Search Results (4)

To mitigate large-scale blackout risks in urban distribution systems under typhoon-induced extreme weather and to reduce post-disaster restoration costs, this study proposes a resilience-oriented spatiotemporal co-optimization framework integrating transportation networks, power grids, and distributed energy resources. First, a city-scale typhoon spatiotemporal model is established, integrating static wind field, dynamic evolution, and trajectory-based mobility with urban-geometry-driven wind speed correction to characterize the spatiotemporal progression of extreme wind hazards. Second, the time-varying failure rates of distribution network components are quantified by explicitly accounting for network topology correlations, while the spatiotemporal dispatchability and output characteristics of distributed resources under disaster conditions are systematically modeled. Third, a pre-disaster proactive deployment model is formulated to minimize load curtailment costs and resource allocation expenditures. The model integrates active network reconfiguration with coordinated placement of distributed generation (DG) and mobile energy storage systems (MESSs), enabling resilience-enhancing pre-positioning strategies. Subsequently, a post-disaster restoration scheduling model is developed with the objective of minimizing unserved load. By embedding traffic flow constraints and optimal path computation under disrupted transportation conditions, the proposed framework realizes spatiotemporal coordination among MESSs, DG, and electric vehicles (EVs), thereby accelerating system-level recovery. Finally, the effectiveness of the proposed strategy is validated on a 51-node urban distribution system located in eastern coastal China, demonstrating significant improvements in restoration performance and resilience enhancement. Full article

In solving descriptive geometry (DG) problems, board (i.e., hand drawing) methods are frequently used, despite this discipline is still very important to enhance spatial vision. These methods are very different from CAD tools which are used in the field of design. CAD facilitates the realization of geometric constructions and transformations (i.e., rotation, translation, copying, scaling, alignment, and symmetry, among others) are performed analytically. For this reason, a 3D DG problem-solving methodology using CAD and orthographic projection (CADOP) is introduced. Once the principles of DG, orthographic projection, and CAD fundamentals and tools are described, CADOP is applied to obtain (i) orthogonal views; (ii) principal lines of a plane; (iii) true-size view of a plane; (iv) parallelism, perpendicularity, and distance, and (v) angles. Considering the user coordinate system in CADOP allows one to place the horizontal plane in the suitable position to solve DG problems directly in one step. In the traditional methods, the use of auxiliary views must be carried out in several steps instead. The dynamic management of the 3D view of the scene is facilitated in CADOP, improving its understanding, and achieving the precision inherent in analytical calculations. Full article

The rapid changes in information and communication technology (ICT), the increasing availability of processing power, and the complexity of mathematical software demand a radical re-thinking of science, technology, engineering, arts, and mathematics (STEAM), as well as mathematics education. In the transition to technology-based classrooms, the constant use of educational software is a requirement for sustainable STEAM and mathematics education. This software supports a collaborative and actionable learning environment, develops 21st-century skills, and promotes the adoption of active and innovative methodologies. This paper focuses on learning and teaching mathematics and analyzes the role and utility of ICT tools in education as computer algebra systems (CAS) and dynamic geometry systems (DGS) in implementing active and innovative teaching methodologies related to sustainable STEAM education. Likewise, it highlights the necessity for learners to have extensive knowledge of mathematical theory, an essential asset to ensure the reliable and effective use of mathematical software. Through a practical experiment, this study aims to highlight that a mixed teaching method can significantly improve the sustainability of math knowledge. It provides various solid examples of CAS and DGS applications to emphasize its usage rooted in a mathematical background to enable learners to identify when the computer solution is unreliable. The study highlights that the proper use of CAS and DGS is an efficient method of deepening our understanding of mathematical notions and solving tasks in STEAM subjects and real-life applications. This paper’s goal is to direct our attention to the proper and intelligent use of computer tools, especially symbolic calculators, such as CAS and DGS, without providing an in-depth analysis of the challenges of these technologies. The outcomes of the paper should offer educators and learners new elements of active strategies and innovative learning models that can be immediately applied in education. Full article

Our goal is to discuss the different issues that arise when attempting to visualize a joints-and-bars cube through GeoGebra, a widespread program that combines dynamic geometry (DGS) and computer algebra systems (CAS). As is standard in the DGS framework, the performance of the graphic model (i.e., the positions of the other vertices when dragging a given one) must correspond to a mathematically rigorous, symbolic computation-driven output. This requirement poses both computational algebraic geometry and dynamic geometry programming challenges that will be described, together with the corresponding proposed solutions. Among these, we include a complete determination of the dimension of the cubic linkage from an algebraic perspective, and introduce advanced 3D visualizations of this structure by using the GeoGebra software. Full article