On the classification of discrete Hirota-type equations in 3D

In the series of recent publications we have proposed a novel approach to the classification of integrable differential/difference equations in 3D based on the requirement that hydrodynamic reductions of the corresponding dispersionless limits are `inherited' by the dispersive equations. In this paper we extend this to the fully discrete case. Our only constraint is that the initial ansatz possesses a non-degenerate dispersionless limit (this is the case for all known Hirota-type equations). Based on the method of deformations of hydrodynamic reductions, we classify discrete 3D integrable Hirota-type equations within various particularly interesting subclasses. Our method can be viewed as an alternative to the conventional multi-dimensional consistency approach.Comment: 29 page

Slim accretion discs: a model for ADAF-SLE transitions

We numerically construct slim, global, vertically integrated models of optically thin, transonic accretion discs around black holes, assuming a regularity condition at the sonic radius and boundary conditions at the outer radius of the disc and near the black hole. In agreement with several previous studies, we find two branches of shock-free solutions, in which the cooling is dominated either by advection, or by local radiation. We also confirm that the part of the accretion flow where advection dominates is in some circumstances limited in size: it does not extend beyond a certain outer limiting radius. New results found in our paper concern the location of the limiting radius and properties of the flow near to it. In particular, we find that beyond the limiting radius, the advective dominated solutions match on to Shapiro, Lightman & Eardley (SLE) discs through a smooth transition region. Therefore, the full global solutions are shock-free and unlimited in size. There is no need for postulating an extra physical effect (e.g. evaporation) for triggering the ADAF-SLE transition. It occurs due to standard accretion processes described by the classic slim disc equations.Comment: 12 pages, 7 figures, MNRAS accepte

Hydrodynamic Flow as Congruence of Geodesic Lines in Riemannian Space-Time

It is shown that small elements of perfect fluid in adiabatic processes move along geodesic lines of a Riemannian space-time.Comment: 5 pages, Latex. Final versio

Mass of the higgs versus fourth generation masses

The predicted value of the higgs mass $m_H$ is analyzed assuming the existence of the fourth generation of leptons ($N, E$) and quarks ($U, D$). The steep and flat directions are found in the five-dimensional parameter space: $m_H$, $m_U$, $m_D$, $m_N$, $m_E$. The LEPTOP fit of the precision electroweak data is compatible (in particular) with $m_H \sim 300$ GeV, $m_N \sim 50$ GeV, $m_E \sim 100$ GeV, $m_U +m_D \sim 500$ GeV, and $|m_U -m_D| \sim 75$ GeV. The quality of fits drastically improves when the data on b- and c-quark asymmetries and new NuTeV data on deep inelastic scattering are ignored.Comment: 8 pages, 4 figure