As a consequence, for a given accuracy, an upper bound exists for the interfacial heat and mass fluxes that can be simulated.
No upper bound exists: with proper joint preparation and use of multiple passes, materials of virtually unlimited thicknesses can be joined.
Assume that ((mathbb {X}, le)) is a partially ordered set such that every pair of elements of X has a lower bound or an upper bound, and there exists a metric d on (mathbb {X}) such that ((mathbb {X}, le)) is a complete metric space.
Case B. If is not comparable to then there exists an upper bound or alower bound of and, that is, there exists such that Then by using monotonicity character of we have (2.45).
Case 2. If is not comparable to, then there exists an upper bound or lower bound of.
If x∗ is not comparable to y∗, then there exists an upper bound or a lower bound of x∗ and y∗.
In this case, there exists an upper bound or a lower bound Z = ( z 1, z 2 ) ∈ X 2 of Z ∗ and Z ¯.
Case 2. If is not comparable to then there exists an upper bound or a lower bound of and Then, is comparable to and.
From the figure, we observe that there exists an upper bound and a lower bound for the power ratio to satisfy the outage probability constraints when other parameters are fixed for the cognitive network with cooperative relaying.
P is reproducing; every pair (x,yin X ) has a lower bound; every pair (x,yin X ) has an upper bound; (forall xin X), there exists (ugeq0) such that (xleq u); (forall xin X), there exists (uleq0) such that (xgeq u).
An interesting question is whether an upper bound for reasonable insulin concentrations exists.
