Recursion Operators of Some Equations of Hydrodynamic Type

We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N=2 and N=3 containing the equations of shallow water waves and its generalizations with their first two higher symmetries and their recursion operators. We also discuss a reduction of $N+1$ systems to $N$ systems of some new equations of hydrodynamic type.Comment: Latex File (amssymb), 22 page

Exact static solutions in four dimensional Einstein-Maxwell-Dilaton gravity

Classes of exact static solutions in four-dimensional Einstein-Maxwell-Dilaton gravity are found. Besides of the well-known solutions previously found in the literature, new solutions are presented.It's shown that spherically symmetric solutions, except the case of charged dilaton black hole, represent globally naked strong curvature singularities.Comment: 8 pages, late

On the naming of innovation districts

Name plays a fundamental role in defining and differentiating a company within a category. In this paper we identify how the leaders of 7 innovation districts (22@Barcelona, Ann Arbor Spark, EECi, Porto Digital, Ruta N – Medellín, SK-Skolkovo and TusPark) understand the construction of the names of their innovation districts. We take an inductive approach utilizing two types of data: exploring the innovation district directors' understanding through direct semi-structured interviews and analyzing secondary data consisting of website and brochures. We show how innovation district leaders use more than one classification name for their organization and that these names either tend towards a more strategic or institutional posture. We contribute by extending existing naming theory to include innovation districts, a complex organization composed by actors of the Triple Helix. We also contribute by providing managerial guidance to assist in understanding the importance of the role of their organization's name in long-term positioning

Relativistic Compact Objects in Isotropic Coordinates

We present a matrix method for obtaining new classes of exact solutions for Einstein's equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein's equations to two independent Riccati type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic type fluid with an equation of state $p=\gamma \rho$ is discussed in detail.Comment: 9 pages, no figures, accepted for publication in Pramana-Journal of Physic

All stationary axi-symmetric local solutions of topologically massive gravity

We classify all stationary axi-symmetric solutions of topologically massive gravity into Einstein, Schr\"odinger, warped and generic solutions. We construct explicitly all local solutions in the first three sectors and present an algorithm for the numerical construction of all local solutions in the generic sector. The only input for this algorithm is the value of one constant of motion if the solution has an analytic centre, and three constants of motion otherwise. We present several examples, including soliton solutions that asymptote to warped AdS.Comment: 42 pages, 9 figures. v2: Changed potentially confusing labelling of one sector, added references. v3: Minor changes, matches published versio

Chiral models in dilaton-Maxwell gravity

We study symmetry properties of the Einstein-Maxwell theory nonminimaly coupled to the dilaton field. We consider a static case with pure electric (magnetic) Maxwell field and show that the resulting system becomes a nonlinear sigma-model wich possesses a chiral representation. We construct the corresponding chiral matrix and establish a representation which is related to the pair of Ernst-like potentials. These potentials are used for separation of the symmetry group into the gauge and nongauge (charging) sectors. New variables, which linearize the action of charging symmetries, are also established; a solution generation technique based on the use of charging symmetries is formulated. This technique is used for generation of the elecricaly (magneticaly) charged dilatonic fields from the static General Relativity ones.Comment: 9 pages in LaTex; published in Gen. Rel. Grav. 32 (2000) pp 1389-139

Behaviour of Magnetic Tubes in Neutron Star's Interior

It is found from Maxwell's equations that the magnetic field lines are good analogues of relativistic strings. It is shown that the super-conducting current in the neutron star's interior causes local rotation of magnetic flux tubes carrying quantized flux.Comment: 6 pages, no figure

Topologically Massive Gravity and Ricci-Cotton Flow

We consider Topologically Massive Gravity (TMG), which is three dimensional general relativity with a cosmological constant and a gravitational Chern-Simons term. When the cosmological constant is negative the theory has two potential vacuum solutions: Anti-de Sitter space and Warped Anti-de Sitter space. The theory also contains a massive graviton state which renders these solutions unstable for certain values of the parameters and boundary conditions. We study the decay of these solutions due to the condensation of the massive graviton mode using Ricci-Cotton flow, which is the appropriate generalization of Ricci flow to TMG. When the Chern-Simons coupling is small the AdS solution flows to warped AdS by the condensation of the massive graviton mode. When the coupling is large the situation is reversed, and warped AdS flows to AdS. Minisuperspace models are constructed where these flows are studied explicitly