An asymptotic result and a stability criterion for linear nonautonomous delay difference equations

Linear delay difference equations with variable coefficients and constant delays are considered. By the use of an appropriate solution of the so called generalized characteristic equation, an asymptotic result is obtained and a stability criterion is established.     

Understanding organic gas-phase anion molecule reactions

Although ionic reactions in the gas phase seem on the surface to be totally different from those in solution (e.g., they typically occur about 10(12) times more rapidly than their solution analogues and go about as fast at 10 K as they do at room temperature), they can, in fact, exhibit subtle steric, electronic, and isotopic effects. In this Perspective, we show how these differences arise, explain why gas-phase ion reactions can be both fast and selective, and discuss when they can and cannot be classified as "hot" reactions. We also give examples of the use of these reactions to devise new synthetic pathways, investigate reaction mechanisms, and generate important thermochemical data such as bond dissociation energies.     

Energy spectra and asymmetries of neutrons emitted after muon capture

Inclusive energy spectra and the energy dependence of the asymmetry parameter have been measured for neutrons emitted after muon capture in O, Si, Ca and Pb. In addition a neutron-neutron coincidence measurement has been performed for Ca. The results of these measurements confirm the exponential shape of the energy spectra and the positive asymmetry observed by Sundelin and Edelstein. The observation of neutrons with energies above 50 MeV and the observation of simultaneous emission of two high-energy neutrons suggest the importance of short-range nucleonnucleon correlations in this process.     

Neodymium luminescence in chalcogenides of europium-gallium: EuGaS4 and EuGa2Se4

Photoluminescence of chalcogenides of europium-gallium, EuGa₂S₄ and EuGa₂Se₄, doped with neodymium is investigated. The positions of Stark levels are determined from the spectra. The symmetry of luminescence centres is shown to be lower than cubic and the existence of nonequivalent centers is established. At 77 K the decay time of luminescence from the excited levels of Nd³⁺ depends on the spin of the states. That indicates a slow relaxation rate in the crystals under investigation. It is probable that these crystals can be used as effective luminophores.     

On conformal mapping and linear measure

Journal d'Analyse Mathématique -     

Experimental limits on the production of fractionally charged particles in proton-nucleus and neutrino-nucleus collisions

A search for fractionally chargedQ=1/3 (2/3) particles of different properties of interaction produced in (anti)neutrino-nucleus and in protonnucleus collisions was performed using the scintillator system of the CHARM neutrino detector at the CERN SPS. No events of the cases considered were found. In (anti)neutrino beams production was found to be less than a few times 10^?5 per interaction of a beam particle. In a proton beam an upper limit on the production cross section of ～10^?40 cm² was obtained.     

Gas-phase ion-molecule reactions of small nitroalkanes and their deprotonated anions

Gas-phase reactions of nitromethane (1), nitroethane (2), 2-nitropropane (3), 2-methyl-2-nitropropane (4) and nitrocyclopropane (5) were studied at 300 K using the flowing afterglow technique. These nitroalkanes react with gas-phase bases HO(-), CH(3)O(-) and HOO(-) very rapidly with rate coefficients of (2.5-4.3) x 10(-9) cm(3) s(-1) and reaction efficiencies of 60-100%, for example, k = 3.2 x 10(-9) cm(3) s(-1) (86%) for 5 reacting with hydroperoxide anion. Proton transfer (PT) is the only reaction observed for 1 while elimination (E2) is the exclusive pathway for 4 yielding isobutene and NO(2)(-). Both PT and E2 reactions are observed for 2, 3 and 5, the former being the major pathway. Deprotonated anions of 1, 2, 3 and 5 were subjected to reactivity studies with CH(3)I, CO(2), CS(2) and SO(2). Nucleophilic substitution (S(N)2) reaction occurs with CH(3)I while characteristic products CS(2)O(-) and SO(3)(-) are formed from CS(2) and SO(2), respectively, along with competing adduct formation. The SN(2) rate is greater, whereas the reactivities with the triatomic reagents are smaller for deprotonated nitrocyclopropane than for the other acyclic anions. These observations strongly suggest that the reactions of nitroalkane [M - H](-) anions occur through initial attack from the terminal oxygen; the nitrocyclopropane carbanion is more strained and, thus, less stabilized by resonance [R(2)C(-) - NO2 <--> R(2)=NO(2)(-)] resulting in the greater basicity/nucleophilicy and the less negative charge on the oxygen site.     

A facile one‐pot synthesis of tetrahydropyrimidines part 3 Synthesis of [alkanediylbis(3‐alkyl/aralkyl/aryl‐3,6‐dihydropyrimidine‐1,5(2H)‐diyl)bis(arylmethanones) and [1,4‐phenylenebis(3‐phenyl‐3,6‐dihydropyrimidine‐1,5(2H)‐diyl)]bis(phenylmethanone)

A facile one‐pot synthetic strategy has been developed for novel [alkanediylbis(3‐alkyl/aralkyl/ aryl‐3,6‐dihydropyrimidine‐1,5(2H)‐diyl)]bis(arylmethanones) 2a‐c, 2e‐m and [1,4‐phenylenebis(3‐phenyl‐3,6‐dihydropyrimidine‐1,5(2H)‐diyl)]bis(phenylmethanone) 2d by refluxing enaminones 1a‐f in methanol with diamines and formaldehyde.