Sentence examples for vanishing order from inspiring English sources

Note that in the regime we are interested in (vanishing order parameter: 〈 b ˆ μ 〉 = 0 ), 〈 O ˆ μ n 1 n 2 〉 vanishes for n 1 ≠ n 2. The diagonal terms 〈 O ˆ μ n n 〉 yield the probabilities p μ ( n ) to have n particles at the lattice site μ.

It shows that there are some relationships between analytic properties (e.g.,Lp-norm, vanishing order of the nodal point, andN−1 dimensional Hausdorff measure of the nodal set) of the solutions as the functions on the domainΩand Morse indices of the solutions as the critical points of the functionalJ u)=∫Ω [12 |∇u|2−F(x, u)] dxonH10.

There is no nostalgia for a vanishing old order in which everyone knew his or her place.

"Oddly oblique," he concludes, "The Hard Life reads as... a rather mild attack on the pretenses of Catholicism and an already vanishing social order".

Let M0 be the submodule of functions vanishing to order k on a hypersurface Z in Ω.

In this paper we present a solution of the free analogue of this question and show that the only distributions, whose free sample variance is distributed according to a free χ2-distribution, are the semicircle law and more generally so-called odd laws, by which we mean laws with vanishing higher order even cumulants.

The finite element approximation of variational inequalities with vanishing zero-order term was first studied in [3] and L ∞ error estimates were derived by means of the concept of subsolutions.

His 32-year-reign is the longest in the church's history, and in some ways it was the last of a vanished world order.