Sentence examples for unequal components from inspiring English sources

As a remark, this also shows that for spherical whirls u with f as in Proposition 2.2 (cf. (2.19)), the reduced system (2.17) is equivalent to the original full system (1.6), a conclusion that is not in general true for spherical whirls with unequal components of f merely solving (2.17).

Remark 1 Theorem 2 shows that F has at least one (coupled) fixed point of the form ( x ¯, x ¯ ) ∈ C × C, but, in general, for a bivariate mapping F it is also possible to have coupled fixed points ( x ¯, y ¯ ) with unequal components, i.e., such that x ¯ ≠ y ¯, as shown by the following example.

Example 2 Let X = R (with the usual metric), C = [ − 4, 4 ] and F : C 2 → X be defined by F ( x, y ) = 4 − x 2 − 2 y, ∀ x, y ∈ C. Then F is weakly Lipschitzian with constants a = 8 and b = 2 (in the sense of Definition 1) and F possesses two coupled fixed points ( − 4, − 4 ), ( 1, 1 ) with equal components and two coupled fixed points with unequal components, ( − 1, 2 ) and ( 2, − 1 ).

When glass is subjected to unequal stress components operating on perpendicular planes, it becomes birefringent (that is, doubly refracting).

Using comparisons with numerical simulations and complementary optical data, the highly complex temperature structure evident in A3921 is interpreted as an off-axis merger between two unequal mass components.

This formulation permits unequal breadth and depth taper ratios as well as unequal element lengths.

It then becomes easier understood that, in the regime of polar material response, a thin-walled structure made of ideal fibre-reinforced material deforms plastically when suitable combinations of shear stress values are reached simultaneously, rather than when only one of two unequal shear stress components reaches some maximum absolute value.

If such oriented conduits exist they could allow the directional transport and/or unequal stabilisation of components of the polarity machinery (such as Ds and Ft themselves).

(b) Independent-unequal model: pleiotropy components are independent of each other but have different strengths.

The number of components was unequal for the nitrate concentration and flux models.

The deviations increased for solutions with a substantial chemical loading in combination with unequal diffusivities of the components.