Revista de Matemática: Teoría y Aplicaciones

Measuring, simulation, and evaluation of room impulse responses for acoustical spaces with rectangular geometry

2024-07-31T10:49:58-06:00

In this paper, a closed room with rectangular geometry is selected, in which a comparative study is performed between the acoustical parameters, obtained from the measured room impulse responses using a directional loudspeaker as sound source, and those generated by numerical methods inside a simulation software, where the sound source is omnidirectional. The benefit of approximating an omnidirectional source by the rotation on the horizontal plane of a directional source is also evaluated. Results presented here indicate that the directional loudspeaker can be used to obtain a general characterisation of the acoustics of the room, with error levels that could be tolerated, particularly for midrange frequency bands, with the advantage of representing a low-cost alternative.

A two-level overlapping Schwarz preconditioner for discontinuous Galerkin methods

2024-10-25T10:59:35-06:00

This article introduces a two-level overlapping additive Schwarz algorithm tailored for solving elliptic problems discretized with the symmetric interior penalty discontinuous Galerkin method. The proposed algorithm allows for the use of irregular subdomains, overcoming limitations of other approaches where the coarse mesh was based on triangular elements. Additionally, we provide a brief description of the numerical implementation of the Galerkin method. We present numerical results validating the relevance of our algorithm, including cases where the coefficient of the differential equation is discontinuous—a feature that is particularly relevant to various practical applications.

A robust stability criterion in the heat equation with a conformable fractional derivative defined on a radially symmetric sphere

2024-05-07T11:23:13-06:00

In this paper, we present a robust stability criterion for a heat equation with axial symmetry and with a general time-conformable fractional derivative defined on a sphere. The heat equation is assumed to have a heat source that is represented as a Fourier series with coefficients described by bounded, piecewise continuous functions. The robust stability criterion establishes conditions to guarantee that the solution of the heat equation, along with its partial derivative with respect to the radial axis and its general timeconformable fractional derivative, remains bounded by a predetermined value. The robust stability criterion is obtained by extending the concept of stability under constant-acting perturbations applied to systems of ordinary differential equations. The results are illustrated numerically.

The significance of the Perron-Frobenius eigenvalue for the characterization of a measure of channel occupancy in data networks

2024-08-06T12:03:31-06:00

Telecommunications is currently one of the most important technologies, utilizing various infrastructure elements to enable communication over the Internet. When an internet connection is established, traffic packets are routed from one device to another, taking different paths through routers that process each packet. These networks present multiple challenges in processing, distributing and connecting traffic. To address these challenges it is necessary, on the one hand, to have models that describe the behavior of traffic and its evolution over time, such as the Generalized Markov Fluid Model. On the other hand, it is essential to reserve part of the available resource at each node for ongoing connections. To carry out this reservation process, the Effective Bandwidth is employed. In this paper, we describe the distribution of the buffer in equilibrium for traffic sources modeled by a Generalized Markov Fluid Model, using a system of differential equations. As the main result of this paper, we prove that it is possible for this model to characterize the effective bandwidth when the most probable duration of the buffer busy period prior to overflow becomes larger and larger. Finally, we verify this result numerically from simulated traffic traces.