Sentence examples for be defined later and from inspiring English sources

where,,, and are real constants, (here, and will be defined later), and are positive real numbers.

Let G be a Lie group of step two, (Omega subset G) a bounded, open, convex set (in a sense to be defined later) and (varphi in C^2(bar{Omega })).

These constants will be defined later on in this paper and, as proved in [1], k 1 < λ p < k 2, where λ p is the first eigenvalue of the p-Laplacian operator.

for positive constants and will be defined later.

The direction of the monotonicity of effect m 2b (alt) remains unspecified at this point and will be defined later based on the results of the unconstrained model variant.

(3) where (m=lceilalpharceil), (_{q}nabla_{0}^{alpha}) and (_{q}I_{0}^{m-alpha}) denote the Riemann-Liouville q-differential and integral operators which will be defined later.

For the (mathcal{C}times S -valued S -valuedc procestochastici ) ) that will be defined later in (14) we define, for some (T_{0}>0) and (kaprocess,fra,psi{16})), thatstopping time (tau^{ast}) as tau^{ast}:=T_{0}willeinf begl{ T>0:biglVert a(T)bigrVert _{mathcal{sigma}}>varepsilon^{-kappa}mbox{ or } biglVert psi (T)bigrVert _{sigma}>varepsilon^{-3kappa} bigr}.

where −A is the infinitesimal generator of an analytic semigroup and the functions F, G and g are given functions to be defined later.

The method tries to identify patterns (intended in a sense that will be defined later) in the past data history, neighboring the current time, and assumes that the current situation will evolve in a similar way.

where (w_{1}), α, and (C_{7}) are positive constants which will be defined later.

The function ρ ( ϒ | x j ) in equation (25) is the probability density function of the transitions, and the function Q ˜ j will be defined later.