Sentence examples for for a given ξ from inspiring English sources

For a given ξ ∈ A, differentiating (5.8) w.r.t.

This gives the solution at a given ξ i.

For any given ξ ∈ R, using the fact that y is increasing and (4.4), it follows that y ¯ ≤ y.

Remark 2 For given ξ, the second-stage problem can be solved explicitly: by (16) and (17), in village j, vehicle k can deliver a maximal amount of min ∑ i ∈ V ξ i w i ψ (d ij ) y ij, γ j z jk.

From now on, for a given function ξ ∈ L ∞ [ 0, ∞ ], we denote the essential supremum and infimum of ξ by ξ ∗ and ξ ∗, respectively.

For convenience, for a given function ξ ∈ L∞[0, T], we denote the essential supremum and infimum of ξ by ξ* and ξ*, respectively.

The height H ( P ) of the polynomial P is defined by H ( P ) = max n ( | a n |, …, | a 0 | ). and if the degree of P is denoted by deg ( P ), then deg ( P ) = n, and for a given arbitrary complex number ξ, it can be written as ω n ( H, ξ ) = min n { | P | : deg ( P ) ≤ n, H ( P ) ≤ H, P ≠ 0 }, where n and H are positive integers; see [5].

valid for a given a sequence { ξ n } n ≥ 1 of non-degenerate, independent and identically distributed (i.i.d).i.d

Under these assumptions, the joint probability density function of the noisy observations y for a given unknown deterministic parameter vector ξ is as follows: where.

For a given R, the switching probability ξ(R) is xi(R) = sumlimits_{l = leftlceil {frac{{R - frac{Upsilon}{{BW}} + H}}{2}} rightrceil + 1}^{H} {Pr { H_{d} = l} } (30).

Let the true logit transformed 1 - specificity and sensitivity for a given threshold j be denoted by ξ ij and η ij respectively, where ξ ij 's and η ij 's are ordered in the j index.