In fact, if it is not true, then there exists a sequence of initial functions such that (3.34).
As the illustrated example shown in Figure 2, a sequence of initial modeled background frames B ^ t (t = 1,2,…) will be obtained in the initial modeled background processing procedure.
For example, we may define such a sequence of initial conditions by Θ 0 k, n = argmin i = 1, …, l ( k, n ) | i l ( k, n ) − 1 | D k, n | ∫ D k, n ν ( 0, x ) d x |.
If (40) were not true, then there would exist a sequence of initial values (Y_{n}=(S_{n},I_{n},R_{n},U_{n},V_{n})inmathbb{R}_^{5}) ((n=1,2,ldotsuchsuch that liminf_{trightarrowinfty}I t, Y_{n})< frac{varepsilon}{n^{2}}.
It is easy to see that such a sequence of initial conditions Θ 0 n, n ∈ N, can be found for any deterministic initial condition ν 0 under some reasonable conditions on the domain D and the sequence of partitions D n.
Then there exists ε 0 and a sequence of initial data u k ( 0 ) satisfying inf η ∥ u k ( 0 ) − φ ∥ H 2 → 0 ; however, sup t inf η ∥ u k ( t ) − φ ∥ H 2 ≥ ε 0, where u k ( t ) is a solution of Eq. (12) with initial datum u k ( 0 ).
Current evidence suggests a sequence of treatments consisting of initial diathermy vaporisation followed by either holmium laser enucleation or transurethral resection, repeated if necessary on failure or relapse, are cost effective strategies for surgical treatment of symptoms presumed to be caused by benign enlargement of the prostate.
Let ((u_{n}^{0},u_{n}^{1},theta^{0}_{n},chi^{0}_{n})) be a given sequence of initial data in B. Then the corresponding sequence ((u_{n},u_{tn},theta_{n},chi_{n})) of solutions of problem (28 - 33) is uniformly bounded in (mathbb{H}_{0}), because B is bounded and positively invariant.
Model simulations highlight for the first time the necessity of a temporal sequence of initial, transient MET receptor (met proto-oncogene, hepatocyte growth factor receptor) and subsequent, continuous epidermal growth factor/integrin signalling to trigger and sustain migration by autocrine signalling that is integrated through the Focal adhesion kinase protein.
The first term describes the case when the packet was forwarded after an initial wait, and the second term describes the case for a sequence of forwards without an initial wait.
On this basis, we outline a sequence of events for the initial stages of the catalytic cycle.
