Sentence examples for outer basis from inspiring English sources

As introduced, we use the subscripts ˘ and ˆ to indicate the component tuples corresponding to the rotating outer basis { a 1 ( t ), a 2 ( t ), a 3 ( t ) } and the cylindrical basis { e x, e r, e ϕ }, respectively.

As a consequence of a row-wise homogenization, the air flow (2) can be treated as stationary not only in the rotating outer basis { a 1 ( t ), a 2 ( t ), a 3 ( t ) }, but also in a fixed outer one.

Note that to an arbitrary vector field z = ∑ i = 1 3 z ˘ i a i = ∑ i = 1 3 z i d i ∈ E 3, we indicate the component tuples corresponding to the rotating outer basis and the director basis by z ˘ = ( z ˘ 1, z ˘ 2, z ˘ 3 ) ∈ R 3 and z = ( z 1, z 2, z 3 ) ∈ R 3, respectively.

The director basis can be transformed into the rotating outer basis by the tensor-valued rotation R, that is, R = a i ⊗ d i = R i j a i ⊗ a j ∈ E 3 ⊗ E 3 with associated orthogonal matrix R = ( R i j ) = ( d i ⋅ a j ) ∈ SO ( 3 ).

We introduce the rotating outer orthonormal basis { a 1 ( t ), a 2 ( t ), a 3 ( t ) } satisfying ∂ t a i = Ω × a i, i = 1, 2, 3, where Ω is the angular frequency of the centrifugal disk.

Let ({mathbf{e}_{mathbf{1}}, mathbf {e}_{mathbf{2}}, mathbf{e}_{mathbf{3}}}) be a fixed outer orthonormal basis, then we consider a beam in the (mathbf{e}_{mathbf{1}} - mathbf{e}_{mathbf{1}} - mathbf{e

In this chapter, we survey the major progress that has been made for understanding the molecular basis of outer segment architecture.

The colorful agate sample is mainly divided into two growth zones: the inner and outer halves on the basis of ~0.2-mm-thick white band (Fig. 1a).

The castle was increasingly rigorously maintained, and during the 1910s and 1920s the larger trees around the castle were cut down, and the animals were cleared from the inner and outer baileys on the basis that they posed a health and safety risk to visitors.

On a daily basis, the outer segment tips of photoreceptors are phagocytosed into the RPE, and digested in phago-lysosomes within the RPE [ 7].

However, it is not possible to say whether this carbohydrate material is extracellular in the form of slime, as a capsule more tightly associated with the outside of the cell, or lipopolysaccharide which forms the basis of the outer leaflet of Gram negative outer membrane.