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A mapping f : C → C is called contractive with a contraction coefficient if there exists a constant ρ ∈ ( 0, 1 ) such that ∥ f ( x ) − f ( y ) ∥ ≤ ρ ∥ x − y ∥, ∀ x, y ∈ C. (1.6).
Hence is a contraction with contraction coefficient.
Then is a contraction with contraction coefficient.
then is a contraction with contraction coefficient (2.5).
Hence, S is a contraction with contraction coefficient τ t.
Hence, G is a contraction with contraction coefficient τ t.
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Crack-free and high-density composites were obtained despite the different contraction coefficients of the layers during the sintering.
The strain distribution is very heterogeneous due to the difference between the thermal contraction coefficients of aggregates and mastic (i.e., bitumen and filler).
The data are analyzed in terms of a development of the simple energy balance incorporating flow contraction coefficients to quantify deviations from ideal flow.
Bubble column geometry, i.e. draft-tube diameter, affects both bubble entrainment and the flow contraction coefficients, and interacts with the fluid properties to affect both gas hold-up and liquid circulation.
where the step size τ n is given by (1.12), g : H 1 → H 1 is a contraction with contractive coefficient δ ∈ ( 0, 1 ), and { α n } is a real sequence in ( 0, 1 ).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com