Sentence examples for implies and is implied by from inspiring English sources

As an application of our local observer design, we consider a class of nonlinear systems with an input generator (exosystem) and show that for this class of nonlinear systems, under some stability assumptions, the existence of local exponential observers in the presence of inputs implies and is implied by the existence of local exponential observers in the absence of inputs.

As an application of our local observer design, we consider a class of discrete-time nonlinear systems with an input generator (exosystem) and show that for this class of nonlinear systems, under some stability assumptions, the existence of local exponential observers in the presence of inputs implies and is implied by the existence of local exponential observers in the absence of inputs.

We also show that for the general class of discrete-time nonlinear systems considered, under some stability assumptions, the existence of local exponential observers in the presence of inputs implies, and is implied by the existence of local exponential observers in the absence of inputs.

We also show that for the general class of nonlinear systems considered, under some stability assumptions, the existence of local exponential observers in the presence of inputs implies, and is implied by, the existence of local exponential observers in the absence of inputs.

Property (iii) is direct since any equilibrium point of (1.1) in R 0 + implies and is implied by the condition g ( x ) = 0.

In symbolic logic there is a similar self-duality if "implied" and "is implied by" are interchanged, along with the logical connectives "and" and "or".

In contrast, Oba neither implies nor is implied by Oab, and this is expressed by saying that O propositions do not convert.

Supervenience physicalism neither implies nor is implied by token physicalism.

Actually, DDI neither implies nor is implied by divine impassibility.

Notice also that these conditions do not imply continuity and that condition (D) is implied by condition (C) for x, y such that (1/2)d x, T x)) = d x, y).

Given that strict implication (p⇒q) is defined as ¬◊(p∧¬q), it follows that an impossible proposition implies anything, and that a necessary proposition is implied by anything.