Abstract: We study a higher order dispersion nonlinear Schr6dinger (NLS) equation with the k-Laplacian (-Δ)k, and the potential term expressed as a power nonlinearity (for any positive power). When k = 1 we recover the NLS with the standard Laplacian and when k = 2 we get the bi-harmonic NLS. We investigate well-posedness of solutions…
Abstract: Families of periodic arrays are useful in a variety of applications, including multiple target recognition, optical communications, and digital watermarking. In video watermarking, these arrays can be employed as watermarks to ensure copyright protection and to verify the authenticity of the original video. In video watermarking, watermarks based on periodic arrays can be embedded…
Abstract: Modem education requires our students to develop 21st-century problem-solving skills. This presentation offers an in-depth look at the integration of Computer Science and Computational Thinking at the primary and secondary education levels. Through a practical approach, we will discuss how gamification—highlighting the highly successful model of the Bebras Challenge—can motivate students and facilitate the…
Abstract: Materials Science & Engineering has experienced an enormous growth in the last century. Underpinned by nanotechnology and other interdisciplinary endeavors, the field is avid for more practitioners, science and engineering majors. In this seminar, the speaker will relate his research in the last decade as a UPRM professor. Place: Monzón 201 Hour: 10:30 a.m.
Abstract: This talk presents a structured overview of stochastic differential equations (SDEs), beginning with classical Itô diffusions and progressively incorporating jumps, regime switching, and interacting particle systems. We then introduce McKean—Vlasov equations, where the dynamics depend on the law of the solution itself, highlighting their nonlinear and mean-field nature. Particular emphasis is placed on conditional…
Abstract: The COVID-19 pandemic has highlighted significant challenges for public health systems worldwide, demonstrating not only the lethality of infectious diseases but also the critical role of public behavior that influence case numbers and mortality rates, particularly in geographically isolated regions like Puerto Rico. This study presents a metapopulation model framework to analyze the transmission…
Abstract: Functional magnetic resonance imaging (fMRI) is a noninvasive tool for studying regions related to some particular stimulus. To find these regions, the stimulus is typically applied in the form of event-related or block-design. Due to this, fMRI experiments have a natural seasonal pattern. In this work, we used different seasonal time series models in…
Abstract: The fractional Schrodinger equation generalizes the standard Schrodinger equation by incorporating fractional derivatives, extending traditional quantum mechanics through fractional calculus. This approach provides a more flexible framework for modeling quantum systems with anomalous diffusion or complex geometries. Research in this field is dynamic, with ongoing exploration of both theoretical foundations and experimental implications, offering…
Abstract: In this presentation, we explore the growing threat of antimicrobial resistance (AMR), a major global public health issue that complicates the elimination of harmful microorganisms in the host. Mathematical models have significantly contributed to the understanding of AMR dynamics and identifying strategies to combat bacterial infections, although they have primarily focused on single bacterial…
Abstract: Rotation symmetric Boolean functions were introduced by Pieprzyk and Qu in 1999. They proved that these functions have efficient and secured cryptographic implementations. Later, in 2007, Kavut and Yucel found a function that exceed the Bent concatenation bound in this new class of functions. Concepts such as affine equivalence, Hamming weight, and nonlinearity have…