Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface

Given an oriented Riemannian surface (Sigma, g), its tangent bundle T Sigma enjoys a natural pseudo-Kahler structure, that is the combination of a complex structure 2, a pseudo-metric G with neutral signature and a symplectic structure Omega. We give a local classification of those surfaces of T Sigma which are both Lagrangian with respect to Omega and minimal with respect to G. We first show that if g is non-flat, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in R(3) or R(1)(3) induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS(2) or TH(2) respectively. We relate the area of the congruence to a second-order functional F = f root H(2) - K dA on the original surface. (C) 2010 Elsevier B.V. All rights reserved.

Associated Family of G-Structure Preserving Minimal Immersions in Semi-Riemannian Manifolds

We prove the existence of an associated family of G-structure preserving minimal immersions into semi-Riemannian manifolds endowed with a compatible infinitesimally homogeneous G-structure. We will study in more details minimal embeddings into product of space forms.

NONSTATIONARY MIXING AND THE UNIQUE ERGODICITY OF ADIC TRANSFORMATIONS

We define topological and measure-theoretic mixing for nonstationary dynamical systems and prove that for a nonstationary subshift of finite type, topological mixing implies the minimality of any adic transformation defined on the edge space, while if the Parry measure sequence is mixing, the adic transformation is uniquely ergodic. We also show this measure theoretic mixing is equivalent to weak ergodicity of the edge matrices in the sense of inhomogeneous Markov chain theory.

Comparison for three Classification Techniques

In this paper we show the results of a comparison simulation study for three classification techniques: Multinomial Logistic Regression (MLR), No Metric Discriminant Analysis (NDA) and Linear Discriminant Analysis (LDA). The measure used to compare the performance of the three techniques was the Error Classification Rate (ECR). We found that MLR and LDA techniques have similar performance and that they are better than DNA when the population multivariate distribution is Normal or Logit-Normal. For the case of log-normal and Sinh(-1)-normal multivariate distributions we found that MLR had the better performance.

GENOTYPE CHARACTERIZATION OF THE Haematobia irritans (DIPTERA: MUSCIDAE) FROM BRAZIL, DOMINICAN REPUBLIC AND COLOMBIA BASED ON RANDOMLY AMPLIFIED POLYMORPHIC DNA (RAPD) ANALYSIS

Blood-sucking flies are important parasites in animal production systems, especially regarding confinement conditions. Haematobia irritans, the horn fly, is one of the most troublesome species within bovine production systems, due to the intense stress imposed to the animals. H. irritans is one of the parasites of cattle that cause significant economic losses in many parts of the world, including South America. In the present work, Brazilian, Colombian and Dominican Republic populations of this species were studied by Random Amplified Polymorphic DNA(RAPD) to assess basically genetic variability between populations. Fifteen different decamer random primers were employed in the genomic DNA amplification, yielding 196 fragments in the three H. irritans populations. Among h. irritans samples, that from Colombia produced the smallest numbers of polymorphic hands. This high genetic homogeneity may be ascribed to its geographic origin, which causes high isolation, low gene flow, unlike the other American populations, from Brazil and Dominican Republic. Molecular marker fragments, which its produced exclusive bands, detected in every sample enabled the population origin to be characterized, but they are also potentially useful for further approaches such as the putative origin of Brazilian, Colombian and Dominican Republic populations of horn fly from South America. Similarity indices produced by chemo metric analysis showed the closest relationships between flies from Brazil and Dominican Republic, while flies from Colombia showed the greatest genotypic differentiation relative to the others populations.

Mått för att mäta kodkvalitet undersystemutvecklingsprocessen

Viljan att hålla en hög kvalitet på den kod som skrivs vid utveckling av system och applikationerär inte något nytt i utvecklingsvärlden. Flera större företag använder sig av olika mått för attmäta kvaliteten på koden i sina system med målet att hålla en hög driftsäkerhet.Trafikverket är en statlig myndighet som ansvarar för driften av bland annat de system somhåller igång Sveriges järnvägsnät. Eftersom systemen fyller en viktig del i att säkra driften ochse till att tågpositioner, planering av avgångar och hantering av driftstörningar fungerar dygnetrunt för hela landet anser de att det är viktigt att sträva efter att hålla en hög kvalitet påsystemen.Syftet med det här examensarbetet var att ta reda på vilka mått som kan vara möjliga attanvända under systemutvecklingsprocessen för att mäta kvaliteten på kod och hur måtten kananvändas för att öka kvaliteten på IT-lösningar. Detta för att redan på ett tidigt stadie kunnamäta kvaliteten på den kod som skrivs i både befintliga och nyutvecklade system.Studien är en fallstudie som utfördes på Trafikverket, de olika måtten som undersöktes varcode coverage, nivån på maintainability index och antalet inrapporterade incidenter för varjesystem. Mätningar utfördes på sju av Trafikverkets system som i analysen jämfördes motantalet rapporterade incidenter. Intervjuer utfördes för att ge en bild över hur arbetssättet vidutveckling kan påverka kvaliteten. Genom litteraturstudier kom det fram ett mått som inte kundeanvändas praktiskt i det här fallet men är högst intressant, detta är cyclomatic complexity somfinns som en del av maintainability index men som även separat påverkar möjligheten att skrivaenhetstest.Resultaten av studien visar att måtten är användbara för ändamålet men bör inte användassom enskilda mått för att mäta kvalitet eftersom de fyller olika funktioner. Det är viktigt attarbetssättet runt utveckling genomförs enligt en tydlig struktur och att utvecklarna både harkunskap om hur man arbetar med enhetstest och följer kodprinciper för strukturen. Tydligakopplingar mellan nivån på code coverage och inflödet av incidenter kunde ses i de undersöktasystemen där hög code coverage ger ett lägre inflöde av incidenter. Ingen korrelation mellanmaintainability index och incidenter kunde hittas.

Vector Theory of Spontaneous Lorentz Violation

Classical electromagnetism predicts two massless propagating modes, which are known as the two polarizations of the photon. On the other hand, if the Lorentz symmetry of classical electromagnetism is spontaneously broken, the new theory will still have two massless Nambu-Goldstone modes resembling the photon. If the Lorentz symmetry is broken by a bumblebee potential that allows for excitations out of the minimum, then massive modes arise. Furthermore, in curved spacetime, such massive modes will be created through a process other than the usual Higgs mechanism because of the dependence of the bumblebee potential on both the vector field and the metric tensor. Also, it is found that these massive modes do not propagate due to the extra constraints.