A result of Ladas; Lakshmikantham, and Papadakis [1] concerning oscillation caused by lag in linear first order retarded argument differential equations is generalized to the sublinear case. Examples showing that such generalization to the superlinear case is impossible are given. 0. Introduction. It is known ([1], for example) that (A) g e C(R, R), g(t) < t for t e R, g(t) is strictly increasi...

Fluctuation theorems provide a correspondence between properties of quantum systems in thermal equilibrium and work distribution arising non-equilibrium process that connects two with Hamiltonians $H_0$ $H_1=H_0+V$. Building upon these theorems, we present algorithm to prepare purification the state $H_1$ at inverse temperature $\beta \ge 0$ starting from $H_0$. The complexity algorithm, given ...