Sentence examples for degree powers from inspiring English sources

Upon formal substitution, equating to zero the coefficients of zero and first degree powers of ε, we get the following one-parameter Lie group of infinitesimal transformations in the ( t, x, w 0, w 1 ) -space t ˆ = t + a ξ 0 1 ( t, x, w 0 ) + O ( a 2 ), (11).

Upon formal substitution of (7) in (2), equating to zero the coefficients of zero and first degree powers of ε, we arrive at the following system of PDEs: L 0 : = w 0 t t − f ( w 0 x ) w 0 x x = 0, (9).

Equating to zero the coefficients of zero and first degree powers of ε, we obtain an approximate Lie operator which permits to solve in hierarchy the invariance condition of the system (9 - 10) starting from the classification of unperturbed nonlinear wave equation (3).

This is evident in the right panel of Fig. 1 which shows degree power (top) and degree correlation (bottom) for the first time derivative (secular variation) of the core field.

Parameters like average clustering coefficient, topological coefficient, average degree, power law distribution of degrees and betweenness centrality have been assessed to capture the topology of the networks.

As result, a high degree power-law polynomial function (that is, ψ≫1) converges to equation (4) as <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0004852.e064.PNG" class= inline-graphic"/> approaches 0 (equation 6).

The co-existence of scale-freeness, indicated by the degree power-law relationships, and modularity, indicated by high clustering coefficients deserves particular attention, since folk knowledge typically equates "scale-free" with "random", and "modular" with "structural".

Temperatures typically hit 100 degrees, power outages drag on for hours, heatstroke is common, and while monsoon rains bring some relief, they bring great ruin through widespread flooding.

Nonetheless, the first-degree power-law polynomial function describes only one of many hydrodynamics-based functional forms of activity metabolism.

The first-degree power-law polynomial function is frequently used to describe activity metabolism for steady swimming animals.

Consequently, the first-degree power-law polynomial function yields incorrect parameter values of energetic costs if activity metabolism is governed by the power-law polynomial function of any degree greater than one.