Then, in any nonempty open subinterval I of ((0, infty)), there exits a number h with the property that for each k, (nhin G_{k}) for infinitely many integers n. (1) For each (h>0) such that ((1-e^{(lambda-q_{m})h})E^{m}{e^{lambdatau^_{m}}}<1), we write (p^{h}_{ij}(n)) for the transition function of h-skeleton ({X_{nh}}_{n=1}^{infty}).
We say that ({Y_{n}}^{infty}_{n=0}) is ρ-geometrically ergodic (for short, geometrically ergodic) if there exits a number ρ with (0
But these are not hermetically sealed environments, and pathogens can enter and exit a CAFO in a number of ways other than via swine workers (or flies, another proven vector of CAFO diseases).
If there exits a positive number k ≤ k λ ( r ) such that (39) is still valid as we replace k λ ( r ) by k, then, in particular, (22) is valid ( a ˜ n, f ˜ ( x ) are taken as (21)).
A mapping A of C into itself is called L-Lipschitz continuous if there exits a positive number L such that ∥ A x − A y ∥ ≤ L ∥ x − y ∥, ∀ x, y ∈ C. A mapping A of C into H is called α-inverse-strongly monotone if there exists a positive real number α such that 〈 x − y, A x − A y 〉 ≥ α ∥ A x − A y ∥ 2. for all x, y ∈ C ; see [9 14].
A real function (f(x),x>00,) is said to be in the space (C_{mu },muu in {mathbb {R}}) if there exits a real number (lambda > mu ), such that ( f(x)=x^{lambda }g(x)), where (g(x in C[0,infty )) and it is said to be in the space (C^{m}_{mu }) if and only if (f^{(m)}in C_{mu }) for (min mathbb {N}).
Roughly 3.5% of the companies that have gone through an accelerator in the top 10 have exited successfully, a number that is low, but not necessarily surprising given how new the phenomenon is relative to the typical number of years it takes for a seed stage startup to reach a successful exit.
Beyond Carlyle Group's private equity investment in Beats — which was the largest commitment to the wearables market, according to CrunchBase data (and should the Apple deal close, one of the largest exits) — a number of venture capital's top firms have placed their own significant equity and debt bets on wearables.
Choose a constant M> such that g ( u ∗ ( k ) ) > M for k ∈ [ 1, T ] Z. Since g is uniformly continuous on [ 0, ∥ u ∗ ∥ + 1 ], there exits a sufficiently small number ϵ > 0 such that for all u ∈ E : ∥ u − u ∗ ∥ ≤ ϵ, | g ( u ( k ) ) − g ( u ∗ ( k ) ) | < λ ∗ − λ λ M, k ∈ [ 0, T + 1 ] Z.
