Sentence examples for above implications from inspiring English sources

None of the above implications is reversible.

The converses of above implications in Proposition 3 are not always true as we have seen in the following examples.

While the above implications underlie the learners' interactional feedback exchanges in the learning space, interaction exchanges in the social space should not be discouraged by instructors, especially in the CAPR.

It is clear that the inverse of the above implication does not hold.

end{cases} Assume that there exists (r in[0,1)) such that psi(r d x,Tx leq d x,y quad Longrightarrowquad H(Tx,Ty leq rM_{d} x,y) for all (x,yin X), where M_{d} x,y)=max biggl{ d x,y),d x,Tx),d y,Ty), frac {d x,Ty)+d y,Tx)}{2} biggr}. Then T has a fixed point. We remark that the right-hand side of the above implication is known as Ćirić type contractive condition, see [10, 11, 18].

The above policy implications are short-run remedial measures.

The detailed investigations on the above two implications are in progress.

The bifunction h : Γ × R n → R ∪ is said to be η-pseudomonotone on Γ if, for any x, y ∈ Γ, h ( x ; η ( y, x ) ) ≥ 0 ⇒ h ( y ; η ( x, y ) ) ≤ 0. The above implication is equivalent to the following implication: h ( y ; η ( x, y ) ) > 0 ⇒ h ( x ; η ( y, x ) ) < 0. Next, we present some properties for pseudoinvexity.

In addition to the above methodological implication, this study needs to mention that it is not easy for us to maintain a social balance (so, sustainability) between economic development and environmental protection.

Combine this with anticipated debt levels and the possible changes in working behaviour discussed above, with its implications for access to finance, and the last decades of the 20th century will be remembered as the halcyon days of home ownership.

Based on the above findings, the implications and suggestions are provided for future research.