Sentence examples for implications I from inspiring English sources
The implications (i) (ii) and (ii) (iii) follow immediately from Theorems 3.4 and 3.5 and the definition of recession cone.
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].
From a policy point of view, these findings have two important implications: (i) Bankruptcy costs increase the instability of the financial system significantly.
The equivalence of the methods has two implications: (i) the crossover component is 'universal' as it is valid also for large coupling constants; (ii) the 'macroscopic' stability is fully contained in our 'microscopic' analysis.
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.
This will have three major implications: (i) to design novel intervention studies that aim to strengthen protective factors and cognitive reserve, (ii) to provide an in vivo test system for the mode of action of potentially protective interventions, and (iii) to serve as a secondary endpoint for the effectiveness of interventions.
How conscious were you of trying not to make this story too direct and obvious of an implication — i.e., TV is driving us mad.
Proof The implication (i) → (ii) is obvious.
We prove the implication (i) ⇒ (ii).
Proof We first prove the implication ((i) ⇒ (ii)).
The implication (i) (vii) is exactly Theorem 3.3.
