Theorem 3.2 For any set-valued mapping F : K → 2 H such that F ( x ) = x − G ( x ), where G : H → 2 H is an upper semi-continuous compact mapping with nonempty closed convex values, if there does not exist an exceptional family of elements for GVI ( F, K ), then there exists a solution of GVI ( F, K ).
Roughly speaking, these two values correlate with each other, but there exists a group of exceptional genes that have larger linker ratios than expected.
So my wife and I drove 40 minutes down Highway 1, surely as beautiful a stretch of road as exists anywhere, and had an exceptional lunch high above the ocean at the glass and steel restaurant attached to the recently opened Post Ranch Inn.
This shows that in Theorem 1.2, there exists one possible exceptional solution with σ ( f ) < max { σ ( B ), 1 } + 1.
Under Tusk's proposal, Britain would be able to initially withhold in-work benefits to migrant workers if "an exceptional situation exists on a scale that affects essential aspects of its social security system," before gradually introducing those benefits over a period of four years.
Section 4 is devoted to the case n = 2, where there exist some exceptional boundaries in which we need to add a constant vector to the simple layer potential.
Thereby the goal is to obtain finite expressions in terms of known functions like elementary, Liouvillian or special functions that annihilate the given differential equation upon substitution; they exist only in exceptional cases.
For an exceptional and motivated candidate, possibility exists for collaboration in workshops and published reports targeting water decision makers.
Our military exists only to protect the things that make America an exceptional democracy.
Besides an exceptional amount of volcanic and volcaniclastic deposits, there exist many localities with intensive hydrothermal activity.
