Sentence examples for defined at point from inspiring English sources
[3] For a function f : T → ℝ (the range ℝ of f may be actually replaced by Banach space), the (delta) derivative is defined at point t by f Δ ( t ) = f ( σ ( t ) ) - f ( t ) σ ( t ) - t, if f is continuous at t and t is right-scattered.
This will still rule out local observables since any quantities defined at points or regions of the spacetime manifold will clearly fail to be diffeomorphism invariant.
In the section "Deficiencies of the Conventional Formulation of QFT" we already saw that, strictly speaking, field operators cannot be defined at points but need to be smeared out in the (finite and arbitrarily small) vicinity of points, giving rise to smeared field operators φˆ(f), which represent the weighted average field value in the respective region.
Significant associations were defined at point-wise P < 0.001 to ensure an average of one significant (and spurious) association per SNP across the 1000 replicates.
Thus, the Hessian matrix is positive define at point (left( {t_{1},t_{2} } right) = left( {t_{1}^,t_{2}^ right)).
A low cut-off point is defined at the point where the number of probes predicted to show that particular signal by the fitted distribution drops below the observed number.
This work deals with nonlinear systems whose relative degree is not defined at any point xo, where xo belongs to the reference signal.
"As far as how a peanut deficient in these proteins would actually be utilised by industry is less well defined at this point".
In fact, the derivatives above are defined at any point in any quasi-static process whether that process is constant volume, constant pressure, or neither.
The linear cortical magnification factor M v r can be defined at any point r for arbitrary directions v.
