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We have the following equivalent description of continuous functions of ultrapolynomial growth of class ({M_p}).
To say 'translated' is to imply that dynamical systems tools provide an alternative (and equivalent) description of the dynamics.
The Fourier transform is an equivalent description of time-dependent data, and represents its decomposition into its frequency components.
In the remaining two cases the 'effective shunt' model and the two-parameter model provide an equivalent description of the data.
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Duality is the relation between two equivalent descriptions of the same quantum physics in different classical terms.
String theory and quantum field theory leverage exact and infrared dualities to provide equivalent descriptions of physical objects, some of which admit rigorous definitions; dual pairs of objects are sometimes even formalized using two a priori distinct areas of mathematics.
In this paper affine Lie algebras are used to describe a theta function and Brownian motion in the framework of affine Lie algebras is used to verify some equivalent descriptions of a theta function such as those given by Macdonald and Kostant.
Though, these two approaches are radically different perspectives, SD and ABM models must deliver equivalent descriptions of the systems at the aggregate levels.
I will then describe two equivalent descriptions of the irreducible components of ({mathfrak {M}}_g (G)), surveying known irreducibility results for some special groups.
In physics, duality means that two equivalent descriptions of a particular physical situation exist, using different physical concepts.
Almost immediately a crisis arose because these two presumably equivalent descriptions of evolution, genotype and phenotype, were contradictory.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com