Sentence examples for matrix of type from inspiring English sources

If (theta -1notin {mathbb {J}}), then (C^{(overline{{mathbb {J}}},d)}) is the Cartan matrix of type (D_theta ) (4.23).

If (theta -1notin {mathbb {J}}), then (C^{({mathbb {J}},c)}) is the Cartan matrix of type (C_theta ) as in (4.15).

If (theta -1notin {mathbb {J}}), then (C^{({mathbb {J}},d)}) is the Cartan matrix of type (D_theta ) (4.23).

The bundle of Cartan matrices ((C^{a_j})_{jin mathbb {I}_3}) is constant: (C^{a_j}) is the Cartan matrix of type (G_2) as in (4.43) for any (j in mathbb {I}_3).

By the definition (2.24), (C^{mathbf{A}_{theta }(q;{mathbb {J}})}) is the Cartan matrix of type (A_{theta }) for all ({mathbb {J}}in texttt {A}_{theta, j}), thus coincides with (C^{{mathbb {J}}}).

The bundle of Cartan matrices ((C^{{mathbb {J}}})_{{mathbb {J}}in texttt {B}_{theta, j}}) is constant: (C^{{mathbb {J}}}) is the Cartan matrix of type (B_theta ) as in (4.7) for any ({mathbb {J}}in texttt {B}_{theta, j}).

We examined activation of the extracellular signal-regulated kinase (ERK) signaling pathway by vascular smooth muscle cells (VSMC) in response to 2D and 3D matrices of type I collagen, fibrin, or a 1 1 composite mixture of these proteins.

In the present study we investigated the morphology and biosynthetic activity of human articular chondrocytes seeded on porous matrices of type I/III collagen (Chondrogide™, Geistlich Biomaterials, Wolhusen, Switzerland).

Here, the mean is calculated from each of the cells containing in column i and row j of each of the n matrices of type A. Subsequently, for each model m, the absolute difference between and the mean are computed and averaged over the number of residues L of the model [ formula (2), Figure 1, panel II].

This is, the evolutionary process is a Markov process with uniform distribution at the root and is specified by transition matrices of type a i b i c i d i b i a i d i c i c i d i a i b i d i c i b i a i on each branch e i.

We then create a character matrix of habitat type and morphological characters, which we use to infer ancestral character states and test for correlation between habitat and morphology.