INEQUALITIES FOR ZEROS of JACOBI POLYNOMIALS VIA OBRECHKOFF'S THEOREM

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Finiteness theorem for topological contact equivalence of map germs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CP trajectory diagram - a tool for a pictorial representation of CP and matter effects in neutrino oscillations

We introduce a CP trajectory diagram in bi-probability space as a powerful tool for a pictorial representation of the genuine CP and the matter effects in neutrino oscillations. The existence of correlated ambiguity in the B is uncovered. The principles of tuning the beam energy for a determination of CP-violating phase delta and the sign of Deltam(13)(2) given baseline distance are proposed to resolve the ambiguity and to maximize the CP-odd effect. We finally point out, quite contrary to what is usually believed, that the ambiguity may be resolved with similar to 50% chance in the super-JHF experiment despite its relatively short baseline of 300 km. (C) 2003 Elsevier B.V. B.V. All rights reserved.

CP and T trajectory diagrams for a unified graphical representation of neutrino oscillations

Recently the CP trajectory diagram was introduced to demonstrate the difference between the intrinsic CP violating effects to those induced by matter for neutrino oscillation. In this Letter we introduce the T trajectory diagram. In these diagrams the probability for a given oscillation process is plotted versus the probability for the CP- or the T-conjugate processes, which forms an ellipse as the CP- or T-violating phase is varied. Since the CP- and the T-conjugate processes are related by CPT symmetry, even in the presence of matter, these two trajectory diagrams are closely related with each other and form a unified description of neutrino oscillations in matter. (C) 2002 Published by Elsevier B.V. B.V.

Husserl on Geometry and Spatial Representation

Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl's ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl.

Comparative genomic hybridization analysis detects frequent over-representation of DNA sequences at 3q, 7p, and 8q in head and neck carcinomas

Comparative genomic hybridization (CGH) was used to identify chromosomal imbalances in 19 samples of squamous cell carcinoma of the head and neck (HNSCC). The chromosome arms most often or er-represented were 3q (48%), 8q (42%), and 7p (32%); in many cases, these changes were observed at high copy number. Other commonly over-represented sites were 1q, 2q, 6p, 6q, and 18q. The most frequently under-represented segments were 3p and 22q. Loss of heterozygosity of two polymorphic microsatellite loci from chromosome 22 was observed in two tongue tumors, in agreement with the CGH analysis. Gains of 1q and 2q material were detected in patients exhibiting a clinical history of recurrence and/or metastasis followed by terminal disease. This association suggests that gain of 1q and 2q map be a new marker of head and neck tumors with a refractory clinical response. (C) 2000 Elsevier B.V. All rights reserved.

Representation and analysis of soccer players' actions using principal components

This paper proposes the use of the Principal Components Analysis (PCA) method to represent and to analyse soccer players' actions distribution in the pitch. The seven games of the Brazilian National Team during the 2002 World Cup were analysed. The player's position actions were measured from videotapes in a computer interface. The results were: a) the graphical representation, given by two orthogonal segments in the two directions of maximal variability and centred at the mean of each player's actions position; b) the eccentricity measurement, given by the variability ratio and c) the actions zone area, given by variability product. The results showed that the individual characteristics of acting were well represented by the PCA, allowing comparisons among games and providing insights related to the tactical organisation of the team.

Collisional semiclassical approximations in phase-space representation

The Gaussian wave-packet phase-space representation is used to show that the expansion in powers of a of the quantum Liouville propagator leads, in the zeroth-order term, to results close to those obtained in the statistical quasiclassical method of Lee and Scully in the Weyl-Wigner picture. It is also verified that, propagating the Wigner distribution along the classical trajectories, the amount of error is less than that coming from propagating the Gaussian distribution along classical trajectories.

Blumenthal's theorem for Laurent orthogonal polynomials

We investigate polynomials satisfying a three-term recurrence relation of the form B-n(x) = (x - beta(n))beta(n-1)(x) - alpha(n)xB(n-2)(x), with positive recurrence coefficients alpha(n+1),beta(n) (n = 1, 2,...). We show that the zeros are eigenvalues of a structured Hessenberg matrix and give the left and right eigenvectors of this matrix, from which we deduce Laurent orthogonality and the Gaussian quadrature formula. We analyse in more detail the case where alpha(n) --> alpha and beta(n) --> beta and show that the zeros of beta(n) are dense on an interval and that the support of the Laurent orthogonality measure is equal to this interval and a set which is at most denumerable with accumulation points (if any) at the endpoints of the interval. This result is the Laurent version of Blumenthal's theorem for orthogonal polynomials. (C) 2002 Elsevier B.V. (USA).

Homonymy in natural language processes: A representation using Pustejovsky's Qualia Structure and ontological information

This paper presents a proposal for the semantic treatment of ambiguous homographic forms in Brazilian Portuguese, and to offer linguistic strategies for its computational implementation in Systems of Natural Language Processing (SNLP). Pustejovsky's Generative Lexicon was used as a theoretical model. From this model, the Qualia Structure - QS (and the Formal, Telic, Agentive and Constitutive roles) was selected as one of the linguistic and semantic expedients for the achievement of disambiguation of homonym forms. So that analyzed and treated data could be manipulated, we elaborated a Lexical Knowledge Base (LKB) where lexical items are correlated and interconnected by different kinds of semantic relations in the QS and ontological information.

Ordering ambiguity versus representation

In this work we show that the ordering ambiguity on quantization depends on the representation choice. This property is then used to solve unambiguously some particular systems. Finally, we speculate on the consequences for more involved cases.

Incorporating voltage/reactive representation to short-term generation scheduling models

This paper proposes a methodology to incorporate voltage/reactive representation to Short Term Generation Scheduling (STGS) models, which is based on active/reactive decoupling characteristics of power systems. In such approach STGS is decoupled in both Active (AGS) and Reactive (RGS) Generation Scheduling models. AGS model establishes an initial active generation scheduling through a traditional dispatch model. The scheduling proposed by AGS model is evaluated from the voltage/reactive points of view, through the proposed RGS model. RGS is formulated as a sequence of T nonlinear OPF problems, solved separately but taking into account load tracking between consecutive time intervals. This approach considerably reduces computational effort to perform the reactive analysis of the RGS problem as a whole. When necessary, RGS model is capable to propose active generation redispatches, such that critical reactive problems (in which all reactive variables have been insufficient to control the reactive problems) can be overcome. The formulation and solution methodology proposed are evaluated in the IEEE30 system in two case studies. These studies show that the methodology is robust enough to incorporate reactive aspects to STGS problem.

Representation in cognitive neuroscience

This article discusses the possible representational nature of two brain cognitive functions: perceptual and executive. Assuming the Newellian definition of representational processes as those that establish an isomorphic relation between two structures, I claim that perceptual processes generate only a partial correspondence (between stimuli properties and brain states) and therefore should not be properly conceived as representational. on the other hand, executive processes encompass the combination of copies (i.e., representations) of perceptual patterns, generating new patterns that subserve behavior. In summary, I criticize the notion of perceptual representations, and propose that brain representational processes are related to executive functions, having a pragmatic dimension.