"Pitágoras: estendendo a dimensão do teorema"

Dissertação (mestrado profissional) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Programa de Pós-Graduação em Matemática, Florianópolis, 2016.Conforme relatos históricos, é sabido que o Teorema de Pitágoras já era utilizado antes mesmo do nascimento do famoso matemático e filósofo grego. Neste trabalho, com auxílio de ferramentas da Álgebra Linear é da Geometria Analítica, será investigada uma generalização desse importante Teorema. O caso mais conhecido é o do R2 (em correspondência com o plano euclidiano), entretanto, será visto que existe um certo padrão matemático também para o R3 e R4 . Ainda, será apresentado um plano de aula, em que o Teorema de Pitágoras no R3 poderá ser visualizado e compreendido por estudantes do Ensino Médio, através do software GeoGebra e conceitos da Geometria Analítica, estudados em sala.Abstract : According to historical accounts, it is known that the Pythagoreantheorem was already used even before the birth of the famous mathematicianand Greek philosopher. In this paper, with the aid of thetools Linear Algebra and Analytic Geometry, a generalization of thisimportant theorem will be investigated. The best known case is thatof R2 (corresponding to the Euclidean plane), however, it will be seenthat there is a certain mathematical pattern also for R3 and R4. It willalso be presented in the \\Pythagoras' theorem in R3" a lesson that canbe understood by high school students through the software GeoGebraand concepts of analytic geometry , studied in class

Process development for an effective COVID-19 vaccine candidate harboring recombinant SARS-CoV-2 delta plus receptor binding domain produced by Pichia pastoris

Abstract Recombinant protein-based SARS-CoV-2 vaccines are needed to fill the vaccine equity gap. Because protein-subunit based vaccines are easier and cheaper to produce and do not require special storage/transportation conditions, they are suitable for low-/middle-income countries. Here, we report our vaccine development studies with the receptor binding domain of the SARS-CoV-2 Delta Plus strain (RBD-DP) which caused increased hospitalizations compared to other variants. First, we expressed RBD-DP in the Pichia pastoris yeast system and upscaled it to a 5-L fermenter for production. After three-step purification, we obtained RBD-DP with > 95% purity from a protein yield of > 1 g/L of supernatant. Several biophysical and biochemical characterizations were performed to confirm its identity, stability, and functionality. Then, it was formulated in different contents with Alum and CpG for mice immunization. After three doses of immunization, IgG titers from sera reached to > 106 and most importantly it showed high T-cell responses which are required for an effective vaccine to prevent severe COVID-19 disease. A live neutralization test was performed with both the Wuhan strain (B.1.1.7) and Delta strain (B.1.617.2) and it showed high neutralization antibody content for both strains. A challenge study with SARS-CoV-2 infected K18-hACE2 transgenic mice showed good immunoprotective activity with no viruses in the lungs and no lung inflammation for all immunized mice