The Gandy–Hyland functional and a computational aspect of Nonstandard Analysis
Computability, 2017 In this paper, we highlight a new computational aspect of Nonstandard Analysis relating to higher-order computability theory. In particular, we prove that the Gandy–Hyland functional equals a primitive recursive functional involving nonstandard numbers inside Nelson’s internal set theory.
Sam Sanders
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A dynamically consistent nonstandard finite difference scheme for a predator–prey model
Advances in Difference Equations, 2019 The interaction between prey and predator is one of the most fundamental processes in ecology. Discrete-time models are frequently used for describing the dynamics of predator and prey interaction with non-overlapping generations, such that a new ...
Muhammad Sajjad Shabbir +4 more
doaj +2 more sources
Analysis and optimal boundary control of a nonstandard system of phase field equations [PDF]
Milan Journal of Mathematics, 2012 We investigate a nonstandard phase field model of Cahn-Hilliard type. The model describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs.
Colli, Pierluigi +2 more
core +5 more sources
Distributed optimal control of a nonstandard nonlocal phase field system with double obstacle potential [PDF]
, 2016 This paper is concerned with a distributed optimal control problem for a nonlocal phase field model of Cahn-Hilliard type, which is a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion.
Colli, Pierluigi +2 more
core +5 more sources
Stochastic Two-Scale Convergence in the Mean in Orlicz-Sobolev’s Spaces and Applications to the Homogenization of an Integral Functional [PDF]
Asymptotic Analysis, 2023 In this article, we study the stochastic homogenization for a family of integral functionals with convex and nonstandard growth integrands defined on Orlicz-Sobolev’s spaces. One fundamental in this topic is to extend the classical compactness results of
Dongho Joseph +2 more
semanticscholar +1 more source
BioMed Research International, 2021 In this study, 16S rRNA high-throughput sequencing technology was used to analyze the composition and diversity of bacterial and fungal communities in mushroom residue samples at different composting stages.
Chaonan Wang +4 more
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On Optimizing the Conditional Value-at-Risk of a Maximum Cost for Risk-Averse Safety Analysis [PDF]
IEEE Transactions on Automatic Control, 2021 The popularity of Conditional Value-at-Risk (CVaR), a risk functional from finance, has been growing in the control systems community due to its intuitive interpretation and axiomatic foundation. We consider a nonstandard optimal control problem in which
Margaret P. Chapman +2 more
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Statelets: Capturing recurrent transient variations in dynamic functional network connectivity
Human Brain Mapping, 2022 Dynamic functional network connectivity (dFNC) analysis is a widely used approach for capturing brain activation patterns, connectivity states, and network organization.
M. A. Rahaman +4 more
semanticscholar +1 more source
Time averaging for functional differential equations
Journal of Applied Mathematics, 2003 We present a result on the averaging for functional differential equations on finite time intervals. The result is formulated in both classical mathematics and nonstandard analysis; its proof uses some methods of nonstandard analysis.
Mustapha Lakrib
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