Then, in virtue of the continuity of, we see that.
In virtue of the continuity of f t, x) and I i (x)(1 ≤ i ≤ m), the right-hand side tends to zero uniformly as |x - y| → 0. Consequently, {Φx : x ∈ U} is the set of equicontinuous functions.
Then in virtue of the continuity of (v_{n}(t)), we see that (v_{n}(t^)inpartialSigma). Hence Ebigl v_{n}bigl(t^bigr bigr)=frac{1}{2n}S^{n} quad mbox{or} quad int_{mathcal{C}}|nabla v_{n}|^{2},dx,dy=int_{Omegatimes{0}}|v_{n}|^{2^,dx, which contradicts (4.1).
Then, for any u ∈ B, in virtue of the continuities of f t, u) and I k (u), there exist c > 0, c k > 0 such that f ( t, u ) ≤ c, I k ( u ) ≤ c k, k = 1, 2, …, m.
In our case, exploiting the previous analysis and by virtue of continuity arguments, we surmise that, for small-enough variations of the parameter values, the DA's represent good initial guesses.
Remark 3.1 Estimates (3.11) and (3.12) are also true for t ∈ [ 0, t 0 ] by virtue of continuity and boundedness of E ( t ) and ξ.
It may be rational for me to anticipate only the experiences of my biological continuers, for instance, but it won't be in virtue of my biological continuity with them that it's rational to do so; rather, it seems rational only in virtue of the psychological relations they are expected to bear to me.
In virtue of its accuracy and of the C0-continuity requirement for shape functions, RZT can be adopted to derive reliable and computationally efficient finite elements suited for large-scale analyses of sandwich structures.
For example, it looks as if we can say that the adult Russell is identical with the infant Russell in virtue of the existence of certain spatiotemporal and causal continuities between his infant state in 1873 and his adult state in (say) 1950 that are characteristic of the continued existence of a human being.
In virtue of what, precisely, would you distinguish them aesthetically?
