Sentence examples for be equivalent for any from inspiring English sources

As a generalized of Corollary 2, G m and G n will be equivalent for any real m,n.

Efficiency of amplification was shown to be equivalent for all primers.

Predictive performance of all measures may not be equivalent for all age groups.

Result: These are equivalent for any finite graph E : 1. L C ( E ) is simple.

Result: These are equivalent for any finite graph E : 1. L C ( E ) is purely infinite simple.

Suppose that,, are Jackson-type operators on the spherical cap,, then the following are equivalent for any,, (i) ; (ii).

Hence the norms (Vert uVert _{mathcal{H}_{t}}^{2}) and (Vert uVert _{mathcal {H}_{tau}}^{2}) are equivalent for any fixed (t, tauinmathbb{R}), but the equivalent constant blows up when (trightarrow+infty).

Then the following three assertions are equivalent for any u, (vin L^{p}(Omega,mu)): (1) We have Vert uVert _{p}^{p}= int_{Omega} vert uvert ^{p-2}uv,dmu.

Interestingly, if the MMSE decoder is employed for PSVD approach and Φ n k = β k I u k, the PMMSE-IAP, PMMI-IAP, and PSVD-IAP are equivalent for any L k. Thus, if L k  = P k /m k, Φ n k = β k I u k and the MMSE decoder is employed for PSVD approach, the PMMSE-IAP, PMMI-IAP, PSVD-IAP, and PSVD-ATP are equivalent.

Although the fluctuations in mean prevalence rates are larger for smaller network sizes, the means are equivalent for any network size.

Thus, for the exponential payoff to fitness mapping, we find that ϕ A > ϕ B and risk dominance of A are equivalent for any intensity of selection in large populations.