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Ordinary Differential Equations [PDF]
, 2021 AbstractIn this chapter, we discuss a first application of the time derivative operator constructed in the previous chapter. More precisely, we analyse well-posedness of ordinary differential equations and will at the same time provide a Hilbert space proof of the classical Picard–Lindelöf theorem (There are different notions for this theorem.
Christian Seifert +2 more
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nmODE: neural memory ordinary differential equation
Artificial Intelligence Review, 2023 Brain neural networks are regarded as dynamical systems in neural science, in which memories are interpreted as attractors of the systems. Mathematically, ordinary differential equations (ODEs) can be utilized to describe dynamical systems.
Zhang Yi
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Neural ordinary differential equation and holographic quantum chromodynamics [PDF]
Machine Learning: Science and Technology, 2020 The neural ordinary differential equation (neural ODE) is a novel machine learning architecture whose weights are smooth functions of the continuous depth. We apply the neural ODE to holographic QCD by regarding the weight functions as a bulk metric, and
K. Hashimoto, Hong-ye Hu, Yi-Zhuang You
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Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper, we present some uniqueness results for systems of ordinary differential equations. All of them are linked by a weak transversality condition at the initial condition, which generalizes those in the previous literature. Several examples are
José Ángel Cid +2 more
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Қарағанды университетінің хабаршысы. Математика сериясы, 2021 In the present paper the initial value problem for the second order ordinary differential equation with damping term and involution is investigated. We obtain equivalent initial value problem for the fourth order ordinary differential equations to the ...
A. Ashyralyev +2 more
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Mathematics, 2021 Discussions are presented by Morita and Sato in Mathematics 2017; 5, 62: 1–24, on the problem of obtaining the particular solution of an inhomogeneous ordinary differential equation with polynomial coefficients in terms of the Green’s function, in the ...
Tohru Morita, Ken-ichi Sato
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Mendel, 2022 This paper examines the implementation of simple combination mutation of differential evolution algorithm for solving stiff ordinary differential equations.
Werry Febrianti +2 more
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Gluon dynamics from an ordinary differential equation
European Physical Journal C: Particles and Fields, 2021 We present a novel method for computing the nonperturbative kinetic term of the gluon propagator from an ordinary differential equation, whose derivation hinges on the central hypothesis that the regular part of the three-gluon vertex and the ...
A. C. Aguilar +2 more
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Elastic transformation method for solving ordinary differential equations with variable coefficients
AIMS Mathematics, 2022 Aiming at the problem of solving nonlinear ordinary differential equations with variable coefficients, this paper introduces the elastic transformation method into the process of solving ordinary differential equations for the first time.
Pengshe Zheng +3 more
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Linearisation of a second-order nonlinear ordinary differential equation
Acta Polytechnica, 2023 We analyse nonlinear second-order differential equations in terms of algebraic properties by reducing a nonlinear partial differential equation to a nonlinear second-order ordinary differential equation via the point symmetry f(v)∂v.
Adhir Maharaj +3 more
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