As fórmulas de Euler em projeção estereográfica e seu significado físico no levantamento de indicatrizes óticas

As fórmulas de Euler são deduzidas a partir de triângulos esféricos obtidos da representação estereográfica das rotações φ, θ, ψ. Um exemplo de aplicação a uma secção arbitrária de gipsita é incluído.

World catalog of the genera of Pselaphidae (Coleoptera) / Alfred F. Newton, Jr., Donald S. Chandler.

n.s. no.53(1989)

Contributions to the paleontology of the upper cretaceous series / by William Newton Logan, A.M. ; Oliver Cummings Farrington, Ph.D. Curator, Dept. of Geology.

v.1:no.6(1899)

Current classification and family-group names in Staphyliniformia (Coleoptera) / Alfred F. Newton, Jr., Margaret K. Thayer.

n.s. no.67(1992)

La Phoronomia (1716) de Jacob Hermann (1678 -1733): entre la filosofía natural y la mecánica analítica

La "Phoronomia", primer libro de mecánica escrito tras los "Principia", es representativo del proceso de transición que transformó la dinámica a principios del XVIII y que concluye con la "Mecánica" de Euler (1736). Está escrita en estilo geométrico y algebraico, y mezcla los conceptos y métodos de Leibniz y Newton de forma idiosincrásica. En esta obra se encuentra por primera vez la segunda ley de Newton escrita en la forma en que hoy la conocemos, así como un intento de construcción de la estática y la dinámica de sólidos y fluidos basado en reglas generales diferenciales.

The Euler characteristic of a category

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula is proved for the cardinality of a colimit of sets, generalizing the classical inclusion-exclusion formula. Both rest on a generalization of Rota's Möbius inversion from posets to categories.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Notes on Agents’ Behavioral Rules Under Adaptive Learning and Studies of Monetary Policy

These notes try to clarify some discussions on the formulation of individual intertemporal behavior under adaptive learning in representative agent models. First, we discuss two suggested approaches and related issues in the context of a simple consumption-saving model. Second, we show that the analysis of learning in the NewKeynesian monetary policy model based on “Euler equations” provides a consistent and valid approach.

Finiteness obstructions and Euler characteristics of categories

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

Symmetric planar central configurations of five bodies: Euler plus two

We study planar central configurations of the five-body problem where three of the bodies are collinear, forming an Euler central configuration of the three-body problem, and the two other bodies together with the collinear configuration are in the same plane. The problem considered here assumes certain symmetries. From the three bodies in the collinear configuration, the two bodies at the extremities have equal masses and the third one is at the middle point between the two. The fourth and fifth bodies are placed in a symmetric way: either with respect to the line containing the three bodies, or with respect to the middle body in the collinear configuration, or with respect to the perpendicular bisector of the segment containing the three bodies. The possible stacked five-body central configurations satisfying these types of symmetries are: a rhombus with four masses at the vertices and a fifth mass in the center, and a trapezoid with four masses at the vertices and a fifth mass at the midpoint of one of the parallel sides.

A web-based pilot study of inter-pathologist reproducibility using the ISHLT 2004 working formulation for biopsy diagnosis of cardiac allograft rejection: The European experience.

BACKGROUND: The aim of this study was to assess, at the European level and using digital technology, the inter-pathologist reproducibility of the ISHLT 2004 system and to compare it with the 1990 system We also assessed the reproducibility of the morphologic criteria for diagnosis of antibody-mediated rejection detailed in the 2004 grading system. METHODS: The hematoxylin-eosin-stained sections of 20 sets of endomyocardial biopsies were pre-selected and graded by two pathologists (A.A. and M.B.) and digitized using a telepathology digital pathology system (Aperio ImageScope System; for details refer to http://aperio.com/). Their diagnoses were considered the index diagnoses, which covered all grades of acute cellular rejection (ACR), early ischemic lesions, Quilty lesions, late ischemic lesions and (in the 2005 system) antibody-mediated rejection (AMR). Eighteen pathologists from 16 heart transplant centers in 7 European countries participated in the study. Inter-observer reproducibility was assessed using Fleiss's kappa and Krippendorff's alpha statistics. RESULTS: The combined kappa value of all grades diagnosed by all 18 pathologists was 0.31 for the 1990 grading system and 0.39 for the 2005 grading system, with alpha statistics at 0.57 and 0.55, respectively. Kappa values by grade for 1990/2005, respectively, were: 0 = 0.52/0.51; 1A/1R = 0.24/0.36; 1B = 0.15; 2 = 0.13; 3A/2R = 0.29/0.29; 3B/3R = 0.13/0.23; and 4 = 0.18. For the 2 cases of AMR, 6 of 18 pathologists correctly suspected AMR on the hematoxylin-eosin slides, whereas, in each of 17 of the 18 AMR-negative cases a small percentage of pathologists (range 5% to 33%) overinterpreted the findings as suggestive for AMR. CONCLUSIONS: Reproducibility studies of cardiac biopsies by pathologists in different centers at the international level were feasible using digitized slides rather than conventional histology glass slides. There was a small improvement in interobserver agreement between pathologists of different European centers when moving from the 1990 ISHLT classification to the "new" 2005 ISHLT classification. Morphologic suspicion of AMR in the 2004 system on hematoxylin-eosin-stained slides only was poor, highlighting the need for better standardization of morphologic criteria for AMR. Ongoing educational programs are needed to ensure standardization of diagnosis of both acute cellular and antibody-mediated rejection.