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Except for particular cases, the classical expressions of the Eshelby or Hill polarization tensors, depend, respectively, on a simple or double integral for a fully anisotropic two-dimensional or three-dimensional elastic body.
Contrary to 2-dimensional differential systems where the Poincaré-Bendixson theorem gives general conditions for the existence of periodic orbits, there is no such equivalent theorem concerning the existence of periodic orbits for 3-dimensional differential system except for particular systems such as competitive or cooperative systems [26].
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These influential experiments showed that the differentiated state was reversible and not accompanied by irreversible gene loss, excepting for particular lineages like B and T cells; differentiation was the result of epigenetic regulation of gene expression.
Dysregulated interactions were defined as those exhibiting mutual information (essentially, correlation) in all samples except for a particular phenotype (loss-of-correlation) or lack of mutual information in all samples except for a particular phenotype (gain-of-correlation).
This would have been a really admirable debut except for one particular clue that I thought was a bit insensitive given the economic downturn.
They have discovered that a type of ant causes all vegetation to die except for the particular tree – "thin, bare and bleached looking... with crooked branches that reached towards the sky like claws" – which acts as host for the ant.
She still half-consciously considers N.Y. to be inhabited by a population that knows exactly what's going on & from which she is naturally excluded, except for a particular moment once in a while.
From the questionnaire results, this technique was relatively acceptable for 3 years, except for this particular point.
Generally, (Y_{q,lambda}) previously introduced cannot be explicitly computed, except for few particular values of q, such as (q=1) and (q=1/2).
But most fourth-order time-dependent PDEs have no closed-form solutions except for certain particular types of linear or quasi-linear equations.
It was demonstrated that most matrices R l have full rank when l is not a multiple of n, except for some particular cases which depend on codes (generator matrix).
Write better and faster with AI suggestions while staying true to your unique style.
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