It is easy to see that Δ ˜ ( x ) is nonempty for every x such that θ λ ( x ) > 0. Now we give the first algorithm.
Therefore H t, x ˜ ( i i ) is nonempty for every φ ( t − t 0 ) ∈ H 0 ⊂ C σ. Now, we show that this (ii -sheaf solutii -sheafique.
We have revealed (s_{i}^{0}in T_{i}(x)), which illustrates that (T_{i}(x)) is nonempty for every (xin S).
Hence, Δ ˆ ( x ) is nonempty for every x such that θ λ ( x ) > 0. Next, we will give the second algorithm.
The sets, for, that are nonempty, are exactly the Nielsen root class of at and a class is essential if and only if is nonempty for every map homotopic to.
(T_{r}(x)) is nonempty for every (xin E); (T_{r}) is single-valued; (langle T_{r}x-T_{r}y,J(T_{r}x-x rangleleq langle T_{r}x-x rangleleq{r}y-y)ranglangleor all (x, yin E); (F(T_{r})=MEP(h,phi)); (MEP(h,phi)) is nonempty, closed, and convex.
Suppose that (mathcal {D}) is a set of maps from (Omegatimes mathfrak {R}) to the power set of (L^{2}(mathcal {O} times L^{2}(mathcal {O})) such that (D omega,r)) is nonempty for every ((omega,r inOmegatimes mathfrak {R}) and (Dinmathcal {D}).
The saturation condition represents the maximum load in a stable condition, i.e., the queue for arriving packets is assumed to always be nonempty for each node in the network.
If the set (mathbb{O}_{k} omega)) of orbits of (varphi omega, cdot )) is nonempty, for almost every (omegainOmega), then φ admits a random k-orbit.
Note that it can be shown that the sets H* t) and H* t) are nonempty for almost every t ∈ [0, ω] and thus we can define h * ( t ) = sup H * ( t ) for almost every t ∈ [ 0, ω ]. and h * ( t ) = inf H * ( t ) for almost every t ∈ [ 0, ω ].
