Sentence examples for proved in a general from inspiring English sources

The theorem is proved in a general setting.

Numerical simulations of individual models indicate that the minimum tumor size during these oscillations can decline exponentially with the viral replication rate β, although again this could not be proved in a general setting.

We prove in a general environment that there is a nontrivial set of parameters for which the principal strictly prefers not to be fully informed, regardless of the equilibrium played.

All the results are proved in a more general setting, namely for noncommutative Lp spaces.

Remark 3.2 (1) The relation (a) ⇔ (b) was essentially proved in a very general result in [18].

The relation (a) ⇔ (b) was essentially proved in a very general result in [18].

To build such a decoder, Meerwald and Furon [12] previously noted that Abbe and Zheng [11] proved in a more general context that under certain conditions on the set of allowed pirate strategies (vec {Theta }), a decoder that works against the worst-case attack (vec {theta }^ in vec {Theta }) also works against arbitrary other attacks (vec {theta } in vec {Theta }).

The development of model theory has led to a more general outlook that enabled the Swedish logician Per Lindström to prove in 1969 a general theorem to the effect that, roughly speaking, within a broad class of possible logics, elementary logic is the only one that satisfies the requirements of axiomatizability and of the Löwenheim-Skolem theorem.

Then for every predicate E x) of expressions of L defined in L+ one can prove in L+ a general sentence of the form ∀n[¬E(d(φ(n)))↔ψ(n)], where ψ(n) is a formula with one free variable entirely constructed in L (through the arithmetization of the L+ predicate "¬E(d(φ(n)))").

Especially in 2015, the Hyers-Ulam stability of the first-order matrix difference equations has been proved in [17] in a general setting.

Sure enough, he is a fine leading man, as he proved in The General and In Bruges, but it is as a miniaturist that he is arguably most prized.