2 Semiclassical Transport Theory 3 2.1 Langrangian vs Eulerian Analysis Techniques . . . . . . . . . . . . . . . . . 3 2.2 Various Lifetime and Relaxation Time Constants . . . . . . . . . . . . . . . 4 2.2.1 Lifetime Constant (τ) . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 φ (Momentum) Relaxation Time Constant (τΦ) . . . . . . . . . . . . 7 2.2.3 Average φ(momentum) Relaxation T...

The Hamilton-Jacobi equation for the string cosmology is solved using the gradient expansion method. The zeroth order solution is taken to be the standard pre-big bang model and the second order solution is found for the dilaton and the three-metric. It indicates that corrections generated by inhomogeneities of the seed metric are suppressed near the singularity and are growing towards the asym...

In this paper, transverse and longitudinal vibration of nonlinear plate under exciting of orbiting mass is considered based on first-order shear deformation theory. The nonlinear governing equation of motion are discretized by the finite element method in combination with Newmark’s time integration scheme under von Karman strain-displacement assumptions. For validation of method and formulation...

Let G = (V, E), V {v1, v2,..., vn}, be a simple connected graph of order n and size m, without isolated vertices. Denote by d1 ? d2 ?... dn, di d(vi) sequence vertex degrees G. The general zeroth-order Randic index is defined as 0R?(G) ?ni =1 d?i, where an arbitrary real number. corresponding coindex via 0R??(G) ?ni=1(n?1?di)d?i. Some new bounds for the relationship between 0R??(G?) 0R???1(G?) ...

We study a class of cooperative multi-agent optimization problems, where each agent is associated with local action vector and cost, the goal to cooperatively find joint profile that minimizes average costs. consider setting gradient information not readily available, agents only observe their costs incurred by actions as feedback determine new actions. propose zeroth-order scheme provide expli...