Sentence examples for dropping the dependence from inspiring English sources

In order to achieve rate (21), we consider the specific distributions (dropping the dependence on the time index with a slight abuse of notation) and, with independent of.

In order to achieve rate (8), we further specialize the distributions as and as (dropping the dependence on the time index with a slight abuse of notation) (B.2). where, independent of all and " " denotes convolution.

Hence, one often drops the dependence on the initial condition in (A5).

We drop the dependence on T of the estimated matrices and vectors.

For simplicity, we drop the dependence in t: F ( x ) = x 1 + α sin ( log ( 1 + x ) ).

In the following, we focus on a specific set of active MSs and, furthermore, we drop the dependence on the block index for simplicity of notation.

fWe shall henceforth, without loss of generality, drop the dependence of π on the signals St. gWe assume c < p 3 S 2, ~ S 1, π 3 with probability 1. hWe assume that this return is based on a known success probability (no learning needs to take place on the part of the VC about the parameters).

For conciseness, in the sequel we shall drop the dependence of v on (x, u, e) from the notation.

Substituting back into \ \bF\) and expanding to first order in \(\varepsilon(t)\) (considering only the perturbations at \(t = 0\) and dropping the explicit dependence on \(t\) from \(\varepsilon)\) yields where the matrix \ \bJ \bx)\) is the \(n\times n\) Jacobian matrix of partial derivatives of \ \bF\) evaluated at the point \ \bx\).

But DSM-5, the latest edition, dropped the term "dependence" in 2013 as the label for addiction.

In order to prove the existence of extremal elements of the solution set, we drop the -dependence of the operator.