the assignments.     

Centrality dependence of charged particle multiplicity in Au-Au collisions at square root of (s)NN = 130 GeV

We present results for the charged-particle multiplicity distribution at midrapidity in Au-Au collisions at square root of [s(NN)] = 130 GeV measured with the PHENIX detector at RHIC. For the 5% most central collisions we find dN(ch)/d eta(vertical line eta = 0) = 622+/-1(stat)+/-41(syst). The results, analyzed as a function of centrality, show a steady rise of the particle density per participating nucleon with centrality.     

The Reaction of Coumalic Acid with Benzoquinone: Formation of a Spirobutenolide

Abstract

Although additions of α-pyrones to dienophiles have received extensive study,¹ there have been few reports of additions of α-pyrones to quinones.² In attempts to add benzoquinone (1) to coumalic acid (2), we have found that keeping these compounds in methanol and acetic acid in the presence of sodium acetate for 4 hours at 0°C followed by removal of the solvents under reduced pressure and purification by flash chromatography gave compound 3 ³ (22%⁴) mp 158–161°C raised to mp 160–162°C (benzene) UV (MeOH) λ;306 nm (ε 4700), 215 (12,500); IR (CHCl₃) v_max 3340, 1770 cm^?1; ¹H NMR ((CD₃)₂CO) δ 3.5 (s, 3H), 5.52 (s, 1H), 6.35 (d, J=5 Hz, 1H), 6.55 (m, 1H), 6.85 (m, 2H), 7.55 (d, J=5 Hz, 1H); ¹³C 171.5, 153.8, 153.4, 150.9, 122.3, 121.8, 119.6, 111.8, 110.8, 94.7, 56.9; mass specteum m/e (relative intensity) 234.0530 (54), 202.0267 (100), 174.0320 (34), 146.0367 (88), 98.0371 (47); m/e calcd for C₁₂H₁₀O₅.     

Application of Mössbauer Spectroscopy to the Study of Corrosion

Corrosion research, and the need to fully understand the effects that environmental conditions have on the performance of structural steels, is one area in which Mössbauer spectroscopy has become a required analytical technique. This is in part due to the need to identify and quantify the nanophase iron oxides that form on and protect certain structural steels, and that are nearly transparent to most other spectroscopic techniques. A review is given of the most recent Mössbauer characterization of rusts that have formed on structural steels exposed to different environments. Mössbauer spectroscopy is playing an important role in a new corrosion program in the United States in which steel bridges, old and new, are being evaluated for corrosion problems that may reduce their serviceable lifetimes. Mössbauer spectroscopy has been used to characterize the corrosion products that form the protective patina on weathering steel, as well those that form in adverse environments in which the oxide coating is not adherent or protective to the steel. Mössbauer spectroscopy has also become an important analytical technique for investigating the corrosion products that have formed on archeological artifacts, and it is providing guidance to aid in the removal of the oxides necessary for their preservation.