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Uma introdução histórica à geometria hiperbólica e aplicações trigonométricas

2026-08-07T13:53:40Z

Título: Uma introdução histórica à geometria hiperbólica e aplicações trigonométricas Autor(es): Santos, Gabriel dos Abstract: This work analyzes the historical and mathematical evolution of geometry, focu-sing on the rupture of the Euclidean dogma and the consolidation of hyperbolic geometry as a foundation for modern physics. The research aims to describe the transition from Euclid’s axiomatic system to non-Euclidean models, demonstrating how the negation of the fifth postulate grounds new understandings of space. The method utilizes a bibliographic and documental review of a deductive nature, based principaly in Barbosa’s works to reconstruct the logical rigor of geometric demonstrations(BARBOSA, 2007). The discussion covers the failed attempts by mathematicians such as Ptolemy, Proclus, and Saccheri to prove the parallel postu-late, culminating in the independent discovery by Gauss, Bolyai, and Lobachevsky. The text details elementary properties of neutral and hyperbolic geometry, suchas Saccheri and Lambert quadrilaterals, generalized triangles, and hyperbolic tri-gonometry. The results highlight that hyperbolic geometry provides the necessarymathematical framework for Einstein’s Theory of Relativity.

Efeito da idade, do período e da coorte de nascimento na mortalidade por câncer de orofaringe nas unidades federativas brasileiras entre 1999 e 2023

2026-08-04T12:37:15Z

Título: Efeito da idade, do período e da coorte de nascimento na mortalidade por câncer de orofaringe nas unidades federativas brasileiras entre 1999 e 2023 Autor(es): Sousa, Matheus Barbosa Abstract: Oropharyngeal Cancer (OC) has demonstrated a global epidemiological transition in recent decades, occurring more frequently in young individuals non-exposed to tobacco or alcohol, the classic risk factors. This phenomenon, compared to an epidemic in some countries, is primarily driven by Human Papillomavirus (HPV) infection, associated with changes in sexual behavior. Age-Period-Cohort (APC) analysis identifies variations in the epidemiology of this neoplasm, enabling an investigation of this effect on OC mortality across Brazil's Federative Units (FU). This study aimed to analyze the APC effect on OC mortality in the 27 Brazilian FU from 1999 to 2023, identifying potential determinants for the observed effects and comparing them among the FU. This was an observational ecological study, since population aggregates were used as units of analysis. Thus, Population and death records, obtained from the Mortality Information System (SIM) and IBGE, were grouped into 5-year intervals. A Poisson regression model was applied, calculating the relative risk (RR) for each cohort. Data analysis utilized Deviance statistics and the approach proposed by Carstensen. A total of 77,293 deaths were identified, 84% of which were male. Results demonstrated regional heterogeneity. An increased risk of death from OC was observed in young cohorts in the North and Northeast, represented by Amazonas in the 1989-1993 cohort (RR= 5.40; 95%CI: 1.02 – 28.55) and Maranhão in the 2004-2008 cohort (RR= 13.38; 95%CI: 1.17 – 152.40). Furthermore, a reduction in mortality risk was recorded in more recent cohorts in the South, specifically in Paraná in the 1999-2003 cohort (RR= 0.20; 95%CI: 0.06 – 0.69), Santa Catarina in the 1994-1998 cohort (RR= 0.18; 95%CI: 0.06 – 0.53), and Rio Grande do Sul in the 1994-1998 cohort (RR= 0.22; 95%CI: 0.10 – 0.49); and in the Southeast, notably São Paulo in the 2004-2008 cohort (RR= 0.33; 95%CI: 0.11 – 0.97) and Rio de Janeiro in the 1999-2003 cohort (RR= 0.35; 95%CI: 0.14 – 0.91), in addition to Rondônia and Mato Grosso. Thus, Brazil presents heterogeneous OC mortality epidemiology; the South and Southeast reflect the success of tobacco control policies, while in the North and Northeast, HPV emerges as a potential cause of increased risk in current cohorts. Therefore, the need for expanded HPV vaccination coverage and public policies focused on early diagnosis is evident.

Tendência temporal e fatores associados ao prognóstico dos acidentes ofídicos no estado de Sergipe no período de 2010 a 2024

2026-08-04T11:36:19Z

Título: Tendência temporal e fatores associados ao prognóstico dos acidentes ofídicos no estado de Sergipe no período de 2010 a 2024 Autor(es): Oliveira, Leonardo de Abstract: Introduction: Snakebite envenoming represents a severe public health problem in Brazil and a neglected tropical disease with high socioeconomic impact, especially in the Northeast region, where it is frequently characterized as an occupational accident among vulnerable rural populations. Objectives: To analyze the temporal trend, spatial distribution, and factors associated with the prognosis of snakebites notified in the state of Sergipe between 2010 and 2024. Material and Methods: This is an observational, retrospective, ecological time-series epidemiological study with an analytical approach, conducted using secondary data from the Notifiable Diseases Information System. The temporal trend was analyzed using log-linear regression (Negative Binomial) and the spatial distribution using Global and Local Moran’s indices (LISA), while factors associated with severity and death were investigated using Firth’s logistic regression. Results: A total of 2,731 cases were notified during the period, with a predominance of male victims of economically active age, with the Bothrops genus being responsible for the majority of notifications. Multivariate analysis identified a delay in medical care exceeding six hours as the main independent predictor of severity (OR = 4.13) and death (OR = 5.23). Age equal to or greater than 60 years was associated with a higher risk of fatal outcome, and accidents caused by the Crotalus and Micrurus genera presented high clinical severity. The temporal analysis revealed a stationary trend in incidence, with marked seasonality from May to August, while the spatial distribution revealed heterogeneity, with the formation of high-risk clusters. Conclusion: Snakebite envenoming in Sergipe presents an epidemiological pattern strongly influenced by social, occupational, environmental, and climatic determinants. The time elapsed between the bite and antivenom therapy constitutes the main modifiable prognostic determinant, reinforcing the need for strategies to decentralize medical care and provide differentiated care to the elderly population to reduce lethality and sequelae caused by snakebites.

Avaliação do conhecimento dos estudantes de medicina sobre a abordagem diagnóstica e terapêutica precoces das cefaleias primárias e secundárias

2026-08-04T11:15:27Z

Título: Avaliação do conhecimento dos estudantes de medicina sobre a abordagem diagnóstica e terapêutica precoces das cefaleias primárias e secundárias Autor(es): Cardoso, Tarcísio Nascimento Abstract: Headaches represent one of the main neurological conditions in emergency care, making it imperative for future physicians to have the competence for their effective management. This study's primary objective was to assess the knowledge level of medical students at the Federal University of Sergipe – Lagarto Campus regarding the early diagnostic and therapeutic approach to primary and secondary headaches. The method used was a quantitative and descriptive study. The research involved applying a 30-item structured online questionnaire, previously tested in a pilot group with students and specialists. The sample comprised 116 medical students from the basic, clinical, and internship cycles. Performance was analyzed using descriptive statistics, with results indicating a statistically significant progression of knowledge with advancement in the course, as evidenced by the Kruskal-Wallis test (H=54.98, p<0.001). The Dwass-Steel-Critchlow-Fligner post-hoc test confirmed that the overall score was significantly different among all three groups (Basic vs. Clinical p<0.001; Basic vs. Internship p<0.001; and Clinical vs. Internship p=0.023). Additionally, the instrument's psychometric quality was rigorously assessed using Item Response Theory (IRT) with the Rasch Model. Although the mastery of basic and emergency topics, such as acute treatment and evident warning signs, is consolidated, the item analysis revealed critical gaps. The diagnostic criteria for chronic migraine, the prophylactic management of primary headaches, and the interpretation of warning signs in more complex scenarios were shown to be deficient aspects in the studied population. The findings directly signal weaknesses in training, contextualized in the discussion as part of a global curricular gap, suggesting the need for programmatic reinforcement in teaching specific clinical guidelines. Such intervention is crucial to prepare future professionals to deal with the complexity of headaches, promoting greater diagnostic accuracy and enhancing patient safety and quality of life.