Then Theorem 2.1 implies that the mapping L : C 1 ( S ¯ T ) ⊃ K → L 2 ( 0, T ; V ) is well defined and unique.
Combining this and assumption (A5), the projection Pr F ∩ Sol ( f, C ) x 0 is well defined and there exits a unique point p such that p = Pr F ∩ Sol ( f, C ) x 0. So, we have 0 ≤ 〈 x 0 − x n, x n − p 〉 = 〈 x 0 − x n, x n − x 0 + x 0 − p 〉 ≤ − ∥ x 0 − x n ∥ 2 + ∥ x 0 − x n ∥ ∥ x 0 − p ∥, and hence ∥ x 0 − x n ∥ ≤ ∥ x 0 − p ∥. Then the sequence { x n } is bounded.
There exists a positive solution of (2.6) defined on ([0,infty)) with the initial condition (3.1), which is unique. Furthermore, the solution semiflow (Phi(t)) of (2.6), defined by ([Phi(t phi](xi)=(P_{t}(xi),S_{t}(xi))^{T}), is well defined and has a global attractor in X.
Given that the genetic defect is well defined and musical training in affected subjects is negligible, WS offers a unique opportunity to probe training-independent auditory system properties.
One of the most unique features of Giardia is its lack of organellar structures as for example a well defined mitochondria, Golgi bodies and endoplasmic reticulum, in spite of being an eukaryote.
This seems to be a unique feature of community engagement in rural African settings where the community structure is well defined and recognised and where there is some community cohesiveness [ 1].
are well defined and achievable.
(iii) For each face f ⊂ ∂ P, all points on F (f ) (also on boundaries and vertices) possess a well defined tangent plane (the limit of the tangent planes, when we go to the vertex, is unique).
My sound has developed... into a stronger, more defined and unique direction.
As an example, we show how membrane lasers that were designed to produce a well-defined and unique lasing spectrum can be used as counterfeit-resilient, barcode-type security labels on bank notes.
When using Voronoi diagrams, every cell has a well-defined and unique coverage area, i.e., no overlapping or gap between the coverage areas of two neighboring cells can occur.
