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13 papers · 1 filter
Strong Connections and Chern-Connes Pairing in the Hopf-Galois Theory
L. Dabrowski, H. Grosse, P. M. Hajac
We reformulate the concept of connection on a Hopf-Galois extension in order to apply it in computing the Chern-Connes pairing between the cyclic cohomology $HC^{2n}…
On separable Schrödinger equations
Renat Zhdanov, Alexander Zhalij
We classify (1+3)-dimensional Schrödinger equations for a particle interacting with the electromagnetic field that are solvable by the method of separation of variables. As a resul…
Differential Equations for F_q-Linear Functions
Anatoly N. Kochubei
We study certain classes of equations for -linear functions, which are the natural function field counterparts of linear ordinary differential equations. It is shown that, in…
Nature of singularities in gravitational collapse
Andrzej Krolak
We discuss several aspects of cosmic censorship hypothesis. There is evidence both in favor and against the hypothesis. On one hand one can prove that cosmic censorship holds in se…
Lro in Lattice Systems of Linear Classical and Quantum Oscillators. Strong N-N Pair Quadratic Interaction
W. I. Skrypnik
For systems of one-component interacting oscillators on the d-dimensional lattice, d>1, whose potential energy besides a large nearest-neighbour (n-n) ferromagnetic translation-inv…
Completely integrable systems: a generalization
Dmitry Alekseevsky, Janusz Grabowksi, Giuseppe Marmo +1
We present a slight generalization of the notion of completely integrable systems to get them being integrable by quadratures. We use this generalization to integrate dynamical sys…