Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

Adaptation of the reservoir fish assemblage index (RFAI) for assessing the Barra Bonita Reservoir (São Paulo, Brazil)

In order to evaluate the environmental condition of the Barra Bonita Reservoir, we adapted the Index of Biotic Integrity (IBI). We chose 24 sampling sites in which three types of habitats were sampled: the mouths of tributaries, the central reservoir and the lateral reservoir. Fish were caught in two seasons (dry and rainy) using 10 gillnet gangs, with meshes ranging from 3 to 12 cm between opposite knots, and funnel traps. Abiotic and biotic variables were measured. Due to the artificial nature of the reservoir, the term biotic integrity was considered inappropriate and the term RFAI (Reservoir Fish Assemblage Index) was adopted. Twelve metrics from sixteen possibles were selected using the Pearson correlation coefficient. The reference conditions were set up based on the criteria of the best condition observed. For each metric, a score of 1, 3 or 5 was assigned as it strongly departs (1), slightly departs (3) or approaches (5) the reference condition. The index value is the sum of the metrics partial scores and ranges from 12 to 60. To evaluate the importance of the unit of measurement of the metric, the index was calculated in fish number (RFAI(N)) and in weight (RFAI(w)). The correlation between RFAIN and RFAIw was very high (r = 0.90, n = 46) indicating that the unit of measurement does not influence the final result of the index. Most of the sampling sites were classified in the 'reasonable' RFAI category. Only the central sites were classified as 'poor'. To validate the RFAI, another index, the Habitat Quality Index (HQI), was built starting from the physiochemical and habitat variables collected. The correlation of the RFAI with the HQI was highly significant (RFAIN, r = 0.37; RFAI(w), r = 0.47; n = 46), indicating that they respond in the same way to environmental degradation. The HQI metrics which most affect RFAI were depth, surrounding landscape and macrophyte presence/absence. Copyright C) 2007 John Wiley & Sons, Ltd.

Geometric Algebra and Einstein’s Electron

This thesis entitled Geometric algebra and einsteins electron: Deterministic field theories .The work in this thesis clarifies an important part of Koga’s theory.Koga also developed a theory of the electron incorporating its gravitational field, using his substitutes for Einstein’s equation.The third chapter deals with the application of geometric algebra to Koga’s approach of the Dirac equation. In chapter 4 we study some aspects of the work of mendel sachs (35,36,37,).Sachs stated aim is to show how quantum mechanics is a limiting case of a general relativistic unified field theory.Chapter 5 contains a critical study and comparison of the work of Koga and Sachs. In particular, we conclude that the incorporation of Mach’s principle is not necessary in Sachs’s treatment of the Dirac equation.

Implementation for spatial data of the shared nearest neighbour with metric data structures

Dissertação para obtenção do Grau de Mestre em Engenharia Informática

Metric properties of the braided Thompson's groups

"Vegeu el resum a l'inici del document del fitxer adjunt."

Induced quantum metric fluctuations and the validity of semiclassical gravity

We propose a criterion for the validity of semiclassical gravity (SCG) which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrinsic and induced fluctuations. These fluctuations can be described by the Einstein-Langevin equation obtained in the framework of stochastic gravity. Specifically, the Einstein-Langevin equation yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. The homogeneous solutions of the Einstein-Langevin equation are equivalent to the solutions of the perturbed semiclassical equation, which describe the evolution of the expectation value of the quantum metric perturbations. The information on the intrinsic fluctuations, which are connected to the initial fluctuations of the metric perturbations, can also be retrieved entirely from the homogeneous solutions. However, the induced metric fluctuations proportional to the noise kernel can only be obtained from the Einstein-Langevin equation (the inhomogeneous term). These equations exhibit runaway solutions with exponential instabilities. A detailed discussion about different methods to deal with these instabilities is given. We illustrate our criterion by showing explicitly that flat space is stable and a description based on SCG is a valid approximation in that case.

Parasites of the freshwater fish trade in Brazil: science metric study

This paper presents a science metric study of parasites of fish farming in Brazil, including a significant review of the literature. The methodology used was based on researching articles in three different databases, carried out ​on May 2012: ISI (Institute for Scientific Information), SciELO (Scientific Electronic Library Online), and Google Academic. The number of articles on fish parasites is mounting (currently over 110), having much increased since 1995. However, the quantity is still low compared with the amount of papers on parasites of fish from natural environments. In Brazil, the farmed fish that have been studied the most are pacu, tilapia and tambaqui. Monogeneans represent the most prevalent group, followed by protozoa and crustaceans. The regions most researched were the southeast and south, making up 84% of the total literature. The main issue addressed in articles was pathology, followed by treatment and record. In conclusion, the treatment of parasitic diseases of farmed fish in Brazil is still incipient, highlighting the importance and usefulness of management practices to prevent the occurrence of health problems.

Slicing the metric space to provide quick indexing of complex data in the main memory

Searching in a dataset for elements that are similar to a given query element is a core problem in applications that manage complex data, and has been aided by metric access methods (MAMs). A growing number of applications require indices that must be built faster and repeatedly, also providing faster response for similarity queries. The increase in the main memory capacity and its lowering costs also motivate using memory-based MAMs. In this paper. we propose the Onion-tree, a new and robust dynamic memory-based MAM that slices the metric space into disjoint subspaces to provide quick indexing of complex data. It introduces three major characteristics: (i) a partitioning method that controls the number of disjoint subspaces generated at each node; (ii) a replacement technique that can change the leaf node pivots in insertion operations; and (iii) range and k-NN extended query algorithms to support the new partitioning method, including a new visit order of the subspaces in k-NN queries. Performance tests with both real-world and synthetic datasets showed that the Onion-tree is very compact. Comparisons of the Onion-tree with the MM-tree and a memory-based version of the Slim-tree showed that the Onion-tree was always faster to build the index. The experiments also showed that the Onion-tree significantly improved range and k-NN query processing performance and was the most efficient MAM, followed by the MM-tree, which in turn outperformed the Slim-tree in almost all the tests. (C) 2010 Elsevier B.V. All rights reserved.

The Wijsman hyperspace of a metric hereditarily Baire space is Baire

In this paper, we show that the Wijsman hyperspace of a metric hereditarily Baire space is Baire. This solves a recent question posed by Zsilinszky. (C) 2009 Elsevier B.V. All rights reserved.

Metric-scalar gravity with torsion and the measurability of the non-minimal coupling

The measurability of the non-minimal coupling is discussed by considering the correction to the Newtonian static potential in the semiclassical approach. The coefficient of the gravitational Darwin term (GDT) gets redefined by the non-minimal torsion scalar couplings. Based on a similar analysis of the GDT in the effective field theory approach to non-minimal scalar, we conclude that for reasonable values of the couplings the correction is very small.

THE PARAMETERS OF THE LEWIS METRIC FOR THE WEYL CLASS

We provide physical interpretation for the four parameters of the stationary Lewis metric restricted to the Weyl class. Matching this spacetime to a completely anisotropic, rigidly rotating, fluid cylinder, we obtain from the junction conditions that one of these parameters is proportional to the vorticity of the source. From the Newtonian approximation a second parameter is found to be proportional to the energy per unit of length. The remaining two parameters may be associated to a gravitational analog of the Aharanov-Bohm effect. We prove, using the Cartan scalars, that the Weyl class metric and static Levi-Civita metric are locally equivalent, i.e., indistinguishable in terms of its curvature.

On the parameters of the Lewis metric for the Lewis class

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analytical form of the Probability Density Function of travel times in rectangular zone with Tchebyshev’s metric

Geometrical dependencies are being researched for analytical representation of the probability density function (pdf) for the travel time between a random, and a known or another random point in Tchebyshev’s metric. In the most popular case - a rectangular area of service - the pdf of this random variable depends directly on the position of the server. Two approaches have been introduced for the exact analytical calculation of the pdf: Ad-hoc approach – useful for a ‘manual’ solving of a specific case; by superposition – an algorithmic approach for the general case. The main concept of each approach is explained, and a short comparison is done to prove the faithfulness.