Oscillation Results for Emden–Fowler Type Differential Equations

AbstractThe third order nonlinear differential equationx‴+a(t)x′+b(t)f(x)=0, (∗)is considered. We present oscillation and nonoscillation criteria which extend and improve previous results existing in the literature, in particular some results recently stated by M. Greguš and M. Greguš, Jr., (J. Math. Anal. Appl.181, 1994, 575–585). In addition, contributions to the classification of solutions are given. The techniques used are based on a transformation which reduces (∗) to a suitable disconjugate form. To this aim auxiliary results on the asymptotic behavior of solutions of a second order linear differential equation associated to (∗) are stated. They are presented in an independent form because they may be applied also to simplify and improve other qualitative problems concerning differential equations with quasiderivatives

Chemistry in Evaporating Ices: Unexplored Territory

We suggest that three-body chemistry may occur in warm high density gas evaporating in transient co\textendash desorption events on interstellar ices. Using a highly idealised computational model we explore the chemical conversion from simple species of the ice to more complex species containing several heavy atoms, as a function of density and of adopted three body rate coefficients. We predict that there is a wide range of densities and rate coefficients in which a significant chemical conversion may occur. We discuss the implications of this idea for the astrochemistry of hot cores.Comment: Accepted in Ap

Giant g factor tuning of long-lived electron spins in Ge

Control of electron spin coherence via external fields is fundamental in spintronics. Its implementation demands a host material that accommodates the highly desirable but contrasting requirements of spin robustness to relaxation mechanisms and sizeable coupling between spin and orbital motion of charge carriers. Here we focus on Ge, which, by matching those criteria, is rapidly emerging as a prominent candidate for shuttling spin quantum bits in the mature framework of Si electronics. So far, however, the intrinsic spin-dependent phenomena of free electrons in conventional Ge/Si heterojunctions have proved to be elusive because of epitaxy constraints and an unfavourable band alignment. We overcome such fundamental limitations by investigating a two dimensional electron gas (2DEG) confined in quantum wells of pure Ge grown on SiGe-buffered Si substrates. These epitaxial systems demonstrate exceptionally long spin relaxation and coherence times, eventually unveiling the potential of Ge in bridging the gap between spintronic concepts and semiconductor device physics. In particular, by tuning spin-orbit interaction via quantum confinement we demonstrate that the electron Land\'e g factor and its anisotropy can be engineered in our scalable and CMOS-compatible architectures over a range previously inaccessible for Si spintronics

On the integral characterization of principal solutions for half-linear ODE

We discuss a new integral characterization of principal solutions for half-linear differential equations, introduced in the recent paper of S. Fisnarova and R. Marik, Nonlinear Anal. 74 (2011), 6427-6433. We study this characterization in the framework of the existing results and we show when this new integral characterization with a parameter $\alpha$ is equivalent with two extremal cases of the integral characterization used in the literature. We illustrate our results on the Euler and Riemann-Weber differential equations