Federal University of Itajubá

Abstract Picard's method of successive approximations is utilized to address the linear differential equation that governs the behaviour of the damped forced harmonic oscillator under the influence of an arbitrary forcing function. With the time-dependent substitution $\chi(t) = e^{-\gamma t}x(t)$, the first derivative term vanishes and the differential equation reduces to a second-order ODE without damping for $x(t)$. This modified equation takes the form of an inhomogeneous Volterra integral equation of the second type, incorporating two initial conditions. Initiating the iterative process of successive approximations with a meticulously selected zero-order approximation, we demonstrate the emergence of convergent sequences of partial sums, culminating in the derivation of a closed-form solution. The straightforward approach employed in this paper to analyze the damped and forced harmonic oscillator is accessible to undergraduate students in physics, engineering, and mathematics, without requiring sophisticated mathematical tools. Moreover, it facilitates a direct physical analysis of the problem and serves as an insightful example of the application of Taylor series expansion. As specific examples, presented merely as illustrative applications that have not yet been addressed in the literature (at least not in this context for the second example), we consider an oscillator driven by a Gaussian-like force and by a normalized exponential force. These examples can be seen as regularized generalizations of an impulsive, delta-like force.

Real-world problems can be quite challenging, containing multiple variables and objectives with equations over their domain that may be completely unknown. A very common approach in the industry is to use Response Surface Methodology (RSM) to obtain approximate model equations. However, optimization with Artificial Intelligence has been a promising tool to explore multi-objective black-box optimization problems. To illustrate this general problem, this study presents the structural optimization of an isogrid tube that has four responses with no explicit equations: mass, natural frequency, critical buckling load, and Tsai-Wu failure criteria for compression. A metaheuristic (MH) will be applied to three different methodologies that will be compared: i) Direct link between the MH and the structure in the Finite Element software (more expensive and realistic option), ii) Link between the MH and the polynomials found through RSM, and iii) Link between the MH and the best supervised machine learning algorithm found among more than 20 models for each response. The machine learning results found are close to the real in convergence, coverage, and presentation of the true nature of these tradeoffs, but with 96% less computational cost. Hyperparameters of all ML models were tuned using Bayesian Optimization with cross-validation.

ABSTRACT A recent article discusses the design of chain sampling plans based on the Cpm index where a sample is randomly selected from the lot, and the C pm value of the sample is compared with the threshold ( k a ). If the C pm is lower than k a , the lot is rejected, otherwise, the C pm values of previous m lots are examined; if m ‐1 of the C pm values exceed k a and the remaining C pm value exceeds one or both thresholds ( k r , k a ), the lot is accepted, otherwise the lot is also rejected. In this article, we adopted the criteria of C pm s lower than k r (instead of k a ) to reject the current lot. In this way, current lots with C pm s in the interval ( k r , k a ) can still be accepted; in fact, they are accepted if the C pm s of their preceding m lots exceed k a . We found that the original lot sentencing procedure, without the proposed modifications, increase the average sample size required by the CPM‐based chain sampling plan by 18%, 26%, and 28% for m = 1, 2, and 3, respectively. An algorithm has been developed to find the minimum sample size n required by the chain sampling plan to satisfy the producer and consumer risks. It is a very fast ( n , k r ) search algorithm that intelligently exploits the fact that the second threshold k a can be expressed as a function of ( n , k r ).

Large Language Models (LLMs) have gained attention for addressing coding problems, but their effectiveness in fixing code maintainability remains unclear. This study evaluates LLMs capability to resolve 127 maintainability issues from 10 GitHub repositories. We use zero-shot prompting for Copilot Chat and Llama 3.1, and few-shot prompting with Llama only. The LLM-generated solutions are assessed for compilation errors, test failures, and new maintainability problems. Llama with few-shot prompting successfully fixed 44.9 % of the methods, while Copilot Chat and Llama zero-shot fixed 32.29 % and 30 %, respectively. However, most solutions introduced errors or new maintainability issues. We also conducted a human study with 45 participants to evaluate the readability of 51 LLM-generated solutions. The human study showed that 68.63 % of participants observed improved readability. Overall, while LLMs show potential for fixing maintainability issues, their introduction of errors highlights their current limitations.

Abstract The combination of acidizing and hydraulic fracturing, or proppant-acid fracturing, seems to be a very logical approach to achieve the maximum stimulated volume in tight gas reservoirs, since the acid solution can stimulate the deep microfracture network far beyond the main propped fracture. However, this hybrid stimulation method sparks concerns that acidizing can increase proppant embedment and decrease the propped fracture conductivity. To understand how acidizing may be responsible for reducing conductivity, this article initially delves into the analysis of microscopic images of carbonate and siltstone specimens associated with a low permeability or tight gas reservoir in the São Francisco basin, in Minas Gerais, a kind of reservoir which is becoming considerably more important in recent years due to energy transition initiatives. The microscopic analysis revealed that thin, well-defined layers emerged on the acidized surface of some of the studied specimens. Then additional nanoindentation and proppant embedment tests showed that these new layers are weaker compared to the original rock matrix and are ultimately responsible for fracture conductivity decline. The findings in this study serve as an important piece of information for reservoir stimulation professionals that may consider the combination of acid stimulation and hydraulic fracturing in tight gas formations.

This study investigates the microstructure and corrosion behavior of WC-NiSi cemented carbide produced by conventional powder metallurgy, with comparative analysis against traditional WC-Co cemented carbide. Microstructural characterization was carried out using scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), and X-ray diffraction (XRD) before and after corrosion testing. Electrochemical performance was evaluated in a 3.5 wt.% NaCl solution through open-circuit potential (OCP) measurements, linear potentiodynamic polarization, and electrochemical impedance spectroscopy (EIS). The WC-NiSi cemented carbide exhibited a microstructure similar to WC-Co, although with a slightly higher porosity and increased presence of binder islands. Electrochemical assessments revealed that the cemented carbide with NiSi binder demonstrated more noble corrosion potentials, reduced current density, and higher overall impedance compared to its Co binder counterpart, indicating enhanced corrosion resistance.

Abstract This work is a guide for researchers in the area of mathematics education and aims to contribute to good writing and structuring of journal articles for publication in journals, since authors who construct a persuasive and convincing argument are more likely to influence the readers and gain acceptance within the research community. To address the research question – How to write a good article in mathematics education? –, a non-systematic literature review was conducted, analyzing texts from seven journals that are among the top ten international mathematics education journals. The results offer guidance on writing the main sections of a typical paper – title, abstract, introduction, literature review, theoretical framework, methodology, results, discussions and conclusion – as well as guidance on structuring the article as a whole.

Resumo Considerando o aumento da oferta de disciplinas específicas de História da Matemática (HM) nos cursos de formação de professores, realizamos esta investigação com objetivo de descrever e analisar as contribuições de uma disciplina de História da Matemática para a formação de professores, mais especificamente, para a mobilização de Conhecimentos Matemáticos para o Ensino. Assim, a pesquisa teve como foco os conhecimentos mobilizados por sete futuros professores, ao longo de um semestre da disciplina de HM presente no currículo de um curso de licenciatura de uma universidade federal, adotando como referência o modelo Conhecimento Matemático para o Ensino, proposto por Ball, Thames e Phelps em 2008, que é conhecido pela sigla MKT. Os dados da investigação emergiram a partir de gravações audiovisuais das aulas, do diário de campo, das atividades realizadas pelos estudantes e das entrevistas realizadas após o término da disciplina. As análises indicam que os licenciandos expressaram conhecimentos referentes aos três subdomínios do Conhecimento Específico do Conteúdo, sobretudo, relativo ao Conhecimento Especializado do Conteúdo aparecendo com maior frequência nas atividades acerca da Matemática na Antiguidade. Também, evidenciaram-se, de maneira expressiva, conhecimentos referentes a todos os subdomínios do Conhecimento Pedagógico do Conteúdo, de modo especial, aos subdomínios: Conhecimento do Conteúdo e dos Estudantes e Conhecimento do Conteúdo e Ensino. Assim, os resultados desta investigação indicam que a disciplina História da Matemática tem o potencial de possibilitar aos licenciandos a mobilização de relevantes conhecimentos para a docência e, portanto, tal disciplina pode contribuir para a formação inicial de professores.