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On the other hand, since the eigenvalues (lambda_{n}) are simple, we find from (2.25) that the maximal multiplicity of (theta_{n}) is two.
As the effects of discretization errors are eliminated by employing a sufficiently large number of collocation points (≥ 20) for reactor axis discretization, maximal multiplicity of five steady states appears.
Thus, τ can be factorized as tau omega)=cos^{n}biggl(frac{omega}{2}biggr)mathcal{L}( omega), where n is the maximal multiplicity of the zeros of τ at π and (mathcal{L} omega)) is a trigonometric polynomial with (mathcal {L}(0)=1).
A multiplicity-slice (m-slice) [ 10] is then applied to the graph, giving a multiplicity value to each gene in the network derived from the maximal multiplicity of the links within a gene's set of directly connected genes.
Also note that since i is chosen from the set { i : x i = y1}, there are O(μ(x)) choices for i, where μ(x) is the maximal multiplicity of a character in x.
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A third dimension is added to the network by assigning a maximal multiplicity to each cancer or gene.
It should be emphasized that exactly the same (nonimprovable) asymptotic estimate holds for the solution of the exact pantograph equation (4.2) provided that all eigenvalues of have negative real parts and the maximal geometric multiplicity of eigenvalues of with the maximal real part is equal to 1 (see [15, 16]).
In all cases, we have few units with maximal multiplicity, indeed Zipf curves initially slope down steeply.
Further, the maximal size and multiplicity of SBI in the two-vessel (1.00 and 1.44) and three-vessel (0.94 and 1.26) groups were significantly higher than those of the zero-vessel (0.27 and 0.50) CAD group (P = 0.0002, P = 0.0025, respectively).
This is because multiplicity of roots in minimal polynomial coincides with maximal size of the Jordan blocks.
Multiplicity of activity predominates.
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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
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