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A Review of Earthquake Landslide Hazard Assessment Methods
No full textLandslides triggered by earthquakes are large in scale and wide in scope, making them one of the most serious geological disasters. Earthquake landslide hazard assessment has become an important part of disaster reduction and prevention work. Based on existing research and assessment practices, such an assessment is divided into two levels: individual landslide assessment and regional landslide assessment. The individual assessment, mainly required by specific engineering seismic issues, serves as the foundation of earthquake landslide hazard assessment. It includes two analysis methods: qualitative analysis based on causal relationships (e.g., comprehensive indicator modeling, logistic regression, neural network modeling, information quantity evaluation) and mechanical analysis based on physical-mechanical mechanisms (e.g., quasi-static method, Newmark method, dynamic time-history method). This paper summarizes the characteristics and problems of these two methods. Regional assessment caters to regional strong earthquake geological disaster rescue deployment, future earthquake defense planning, and engineering construction strategic layout. It has two strategies—“from region to individual” (earthquake-focused, coarse-to-fine) and “from individual to region” (landslide-focused, point-to-area)—which differ in observation angles and technical routes. Currently, the individual assessment can estimate landslide hazard probability by considering potential seismic source ori-entations, but the regional assessment lags, e.g., ignoring such orientations and lacking the application of the dynamic time-history method. Thus, this paper proposes establishing slope seismic resistance fields and multi-azimuth seismic impact fields, then overlaying them to determine regional earth-quake landslide distribution probability, and points out future research directions
Coloración en gráficas de mapas en la Tierra y mapas en la Luna
No full textLa ''coloración de mapas'' es un problema clásico en la ''Teoría de Grafos'', donde cada país se modela como un vértice y las fronteras entre países como aristas. El ''Teorema de los Cuatro Colores'' establece que cualquier mapa plano puede colorearse con cuatro colores sin que dos regiones adyacentes compartan el mismo color. En este artículo, exploramos la generalización del problema de coloración de mapas al caso de la Tierra y la Luna, conocido como el '''Earth Moon Problem''', propuesto por Ringel. Este problema busca determinar el número mínimo de colores necesarios para colorear un mapa donde cada país en la Tierra y su colonia lunar deben recibir el mismo color, respetando la restricción de que las regiones adyacentes en cualquiera de los dos cuerpos celestes deben tener colores distintos. Nuestro principal aporte es demostrar que el problema de la ''3-coloración'' de la Tierra-Luna es ''NP-completo'', mediante una reducción desde ''3-SAT'', lo que implica que no existe un algoritmo eficiente para resolverlo en general (suponiendo P ≠ NP). Además, complementamos demostraciones previas que aparecían incompletas en la literatura y modelamos el problema como un ''problema de satisfacción de restricciones'' (CSP), lo que permite un análisis más profundo de su complejidad computacional. Este trabajo no solo aporta una nueva demostración de que el problema de coloración de la Tierra-Luna con 3 colores es NP-completo, sino que también abre la puerta a futuros estudios sobre su dificultad para diferentes números de colores. Por último, describir el problema de coloración de la Tierra-Luna a través de grafos, un caso abierto en la coloración de grafos que extiende el problema de la coloración de mapas planos. En términos de grafos, esto se puede reformular como la búsqueda del '''número cromático máximo''' de un grafo G que es la unión de dos grafos planares (sobre el mismo conjunto de vértices). Se demuestra mediante inducción que G es 12-coloreable, como observó Heawood. Ringel conjeturó que el Problema de la Tierra-Luna era 8-coloreable pero Sulanke reportó un ejemplo que requiere 9 colores, aún no se conoce si existen configuraciones que requieran 10, 11 o 12 colores
A simple overview of least squares
No full textIn this work we aim to give an overview of least squares for curve fitting. The idea is to illustrate, for a broad audience, the mathematical foundations and practical methods used to solve this simple problem. We will consider four methods: the normal equations method, the QR factorization, the singular value decomposition (SVD), as well as a new approach based on neural networks. The last approach is not as common as the others, but it is very interesting because, in modern days, it has become a very important tool in many branches of modern knowledge, like data science (DS), machine learning (ML) and artificial intelligence (AI).
 
Optimal Control Strategies for COVID-19 Epidemic Management: A Mathematical Modeling Approach Using the SEIQR Framework
Get PDFThe COVID-19 pandemic has necessitated the development of robust mathematical models to understand and mitigate its impact. This study presents a compartmental model for the Indian pandemic COVID-19 dynamics, incorporating key compartments such as susceptible, exposed, infected, quarantined, and recovered populations. The positivity and boundedness of solutions are rigorously analyzed to ensure that the model remains biologically meaningful over time. A detailed exploration of the basic reproduction number
Stability in the Sense of Hyers-Ulam of Proportional Fractional Stochastic Integral Equations
Get PDFThis work investigates the existence, uniqueness, and stability in the sense of Hyers-Ulam for a class of proportional fractional Itô-Doob stochastic integral equations (PFIDSIE). To establish these properties, we employ the Banach fixed point theorem (BFPT) in combination with several fundamental mathematical inequalities that provide insight into the structure of PFIDSIEs. The approach is structured to demonstrate not only the theoretical foundation of the existence and uniqueness of solutions but also the stability of these solutions in the Hyers-Ulam sense, which ensures that approximate solutions remain close to the exact solution under small perturbations. The results contribute to the broader field of fractional stochastic differential equations, particularly in situations where fractional dynamics and stochastic processes intersect. Furthermore, the findings are illustrated through three examples, showcasing the applicability and utility of the developed theory in practical settings.OPEN ACCESS Received: 29/01/2025 Accepted: 14/03/2025 Published: 20/04/202
A Numerical Study on MHD 3-D Casson-Nanofluid Flow Past an Exponentially Stretching Sheet with Double Cattaneo-Christov Diffusion Effects
Get PDFA numerical study of a three-dimensional steady-state flow of a viscous incompressible Casson fluid containing nanofluid particles interacting with a stretching sheet is the primary focus of this work. The equations for concentration and energy include the Cattaneo-Christov double diffusion effects. This work transforms deriving the controlling boundary layer equations into similarity equations using non-linear similarity transformations in three-dimensional analyses. To evaluate this study, the following was done. In the case of the combined Runge-Kutta method and the shooting approach, it is possible to provide an analytical solution for the obtained equations. Moreover, a comparative analysis of the collected data with previously published results under certain circumstances demonstrates a significant concordance between the two sets of findings. The problem is governed by thirteen physical parameters. Figures and tables are used to depict the effects of different characteristics in the following chapters, including temperature, velocity, and concentration profiles, on distinct flow distributions.OPEN ACCESS Received: 08/01/2025 Accepted: 28/03/2025 Published: 20/04/202
MTNet: Multi-Task Underwater Image Enhancement Method Based on Retinex
Get PDFUnderwater images play a critical role in underwater exploration and related tasks. However, due to light attenuation and other underwater factors, underwater images often suffer from color distortion and low contrast, which to some extent limit the efficiency and safety of underwater exploration. To meticulously address these issues and enhance the accuracy and reliability of underwater exploration, this paper proposes a multi-task underwater image enhancement method based on Retinex theory. This method divides the underwater image enhancement task into several sub-tasks, including image decomposition, color correction, detail reconstruction, and illumination adjustment. Specialized sub-networks— DecomNet, DecolorNet, and DelightNet—are designed to specifically address these problems, thereby alleviating color distortion, enhancing image details, and improving contrast. Experiments conducted on several publicly underwater image datasets indicate that the quality of underwater images is significantly improved after enhancement with the proposed method, compared to other representative underwater image processing techniques. For example, on the real-world dataset Underwater Image Enhancement Benchmark, the MSE, Structural Similarity Index Measure, and Peak signal-to-noise ratio scores achieved were 453.480, 0.901, and 25.145, respectively. This study holds significant implications for underwater exploration, with potential applications in the fields of marine research and underwater archaeology.OPEN ACCESS Received: 03/11/2024 Accepted: 27/12/2024 Published: 20/04/202
Manufacturing of Thermoplastic Composite Upper Wing Skin by In-situ consolidation (ISC)
No full textThe OUTCOME Thermoplastic Upper Skin consortium is a European project framed within the Airframe ITD research platform of CleanSky2, funded by the EU's Horizon 2020 program. It is focused on developing, manufacturing, and validating a thermoplastic composite upper wing skin for future application in Airbus Defence and Space transport aircraft.
The upper skin consists of a stiffened panel of approximately 4 meters in length, with six integrated stringers. These elements were joined through a co-consolidation process, where they were welded simultaneously with the tape layup of the skin using In-Situ Consolidation (ISC). The integrated stringers were manufactured in a previous stage using an oven consolidation process. The skin lamination was carried out through ISC using an automated tape laying equipment such as AFP MTorres, assisted by a laser and utilizing PEEK APC-2/AS4 material with a ¼" tow width.
Throughout the project, a campaign of structural tests was conducted to obtain the mechanical properties and allowable values for the design of the outer wing box's upper skin. Detailed and subcomponent specimens (stiffened panels) were also designed, manufactured, and tested with the aim of validating the design, analysis methodology, manufacturing method, and quality control procedure. The activity will conclude at the end of the year with the ground structural testing of the wing box, of which the element is a part, completing the testing pyramid
Additive preforming technology applied to carbon-reinforced composites
No full textManufacturing composite materials by conventional methods is known to be costly as it requires many steps, equipment and tooling. The challenge this presents can benefit from the moldless approach and rapid, automated prototyping enabled by additive manufacturing. Today, additive technologies are changing the manufacturing processes of plastics and composites, allowing short series to be automated and scalable for adaptation to long series, always oriented to final part production. In addition, the mechanical limitations presented by 3D printing processes of polymeric materials have been enhanced by the reinforcement of short or continuous carbon and glass fibers, mainly. Moreover, the hybridization of additive technologies with conventional processes makes it possible to overcome their current limitations, taking advantage of many of their benefits and increasing the fields of application.
In this context, the idea of developing a technology that allows obtaining intermediate parts or preforms with high geometric complexity, which require a subsequent process, such as resin transfer molding (RTM), that confers mechanical performance similar to that of composites. In this work, an alternative method of manufacturing carbon fiber reinforced preforms using an additive process based on Fused Fusion Deposition Modeling (FDM) is detailed, as well as the production of composites from these preforms. Thus, the 3D preform is manufactured from fiber filaments coated with a thermoplastic binder. Then, this preform is subjected to a thermosetting resin injection process in a mold to obtain the final composite. In summary, a new method of additive preforming in combined with RTM is proposed to manufacture carbon fiber reinforced polymer composites (CFRPC)