Large deviations for random walks under subexponentiality: the big-jump domain

For a given one-dimensional random walk $\{S_n\}$ with a subexponential step-size distribution, we present a unifying theory to study the sequences $\{x_n\}$ for which $\mathsf{P}\{S_n>x\}\sim n\mathsf{P}\{S_1>x\}$ as $n\to\infty$ uniformly for $x\ge x_n$. We also investigate the stronger "local" analogue, $\mathsf{P}\{S_n\in(x,x+T]\}\sim n\mathsf{P}\{S_1\in(x,x+T]\}$. Our theory is self-contained and fits well within classical results on domains of (partial) attraction and local limit theory. When specialized to the most important subclasses of subexponential distributions that have been studied in the literature, we reproduce known theorems and we supplement them with new results.Comment: Published in at http://dx.doi.org/10.1214/07-AOP382 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

An evolution equation as the WKB correction in long-time asymptotics of Schrodinger dynamics

We consider 3d Schrodinger operator with long-range potential that has short-range radial derivative. The long-time asymptotics of non-stationary problem is studied and existence of modified wave operators is proved. It turns out, the standard WKB correction should be replaced by the solution to certain evolution equation.Comment: This is a preprint of an article whose final and definitive form has been published in Comm. Partial Differential Equations, available online at http://www.informaworld.co

Nuclear collective motion with a coherent coupling interaction between quadrupole and octupole modes

A collective Hamiltonian for the rotation-vibration motion of nuclei is considered, in which the axial quadrupole and octupole degrees of freedom are coupled through the centrifugal interaction. The potential of the system depends on the two deformation variables $\beta_2$ and $\beta_3$. The system is considered to oscillate between positive and negative $\beta_3$-values, by rounding an infinite potential core in the $(\beta_2,\beta_3)$-plane with $\beta_2>0$. By assuming a coherent contribution of the quadrupole and octupole oscillation modes in the collective motion, the energy spectrum is derived in an explicit analytic form, providing specific parity shift effects. On this basis several possible ways in the evolution of quadrupole-octupole collectivity are outlined. A particular application of the model to the energy levels and electric transition probabilities in alternating parity spectra of the nuclei $^{150}$Nd, $^{152}$Sm, $^{154}$Gd and $^{156}$Dy is presented.Comment: 25 pages, 13 figures. Accepted in Phys. Rev.

Anomalous biased diffusion in a randomly layered medium

We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The long-time behavior of the particle position is studied in the frame of a continuous-time random walk on a semi-infinite one-dimensional lattice. We formulate the conditions for anomalous diffusion, derive the diffusion laws and analyze their dependence on the particle mass and the distribution of the random force.Comment: 19 pages, 1 figur

Effect of perennial grasses on nutrient supplies of Southern black soil and subsequent crop yield

oai:ojs.european-science.com:article/4The present paper gives the comprehensive analysis of the effect of traditional and nontraditional grasses on soil nutrition status and subsequent crop yield. Substantial contribution of perennial grasses to soil organic matter accumulating is assessed. It has been observed that humus content and nutrition components changed throughout grass cultivation. Phytomelioration impact of five leguminous species and three nonleguminous on Southern black soil fecundity is overviewed. Among spring wheat yield components, the significance of influence of different grasses is underlined. The study evaluates the benefits of legume grasses in comparison to nonlegumes