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Other choices for (H 0)) represent other forms of stochastic calculus (e.g. (H 0) = 1/2) is the choice consistent with Stratonovich calculus).2 Although the generating functional (11) differs from those introduced in Sect. 2 because it is complex and has two source functions J and (tilde{J}), it still obeys Wick's theorem.
Because they believe in tolerance -- a good thing -- and it only makes sense that they not tolerate actions and words that exclude gays or represent other forms of intolerance.
"They're grateful, but they're also annoyed, because they're conscious of the negative political impact of Jean-Marie Le Pen's presence within the party," he said, explaining that the younger generation of FN voters is particularly tired of the elder Le Pen's incendiary comments, "even though they themselves represent other forms of radicalism".
As such, the hypothesis is that these conserved and similar motifs are indicative of the phenotype epilepsy and can be modeled by using lattice paths to represent other forms of epilepsy.
This apparent contradiction between the results obtained with the propidium iodide staining and MTT reduction is not clear, but it is possible that while the former reflects the extent of necrosis alone, the latter may represent other forms of cell death.
Remaining traces of covalently linked dimers seen with the mutant may either be explained by crosslinks to subunits of the endogenously expressed native enzyme, or represent other forms of covalent complexes resistant to DTT and SDS, for example, containing diselenide linkages that were previously shown not to be resolved in reducing SDS-PAGE analyses.
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But three dancers represented other forms: Liliana de León (flamenco), John Pennington (modern dance) and Mythili Prakash (Indian Bharata Natyam).
The specificity of the deficit for C9ORF72-associated frontotemporal dementia requires further corroboration through comparison with larger cohorts of patients representing other forms of genetic and sporadic frontotemporal dementia.
The points in between represent the other forms of communication, and the loose sketch suggests an inverse relationship between the scope of the information and the number of people involved in its production.
There will be a committee with about a dozen unsecured creditors; other committees representing other kinds of creditors may be formed as well.
In addition, two more items representing other standards were included on half of the field-test forms and two other items were included on the other half.
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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