Roshan, Mahmood
Published in
The European Physical Journal C

We find some new exact cosmological solutions for the covariant scalar–tensor–vector gravity theory, the so-called modified gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non-vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vec...

Kuzakon’, V. M.
Published in
Ukrainian Mathematical Journal

We introduce the notion of absolutely developable and biholomorphic vector fields defined on almost Hermitian manifolds. It is shown that any developable vector field on a K¨ahlerian manifold is an absolutely developable vector field. It is also proved that, on a nearly Kählerian manifold, an absolutely developable vector field ξ preserves the almo...

Dolov, M. V. Kruglov, E. V.
Published in
Differential Equations

We obtain a sharp bound for the number of distinct linear particular integrals of a polynomial vector field with coprime components the maximum of whose degrees is not less than 2.

Nesterenko, M.
Published in
Physics of Particles and Nuclei Letters

Two main approaches to the construction of realizations are discussed. The practical calculation algorithm, based on the method of I. Shorokov is proposed. A new realization of the Poincaré algebra p(1, 3) is presented as an example.

Gauduchon, Paul Moroianu, Andrei Ornea, Liviu
Published in
Mathematische Annalen

We prove that any compact homogeneous locally conformally Kähler manifold has parallel Lee form.

Noarov, A. I.
Published in
Doklady Mathematics

Miwa, Libardi Alice Kimie Sharko, Vladimir
Published in
Ukrainian Mathematical Journal

Let M2n+1 be a C(ℂPn) -singular manifold. We study functions and vector fields with isolated singularities on M2n+1. A C(ℂPn) -singular manifold is obtained from a smooth manifold M2n+1 with boundary in the form of a disjoint union of complex projective spaces ℂPn ∪ ℂPn ∪ . . . ∪ ℂPn with subsequent capture of a cone over each component of the boun...

Bramham, Barney
Published in
Inventiones mathematicae

It is an open question in smooth ergodic theory whether there exists a Hamiltonian disk map with zero topological entropy and (strong) mixing dynamics. Weak mixing has been known since Anosov and Katok first constructed examples in 1970. Currently all known examples with weak mixing are irrational pseudo-rotations with Liouvillean rotation number o...

Weigant, W. Plotnikov, P. I.
Published in
Doklady Mathematics

Braso, L. Petrahe, M.
Published in
Journal of Mathematical Sciences

We review two models of optimal transport where congestion effects during the transport can possibly by taken into account. The first model is Beckmann's one, where the transport activities are modeled by vector fields with given divergence. The second one is the model by Carlier et al., which is in turn a continuous reformulation of Wardrop's mode...