We work with varieties over a field k of characteristic 0, though many arguments go through without this assumption. The notation D(X) is reserved for the bounded derived category of coherent sheaves on a variety X, namely D(X) := D c(X). The core of this paper is concerned with the construction of a “constant” t-structure on the bounded derived category of coherent sheaves D(X×S), with X and S...

The paper presents new criteria for bijectivity/transitivity of Tfunctions and fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz p-adic functions and to study measure-preservation/ergodicity of these.

This task has relied upon a combination of computer simulation and experimental testing. Computer crash simulation models were developed and validated for use in the study of factors influencing injury risk of wheelchair occupants in a crash. A wheelchair transportation-specific Injury Risk Assessment method was developed and used in the comparison of injury risk associated with various wheelch...

We obtain Kamenev-type oscillation criteria for the second-order quasilinear differential equation (r(t)|y′(t)|α−1y′(t))′ + p(t)|y(t)|β−1y(t) = 0 . The criteria obtained extend the integral averaging technique and include earlier results due to Kamenev, Philos and Wong.

Oscillation criteria are established for the second order neutral delay differential equation with distributed deviating argument (r(t) (x(t))Z′(t))′ + ∫ b a q(t, )f [x(g(t, ))] d ( )= 0, t t0, where Z(t)= x(t)+p(t)x(t − ). These results are extensions of the integral averaging techniques due to Coles and Kamenev, and improve some known oscillation criteria in the existing literature. © 2006 El...

By using Riccati transformation technique, we will establish some new oscillation criteria for the even order neutral delay differential equations z t n q t f x σ t 0, t ≥ t0, where n is even, z t x t p t x τ t , 0 ≤ p t ≤ p0 < ∞, and q t ≥ 0. These oscillation criteria, at least in some sense, complement and improve those of Zafer 1998 and Zhang et al. 2010 . An example is considered to illust...