Inverse two-sided Laplace transform for probability density functions
Journal of Computational and Applied Mathematics, 1998 The author studies numerical inversion of the two-sided Laplace transform corresponding to a positive function, typically a probability density function. He consideres the problem where the data are the values of the first \(M\) derivatives of \(F(s)\) at the origin, related to the moments \(\mu_j\), \(j= 0,1,\dots, M\) of the function \(f(t)\) through
Aldo Tagliani
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Adaptive Two Sided Laplace Transforms: A Learnable, Interpretable, and Scalable Replacement for Self-Attention [PDF]
We propose an innovative, learnable two-sided short-time Laplace transform (STLT) mechanism to supplant the traditional self attention in transformer-based LLMs. Our STLT introduces trainable parameters for each Laplace node, enabling end-to-end learning of decay rates , oscillatory frequencies, and window bandwidth T. This flexibility allows the model
Kiruluta, Andrew
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Complex Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior [PDF]
, 2019 We provide several Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior. Our results generalize and improve various known versions of the Ingham-Fatou-Riesz theorem and the Wiener-Ikehara theorem.
Debruyne, Gregory, Vindas Diaz, Jasson
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Wave propagation in a infectious disease model with non-local diffusion
Advances in Difference Equations, 2019 In this paper, we propose a nonlocal diffusion infectious disease model with nonlinear incidences and distributed delay to model the transmission of the epidemic.
Yueling Cheng, Dianchen Lu
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Some exact results for a trapped quantum gas at finite temperature [PDF]
, 2002 We present closed analytical expressions for the particle and kinetic energy spatial densities at finite temperatures for a system of noninteracting fermions (bosons) trapped in a d-dimensional harmonic oscillator potential.
Akira Suzuki +21 more
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Mathematics, 2019 In this paper, we study the traveling wave solutions for a nonlocal dispersal SIR epidemic model with standard incidence rate and nonlocal delayed transmission.
Kuilin Wu, Kai Zhou
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Traveling Wave Solutions for Epidemic Cholera Model with Disease-Related Death
The Scientific World Journal, 2014 Based on Codeço’s cholera model (2001), an epidemic cholera model that incorporates the pathogen diffusion and disease-related death is proposed. The formula for minimal wave speed c∗ is given.
Tianran Zhang, Qingming Gou
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Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion
Mathematical Biosciences and Engineering, 2017 This paper is concerned with invasion entire solutions of a monostable time periodic Lotka-Volterra competition-diffusion system. We first give the asymptotic behaviors of time periodic traveling wave solutions at infinity by a dynamical approach coupled
Li-Jun Du, Wan-Tong Li, Jia-Bing Wang
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A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms
Abstract and Applied Analysis, 2016 This paper investigates the two-sided first exit problem for a jump process having jumps with rational Laplace transform. The corresponding boundary value problem is solved to obtain an explicit formula for the first passage functional.
Djilali Ait-Aoudia
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The two-sided Laplace transformation over the Cayley-Dickson algebras and its applications [PDF]
Journal of Mathematical Sciences, 2009 55 ...
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