However, as k tends to infinity
, our error becomes unbounded, and so we cannot achieve Cohen's result for the infinitary case.
In the case of the recovered images, being exactly the same recovered image, a MSE of 0 is obtained, so the PSNR tends to infinity
, proving, thus, that the information is not lost and that the image has not been distorted, excluding the cases in which the MSE is very big and stays out of the range in which the visual distortion is noticeable.
The refraction index for normally incident light tends to infinity
when the longitudinal (along the wires) optical axis of the metamaterial makes an angle [[phi].sub.*] with the normal to the interface (the resonance cone generatrix is along the normal).
Passing to the limit in (66) when n tends to infinity
and gathering together (68)-(72), we obtain
And the value of the cosmological constant (Eq.) tends to zero as x tends to infinity
For all solutions of system (3.1), if exp(y(t)) does not tend to 0 as t tends to infinity
, Lemma 4.4 follows from Lemma 4.2.
We will show that [p.sub.j] converges to the function p(r) for the Bessel process as [DELTA]r decreases to zero and k tends to infinity
in such a way that 1 + k [DELTA]r remains equal to N.
The rationale for the ALF method is based on the fact that when [[lambda].sup.k] is bounded and [c.sup.k] [right arrow] [infinity], then the term [lambda]h (x; V) + (c/2)[h.sup.2] (x; V) tends to infinity
if h(x; V) [not equal to] 0 and is equal to 0 if h(x; V) = 0.
First, we note that the norm of the iterates grows (moreover, each Fourier coefficient tends to infinity
); that is, these functions have unbounded orbits under the action of C.
(ii) Bulk viscous stress n is positive valued and tends to infinity
with the evolution of time for flat and closed Universe whereas it is negative-positive valued for open Universe in 0.7 < [[alpha].sub.4] [less than or equal to] 0.8 and [[alpha].sub.2] = 0.5.
If the tail of p is subexponential, that is, [[summation].sub.k [greater than or equal to] n] [p.sub.k] = exp(-o(n)), then the estimate of Theorem 3 is useless: it tends to infinity
as [DELTA] [right arrow] 0.