Oscillations of certain second order nonlinear differential equations

A second order nonlinear differential equation

Separation of isomeric disaccharides by traveling wave ion mobility mass spectrometry using CO2 as drift gas

The use of CO₂ as a massive and polarizable drift gas is shown to greatly improve peak‐to‐peak resolution (R_p‐p), as compared with N₂, for the separation of disaccharides in a Synapt G2 traveling wave ion mobility cell. Near or baseline R_p‐p was achieved for three pairs of sodiated molecules of disaccharide isomers, that is, cellobiose and sucrose (R_p‐p = 0.76), maltose and sucrose (R_p‐p = 1.04), and maltose and lactose (R_p‐p = 0.74). Ion mobility mass spectrometry using CO₂ as the drift gas offers therefore an attractive alternative for fast and efficient separation of isomeric disaccharides. Copyright © 2012 John Wiley & Sons, Ltd.     

Oscillatory and asymptotic behavior of solutions of differential equations with deviating arguments

The oscillatory and asymptotic behavior of solutions of a class of nth order nonlinear differential equations, with deviating arguments, of the form (E, δ) L_nx(t) + δq(t) f(x[g₁(t)],…, x[g_m(t)]) = 0, where δ = ± 1 and L₀x(t) = x(t), L_kx(t) = a_k(t)(L_{k ? 1}x(t))^., $\text{k = 1, 2,…, n (}{}^{\mathrm{.}}\text{=}\text{d}\text{dt}\text{)}$, is examined. A classification of solutions of (E, δ) with respect to their behavior as t → ∞ and their oscillatory character is obtained. The comparisons of (E, 1) and (E, ?1) with first and second order equations of the form y^.(t) + c₁(t) f(y[g₁(t)],…, y[g_m(t)]) = 0 and (a_{n ? 1}(t)z^.(t))^. ? c₂(t) f(z[g₁(t)],…, z[g_m(t)]) = 0, respectively, are presented. The obtained results unify, extend and improve some of the results by Graef, Grammatikopoulos and Spikes, Philos and Staikos.     

On oscillation of solutions of higher order forced functional differential inequalities

Oscillation criteria for the class of forced functional differential inequalities x(t){L_nx(t) + f(t, x(t), x[g₁(t)],…, x[g_m(t)]) ? h(t)} ? 0, for n even, and x(t){L_nx(t) ? f(t, x(t), x[g₁(t)],…, x[g_m(t)]) ? h(t)} ? 0, for n odd, are established.     

Chiral calcium organophosphate-catalyzed enantioselective electrophilic amination of enamides

Highly enantioselective direct amination of enamides catalyzed by chiral nonracemic calcium bis(phosphate) complex 3g afforded optically active 1,2-hydrazinoimines 4. Following a subsequent in situ hydrolysis or reduction, 2-hydrazinoketones 5 or syn-1,2-disubstituted 1,2-diamines 6 were obtained in high yields and excellent enantiomeric excess.