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In addition, a backstepping formulation is derived using contraction theory that guarantees the boundedness of state response under bounded disturbances such as wind.
We will derive a contraction.
Since Hilbert spaces satisfy Opial's condition, it follows from Step 5 that lim inf i → ∞ ∥ y n i − w ∥ < lim inf i → ∞ ∥ y n i − W n w ∥ ≤ lim inf i → ∞ [ ∥ y n i − W n y n i ∥ + ∥ W n y n i − W n w ∥ ] ≤ lim sup i → ∞ ∥ y n i − W n y n i ∥ + lim inf i → ∞ ∥ W n y n i − W n w ∥ = lim inf i → ∞ ∥ W n y n i − W n w ∥ ≤ lim inf i → ∞ ∥ y n i − w ∥, which derives a contraction.
The asymptotic convergence of proposed estimator is derived by using contraction theory related to semi-contracting systems.
These best conditions cannot be derived from the contraction mapping principle.
Veteran automotive writer, concours judge and museum curator Ken Gross helped the USPS choose this particular car as an exemplar of the machines that came to be known as hot rods – a term though to be derived from a contraction of "hot roadster".
The term Allāh is derived from a contraction of the Arabic definite article al- "the" and "deity, god" to meaning "the [sole] deity, God" (, ho theos monos).
Therefore we hypothesized that TBC1D1 may have a primary function of mediating signalling inputs derived from muscle contraction.
The term biofertiliser was derived from the contraction of the term biological fertiliser, with biological, implying the use of living organism.
An example of the importance of clustered repeats for human cell physiology can be derived from the contraction of the 3.3 kb (D4Z4) megasatellite located at chromosome 4q35.2 which is associated to FSHD manifestation [8 10].
Under physiological conditions, there is a delicate and balanced release of relaxing factors and endothelium-derived contraction factors that are apparently imbalanced in diabetes.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com