Results 11 to 20 of about 16,016 (265)
Neighborhood filters and PDE’s [PDF]
Numerische Mathematik, 2006 Denoising images can be achieved by a spatial averaging of nearby pixels. However, although this method removes noise it creates blur. Hence, neighborhood filters are usually preferred. These filters perform an average of neighboring pixels, but only under the condition that their grey level is close enough to the one of the pixel in restoration.
Antoni Buades +2 more
openaire +3 more sources
Equivalent transformations and exact solutions to the generalized cylindrical KdV type of equation
Nuclear Physics B, 2020 In this paper, by constructing equivalent transformations (ETs) of the generalized cylindrical KdV (cKdV) types of equations, we transform the variable-coefficient partial differential equations (vc-PDEs) into constant-coefficient PDEs (cc-PDEs) under ...
Hanze Liu +3 more
doaj +1 more source
Fast and Slow Decaying Solutions of Lane–Emden Equations Involving Nonhomogeneous Potential
Advanced Nonlinear Studies, 2020 Our purpose in this paper is to study positive solutions of the Lane–Emden ...
Chen Huyuan, Huang Xia, Zhou Feng
doaj +1 more source
Quantitative Predictive Modelling Approaches to Understanding Rheumatoid Arthritis: A Brief Review
Cells, 2019 Rheumatoid arthritis is a chronic autoimmune disease that is a major public health challenge. The disease is characterised by inflammation of synovial joints and cartilage erosion, which lead to chronic pain, poor life quality and, in some cases ...
Fiona R. Macfarlane +2 more
doaj +1 more source
Unsupervised Legendre–Galerkin Neural Network for Solving Partial Differential Equations
IEEE Access, 2023 In recent years, machine learning methods have been used to solve partial differential equations (PDEs) and dynamical systems, leading to the development of a new research field called scientific machine learning, which combines techniques such as deep ...
Junho Choi, Namjung Kim, Youngjoon Hong
doaj +1 more source
Rocky Mountain Journal of Mathematics, 2004 Based on the first author's construction of hyperreal numbers and hyperfunctionals [Lect. Notes Pure Appl. Math. 238, 81--117, Dekker, New York (2004; Zbl 1094.46508)]. The present paper investigates solvability of linear first order Cauchy problems in a similar setting of generalized functions, the space of extrafunctions.
Burgin, Mark, Ralston, James
openaire +2 more sources
Exact Solutions of Reaction–Diffusion PDEs with Anisotropic Time Delay
Mathematics, 2023 This study is devoted to reaction–diffusion equations with spatially anisotropic time delay. Reaction–diffusion PDEs with either constant or variable transfer coefficients are considered.
Andrei D. Polyanin, Vsevolod G. Sorokin
doaj +1 more source
Comments on whether nonlinear fractional partial differential equations have soliton solutions
Partial Differential Equations in Applied Mathematics, 2022 It is well known that many nonlinear integer-order partial differential equations (PDEs) have soliton solutions, this is an indisputable fact in the field of soliton theory.
Weiguo Rui
doaj +1 more source
PDE-Net: Learning PDEs from Data
CoRR, 2017 In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two objectives at the same time: to accurately predict dynamics of complex systems and to uncover the underlying hidden PDE ...
Zichao Long +3 more
openaire +4 more sources