Results 11 to 20 of about 25,652 (111)
Machine Learning and Knowledge Extraction, 2020 This article presents a new methodology called Deep Theory of Functional Connections (TFC) that estimates the solutions of partial differential equations (PDEs) by combining neural networks with the TFC.
Carl Leake, Daniele Mortari
doaj +1 more source
The class of Clifford-Fourier transforms [PDF]
, 2011 Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general principles, using 4 different yet equivalent definitions of the classical ...
De Bie, H., De Schepper, N., Sommen, F.
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On explosive solutions for a class of quasi-linear elliptic equations [PDF]
, 2012 We study existence, uniqueness, multiplicity and symmetry of large solutions for a class of quasi-linear elliptic equations. Furthermore, we characterize the boundary blow-up rate of solutions, including the case where the contribution of boundary ...
Gladiali, Francesca, Squassina, Marco
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Generating functions of (partially-)massless higher-spin cubic interactions [PDF]
, 2012 Generating functions encoding cubic interactions of (partially-)massless higher-spin fields are provided within the ambient-space formalism. They satisfy a system of higher-order partial differential equations that can be explicitly solved due to their ...
Joung, Euihun +2 more
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A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces [PDF]
, 2012 In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R}^d$. For two-dimensional surfaces embedded in $\mathbb{R}^
Fuselier, Edward J., Wright, Grady B.
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A study of blow-ups in the Keller-Segel model of chemotaxis [PDF]
, 2010 We study the Keller-Segel model of chemotaxis and develop a composite particle-grid numerical method with adaptive time stepping which allows us to accurately resolve singular solutions.
Bertozzi A +15 more
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Efficient Gluing of Numerical Continuation and a Multiple Solution Method for Elliptic PDEs
, 2014 Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as across almost all natural and engineering sciences. Although several excellent
Kuehn, Christian
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Path Integral Solution of Linear Second Order Partial Differential Equations I. The General Construction [PDF]
, 2004 A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions.
Abraham +16 more
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, 2010 We show that the standard Dirac phase factor is not the only solution of the gauge transformation equations. The full form of a general gauge function (that connects systems that move in different sets of scalar and vector potentials), apart from Dirac ...
Brown R A +11 more
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, 2010 We have recently solved the inverse spectral problem for integrable PDEs in arbitrary dimensions arising as commutation of multidimensional vector fields depending on a spectral parameter $\lambda$.
Bogdanov L +21 more
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