Sentence examples for ordinary contraction from inspiring English sources

Shielded contraction can be based on an ordinary contraction operator ÷ and a set R of retractable sentences.

for all x, y ∈ X and φ : [ 0, + ∞ ) → [ 0, + ∞ ) is a function satisfying: (i) φ is continuous and nondecreasing;   (ii) φ ( t ) = 0 if and only if t = 0 ;   (iii) lim t → + ∞ φ ( t ) = + ∞.  . φ is continuous and nondecreasing; φ ( t ) = 0 if and only if t = 0 ; lim t → + ∞ φ ( t ) = + ∞. Note that (1.1) reduces to an ordinary contraction when φ ( t ) : = k t, where 0 ≤ k < 1. Theorem 1.1 ([1.1).

By contrast, some ABS materials underwent an irreversible volumetric expansion over a temperature interval of ∼30 K, which was superimposed on the ordinary thermal contraction.

During ordinary breathing, muscular contraction occurs only on inspiration, expiration being accomplished "passively" by elastic recoil of the lung.

Thus, this states that even if the m-metric m and the ordinary metric d have the same topology, the Banach contraction of the m-metric does not imply the Banach contraction of the ordinary metric d.

So this states that if the m-metric m and the ordinary metric d even have the same topology, but the Banach contraction of an m-metric, this does not imply the Banach contraction of the ordinary metric d. ([5]).

In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories.

Friedman wrote extensively on the Great Depression, which he termed the Great Contraction, arguing that it had been caused by an ordinary financial shock whose duration and seriousness were greatly increased by the subsequent contraction of the money supply caused by the misguided policies of the directors of the Federal Reserve.

For Lewis, no (ordinary) object exists at more than one world, so Vallentyne's contractions, being separate worlds, must contain separate objects.

Harjani and Sadarangani [24] investigated some unidimensional fixed point theorems for generalized contractions in complete partially ordered metric spaces and applications to ordinary differential equations.

Recently, some fixed point results for generalized contraction mappings have been proved by Ri [3] as follows: integral equations; ordinary differential equations; partial differential equations; matrix equations; functional equations.