Time-scale invariance of relaxation processes of density fluctuation in slow neutron scattering in liquid cesium

The realization of idea of time-scale invariance for relaxation processes in liquids has been performed by the memory functions formalism. The best agreement with experimental data for the dynamic structure factor $S(k,\omega)$ of liquid cesium near melting point in the range of wave vectors (0.4 \ang^{-1} \leq k \leq 2.55 \ang^{-1}) is found with the assumption of concurrence of relaxation scales for memory functions of third and fourth orders. Spatial dispersion of the four first points in spectrum of statistical parameter of non-Markovity $\epsilon_{i}(k,\omega)$ at $i=1,2,3,4$ has allowed to reveal the non-Markov nature of collective excitations in liquid cesium, connected with long-range memory effect.Comment: REVTEX +3 ps figure

On the equivalence problem of generalized Abel ODEs under the action of the linear transformations pseudogroup

© 2016, Pleiades Publishing, Ltd. In the present paper we establish the necessary and sufficient conditions for two generalized Abel differential equations to be locally equivalent under the action of the pseudogroup of linear transformations of the form {x ↦ f(x), y ↦ g(x) · y + h(x)}. These conditions are formulated in terms of differential invariants

Lie jets and symmetries of prolongations of geometric objects

The Lie jet Lθλ of a field of geometric objects λ on a smooth manifold M with respect to a field θ of Weil A-velocities is a generalization of the Lie derivative Lvλ of a field λ with respect to a vector field v. In this paper, Lie jets Lθλ are applied to the study of A-smooth diffeomorphisms on a Weil bundle TAM of a smooth manifold M, which are symmetries of prolongations of geometric objects from M to TAM. It is shown that vanishing of a Lie jet Lθλ is a necessary and sufficient condition for the prolongation λA of a field of geometric objects λ to be invariant with respect to the transformation of the Weil bundle TAM induced by the field θ. The case of symmetries of prolongations of fields of geometric objects to the second-order tangent bundle T2M are considered in more detail. © 2011 Springer Science+Business Media, Inc

Product preserving bundle functors on multifibered and multifoliate manifolds

We show that the set of the equivalence classes of multifoliate structures is in one-to-one correspondence with the set of equivalence classes of finite complete projective systems of vector space epimorphisms. After that we give the complete description of all product preserving bundle functors on the categories of multifibered and multifoliate manifolds

Poisson structures on Weil bundles

In the present paper, we construct complete lifts of covariant and contravariant tensor fields from the smooth manifold M to its Weil bundle T AM for the case of a Frobenius Weil algebra A. For a Poisson manifold (M, w) we show that the complete lift w C of a Poisson tensor w is again a Poisson tensor on T AM and that w C is a linear combination of some "basic" Poisson structures on T AM induced by w. Finally, we introduce the notion of a weakly symmetric Frobenius Weil algebra A and we compute the modular class of (T AM, w C) for such algebras