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The generalization of a proposition relating convexity of the function and the corresponding surface to nonsmooth yield and phase-transformation surfaces is provided in this paper, together with the (necessary to the proof) extension of a theorem on nonsmooth elastic potential functions.
Let us give a proposition relating to Dirichlet eta function first before we move forward to give another theorem.
The first proposition relating to the relative role of mortality and fertility in the epidemiological transition has been tested above in the context of the assessment of the demographic transition.
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In "Some Remarks on Logical Form" (1929) he says: "One is often tempted to ask from an a priori standpoint: What, after all, can be the only forms of atomic propositions, and to answer, e.g., subject-predicate and the relational propositions with two or more terms further, perhaps, propositions relating predicates and relations with one another, and so on.
Furthermore, entrepreneurs need to understand the value proposition related to cost and scalability.
The next proposition relates the SSOSC and nondegeneracy condition to nonsingularity of Clarke's Jacobian of the mapping defined by (2.11).
Given a reaction term f belonging to a quite large subset of (mathcal {A}), the following proposition relates the corresponding set of the admissible speeds to some bound on f.
The following proposition relates the definition of optimality in (4.1) and (4.2) with the nonlinear approximation classes in [14 17].
Likewise, the proposition related to initiating conjoint efforts was agreed upon by less experts than the proposition about including patient groups for developing interventions, yet did receive a higher priority ranking.
A second set of propositions relating to a future research agenda was determined by expert consensus.
Convexity of the function is proved by developing two general propositions relating convexity of the yield surface to convexity of the corresponding function.
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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