Sentence examples for takes a finite value from inspiring English sources

Now define the inner product of two such sequences to be〈x, y〉 = x0y0 + x1y1 + x2y2 +⋯.It can be shown that this also takes a finite value Hilbert discovered that it is possible to carry out the basic operations of analysis on Hilbert space.

Since the variance term takes a finite value (the series is absolutely convergent), the variance of lim M → ∞ 1 M ∑ k = 0 M - 1 ln | | h ( k ) | | 2 approaches zero.

Such an effect can be understood by the fact that when r2→∞, the energies determined by Equations (8) and (10) approach E nl → En 0 = ℏ2Π2n2/2μ d2 and when r2 takes a finite value E nl > En 0. Figure 2 The subband energies vary with r 2 at a fixed d.

The diffusion coefficient before degradation is statistically insignificant from zero, whereas the value after photodegradation takes a finite value indicating the significantly increased mobility of the beads resulting from the photodegradation-induced gel to sol transition of the core.

In particular, the interdependence z e (n) may be naturally expected to be continuously decreasing when n increases, to take a finite value z0 at n = 0 (clean filter), and to saturate to zero when n reaches some critical value nsat at which all active centers of the wall become well covered by impurities.

end{aligned} (4.23)The location (r=r_g) is, however, a singularity of the metric (4.23), which comes from the fact that (mathrm{d}b/mathrm{d}r|_{r=r_g}) does not take a finite value (i.e., (b'(0)=0) or (b'(0)=infty), where (b' y)) is the first derivative of b y)).

We give a necessary and sufficient condition on a positive compact operatorTfor the existence of a singular trace (i.e. a trace vanishing on the finite rank operators) which takes a finite non-zero value onT.

The model accounts for the existence of a maximum in the reaction rate at some well-defined value of conversion and for the fragmentation phenomenon, which takes place at a finite value of porosity.

The idea is simple: since the test statistic is discrete, it can only take a finite set of values and there exists a minimum attainable P-value strictly greater than 0. As Tarone showed, one can exploit that to obtain an improved Bonferroni correction factor which exhibits a great increase in statistical power in many cases of interest.

These functional states of expression are modeled trough discrete variables that take a finite number of values.

In flexible process operation there exist physical variables which are allowed to take a finite number of stationary values.