This research delves into the assessment of students’ perspectives regarding virtual internships within Brazilian organizations, a phenomenon accelerated by the global pandemic. Evaluating 78 students’ virtual internships via a survey, the study employs the Fuzzy TOPSIS Class method for analysis. Additionally, a sensitivity analysis was conducted to assess the robustness of the results. Key insights for enhancing virtual internships encompass: emphasizing application and deeper understanding of topics learned during the undergraduate course, enhancing understanding about how organizations work, and fostering comprehension of market dynamics. Among the points best rated by students are the opportunity to explore new subjects, development of soft skills, and supervisors’ competence in managing teams in virtual environments. This paper contributes methodologically by proposing a multicriteria decision-making approach to assess virtual internships. The findings serve as a valuable resource for internship supervisors in companies and higher education institutions, aiding them in guiding students through this pivotal developmental phase that shapes their future careers.

Stokes wave is a classical problem in physics. Various Stokes wave theories in different forms have been developed to help us better understand their characteristics and for engineering applications. Exploring whether these Stokes wave theories can be converted into each other is a mathematical issue. We select three Stokes wave theories with different expansion parameters, all expressed in terms of water depth measured from the mean water level (MWL). Using series reversion to convert between the different expansions, we successfully transform the expressions for the velocity potential, wave profile, and dynamic properties between two of the Stokes wave theories. Through this conversion, we identify an incorrect expression for the water level in one Stokes wave theory.

Autonomous drifting is an advanced technique that enhances vehicle maneuverability beyond conventional driving limits. This survey provides a comprehensive, systematic review of autonomous drifting research published between 2005 and early 2025, analyzing approximately 80 peer-reviewed studies. We employed a modified PRISMA approach to categorize and evaluate research across two main methodological frameworks: dynamical model-based approaches and deep learning techniques. Our analysis reveals that while dynamical methods offer precise control when accurately modeled, they often struggle with generalization to unknown environments. In contrast, deep learning approaches demonstrate better adaptability but face challenges in safety verification and sample efficiency. We comprehensively examine experimental platforms used in the field—from high-fidelity simulators to full-scale vehicles—along with their sensor configurations and computational requirements. This review uniquely identifies critical research gaps, including real-time performance limitations, environmental generalization challenges, safety validation concerns, and integration issues with broader autonomous systems. Our findings suggest that hybrid approaches combining model-based knowledge with data-driven learning may offer the most promising path forward for robust autonomous drifting capabilities in diverse applications ranging from motorsports to emergency collision avoidance in production vehicles.

We examine the modified Hill three-body problem by incorporating the oblateness of the primary body and focus on its asymptotic orbits. Specifically, we analyze and characterize homoclinic and heteroclinic connections associated with the collinear equilibrium points. By systematically varying the oblateness parameter, we determine conditions for the existence and location of these orbits. Our results confirm the presence of both homoclinic orbits, where trajectories asymptotically connect an equilibrium point to itself, and heteroclinic orbits, which establish connections between two distinct equilibrium points, via their stable and unstable invariant manifolds, which are computed both analytically and numerically. To achieve precise computations, we employ differential correction techniques and leverage the system’s inherent symmetries. Numerical calculations are carried out for orbit multiplicities up to twelve, ensuring a comprehensive exploration of the dynamical properties.

In this article, we analyze some curvature restrictions satisfying by the concircular curvature tensor in (2n+1)-dimensional Sasakian manifolds with the generalized Tanaka–Webster connection ∇¯ admitting Ricci–Yamabe solitons. Finally, we give an example of three-dimensional Sasakian manifolds which verifies some of our findings.

This study investigates M/M/n:(m/FIFO) systems with a limited queue capacity (incorporating both “waiting and rejection”). This category of systems can be considered to be mixed-service systems. They operate as queuing systems for customers admitted to the system awaiting service, as well as systems that implement rejection or loss for customers who are denied when the system is full (when all servers and the buffer capacity are occupied). The correlation between the system size and a set of performance measures is analysed for the given arrival and service rates. The system size is determined based on a threshold rate of rejected customers. The correlation between the buffer size and the utilisation factor has direct relevance in the design of real systems (e.g., when the dynamics of the arrival rate can be estimated, it provides a solution for phasing the building of physical waiting places for a specific service capacity). In addition, the analysis of customer rejection probability and average waiting time as a function of the effective utilisation factor could yield practical insights for designing and operating real systems. The second part of this study presents a model for optimising the size of a multi-server system with a finite queue capacity. Initially, the number of servers is determined, assuming that the existing situation does not allow for an increase in the buffer capacity. Then, the case in which both server and buffer capacities become decision variables is presented. The operating losses (which are more straightforward to measure than the related costs) are used as an optimisation criterion.

Among the many (mostly randomized) models proposed in the last decades to study how opinions of a set of individuals interconnected by pairwise relations evolve, a novel deterministic model is introduced in this paper that is able to encompass individual choices, strength and sign of relations, and asynchronism. In particular, asynchronism has been considered until now only in randomized settings. It is here studied in which cases the behavior of the resulting dynamical network is predictable, that is, in which cases the number of opinion configurations encountered by the set of individuals before the dynamical network enters a loop is polynomially bounded by the network size.

An efficient linearization method for solving a system of nonlinear equations was developed, showing good stability and convergence properties. It uses an unconventional and simple strategy to improve the performance of classic methods by a full-rank update of the Jacobian approximates. It can be considered both as a discretized Newton’s method or as a quasi-Newton method with a full-rank update of the Jacobian approximates. A solution to the secant equation presented earlier was based on the Wolfe-Popper procedure. The secant equation was splitted into two equations by introducing an auxiliary variable. A simplified algorithm is given in this paper for the full-rank update procedure.It directly solves the secant equation with the pseudoinverse of the Jacobian approximate matrix. Numerical examples are shown for demonstration purposes. The convergence and efficiency of the suggested method are discussed and compared with the convergence and efficiency of classic linearization methods.

This article is dedicated to the construction of neural networks for the prediction of the current–voltage characteristic (CVC). CVC is the most important characteristic of the mass transfer process in electro-membrane systems (EMS). CVC is used to evaluate and select the optimal design and effective operating modes of EMS. Each calculation of the CVC at the given values of the input parameters, using developed analytical-numerical models, takes a lot of time, so the CVC is calculated in a limited range of parameter changes. The creation of neural networks allowed for the use of prediction to obtain the CVC for a wider range of input parameter values and much faster, saving computing resources. The regularities of the behavior of CVC for various values of input parameters were revealed. During this work, several different neural network architectures were developed and tested. The best predictive results on test samples are given by the neural network consisting of convolutional and LSTM (Long Short-Term Memory) layers.

We present the derivation of generic equations describing the long gravity waves in incompressible fluid with a decaying effect. We show that in this theory, the only restriction to the surface deviation is connected to the stability condition for the waves. Derivation of these generic equations is based on Euler equations for inviscid incompressible fluid and the definition of dynamic pressure which leads to a correct dispersion equation for gravity waves. These derived generic equations for the velocity of fluid and the surface deviation describe the propagation of long gravity waves in incompressible fluid with finite amplitude. We also find the necessary and sufficient conditions for generic equations with dissipation of energy or a decaying effect. The developed approach can significantly improve the accuracy of theory for long gravity waves in incompressible fluid. We also find the quasi-periodic and solitary wave solutions for generic equations with a decaying effect.