Sentence examples for singular behaviours from inspiring English sources

We present the full analysis of the singular behaviours at any orders with respect to the parameter ε where we use a systematic nonlinear treatment initiated in Jung et al.

We take advantage of the discontinuous formulation to study the behaviour of the acoustic eigenfunctions in the vicinity of the liner-splice transition where singular behaviours of the acoustic perturbation are found.

For associative 3-folds, I argue that one cannot define deformation-invariant Gromov-Witten style invariants counting associatives, as there are singular behaviours of associatives which would change the numbers under deformation of the -structure.

These types of singular behaviours [1 11] as well as impulsive phenomena [12 21] often exhibit some blow-up properties [22, 23] which occur in many complex physical processes, for example, in mechanics process [1], the stress near the crack tip in elastic fracture exhibits a singularity of (r^{-0.5}), where r is the distance measured from the crack tip.

Due to the corner singularity a singular behaviour of the solution can be expected.

In fact, the singular behaviour at this point has a great influence on the SIF calculation.

This singular behaviour was ascribed to the presence of calcium in COx water.

Type I singularities are abundant and in fact it is conjectured that they are the generic singular behaviour for the Ricci flow on closed manifolds.

Such problems as velocity distribution of the particles, mean velocity, regular and singular behaviour, critical concentration and particle flux are examined.

The pole expansions yield corrections that remove maximal errors of low order, introduced by singular behaviour of the integrands as the evaluation point approaches the poles.

First, elements modelling the singular behaviour of the sound field are used, and then a novel technique of replacing the mid-element node is presented.