Sentence examples for matrices demonstrated in from inspiring English sources

If there exists any common point, we can simply change the collocation points non-uniformly such that every collocation point may be chosen from ([frac{i}{m},frac{i+1}{m} )), (i=0,1,2,ldots, m-1) in order to include all basis functions and keep the structure of constructed matrices demonstrated in (13), (32), and (33) and for higher order.

This creates a 4 × 4 matrix as demonstrated in Fig. 1 with Actors and Entities form x and y axes respectively, and Time is the repetition of all in the z axis to represent these events occurring Any Time.

An effect of high ethanol concentrations on the CSF matrix was demonstrated in a spiking experiment.

As such, it is assumed that the number of apoptotic chondrocytes may increase following excessive running loading, which contributes to the matrix degradation demonstrated in our study.

This in vivo phenomenon was supported by in vitro observations: satellite cells (SCs) that were exposed to the matrix demonstrated an improvement in myogenesis that was maximized when SCs were cultured on the matrix in a necrotic environment.

The concentration inequality of the TBD matrix is simply demonstrated in Section 4. Subsequently, we can find that the TBD matrix satisfies the restricted isometry property (RIP [7] according to a theorem in[8].

The use of a powerful transfer matrix method is demonstrated in the formulation of the coupled plate-fluid layer system response.

Proliferation of mesangial cells and expansion of the matrix have been demonstrated in many immune-mediated forms of glomerulonephritis including lupus nephritis [ 31] and IgA nephropathy [ 32– 32].

Although the nuclear AT1 in dopamine neurons located in the matrix demonstrated a similar loss of AT1 corresponding with the clinicopathological progression as was observed for the entire neuron AT1, the nuclear AT1 in the nigrosome 1 dopamine neurons did not show reduction and remained at levels characteristic of the neurologically and neuropathologically normal control patients.

An opal PhC with cross-linked PS spheres in a PDMS matrix demonstrated changes color by contact with ink 332– 334 such as silicone based volatile fluids (Mw ∼ 200 g mol−1) that swell the PDMS.

As demonstrated in matrix permeability studies, the improved formation of covalent cross-linkages imposed by lysine facilitated construction of stronger cross-linking structures.