"Half a proton" in the Bogomol'nyi-Prasad-Sommerfield Skyrme model

The BPS Skyrme model is a model containing an $SU(2)$-valued scalar field, in which a Bogomol'nyi-type inequality can be satisfied by soliton solutions. In this model, the energy density of static configurations is the sum of the square of the topological charge density plus a potential. The topological charge density is nothing else but the pull-back of the Haar measure of the group $SU(2)$ on the physical space by the field configuration. As a consequence, this energy expression has a high degree of symmetry: it is invariant to volume preserving diffeomorphisms both on physical space and on the target space. We demonstrate here, that in the BPS Skyrme model such solutions exists, that a fraction of their charge and energy densities are localised, and the remaining part can be any far away, not interacting with the localised part.Comment: 5 pages, no figures; updated to final versio

Review of the Late Pleistocene Soricidae (Mammalia) fauna of the Vaskapu Cave (North Hungary)

The summary of the Late Pleistocene Soricidae remains of the North Hungarian Vaskapu Cave II and VII localities is given in the present paper. Five species (Sorex alpinus SHINZ, 1837, Sorex minutus LINNAEUS, 1766, Sorex araneus LINNAEUS 1758, Crocidura russula HERMANN, 1780 and Crocidura suaveolens PALLAS, 1811) were identified in the fauna. The species composition of the shrew assemblage indicates cold climate with diversified ecotypes in the mountain surroundings, with forests and open grasslands as well. Also the new location (in the Stratigraphical Collection of the Department of Paleontology and Geology at the Hungarian Natural History Museum) with definitive inventory numbers of the formerly published Vaskapu fossils is present here

New analytic solutions of the non-relativistic hydrodynamical equations

New solutions are found for the non-relativistic hydrodynamical equations. These solutions describe expanding matter with a Gaussian density profile. In the simplest case, thermal equilibrium is maintained without any interaction, the energy is conserved, and the process is isentropic. More general solutions are also obtained that describe explosions driven by heat production, or contraction of the matter caused by energy loss.Comment: 6 pages, LaTeX. Submitted to Physics Letters B. Shortened from 9 pages, errors corrected in the "More general solutions" sectio

Compact-like abelian groups without non-trivial quasi-convex null sequences

In this paper, we study precompact abelian groups G that contain no sequence {x_n} such that {0} \cup {\pm x_n : n \in N} is infinite and quasi-convex in G, and x_n --> 0. We characterize groups with this property in the following classes of groups: (a) bounded precompact abelian groups; (b) minimal abelian groups; (c) totally minimal abelian groups; (d) \omega-bounded abelian groups. We also provide examples of minimal abelian groups with this property, and show that there exists a minimal pseudocompact abelian group with the same property; furthermore, under Martin's Axiom, the group may be chosen to be countably compact minimal abelian.Comment: Final versio

Compressibility of rotating black holes

Interpreting the cosmological constant as a pressure, whose thermodynamically conjugate variable is a volume, modifies the first law of black hole thermodynamics. Properties of the resulting thermodynamic volume are investigated: the compressibility and the speed of sound of the black hole are derived in the case of non-positive cosmological constant. The adiabatic compressibility vanishes for a non-rotating black hole and is maximal in the extremal case --- comparable with, but still less than, that of a cold neutron star. A speed of sound $v_s$ is associated with the adiabatic compressibility, which is is equal to $c$ for a non-rotating black hole and decreases as the angular momentum is increased. An extremal black hole has $v_s^2=0.9 \,c^2$ when the cosmological constant vanishes, and more generally $v_s$ is bounded below by $c/ {\sqrt 2}$.Comment: 8 pages, 1 figure, uses revtex4, references added in v