With a lower MSE, the PSNR will tend to infinity
, which means that the image compared with the original is a faithful copy.
On the other hand, since a < [L.sub.0] by assumption, it is possible to choose a suitable [epsilon] [member of] [R.sub.+] with 0 < [epsilon] < a - [L.sub.0] small enough so that [L.sub.0][e.sup.[epsilon]r]/(a - [epsilon]) < 1, which, letting T > 0 tend to infinity
and using (36), immediately yields
The number of rows must tend to infinity
, since the source of the open network may infinite number of requests.
This principle is highlighted in the title of the volume, which borrows from analytic geometry the notion of the asymptote, that is, a straight line whose distance from a curve approaches zero as they tend to infinity
. Ziegler adopts this image to articulate the separation between the author and the character in Decadent fiction, going against the widespread tendency to overlap their respective standpoints as narcissistic self-reproductions of a single persona.
and at this point it remains only to let n tend to infinity
in (32) to prove (29), which was a rewriting of (23).
One alternative approach is presented for large CDMA networks with deterministic access in , and it shows that as both the number of users and the spreading gain tend to infinity
with their ratio converging to a constant, the signal to interference and noise ratio (SINR) of the linear receivers converges in probability to a constant.
Letting m tend to infinity
and using Lemma 1.3 and (2.5) we obtain
The interpretation of the solution (14) is also complicated by the fact that it is defined on the semi-axis 0 < x < [infinity], at the boundaries of which either the amplitude A(x) or the phase [PSI](x) tend to infinity
From Lemma 3 (Corollary 1) it follows that as the cardinality k (or expected cardinality [p.sub.n][2.sup.n]) of a random class tends to infinity, the VC-dimension and the initial-dimension both tend to infinity
. It is still possible however that as this occurs, the event [A.sub.d] of the random class shattering all sets of size d (see Section 2.1) does not occur, even for d = 1.
If the spectrum of the preconditioned matrix is bounded from below ([[lambda].sub.min] [greater than or equal to] [beta] > 0, [beta] independent of n), then [[lambda].sub.max] [right arrow] [infinity] and [beta](n) eigenvalues tend to infinity
, with [beta](n) [right arrow] [infinity] for n [right arrow] [infinity].
Several authors (6) believes that it is not physically possible for the extensional viscosity to tend to infinity
for a finite value of extensional rate.
It is (by Proposition 2.3) bounded from above by some fixed constant on some semicircles, whose radii tend to infinity
. The ordinary maximum principle yields that -V is bounded from above in all of the upper halfplane, and hence, by applying an extended maximum principle, that -V is non-positive in the upper half-plane (see e.g.