Sentence examples for a corresponding approximation from inspiring English sources

Because the CSIT contains no information about the channel estimation error in (8) and the channel decomposition error in (9), the transmitter can only calculate approximations (hat {mathbf {R}}_{u}) and (hat {mathbf {R}}_{u,j}) of the covariance matrices utilizing the angular-domain CSI feedback; this gives a corresponding approximation (hat {tilde {R}}_{u}) of (tilde {R}_{u}).

The corresponding approximation results for a finite family of asymptotically quasi-nonexpansive maps on: (i) uniformly convex Banach spaces [5, 14, 15], (ii) convex metric spaces [13], (iii) CAT spaces [12] are immediate consequences of our results.

Finally, for the regularization properties of dropout, the expectation of the dropout gradient is the gradient of the corresponding approximation ensemble, regularized by an adaptive weight decay term with a propensity for self-consistent variance minimization and sparse representations.

We apply phase reduction and averaging methods to a corresponding Langevin approximation of the master equation in order to determine how intrinsic noise disrupts synchronization of the population oscillators driven by a common extrinsic noise source.

Moreover, the limit theorems of Kurtz [48] can be adapted to prove convergence of solutions of the hybrid model to solutions of a corresponding Langevin approximation in the limit N → ∞ and finite time, where N is the number of ion channels within the membrane [44, 52].

In contrast with the existing finite-time control methods, the corresponding approximation errors in this paper will result in a positive constant (d_{0}) appearing in the right side of the inequality (dot{V}leq-a_{0}V^{wp}).

First, x i, j ( t ) is the sparse representation coefficient vector for representing y i with the atom d j selected to be appended at iteration t, and y i, j ( t ) is the corresponding approximation of y i. Next, D i, j ( t ) is a matrix including t - 1 atoms previously selected in t - 1 iterations and the atom d j at iteration t which are used for representing y i.

The following theorem improves and extends the corresponding approximation results in [6 8, 11 14, 25, 27].

The results also apply to corresponding approximation problems with undiscounted objective functions.

for all φ h ∈ X h and t ∈ [ 0, τ ], where u 0, h ∈ X h is the given approximation of u 0 in X, and F h is the corresponding approximation of F in L 1 ( [ 0, τ ], X ).

In Fig. 1e, the frame is categorized as embeddable, as long as the corresponding approximation and detail coefficients are of sufficiently large magnitude to allow the embedding of watermark bits and synchronization codes.