DM-Artículos
URI permanente para esta colecciónhttps://hdl.handle.net/10953/255
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Ítem On the rates of pointwise convergence for Bernstein polynomials(Birkhäuser, 2025) Adell, José Antonio; Cárdenas-Morales, Daniel; López-Moreno, Antonio JesúsLet f be a real bounded function defined on the interval [0, 1], which is affine on a subinterval (a,b) of [0,1], and let Bnf be its associated nth Bernstein polynomial. We prove that, for any x in (a,b), |Bnf(x)-f(x)| converges to 0 as n tends to infinity at an exponential rate of decay. Moreover, we show that this property is no longer true at the boundary of (a, b). For Bernstein–Kantorovich type operators similar properties hold, whenever f is assumed to be constant instead of affine.Ítem Alternating generalized projection method applied to phase-only synthesis process of satellite reflectarray antennas(Elsevier, 2024-10) Florencio Díaz, Rafael; Escalante, RenéPromising algorithm of alternating generalized projection method (AGP) is proposed for phase-only synthesis process of satellite reflectarray antennas under intersection approach. This promising algorithm is a hybridized algorithm of two specialized algorithms for non-convex sets rescued in the literature: algorithm based on separating hyperplanes and algorithm based on decomposition method in polar cones. Since the sets involved in phase-only synthesis process of satellite reflectarray antennas are non-convex, the conventional von Neumann alternating projection method proposed in the literature does not guarantee convergence to the point in the intersection of the involved sets. In addition, the results of the phase-only synthesis obtained by the different algorithms were compared and promising improvements produced by the proposed hybridized algorithm were shown.Ítem A Linguistic Metric for Consensus Reaching Processes Based on ELICIT Comprehensive Minimum Cost Consensus Models(IEEE, 2023) García-Zamora, Diego; Labella, Álvaro; Rodríguez, Rosa M.; Martínez, LuisLinguistic group decision making (LiGDM) aims at solving decision situations involving human decision makers (DMs) whose opinions are modeled by using linguistic information. To achieve agreed solutions that increase DMs' satisfaction toward the collective solution, linguistic consensus reaching processes (LiCRPs) have been developed. These LiCRPs aim at suggesting DMs to change their original opinions to increase the group consensus degree, computed by a certain consensus measure. In recent years, these LiCRPs have been a prolific research line, and consequently, numerous proposals have been introduced in the specialized literature. However, we have pointed out the nonexistence of objective metrics to compare these models and decide which one presents the best performance for each LiGDM problem. Therefore, this article aims at introducing a metric to evaluate the performance of LiCRPs that takes into account the resulting consensus degree and the cost of modifying DMs' initial opinions. Such a metric is based on a linguistic comprehensive minimum cost consensus (CMCC) model based on Extended Comparative Linguistic Expressions with Symbolic Translation information that models DMs' hesitancy and provides accurate Computing with Words processes. In addition, the linguistic CMCC optimization model is linearized to speed up the computational model and improve its accuracy.Ítem On the uniqueness conjecture for the maximum Stirling numbers of the second kind(Springer, 2021-04-15) Adell, José A.; Cárdenas-Morales, DanielThe Stirling numbers of the second kind S(n,k) satisfy S(n,0) < · · · < S(n,kn) ≥ S(n,kn+1) > · · · > S(n,n). A long standing conjecture asserts that there exists no n ≥ 3 such that S(n,kn) = S(n,kn +1). In this note, we give a characterization of this conjecture in terms of multinomial probabilities, as well as sufficient conditions on n ensuring that S(n,kn)> S(n,kn+1).Ítem Approximation rate and saturation under generalized convergence(American Institute of Mathematical Sciences, 2024-02) Garrancho, Pedro; Martínez-Sánchez, Francisco-Javier; Cárdenas-Morales, DanielIn this paper we prove a quantitative result about the convergence of sequences of functions de ned from linear operators. The notion of conver- gence used here is the one given in [8]. The operators will be assumed to satisfy a shape preserving property associated with certain generalized deriv- ative. We also study the saturation class, from the asymptotic condition that the sequence of operators ful lls. Finally, as applications, we show how the notion of weighted g-statistical convergence, recently studied by A. Adem and M. Altinok [3], can be moved to the setting of approximation theory. Besides, we give a non standard example that shows the applicability of the results.Ítem Stochastic Bernstein polynomials: uniform convergence in probability with rates(Springer, 2020-02-27) Adell, José A.; Cárdenas-Morales, DanielWe introduce stochastic variants of the classical Bernstein polynomials associated with a continuous function f , built up from a general triangular array of random variables. We discuss the uniform convergence in probability of the approximation process that they represent, providing at the same time rates of convergence. In the particular case in which the triangular array of random variables consists of the uniform order statistics, we give a positive answer to a conjectured raised in Wu and Zhou (Adv. Comput. Math. 46, 8, 2020) about an exponential rate of convergence in probability.Ítem Asymptotic and Non-asymptotic Results in the Approximation by Bernstein Polynomials(Birkhäuser - Springer, 2022-06-29) Adell, José A.; Cárdenas-Morales, DanielThis paper deals with the approximation of functions by the classical Bernstein polynomials in terms of the Ditzian–Totik modulus of smoothness. Asymptotic and non-asymptotic results are respectively stated for continuous and twice continuously differentiable functions. By using a probabilistic approach, known results are either completed or strengthened.Ítem Random Linear Operators Arising from Piecewise Linear Interpolation on the Unit Interval(Birkhäuser - Springer, 2022-09-09) Adell, José A.; Cárdenas-Morales, DanielWe introduce a sequence of random linear operators arising from piecewise linear interpolation at a set of random nodes on the unit interval. We show that such operators uniformly converge in probability to the target function, providing at the same time rates of convergence. Analogous results are shown for their deterministic counterparts, derived by taking expectations of the aforementioned random operators. Special attention is paid to the case in which the random nodes are the uniform order statistics, where an explicit form for their associated deterministic operators is provided. This allows us to compare the speed of convergence of the aforementioned operators with that of the random and deterministic Bernstein polynomialsÍtem Estimates in direct inequalities for the Szász–Mirakyan operator(Springer, 2022-12-16) Adell, José A.; Cárdenas-Morales, DanielThis paper deals with the approximation of continuous functions by the classical Szász– Mirakyan operator. We give new bounds for the constant in front of the second order Ditzian–Totik modulus of smoothness in direct inequalities. Asymptotic and non asymptotic results are stated. We use both analytical and probabilistic methods, the latter involving the representation of the operators in terms of the standard Poisson process. A smoothing technique based on a modification of the Steklov means is also applied.Ítem Coherent States for infinite homogeneous waveguide arrays(2021) Guerrero, Julio; López-Ruiz, Francisco F.Perelomov coherent states for equally spaced, infinite homogeneous waveguide arrays with Euclidean E(2) symmetry are defined, and new resolutions of the identity are constructed in Cartesian and polar coordinates. The key point to construct these resolutions of the identity is the fact that coherent states satisfy Helmholtz equation (in coherent states labels) an thus a non-local scalar product with a convolution kernel can be introduced which is invariant under the Euclidean group. It is also shown that these coherent states for the Eucliean E(2) group have a simple and natural physical realization in these waveguide arrays.