Sentence examples for hence equivalent from inspiring English sources
Perhaps, then, if the formulas are not equivalent in meaning, they are nevertheless logically interderivable and hence equivalent in this sense.
So in a very general sense, both sets of estimates on (bar{partial }) might be said to be "equivalent" to elementary calculus, and hence equivalent to each other.
Let R be some criterion of relevance of consequences; let AR be the set of relevant consequences of A. Whatever the criterion R is it has to satisfy the constraint that A be recoverable from (and hence equivalent to ) AR. Popper's account is the limiting one — all consequences are relevant.
This follows from ∂ H ∂ p = q ˙ T + p T ∂ q ˙ ∂ p − ∂ L ∂ q ˙ ∂ q ˙ ∂ p = q ˙ T, ∂ H ∂ q = p T ∂ q ˙ ∂ q − ∂ L ∂ q − ∂ L ∂ q ˙ ∂ q ˙ ∂ q = − ∂ L ∂ q, which, since d d t ( ∂ L ∂ q ˙ ) = ∂ L ∂ q implies p ˙ = ∂ L ∂ q, are hence equivalent to the Lagrange equations.
where f c denotes the maximal frequency offset and x is a random variable uniformly distributed over the interval [-f c, f c ]. Equation (40) is hence equivalent to E [ sinc ( 2 π f Δ T p ) ] = ∫ - 2 π T p f c 2 π T p f c sinc ( x ) p ( x ) d x = 1 2 π T p f c s i ( 2 π T p f c ) (41).
Topologies are hence equivalent when derived from the same baseline model irrespective of network size and density.
Then the joint distribution model is built and hence the equivalent deterministic equations are solved to identify unknown loads.
The proposed structure is shown to add tortuosity to the waveguide, hence higher equivalent fluid density is achieved, while the system elastic modulus remains unchanged.
Hence, the equivalent coefficients in this work are an upper bound value for the magnitude and intensity of the ground motion applied in the analysis.
Three factors suggest the Bank will stick with the status quo: the better-than-expected performance of the economy post Brexit, the recent sharp fall in sterling which is seen as positive for output and hence the equivalent of a loosening of policy, and the need to keep some powder dry for if things get really sticky in 2017.
