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

Ordenamiento Territorial Como Propuesta De Desarrollo Económico Local Estudio De Caso: Propuesta De Plan De Desarrollo Y De Ordenamiento Territorial Para El Cantón Alausí, Componente Económico Productivo

An economic development and land use planning proposal for Alausí County, Chimborazo was created as part of this research. The research started with an analysis of the current situation in the productive area of the county. With the help of participative workshops, it was possible to identify principal problems and opportunities; these topics helped in the definition of development strategies. Alausí is a rural area with 76% employment. Most are engaged in farming activities on sandy loam soils with slopes ranging from 15 to 45 degrees. Despite the ruggedness, 39% of the area is appropriate for farming activities, in which the principal products are barley, corn, potato, and fresh milk. Access to technology is a principal barrier to economic growth and profitability in production. It is recommended that the municipality of Alausí implement various projects identified by this research in order to capitalize on the productive area of the county and to improve quality of life

Biofunctionalization of 3D printed collagen with bevacizumab-loaded microparticles targeting pathological angiogenesis

Pathological angiogenesis is a crucial attribute of several chronic diseases such as cancer, age-related macular degeneration, and osteoarthritis (OA). In the case of OA, pathological angiogenesis mediated by the vascular endothelial growth factor (VEGF), among other factors, contributes to cartilage degeneration and to implants rejection. In line with this, the use of the anti-VEGF bevacizumab (BVZ) has been shown to prevent OA progression and support cartilage regeneration. The aim of this work was to functionalize a medical grade collagen with poly (lactic-co-glycolic acid) (PLGA) microparticles containing BVZ via three-dimensional (3D) printing to target pathological angiogenesis. First, the effect of several formulation parameters on the encapsulation and release of BVZ from PLGA microparticles was studied. Then, the anti-angiogenic activity of released BVZ was tested in a 3D cell model. The 3D printability of the microparticle-loaded collagen ink was tested by evaluating the shape fidelity of 3D printed structures. Results showed that the release and the encapsulation efficiency of BVZ could be tuned as a function of several formulation parameters. In addition, the released BVZ was observed to reduce vascularization by human umbilical vein endothelial cells. Finally, the collagen ink with embedded BVZ microparticles was successfully printed, leading to shape-stable meniscus-, nose- and auricle-like structures. Taken altogether, we defined the conditions for the successful combination of BVZ-loaded microparticles with the 3D printing of a medical grade collagen to target pathological angiogenesis

Human adult, pediatric and microtia auricular cartilage harbor fibronectin-adhering progenitor cells with regenerative ear reconstruction potential

Remaining challenges in auricular cartilage tissue engineering include acquiring sufficient amounts of regeneration-competent cells and subsequent production of high-quality neocartilage. Progenitor cells are a resident subpopulation of native cartilage, displaying a high proliferative and cartilage-forming capacity, yet their potential for regenerative medicine is vastly understudied. In this study, human auricular cartilage progenitor cells were newly identified in healthy cartilage and, importantly, in microtia-impaired chondral remnants. Their cartilage repair potential was assessed via in vitro 3D culture upon encapsulation in a gelatin-based hydrogel, and subsequent biochemical, mechanical, and histological analyses. Auricular cartilage progenitor cells demonstrate a potent ability to proliferate without losing their multipotent differentiation ability and to produce cartilage-like matrix in 3D culture. As these cells can be easily obtained through a non-deforming biopsy of the healthy ear or from the otherwise redundant microtia remnant, they can provide an important solution for long-existing challenges in auricular cartilage tissue engineering

Spatial-Selective Volumetric 4D Printing and Single-Photon Grafting of Biomolecules within Centimeter-Scale Hydrogels via Tomographic Manufacturing

Conventional additive manufacturing and biofabrication techniques are unable to edit the chemicophysical properties of the printed object postprinting. Herein, a new approach is presented, leveraging light-based volumetric printing as a tool to spatially pattern any biomolecule of interest in custom-designed geometries even across large, centimeter-scale hydrogels. As biomaterial platform, a gelatin norbornene resin is developed with tunable mechanical properties suitable for tissue engineering applications. The resin can be volumetrically printed within seconds at high resolution (23.68 ± 10.75 µm). Thiol–ene click chemistry allows on-demand photografting of thiolated compounds postprinting, from small to large (bio)molecules (e.g., fluorescent dyes or growth factors). These molecules are covalently attached into printed structures using volumetric light projections, forming 3D geometries with high spatiotemporal control and ≈50 µm resolution. As a proof of concept, vascular endothelial growth factor is locally photografted into a bioprinted construct and demonstrated region-dependent enhanced adhesion and network formation of endothelial cells. This technology paves the way toward the precise spatiotemporal biofunctionalization and modification of the chemical composition of (bio)printed constructs to better guide cell behavior, build bioactive cue gradients. Moreover, it opens future possibilities for 4D printing to mimic the dynamic changes in morphogen presentation natively experienced in biological tissues

Volumetric Bioprinting of Complex Living-Tissue Constructs within Seconds

Biofabrication technologies, including stereolithography and extrusion-based printing, are revolutionizing the creation of complex engineered tissues. The current paradigm in bioprinting relies on the additive layer-by-layer deposition and assembly of repetitive building blocks, typically cell-laden hydrogel fibers or voxels, single cells, or cellular aggregates. The scalability of these additive manufacturing technologies is limited by their printing velocity, as lengthy biofabrication processes impair cell functionality. Overcoming such limitations, the volumetric bioprinting of clinically relevant sized, anatomically shaped constructs, in a time frame ranging from seconds to tens of seconds is described. An optical-tomography-inspired printing approach, based on visible light projection, is developed to generate cell-laden tissue constructs with high viability (>85%) from gelatin-based photoresponsive hydrogels. Free-form architectures, difficult to reproduce with conventional printing, are obtained, including anatomically correct trabecular bone models with embedded angiogenic sprouts and meniscal grafts. The latter undergoes maturation in vitro as the bioprinted chondroprogenitor cells synthesize neo-fibrocartilage matrix. Moreover, free-floating structures are generated, as demonstrated by printing functional hydrogel-based ball-and-cage fluidic valves. Volumetric bioprinting permits the creation of geometrically complex, centimeter-scale constructs at an unprecedented printing velocity, opening new avenues for upscaling the production of hydrogel-based constructs and for their application in tissue engineering, regenerative medicine, and soft robotics

Human adult, pediatric and microtia auricular cartilage harbor fibronectin-adhering progenitor cells with regenerative ear reconstruction potential

Remaining challenges in auricular cartilage tissue engineering include acquiring sufficient amounts of regeneration-competent cells and subsequent production of high-quality neocartilage. Progenitor cells are a resident subpopulation of native cartilage, displaying a high proliferative and cartilage-forming capacity, yet their potential for regenerative medicine is vastly understudied. In this study, human auricular cartilage progenitor cells were newly identified in healthy cartilage and, importantly, in microtia-impaired chondral remnants. Their cartilage repair potential was assessed via in vitro 3D culture upon encapsulation in a gelatin-based hydrogel, and subsequent biochemical, mechanical, and histological analyses. Auricular cartilage progenitor cells demonstrate a potent ability to proliferate without losing their multipotent differentiation ability and to produce cartilage-like matrix in 3D culture. As these cells can be easily obtained through a non-deforming biopsy of the healthy ear or from the otherwise redundant microtia remnant, they can provide an important solution for long-existing challenges in auricular cartilage tissue engineering

One-Step Photoactivation of a Dual-Functionalized Bioink as Cell Carrier and Cartilage-Binding Glue for Chondral Regeneration

Cartilage defects can result in pain, disability, and osteoarthritis. Hydrogels providing a chondroregeneration-permissive environment are often mechanically weak and display poor lateral integration into the surrounding cartilage. This study develops a visible-light responsive gelatin ink with enhanced interactions with the native tissue, and potential for intraoperative bioprinting. A dual-functionalized tyramine and methacryloyl gelatin (GelMA-Tyr) is synthesized. Photo-crosslinking of both groups is triggered in a single photoexposure by cell-compatible visible light in presence of tris(2,2'-bipyridyl)dichlororuthenium(II) and sodium persulfate as initiators. Neo-cartilage formation from embedded chondroprogenitor cells is demonstrated in vitro, and the hydrogel is successfully applied as bioink for extrusion-printing. Visible light in situ crosslinking in cartilage defects results in no damage to the surrounding tissue, in contrast to the native chondrocyte death caused by UV light (365-400 nm range), commonly used in biofabrication. Tyramine-binding to proteins in native cartilage leads to a 15-fold increment in the adhesive strength of the bioglue compared to pristine GelMA. Enhanced adhesion is observed also when the ink is extruded as printable filaments into the defect. Visible-light reactive GelMA-Tyr bioinks can act as orthobiologic carriers for in situ cartilage repair, providing a permissive environment for chondrogenesis, and establishing safe lateral integration into chondral defects

One‐Step Photoactivation of a Dual‐Functionalized Bioink as Cell Carrier and Cartilage‐Binding Glue for Chondral Regeneration

Cartilage defects can result in pain, disability, and osteoarthritis. Hydrogels providing a chondroregeneration-permissive environment are often mechanically weak and display poor lateral integration into the surrounding cartilage. This study develops a visible-light responsive gelatin ink with enhanced interactions with the native tissue, and potential for intraoperative bioprinting. A dual-functionalized tyramine and methacryloyl gelatin (GelMA-Tyr) is synthesized. Photo-crosslinking of both groups is triggered in a single photoexposure by cell-compatible visible light in presence of tris(2,2'-bipyridyl)dichlororuthenium(II) and sodium persulfate as initiators. Neo-cartilage formation from embedded chondroprogenitor cells is demonstrated in vitro, and the hydrogel is successfully applied as bioink for extrusion-printing. Visible light in situ crosslinking in cartilage defects results in no damage to the surrounding tissue, in contrast to the native chondrocyte death caused by UV light (365-400 nm range), commonly used in biofabrication. Tyramine-binding to proteins in native cartilage leads to a 15-fold increment in the adhesive strength of the bioglue compared to pristine GelMA. Enhanced adhesion is observed also when the ink is extruded as printable filaments into the defect. Visible-light reactive GelMA-Tyr bioinks can act as orthobiologic carriers for in situ cartilage repair, providing a permissive environment for chondrogenesis, and establishing safe lateral integration into chondral defects

One-Step Photoactivation of a Dual-Functionalized Bioink as Cell Carrier and Cartilage-Binding Glue for Chondral Regeneration

Cartilage defects can result in pain, disability, and osteoarthritis. Hydrogels providing a chondroregeneration-permissive environment are often mechanically weak and display poor lateral integration into the surrounding cartilage. This study develops a visible-light responsive gelatin ink with enhanced interactions with the native tissue, and potential for intraoperative bioprinting. A dual-functionalized tyramine and methacryloyl gelatin (GelMA-Tyr) is synthesized. Photo-crosslinking of both groups is triggered in a single photoexposure by cell-compatible visible light in presence of tris(2,2'-bipyridyl)dichlororuthenium(II) and sodium persulfate as initiators. Neo-cartilage formation from embedded chondroprogenitor cells is demonstrated in vitro, and the hydrogel is successfully applied as bioink for extrusion-printing. Visible light in situ crosslinking in cartilage defects results in no damage to the surrounding tissue, in contrast to the native chondrocyte death caused by UV light (365-400 nm range), commonly used in biofabrication. Tyramine-binding to proteins in native cartilage leads to a 15-fold increment in the adhesive strength of the bioglue compared to pristine GelMA. Enhanced adhesion is observed also when the ink is extruded as printable filaments into the defect. Visible-light reactive GelMA-Tyr bioinks can act as orthobiologic carriers for in situ cartilage repair, providing a permissive environment for chondrogenesis, and establishing safe lateral integration into chondral defects