Sentence examples for conditions of uniqueness from inspiring English sources

In a plot of the optimal yield vs the dimensionless operating temperature the region is indicated where operation under conditions of uniqueness is feasible.

Whereas under conditions of uniqueness the naphthalene oxidation is shown to be feasible in a tank reactor, the ethylene oxidation cannot be executed economically in a tank reactor.

In a plot of the dimensionless slopes of the heat withdrawal line versus the dimensionless residence time in the reactor the region is indicated, where operation under conditions of uniqueness is feasible.

In this work, we establish the conditions of uniqueness and existence results of positive solutions for a class of fractional integro-differential equations involving the Caputo derivative of order α ((n-1<alpha leq n), (ngeq3)), the explicit cases, including measurable or continuous nonlinear term f, are discussed by adopting new assumption conditions.

Thus, partly inspired by [23], the derivation of the uniqueness conditions is carried out as follows: first, a change of variable is done in order to obtain an equivalent formulation of the problem as a variational inequality (VI) problem; then, the conditions of uniqueness of the solution for the original problem are derived.

In 2010, Lim and Comon proposed a sparse reconstruction method based on low-rank tensor decomposition and analyzed the condition of uniqueness for decomposition [25].

This was not solved satisfactorily by Fraenkel, but the Weyl/Skolem solution works here, too: a functional correspondence is (in effect) just any first-order 2-place predicate ϕ x, y) which satisfies the condition of uniqueness, i.e., ∀x, y, z{[ϕ x, y) ∧ ϕ x, z)] → y = z}.

The proposed design should satisfy all conditions of the uniqueness theorem.

The proposed designs satisfy all conditions of the uniqueness theorem, and as such, cannot be far from minimum weight solutions.

Several fixed point theorems are used for sufficient conditions of existence (uniqueness) solutions of nonlinear differential equations such as Banach's contraction principle, the Leray Schauder nonlinear alternative, and Krasnoselskii's fixed point theorem.

(17) and (18) contains the entire spectrum of nonlinear static responses and satisfies all conditions of the uniqueness theorem; therefore, it cannot be far from a minimum weight solution.