I reproduce a rather simple formal derivation of the Heaps’ law from the generalized Zipf’s law, which I previously published in Russian [7].

This note details the derivation of the generalized advective-diffusive equation system for the 2D space-time incompressible Navier-Stokes governing equations, in conservation form.

We give an alternative derivation of two Painlevé hierarchies. This is done by constructing generalized scaling reductions of the Korteweg-de Vries and dispersive water wave hierarchies. We also construct a generalized scaling reduction of Burgers hierarchy. Corresponding author: P. R. Gordoa. Tel: +34 91 4888243; Fax: +34 91 488 7338; email: [email protected]

We present a canonical derivation of an influence superoperator which generates the reduced dynamics Fermionic quantum system linearly coupled to environment initially at thermal equilibrium. use this formalism derive generalized-Lindblad master equation (in Markovian limit) and generalized version hierarchical equations motion valid in arbitrary parity-symmetry conditions, important for correc...

Here, we investigate symmetric bi-derivations and their generalizations on L? 0 (G)*. For k ? N, show that if B:L?0(G)*x L?0(G)* is asymmetric bi-derivation such [B(m,m),mk] Z(L?0(G)*) for all m (G)*, then B the zero map. Furthermore, characterize generalized biderivations group algebras. We also prove any Jordan 0(G)* a bi-derivation.

Introducing the notions of (inner) σ-derivation, (inner) σ-endomorphism and oneparameter group of σ-endomorphisms (σ-dynamics) on a Banach algebra, we correspond to each σ-dynamics a σ-derivation named as its σ-infinitesimal generator. We show that the σ-infinitesimal generator of a σ-dynamics of inner σ-endomorphisms is an inner σ-derivation and deal with the converse. We also establish a nice...

We derive strain-gradient plasticity from a nonlocal phase-field model of dislocations in plane. After scaling, the elastic interaction we continuous energy with linear growth depending on measure which characterizes macroscopic dislocation density as well effective representing far-field between dislocations. Relaxation and formation microstructures at intermediate scales are automatically inc...