Sentence examples for define the directional from inspiring English sources

Using the obtained continuity results, we will define the directional STFT on distributions.

This project presents an experimental protocol to define the directional dependence of transport properties as measured from healthy cancellous bone when considered as a biologic, porous medium.

In this section, we first define the Directional Binary Pattern (DBP), and then extend it to GDBP, using multiscale and multiorientation Gabor filters.

In order to evaluate the impacts of directional antennas on the antenna factor component, we define the directional improvement factor B DIR as the ratio of the antenna factor component of an DIR network to that one of an OMN network.

For any y ∈ E, we define the directional derivative of f at x by f o ( x, y ) : = lim t → 0 + f ( x + t y ) - f ( x ) t. (7 If the limit as t → 0 + in (7) exists for each y, then the function f is said to be Gâteaux differentiable at x.

As for the maximal operator σ ∗ given by (2.2), we invoke the following lemma in [[21], Lemma 3.2]: We define the directional Hardy-Littlewood maximal function of F for a fixed vector y ′ ∈ S n − 1 by M y ′ F ( x ) = sup r > 0 1 2 r ∫ − r r | f ( x − t y ′ ) | d t.

He defined the directional short-time Fourier transform (DSTFT) and proved several orthogonality results and reconstruction formulas.

Giv defines the directional short-time Fourier transform (DSTFT) of an integrable function (fin L^{1}(mathbb {R}^{n})) with respect to g via DS_{g}f u, b,a):= int_{mathbb {R}^{n}}f(x overline{g ucdot x-b }e^{-2pi i x-b }ea},dx= bigllangle f(x),{overline{g }_{u,b,a}}(x) bigrrangle _{x}, (2.10) where ((u,b,a)inmathbb {Y}^{2n}).

Joining the multi-point descent direction and the quantiles on the optimization parameters permits to define the notion of Directional Extreme Scenarios (DES) without sampling of large dimension design spaces.

This means that (DS^_{overline{g}}) and (DS_{g}) are formal transposes, and we will follow this idea when defining the distributional directional short-time Fourier transform.

To define the Malmquist-Luenberger productivity index, directional distance functions are used with the direction of a vector as g = (0, y, −b) and the technology of periods t and t + 1 as the reference technologies.