A construção ortodoxa dos números : dos números naturais aos complexos

In this work, we investigated the construction of natural, integer, rational, real, complex, quaternion and Octonion numbers. More precisely, the set of real numbers was achieved by applying two methods: Dedekind Cuts and Equivalence Classes of Cauchy Sequences. Our study is only based on using Peano Axioms, which are directly related to the natural numbers, in order to get the basic properties satis ed by these numbers. In addition, we carefully proved the elementary results involving real numbers. This process in question was developed constructively throughout of the concepts of the integer and rational numbers. Next, we show that it is possible to establish the existence of complex numbers along with their more usual arithmetic properties. Finally, we nish each chapter of our work showing some possible applications in each set worked.No presente trabalhos, investigamos, cuidadosamente, a construção do números Naturais, inteiros, Racionais, Reais e Complexos. Sendo que, o conjunto dos números reais foi obtido através dos conhecidos métodos: Cortes de Dedekind e Classes de Equivalência por sequência de Cauchy. O estudo consistiu em utilizar os famosos Axiomas de Peano, ps quais estão relacionados aos números naturais, em ordem a obter as em conhecidas propriedades elementares, satisfeitas para todos esses números. E, a partir deste conhecimento, encontramos rigorosamente as provas dos resultados básicos envolvendo os números reais. Este processo em questão, foi desenvolvida de maneira construtiva através dos números inteiros e racionais. Em seguida, mostramos que é possível estabelecer a existência de números complexos, juntamente com suas propriedades aritméticas mais usuais. Por fim, terminamos cada capítulo do nosso trabalho, mostrando algumas possíveis aplicações em cada conjunto trabalhado

Application of optical coherence tomography enhances reproducibility of arthroscopic evaluation of equine joints

Peer reviewe

Characterizing the Chemical Profile of Incidental Ultrafine Particles for Toxicity Assessment Using an Aerosol Concentrator

Incidental ultrafine particles (UFPs) constitute a key pollutant in industrial workplaces. However, characterizing their chemical properties for exposure and toxicity assessments still remains a challenge. In this work, the performance of an aerosol concentrator (Versatile Aerosol Concentration Enrichment System, VACES) was assessed to simultaneously sample UFPs on filter substrates (for chemical analysis) and as liquid suspensions (for toxicity assessment), in a high UFP concentration scenario. An industrial case study was selected where metal-containing UFPs were emitted during thermal spraying of ceramic coatings. Results evidenced the comparability of the VACES system with online monitors in terms of UFP particle mass (for concentrations up to 95 µg UFP/m3 ) and between filters and liquid suspensions, in terms of particle composition (for concentrations up to 1000 µg/ m3). This supports the applicability of this tool for UFP collection in view of chemical and toxicological characterization for incidental UFPs. In the industrial setting evaluated, results showed that the spraying temperature was a driver of fractionation of metals between UF (<0.2 µm) and fine (0.2– 2.5 µm) particles. Potentially health hazardous metals (Ni, Cr) were enriched in UFPs and depleted in the fine particle fraction. Metals vaporized at high temperatures and concentrated in the UF fraction through nucleation processes. Results evidenced the need to understand incidental particle formation mechanisms due to their direct implications on particle composition and, thus, exposure. It is advisable that personal exposure and subsequent risk assessments in occupational settings should include dedicated metrics to monitor UFPs (especially, incidental).What’s important about this paper: Our work addresses the challenge of characterizing the bulk chemical composition of ultrafine particles in occupational settings, for exposure and toxicity assessments. We tested the performance of an aerosol concentrator (VACES) to simultaneously sample ultrafine particles (UFPs) on filter substrates and as liquid suspensions, in a high UFP concentration scenario. An industrial case study was selected where metal-bearing UFPs were emitted. We report the chemical exposures characterized in the industrial facility, and evidence the comparability of the VACES system with online monitors for UFP particle mass (up to 95 µg UFP/m3) as well as between UFP chemical composition on filters and in suspension. This supports the applicability of this tool for UFP collection in view of chemical and toxicological characterization of exposures to incidental UFPs in workplace settings.Highlights: - The VACES system is a useful tool for UFP sampling in high-concentration settings; - UFP collected simultaneously on filters and in suspension showed good comparability; - UFP chemical profiles were characterized; - Health-hazardous metals Ni and Cr accumulated in UFPs; - Understanding emission mechanisms is key to identifying exposure sources.This work was funded by SIINN ERA-NET (project id: 16), the Spanish MINECO (PCIN-2015-173-C02-01) and the French agency (Region Hauts de France). The Spanish Ministry of Science and Innovation (Project CEX2018-000794-S; Severo Ochoa) and the Generalitat de Catalunya (project number: AGAUR 2017 SGR41) provided support for the indirect costs for the Institute of Environmental Assessment and Water Research (IDAEA-CSIC). We acknowledge support of the publication fee by the CSIC Open Access Publication Support Initiative through its Unit of Information Resources for Research (URICI).info:eu-repo/semantics/publishedVersio

Biofabrication : reappraising the definition of an evolving field

Biofabrication is an evolving research field that has recently received significant attention. In particular, the adoption of Biofabrication concepts within the field of Tissue Engineering and Regenerative Medicine has grown tremendously, and has been accompanied by a growing inconsistency in terminology. This article aims at clarifying the position of Biofabrication as a research field with a special focus on its relation to and application for Tissue Engineering and Regenerative Medicine. Within this context, we propose a refined working definition of Biofabrication, including Bioprinting and Bioassembly as complementary strategies within Biofabrication

Kinematics

In three-dimensional continuum mechanics, the integral-gradient theorem, which is the basis of Green's transformation, often called “the divergence theorem,” is a tool of central importance. All the shapes of bodies should be such as to make the integral-gradient theorem apply whenever the fields integrated are smooth to the degrees ordinarily assumed. The first statement in the theorem makes the sets of finite perimeter a Boolean algebra with respect to intersection and union. This chapter discusses a theorem that relates sets of finite perimeter directly to the integral-gradient theorem. The chapter presents a local analysis of the equilibrium and motion of continuous media. © 1977, Academic Press, Inc

Guidelines for an optimized indentation protocol for measurement of cartilage stiffness: The effects of spatial variation and indentation parameters

Mechanical properties of articular cartilage that are vital to its function are often determined by indentation tests, which can be performed at different scales. Cartilage tissue exhibits various types of structural, geometrical, and spatial variations that pose strict demands on indentation protocols. This study aims to define a reproducible micro-indentation protocol for measuring the effective (average) stiffness of the cartilage surface in a region around 1mm(2). We elucidated how different parameters such as indenter size, indenter depth, and the location of the indentation influence the effective elastic modulus measured in micrometer scale on rat knee cartilage. When an indentation was performed (50μm radial probe, ≈10μm indentation depth) at exactly the same location, the variability was less than 10%, even with a recovery period of 30s. However, there was a high spatial variation and a small change of around 60μm in location could change the modulus values up to as much as 10-20 fold. The effective elastic modulus of cartilage surface layer cannot therefore be reproducibly determined from a few indentations on a cartilage sample, and requires at least 144 (12×12) indentations for a soft spherical probe with a 50μm radius. With higher depths, the spatial variation is slightly lower, allowing slightly lower number of indentations (≈80 measurements or a 9×9 frame) to provide a representative elastic modulus. Using this protocol, we determined an elastic modulus of 2.6±1.9N/mm(2) at the medial side versus a higher modulus of 4.2±2.6N/mm(2) at the lateral side of the tibia of 12 weeks old Wistar rats. Optimized indentation protocols similar to the one presented here are required for revealing such variations in the mechanical properties of cartilage with anatomical location