Sentence examples for a reproducing from inspiring English sources

P is a reproducing cone in X. Proof.

A Hilbert space H defined on a nonempty set E is called a reproducing kernel Hilbert space if there exists a reproducing kernel function (K eta,tau)).

Typically (but not necessarily) there is variation among organisms within a reproducing population.

In addition, a reproducing kernel with polynomial form will be constructed.

Then P is a reproducing cone in X. Lemma 2.4 (Krein-Rutman) [8].

A Hilbert space H which is defined on a non-empty set F is called a reproducing kernel Hilbert space if there exists a reproducing kernel function (R Ftimes Ftomathbb{C}).

Also, a Hilbert space of functions ((mathcal{H}, langle cdot,cdot rangle_{mathcal{H}} )) that possesses a reproducing kernel R is a reproducing kernel Hilbert space (RKHS); we denote it by ((mathcal{H}, langle cdot,cdot rangle_{mathcal{H}},R )).

In the next theorem, we show that Ω is a reproducing kernel space, and we present its reproducing kernel.

Using Lemma 2.1, we prove that the functional space associated with inner norm is a reproducing kernel Hilbert space.

From [17, 18], W 2 1 [ 0, 1 ] is a reproducing kernel Hilbert space and the reproducing kernel is K 1 ( t, s ) = 1 + min { t, s } (2.2).

At [9] prove that function space (W_2^1[a,b]) is a Hilbert space and also it is a reproducing kernel space.