[en] We compute the bulk viscosity in holographic models dual to theories with Lifshitz scaling and/or hyperscaling violation, using a generalization of the bulk viscosity formula derived in arXiv:1103.1657 from the null focusing equation. We find that only a class of models with massive vector fields are truly Lifshitz scale invariant, and have a vanishing bulk viscosity. For other holographic models with scalars and/or massless vector fields we find a universal formula in terms of the dynamical exponent and the hyperscaling violation exponent

[en] Deformations of the smallest Galilei algebra are constructed and deformed algebras are realized by Lie vector fields. For these realization bases of differential invariants and operators of invariant differentiation are constructed in the case of two dependent and one independent variables.

No abstract available

[en] Under certain weak, physically reasonable conditions it is shown that a space-time can have at most one timelike hypersurface orthogonal killing vector field (to within a constant multiple)

[en] We show that C¹-generically, if a divergence-free vector field has the orbital shadowing property then the vector field is Anosov

[en] In this paper we construct a theory of indices of Morse-Bott vector fields on a manifold and use it to solve a famous localization problem for the transfer map. As a consequence, we obtain addition theorems for universal Pontryagin classes in cobordisms. This enables us to complete the construction of the theory of universal characteristic classes, which was begun more than twenty years ago

No abstract available

[en] In this paper, we introduce the category of Yetter-Drinfel'd Hom-modules which is a braided monoidal category and show that the category of Yetter-Drinfel'd Hom-modules is a full monoidal subcategory of the left center of left Hom-module category. Also we study the equivalent relationship between the category of Yetter-Drinfel'd Hom-modules and the category of Hom-modules over the Drinfel'd double. Finally, the Faddeev-Reshetikhin-Takhtajan (FRT) type theorem for the quantum Hom-Yang-Baxter equation is investigated

[en] We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing–Yano forms. A new Lie bracket for conformal Killing–Yano forms that corresponds to slightly modified Schouten–Nijenhuis bracket of differential forms is proposed. We show that conformal Killing–Yano forms satisfy a graded Lie algebra in constant curvature manifolds. It is also proven that normal conformal Killing–Yano forms in Einstein manifolds also satisfy a graded Lie algebra. The constructed graded Lie algebras reduce to the graded Lie algebra of Killing–Yano forms and the Lie algebras of conformal Killing and Killing vector fields in special cases. (paper)

[en] In Ndogmo (2008 J. Phys. A: Math. Theor. 41 025207), the author claims to have determined a complete list of functionally independent differential invariants up to order 2 for the equivalence group of differential equations defined by vector fields when there are two and three independent variables. In this comment, we show that this is not the case. Using the equivariant moving frame method, we derive a complete set of functionally independent differential invariants of orders 1 and 2 for an arbitrary number n ≥ 2 of independent variables. In the particular case n = 2, we obtain six functionally independent invariants, two of which were not found in Ndogmo (2008 J. Phys. A: Math. Theor. 41 025207). In the case n = 3, we get 21 functionally independent invariants, six of which are new. We also give a complete classification of the differential invariants. (comment)