A permutation array is a square binary matrix that contains a single 1 by row and by column. Costas arrays are permutation arrays where the vectors connecting two entries with 1 are distinct. These arrays are useful in applications such as radar and sonar, digital watermarking, and wireless communications in general. In this talk, we will present a generalization of Costas arrays to multiple dimensions, extend the Welch and Lempel constructions to multiple dimensions, and study some of their properties.
Author: ADMIN
An open problem in the theory of discrete dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over the field with two elements. For a family of systems that can be described by monomials (including Boolean AND systems), one can obtain information about the transient of the system from the structure of the monomials. Recent results, see [1], about the Frobenius Number, allow us to present a formula for the transient of fixed-point systems (that is, how long it takes the systems to stabilize)…
Digital communication requires different mechanisms to increase tolerance to errors in communication. Reed-Solomon codes are a class of error-correcting codes defined with polynomials of one variable. Its simple algebraic structure provides many important qualities for protecting against errors. In this talk we will discuss some fundamental concepts of code theory, the construction of Reed-Solomon codes, decoding algorithms and other codes that generalize Reed-Solomon codes. [pdf-embedder url=”https://math.uprrp.edu/wp-content/uploads/2024/09/Charla-Dr-Fernando-Pinero.pdf”]
Congratulations to Jomarie Jiménez González for her successful Dissertation Defense. If the frame below does not scroll on your device click here. [pdf-embedder url=”https://math.uprrp.edu/wp-content/uploads/2024/08/abstract_j_jimenez.pdf”]
The Algebraic Structures in Topology is a conference series that meets every two years in San Juan, Puerto Rico and is partially supported by the National Science Foundation , Purdue University , the Institute of the Mathematical Sciences of the Americas at the University of Miami , and the University of Puerto Rico at Rio Piedras. The conferences will feature a variety of events focusing on recent developments in algebraic topology and their applications to geometry, physics, and data science. The next iteration of the series will occur on June 5 – June 14, 2024. This event will have three…
Congratulations to José Emilio Calderón Gómez for his successful Dissertation Defense. If the frame below does not scroll on your device click here. [pdf-embedder url=”https://math.uprrp.edu/wp-content/uploads/2024/05/abstract_jose_emilio.pdf”] [rev_slider alias=”jose_emi”][/rev_slider]
Congratulations to Angélica M. Rosario Santos for her successful Dissertation Defense. If the frame below does not scroll on your device click here. This defense made history in our graduate program: Angélica M. Rosario Santos is the first Puerto Rican woman to obtain a Doctorate in Mathematics in Puerto Rico. Among others, the Dissertation Committee included doctors: Dr. María E. Pérez (UPRRP), Dr. Marta Álvarez (UPRRP) and Dr. Monica Alexander (U of Toronto). [pdf-embedder url=”https://math.uprrp.edu/wp-content/uploads/2024/05/abstract_angelica.pdf”] [rev_slider alias=”slider-2″][/rev_slider]
Academic Class Schedule — August 2024 The class schedule is subject to changes. Below is the version of the schedule as of April 18, 2024. The document has several pages. If the frame below does not scroll on your device click here. [pdf-embedder url=”https://math.uprrp.edu/wp-content/uploads/2024/05/Horario_2024_2025_1.pdf”]
We consider the problem of finding curves of minimum time of descent, joining two given points over a given frictionless surface and under the influence of gravity. We discuss the existence and minimality of extremals for the corresponding time functional, and find explicit solutions in certain special cases, including a closed form solution for the problem on an inclined plane. A discussion of numerical methods for computing these minimizers is given with several numerical examples for which explicit solutions are not known. This paper is mostly expository. Our main contribution is to put together on a single reference different results…
Let V be a finite dimensional vector space over a field. The collection of all subspaces of V of a fixed dimension can be viewed as a geometric object in the sense that it is a nice projective algebraic variety, known as Grassmann variety. When the base field is finite with q elements, the Grassmann variety can be viewed as the “moduli space” of q-ary linear (error correcting) codes of a fixed length and dimension. Some questions about codes can be profitably studied from this viewpoint. More interestingly, the Grassmann variety itself leads to a special class of linear codes…