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stable if for any real ϕ 0 there exists ε > 0 such that the corresponding solution x ( n ) of (2.3) satisfies | x ( n ) | < ε for all n ∈ N 1 ; asymptotically stable if x ( n ) → 0 as n → ∞ for any real ϕ 0. Remark 2.5 The notion of stability and asymptotic stability for the fractional difference equation (1.1) is defined quite analogously due to Proposition 2.1.
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The lack of decrease in glucose yields with the introduction of the enzyme deactivated lignin rich residues may analogously be due to the non-specific enzyme binding sites on the lignin residue being occupied by deactivated enzyme protein residues.
Topic modeling is a text mining approach, but may be used analogously in toxicogenomics due to the similar data structures between text and gene dysregulation.
Analogously we suppose that, due to the positive inductive effect of three methyl groups, propionate is a weaker Lewis acid than acetate, which in turn is weaker than formate, figure 3a.
Analogously, a jaw joint sound due to an anterior disc displacement with reduction may be slightly annoying to some people, yet highly burdening to others.
Analogously, reduced transcriptional regulation would be due to the lower growth rate under methanol conditions in H. polymorpha[ 38].
For the detachment of links, we analogously assume that links are lost due to mutations at one of two linked nodes, and that the rate of this process does not depend on the properties of the other node that is unaffected by a mutation.
Analogously, maintenance of outcrossing versus selfing may be due to increased fitness variance in populations with higher outcrossing rates [ 12, 13].
Analogously, Mst1 and Mst2 are down-regulated in human soft tissue sarcoma due to CpG island hypermethylation [103].
In this article the word "commitment" is used analogously to radiation protection, where "dose commitment" means an accumulated radiation dose due to inhaled or ingested radionuclides.
Chemical shifts were assigned from this information and by comparison to the reported values for cyclothiazomycin B. Due to the spectral similarity to cyclothiazomycin B, we have assigned the stereochemistry of cyclothiazomycin C analogously to that of the reported compound.
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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