Sentence examples for the inclusion between from inspiring English sources

We will investigate the inclusion between the weighted Orlicz spaces L w 1 Φ 1 ( X ) and L w 2 Φ 2 ( X ).

Now, we can give the necessary and sufficient conditions for the inclusion between the weighted Orlicz spaces L w 1 Φ ( R n ) and L w 2 Φ ( R n ).

In [3], the inclusion between L p spaces is investigated with respect to the measure space ( X, Σ, μ ) and in [4] inclusions between Orlicz spaces are examined for a finite measure space and in general [5, 6].

These treatments include chemical treating with ethyl glycol and heating between 350 and 550 °C; the treatments were applied to separate the inclusion between X-ray peaks for clay minerals.

In this paper, we will investigate the inclusion between weighted Orlicz spaces L w Φ ( X ) with respect to a Young function Φ and a weight w for a general measure space.

Remark 2.1 It is clear that Φ 1 ≺ Φ 2 ( T = 0 ) implies Φ 1 ≺ Φ 2. But Φ 1 ≺ Φ 2 is not sufficient to investigate the inclusion between weighted Orlicz spaces when the measure μ is not finite.

Before we investigate the inclusions between the weighted Orlicz spaces with respect to the Young function and weight, respectively, we will show that, if L w 2 Φ 2 ( X ) ⊆ L w 1 Φ 1 ( X ) then the inclusion map i : ( L w 2 Φ 2 ( X ), ∥ ⋅ ∥ Φ 2, w 2 ) → ( L w 1 Φ 1 ( X ), ∥ ⋅ ∥ Φ 1, w 1 ) is continuous.

Fig. 6 Directed acyclic graph (DAG) showing the inclusions between the linearly bounded lattices partitioning the array space of signal A Fig. 7 Partitioning of the array space of signal A steered by the intensity of memory accesses: the darker the partition, the more it is accessed.

We will investigate the inclusions between the weighted Orlicz spaces L w Φ 1 ( X ) and L w Φ 2 ( X ) with respect to Young functions Φ 1 and Φ 2. Since a weight w satisfies w ≈ w, we get the following consequences of Theorem 2.3.

The novelty to our method is the inclusion of between- and within-community spatial autocorrelation terms and the systematic testing of different exposure models.

The inclusion relations between the Lp-Sobolev spaces and the modulation spaces is determined explicitly.