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Therefore, this example also shows that the implications ((i) ⇒ (iv)) of Theorem 2.3 and ((i) ⇒ (iv)) of Theorem 2.6 are independent of results obtained in [17 19].
Thereby, (breve{partial}^{2} f(bar{x}, bar{x}^)(u)=partial^{2} f(bar{x}, bar{x}^)(u)), which together with Theorem 4.1 shows that the implications (i) ⇒ (ii) holds.
While the data leave no doubt that deaths are indeed being delayed into increasingly older ages, our analysis shows that the implications of such changes for lifespan variability patterns are not pre-determined, but rather depend in intricate ways on the specific pattern of mortality change by age and over time.
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This also shows that the implication from power set to subset collection can not be reversed, as CZF's proof-theoretic strength is way below that of Zermleo set-theory.
The stated deficits in the GMO dossiers and a series of publications that argue against a wider application of the ecological approach in ERA show that the implications of the new legal framework are seen critical by developers of GM crops and scientists advocating their use.
These rulings were legally significant as they appeared to overturn the precedent established in the Overton Park case, which was interpreted as saying that "it must be shown that the implications of not building [a] highway pose an 'unusual situation'".
Our results show that the implications of Wolbachia in genetic differentiation depend on crucial interaction between biological traits such as the genetic system and sib-mating rate.
Now, we show that the implication converse to that from Observation 2.6 does not hold.
(4.1) Then we want to show that the implication (2.6) holds.
In contrast, the present study showed that the implication of PHR1 in the crosstalk between Pi and the sulfate signaling pathway went beyond the regulation of gene expression and that it had an important physiological effect on plant sulfate transport.
It shows that the safety implications of the control room operators' cognitive and cultural issues go far beyond the formal organizational constructs usually implied.
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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