Matemática e Estatística | Artigos em revistas internacionais / Papers in international journals
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Browsing Matemática e Estatística | Artigos em revistas internacionais / Papers in international journals by Field of Science and Technology (FOS) "Ciências Naturais::Matemáticas"
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- Analysis on the cone of discrete Radon measuresPublication . Finkelshtein, Dmitri; Kondratiev, Yuri; Kuchling, Peter; Lytvynov, Eugene; Oliveira, Maria JoãoWe study analysis on the cone of discrete Radon measures over a locally compact Polish space X. We discuss probability measures on the cone and the corresponding correlation measures and correlation functions on the sub-cone of finite discrete Radon measures over X. For this, we consider on the cone an analogue of the harmonic analysis on the configuration space developed in [Y. G. Kondratiev, T. Kuna, Harmonic analysis on configuration space. I. General theory, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5 (2002), 201–233.]. We also study elements of finite-difference calculus on the cone: we introduce discrete birth-and-death gradients and study the corresponding Dirichlet forms; finally, we discuss a system of polynomial functions on the cone which satisfy the binomial identity.
- The discrete generalized exchange-driven systemPublication . Barik, Prasanta Kumar; Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, Rafael; F.P. DA COSTAWe study a discrete model for generalized exchange-driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange-driven growth system and the coagulation-fragmentation system with binary fragmentation. Under reasonable general condition on the rate coefficients we establish the existence of admissible solutions, meaning solutions that are obtained as appropriate limit of solutions to a finite-dimensional truncation of the infinite-dimensional ODE. For these solutions, we prove that, in the class of models, we call isolated both the total number of particles and the total mass are conserved, whereas in those models, we can non-isolated only the mass is conserved. Additionally, under more restrictive growth conditions for the rate equations, we obtain uniqueness of solutions to the initial value problems.
- Finite difference calculus in the continuumPublication . Finkelshtein, Dmitri; Kondratiev, Yuri; Lytvynov, Eugene; Oliveira, Maria JoãoWe describe known and new results on the finite-difference calculus on configuration spaces. We also describe the finite-difference geometry on configuration spaces, relate finite-difference operators to the canonical commutation relations, find explicit form of certain finite-difference Markov generators on configuration spaces, and describe spaces of Newton series defined over the configuration spaces.
- A hybrid method for the time-harmonic inverse acoustic transmission problemPublication . Paixão, João; Serranho, PedroThe inverse transmission problem of scattering an acoustic wave by a penetrable object has several applications in various fields such as radar, sonar, geophysical exploration, medical imaging and non destructive testing. Here we propose a numerical hybrid method to inverse acoustic scattering by penetrable obstacles from far-field data in two-dimensions, that extends an iterative decomposition method to the transmission problem. The proposed method starts by reconstructing the scattered and interior field by imposing the far-field equation and one of the transmission conditions and, in the second step it uses the second transmission condition to update the position of the approximated boundary, by linearization. Also, we compared two approaches for the linearization step: a Newtontype method; and a gradient-type method with a penalty term for high oscillations of the solution. We also support the methods by a convergence result for a related optimization problem. Numerical results from eight incident directions show the method is feasible, though sensitive to noise.
- The MFS-SVD method for the laplace equation in three dimensionsPublication . Antunes, Pedro; Santos, Vinicius; Serranho, PedroThe method of fundamental solutions (MFS) has been widely used to numerically solve boundary value problems involving linear partial differential equations. This method is easy to implement computationally and can be very effective for smooth domains and boundary conditions. The main drawback of the MFS is the ill-conditioning of the associated matrices, which may deteriorate the method’s accuracy. We present three methods to reduce the ill-conditioning of the classical MFS for the Laplace equation defined in bounded star-shaped domains in 3D. The idea is to expand the MFS basis functions in terms of spherical harmonics, in order to use the reduced QR factorization and singular value decomposition to deal with the ill-conditioning, leading to a better function basis that spans the same approximation space as the classical MFS. The numerical results illustrate that these approaches significantly decrease the ill-conditioning, allowing higher accuracy when compared to the classical MFS.
- Tail-adaptive generation of random numbers from a gamma-order normal distribution using the Ziggurat algorithm with a multivariate extensionPublication . Kitsos, Christos P.; Oliveira, Amilcar; Ulrich, Eschcol Nyamsi; Leiva, Victor; Castro, CecíliaThe Ziggurat algorithm is a well-established rejection-sampling method designed for the efficient generation of pseudo-random numbers from unimodal distributions, particularly the standard normal. In this work, we extend and adapt the Ziggurat algorithm to enable the tail-adaptive generation of random numbers from the gamma-order generalized normal distribution |a flexible family characterized by a tail-shaping parameter that governs transitions between light, Gaussian, and heavy-tailed regimes. The resulting algorithm retains the computational speed of the original Ziggurat algorithm while supporting both univariate and multivariate implementations. This extension is especially relevant in simulation-intensive contexts, such as Bayesian modeling, quantitative nance, and machine learning. We provide the mathematical foundation, reproducible implementation details, and extensive benchmarking results that validate the method's efficiency and accuracy. A multivariate extension based on radial decomposition is also introduced, demonstrating the feasibility of generating random variables from symmetric multivariate distributions in practice. To illustrate the practical utility of the proposed algorithm, we present a comprehensive Monte Carlo simulation study evaluating performance across various shape and scale con gurations. Additionally, we apply the method to real-world data from biomedical signal processing, highlighting its robustness and adaptability to empirical settings where tail behavior plays a crucial role.