Sentence examples for assumptions posed from inspiring English sources

Compactness and noncompactness assumptions posed on the potential function V ( x ) are also discussed.

Guastavino [16] and Maffiolo [17] have supported through psychological experiments the assumptions posed by Schafer [18] that sound perception in humans highlights a distinction between sound events, attributed to clearly identified sources, and ambient noise, in which sounds blur together into a generic and unanalyzable background noise.

Section  2 introduces the abstract setting and specifies the assumptions posed on the continuous space X and on the discrete space X (T ).

How to design case studies relying on these theoretical assumptions poses a challenge.

Although these assumptions are valid in some applications and have significantly reduced the complexity of techniques developed, over the last three decades practitioners in various branches of statistics, signal processing, and communications have become increasingly aware of the limitations these assumptions pose in addressing many real-world applications.

The crystallized region is localized near the core surface and hence the assumption posed in deriving Eq. (6) is not violated.

We followed the assumption posed by Morais-Cabral et al. that the potential profile of permeation was symmetrical, which rendered the number of the free parameters less.

This assumption poses limitation on predictive ability of vdW P theory.

A rooted PP assumption poses the constraint that, for any two SNPs in the incidence matrix, not all three combinations (01, 10, 11) exist.

Thus, z ( t, ε ) = T ( t, ε ) z 0 + ∫ 0 t T ( t - s, ε ) f ( s, ε ) d s. is continuously (Frechét) differentiable with respect to ε for ε ∈ P. Now, we present a theorem that is convenient in application since some assumption is posed on the operator A instead of the C0-semigroup T t,ε).

end{aligned} Using the assumption (iv) posed on the function f and dividing both sides of the latter inequality by (f^{1/gamma}y(t)), one can see that begin{aligned} frac{y(t)}{f^{1/gamma} y(t))}&ge f^{1/gamma} biggl( frac{1}{R_{1} t,t_{1})} biggr) int_{t_{1}}^{t} biggl(frac{f(R_{1}(g(s),t_{1}))}{r_{1}(s)} int_{s}^{infty}tilde{Q} u),mathrm {d}u biggr)^{1/gamma},mathrm {d}s.