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Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur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.

Structuralism and the Applicability of Mathematics

In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.

Hydroxyapatite deposition study through polymeric process on commercially pure Ti surfaces modified by laser beam irradiation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Aprender versus ensinar: Charles Sanders Peirce e a universidade americana do final do século XIX

A produção científica e filosófica de Charles Sanders PEIRCE (1839-1914), exigindo como critério para o trabalho intelectual e para a conduta da vida do pensador o absoluto rigor na construção dos conceitos e a estrita verificação experimental, teve por conseqüência desvincular o trabalho científico e filosófico de qualquer função apologética. A afirmação de que todo conhecimento do mundo da experiência e mesmo daquele elaborado pela matemática é intrinsecamente provável e falível se opôs a todo e qualquer dogmatismo e mesmo ao a priori de tradição Kantiana. O interesse pela teoria evolucionista e a coerência inabalável da filosofia e das atitudes de PEIRCE, como professor e pesquisador, encontraram profunda resistência no meio universitário e editorial de seu tempo. Num momento de grave crise na Universidade norte-americana, decorrente das transformações econômicas e políticas ocorridas com a guerra da Secessão (1861-1865), o posicionamento de PEIRCE contribuiu muito provavelmente para sua demissão como professor das Universidades de Harvard e de John Hopkins; para dificultar a publicação de seus escritos e para seu total isolamento nos últimos anos de vida.

Objetos intencionais e existência objetiva

Neste artigo quero apontar para a possibilidade de uma ontologia da matemática que, mesmo mantendo alguns pontos em comum com o platonismo e com o construtivismo, desliga-se destes em outros pontos essenciais. Por objeto matemático entendo o foco referencial do discurso matemático, ou seja, aquilo sobre o qual a matemática fala. Entendo que a existência destes objetos é meramente intencional, presuntiva, mas, simultaneamente, objetiva, no sentido de ser uma existência comunalizada, compartilhada por todos aqueles engajados no fazer matemático. A existência objetiva das entidades matemáticas não está, entretanto, garantida de uma vez por todas, mas apenas enquanto o discurso matemático for consistente. Este é o espírito do critério de existência objetiva enunciado que, acredito, deve sustentar uma ontologia matemática sem o pressuposto da existência independente de um domínio de objetos matemáticos, sem o empobrecimento que lhe impõem as diferentes versões construtivistas e sem a aniquilação que lhe infringe o formalismo sem objetos.

Pure-transvaginal natural orifice transluminal endoscopic surgery (NOTES) ovariohysterectomy in bitches: a preliminary feasibility study

Cirurgia endoscópica por orifícios naturais (NOTES) constitui um acesso cirúrgico relativamente novo para abordagem minimamente invasiva, a qual vem sendo amplamente estudada na medicina humana. Porém, poucos estudos envolvendo sua aplicação na prática cirúrgica de pequenos animais foram realizados até o momento. O objetivo do presente estudo foi avaliar a factibilidade da ovário-histerectomia transvaginal por NOTES pura em cadelas. Cinco cadelas foram avaliadas. A cavidade abdominal foi acessada por um trocarte de 11mm introduzido por uma incisão vaginal. Empregando-se um endoscópio rígido com canal de trabalho, os pedículos ovarianos foram coagulados e seccionados usando-se diatermia bipolar. O corno uterino foi tracionado para o interior do trocarte e exteriorizado juntamente com a cânula. O corpo e vasos uterinos foram coagulados ou ligados com sutura. O coto uterino foi reposicionado na cavidade abdominal e o pneumoperitônio, drenado. O procedimento foi realizado com sucesso em quatro das cinco cadelas. Na primeira tentativa, houve conversão para uma técnica de NOTES-híbrida, devido à quebra de uma pinça de coagulação. O tempo cirúrgico médio foi 52,1 (DP±11,5 minutos) para a técnica de NOTES pura. A OHE por NOTES pura é factível em cadelas, sem resultar em complicações maiores e proporcionando excelente recuperação pós-operatória.

Iterated deferred correction for linear two-point boundary value problems

An analysis of iterated deferred correction based on various classes of implicit Runge-Kutta formulae is given. Out of different possibilities considered, it is shown that those based purely on Lobatto formulae have the best stability. The enhanced stability of Lobatto schemes is very important for the efficient integration of excessively stiff boundary value problems and this is demonstrated by means of some numerical results.

Multiloop superstring amplitudes from non-minimal pure spinor formalism

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRST-invariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the ten-dimensional superspace action which do not involve integration over the maximum number of theta's.

Theoretical study of MgO(001) surfaces: Pure, doped with Fe, Ca, and Al, and with and without adsorbed water

Ab initio calculations of large cluster models have been performed in order to study water adsorption at the five-fold coordinated adsorption site on pure Mg(001) and MgO(001) surfaces doped with Fe, Ca, and Al. The geometric parameters of the adsorbed water molecule have been optimized preparatory to analysis of binding energies, charge transfer, preferential sites of interaction, and bonding distances. We have used Mulliken population analysis methods in order to analyze charge distributions and the direction of charge transfer. We have also investigated energy gaps, HOMO energies, and SCF orbital energies as well as the acid-base properties of our cluster model. Numerical results are compared, where possible, with experiment and interpreted in the framework of various analytical models. (C) 2001 John Wiley & Sons, Inc.

Evaluation of shear bond strength at the interface of two porcelains and pure titanium injected into the casting mold at three different temperatures

Statement of problem. Titanium has physical and mechanical properties, which have led to its increased use in dental prostheses despite casting difficulties due to high melting point and formation of oxide layers which affect the metal-ceramic bond strength.Purpose. This in vitro study evaluated the shear bond strength of the interface of 2 dental porcelains and pure titanium injected into a mold at 3 different temperatures.Material and methods. Using commercially pure (cp) titanium bars (Titanium, Grade I) melted at 1668degreesC and cast at mold temperatures of 430degreesC, 700degreesC or 900degreesC, 60 specimens were machined to 4 x 4 mm, with a base of 5 x 1 mm. The 4-mm surfaces were airborne-particle abraded with 100 mum aluminum oxide before applying and firing the bonding agent and evaluating the 2 porcelains (Triceram/Triline ti and Vita Titankeramik). Ten specimens were prepared for each temperature and porcelain combination Shear bond testing was performed in a universal testing machine, with a 500-kg load cell and crosshead speed of 0.5 mm/min. The specimens were loaded until failure. The interfaces of representative fractured specimens of each temperature were examined with a scanning electron microscope (SEM) and energy dispersive spectrometer (EDS). Data for shear bond strength (MPa) were statistically analyzed by 2-way ANOVA and the Tukey test (alpha = .05).Results. The results showed significant differences for the metal/porcelain interaction effect (P = .0464). There were no significant differences for the 2 porcelains (P = .4250). The Tukey test showed a significant difference between the pair cp Ti 430degreesC Triceram and cp Ti 900degreesC Triceram, with respective mean values and SDs of 59.74 +/- 11.62 and 34.03 +/- 10.35 MPa.Conclusion. Triceram porcelain showed a bond strength decrease with an increase in the mold temperature for casting titanium. The highest bond strength for Vita porcelain and the best metal-ceramic interface observed with the SEM were found with the mold temperature of 700degreesC.

Mathematics teaching life histories in the study of teachers' perceptions of change

The aim of this paper is to discuss teachers' perceptions of change in their thought and/or practice over time and their perceptions of what kind of experiences or challenges might have influenced those changes. Two mathematics teaching life histories of Brazilian teachers are examined, considering a context of curriculum development in the state of São Paulo, Brazil. Reflection on teachers' thought and practice and interest in their own development, including interest in their own learning of mathematics, seemed to be the most important internal aspects influencing change and development. Close support seemed to be the most important external aspect. The retrospective analysis put a good face on personal change and development. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Discrete approximations for strict convex continuous time problems and duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Some superstring amplitude computations with the non-minimal pure spinor formalism

We use the non-minimal pure spinor formalism to compute in a super-Poincare covariant manner the four-point massless one and two-loop open superstring amplitudes, and the gauge anomaly of the six-point one-loop amplitude. All of these amplitudes are expressed as integrals of ten-dimensional superfields in a pure spinor superspace which involves five theta coordinates covariantly contracted with three pure spinors. The bosonic contribution to these amplitudes agrees with the standard results, and we demonstrate identities which show how the t(8) and epsilon(10) tensors naturally emerge from integrals over pure spinor superspace.