Abstract Using the second law of local thermodynamics and the first-order Palatini formalism, we formulate relativistic spin hydrodynamics for quantum field theories with Dirac fermions, such as QED and QCD, in a torsionful curved background.We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic mo

New classes of interpolation spaces of exponential type vectors of complex degrees of positive operators are defined.Properties of the approximation spaces generated by the considered interpolation spaces are investigated.An example of application footjoy weste herren of constructed theory to the regular elliptic boundary problems is considered.In

We establish WKB estimates for linear dynamic systems with a small parameter on a time scale unifying continuous and discrete WKB method.We introduce ackermans lace curtains an adiabatic invariant for dynamic system on a time scale, which is a generalization of adiabatic invariant of Lorentz_s pendulum.As an application we prove that the change of