Computability of the causal boundary by using isocausality

Recently, a new viewpoint on the classical c-boundary in Mathematical Relativity has been developed, the relations of this boundary with the conformal one and other classical boundaries have been analyzed, and its computation in some classes of spacetimes, as the standard stationary ones, has been carried out. In the present paper, we consider the notion of isocausality given by Garc\'ia-Parrado and Senovilla, and introduce a framework to carry out isocausal comparisons with standard stationary spacetimes. As a consequence, the qualitative behavior of the c-boundary (at the three levels: point set, chronology and topology) of a wide class of spacetimes, is obtained.Comment: 44 pages, 5 Figures, latex. Version with minor changes and the inclusion of Figure

The sectional curvature remains positive when taking quotients by certain nonfree actions

We study some cases when the sectional curvature remains positive under the taking of quotients by certain nonfree isometric actions of Lie groups. We consider the actions of the groups $S^1$ and $S^3$ such that the quotient space can be endowed with a smooth structure using the fibrations $S^3/S^1{\simeq}S^2$ and $S^7/S^3\simeq S^4$. We prove that the quotient space carries a metric of positive sectional curvature, provided that the original metric has positive sectional curvature on all 2-planes orthogonal to the orbits of the action.Comment: 26 pages, 1 figure. Changed the spelling of the author's nam

Isocausal spacetimes may have different causal boundaries

We construct an example which shows that two isocausal spacetimes, in the sense introduced by Garc\'ia-Parrado and Senovilla, may have c-boundaries which are not equal (more precisely, not equivalent, as no bijection between the completions can preserve all the binary relations induced by causality). This example also suggests that isocausality can be useful for the understanding and computation of the c-boundary.Comment: Minor modifications, including the title, which matches now with the published version. 12 pages, 3 figure

Spacelike surfaces with free boundary in the Lorentz-Minkowski space

We investigate a variational problem in the Lorentz-Minkowski space \l^3 whose critical points are spacelike surfaces with constant mean curvature and making constant contact angle with a given support surface along its common boundary. We show that if the support surface is a pseudosphere, then the surface is a planar disc or a hyperbolic cap. We also study the problem of spacelike hypersurfaces with free boundary in the higher dimensional Lorentz-Minkowski space \l^{n+1}.Comment: 16 pages. Accepted in Classical and Quantum Gravit

Spin Frustration and Magnetic Exchange in Cobalt Aluminum Oxide Spinels

We report on x-ray diffraction, magnetic susceptibility, electron- spin resonance and heat- capacity studies of Co[Al_1-xCo_x]_2O_4 for Co concentrations 0<x<1. In this spinel system only the A-site Co^2+ cation is magnetic, while the non-magnetic B-site Al^3+ is substituted by the low-spin non-magnetic Co^3+, and it is possible to investigate the complete phase diagram from Co^2+Al^3+_2O_4 to Co^2+Co^3+_2O_4. All samples reveal large negative Curie-Weiss temperatures Theta_CW of the order of -110 K independent of concentration, which is attributed to a high multiplicity of the superexchange interactions between the A-site Co^2+ cations. A pure antiferromagnetic state is found for x = 1.0 and 0.9 with Neel temperatures T_N = 29.5 K and 21.2 K, respectively, as evidenced by lambda-like anomalies in the specific heat. Compositions with 0.3<x<0.75 show smeared out strongly reduced magnetic ordering temperatures. At low temperatures, a T^2.5 dependence of the specific heat is indicative of a spin-liquid state. For x < 0.2 a T^2 dependence of the specific heat and a spin-glass like behavior of the susceptibility below T_f = 4.7 K are observed. The high value of the frustration parameter f = |Theta_CW|/T_f > 10 indicates the presence of strong spin frustration at least for x < 0.6. The frustration mechanism is attributed to competing nearest neighbor and next-nearest neighbor superexchange interactions between the A-site Co^2+ ions.Comment: 19 pages, 9 figures, 46 reference

The region with trapped surfaces in spherical symmetry, its core, and their boundaries

We consider the region $\mathscr{T}$ in spacetime containing future-trapped closed surfaces and its boundary \B, and derive some of their general properties. We then concentrate on the case of spherical symmetry, but the methods we use are general and applicable to other situations. We argue that closed trapped surfaces have a non-local property, "clairvoyance", which is inherited by \B. We prove that \B is not a marginally trapped tube in general, and that it can have portions in regions whose whole past is flat. For asymptotically flat black holes, we identify a general past barrier, well inside the event horizon, to the location of \B under physically reasonable conditions. We also define the core $\mathscr{Z}$ of the trapped region as that part of $\mathscr{T}$ which is indispensable to sustain closed trapped surfaces. We prove that the unique spherically symmetric dynamical horizon is the boundary of such a core, and we argue that this may serve to single it out. To illustrate the results, some explicit examples are discussed, namely Robertson-Walker geometries and the imploding Vaidya spacetime.Comment: 70 pages, 14 figures. Figure 6 has been replaced, and corrected. Minor changes around Propositions 10.3 and 10.4, and some typos correcte

Labrador retrievers under primary veterinary care in the UK: demography, mortality and disorders

Abstract Background Labrador retrievers are reportedly predisposed to many disorders but accurate prevalence information relating to the general population are lacking. This study aimed to describe demography, mortality and commonly recorded diseases in Labrador retrievers under UK veterinary care. Methods The VetCompass™ programme collects electronic patient record data on dogs attending UK primary-care veterinary practices. Demographic analysis covered all33,320 Labrador retrievers in the VetCompass™ database under veterinary care during 2013 while disorder and mortality data were extracted from a random sample of 2074 (6.2%) of these dogs. Results Of the Labrador retrievers with information available, 15,427 (46.4%) were female and 15,252 (53.6%) were male. Females were more likely to be neutered than males (59.7% versus 54.8%, P <  0.001). The overall mean adult bodyweight was 33.0 kg (SD 6.1). Adult males were heavier (35.2 kg, SD 5.9 kg) than adult females (30.4 kg, SD 5.2 kg) (P <  0.001). The median longevity of Labrador retrievers overall was 12.0 years (IQR 9.9–13.8, range 0.0–16.0). The most common recorded colours were black (44.6%), yellow (27.8%) and liver/chocolate (reported from hereon as chocolate) (23.8%). The median longevity of non-chocolate coloured dogs (n = 139, 12.1 years, IQR 10.2–13.9, range 0.0–16.0) was longer than for chocolate coloured animals (n = 34, 10.7 years, IQR 9.0–12.4, range 3.8–15.5) (P = 0.028). Of a random sample of 2074 (6.2%) Labrador retrievers under care in 2013 that had full disorder data extracted, 1277 (61.6%) had at least one disorder recorded. The total number of dogs who died at any date during the study was 176. The most prevalent disorders recorded were otitis externa (n = 215, prevalence 10.4%, 95% CI: 9.1–11.8), overweight/obesity (183, 8.8%, 95% CI: 7.6–10.1) and degenerative joint disease (115, 5.5%, 95% CI: 4.6–6.6). Overweight/obesity was not statistically significantly associated with neutering in females (8.3% of entire versus 12.5% of neutered, P = 0.065) but was associated with neutering in males (4.1% of entire versus 11.4% of neutered, P < 0.001). The prevalence of otitis externa in black dogs was 12.8%, in yellow dogs it was 17.0% but, in chocolate dogs, it rose to 23.4% (P < 0.001). Similarly, the prevalence of pyo-traumatic dermatitis in black dogs was 1.1%, in yellow dogs it was 1.6% but in chocolate dogs it rose to 4.0% (P = 0.011). Conclusions The current study assists prioritisation of health issues within Labrador retrievers. The most common disorders were overweight/obesity, otitis externa and degenerative joint disease. Males were significantly heavier females. These results can alert prospective owners to potential health issues and inform breed-specific wellness checks

Egorov's theorem for transversally elliptic operators on foliated manifolds and noncommutative geodesic flow

The main result of the paper is Egorov's theorem for transversally elliptic operators on compact foliated manifolds. This theorem is applied to describe the noncommutative geodesic flow in noncommutative geometry of Riemannian foliations.Comment: 23 pages, no figures. Completely revised and improved version of dg-ga/970301

Halo properties and secular evolution in barred galaxies

The halo plays a crucial role in the evolution of barred galaxies. Its near-resonant material absorbs angular momentum emitted from some of the disc particles and helps the bar become stronger. As a result, a bar (oval) forms in the inner parts of the halo of strongly barred disc galaxies. It is thinner in the inner parts (but still considerably fatter than the disc bar) and tends to spherical at larger radii. Its length increases with time, while always staying shorter than the disc bar. It is roughly aligned with the disc bar, which it trails only slightly, and it turns with roughly the same pattern speed. The bi-symmetric component of the halo density continues well outside the halo bar, where it clearly trails behind the disc bar. The length and strength of the disc and halo bars correlate; the former being always much stronger than the latter. If the halo is composed of weakly interacting massive particles, then the formation of the halo bar, by redistributing the matter in the halo and changing its shape, could influence the expected annihilation signal. This is indeed found to be the case if the halo has a core, but not if it has a steep cusp. The formation and evolution of the bar strongly affect the halo orbits. A fraction of them becomes near-resonant, similar to the disc near-resonant orbits at the same resonance, while another fraction becomes chaotic. Finally, a massive and responsive halo makes it harder for a central mass concentration to destroy the disc bar.Comment: 6 pages, 3 figures, to appear in "Island Universes - Structure and Evolution of Disk Galaxies" ed. R. S. de Jon