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We illustrate these results using the CLUE-S (Conversion of Land Use and its Effects at Small regional extent) system to forecast land use change for the Deep Creek watershed in the northern Okanagan Valley of British Columbia, Canada.
All entries of the Cauchy matrix of the extent system are nonnegative according to Theorem 1.
The Cauchy matrices of system (14) and the extent system coincide in 0 ≤ s ≤ t < ∞.
Proof Let us extend the coefficients and delays in system (14) on the interval [ − H, 0 ), where H = max i, j = 1, …, n esssup t ≥ 0 τ i j ( t ) as follows: p i i ( t ) = esssup t ≥ 0 p i i ( t ), p i j ( t ) ≡ 0 for i ≠ j, τ i j ( t ) ≡ 0, q i ( t ) ≡ 0 for i, j = 1, …, n, t ∈ [ − H, 0 ), and consider system (14) on [ − H, ∞ ), calling it the extent system.
9 For passenger cars, the extent of residual deformation in lateral direction is classified using a nine-zone extent system.
Besides the above benefits, participation in research rotation allows us to evaluate our residents in the following core competencies – practice based learning, communication skills, and to a certain extent system based practice.
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However, it is as yet unclear which, and to what extent, system-level interventions are being funded by these initiatives, nor is it clear how much funding they allocate to disease-specific activities – through conventional 'vertical-programming' approach.
It remains to be seen to what extent systems biology and proteomics will be able to handle the structural and functional versatility of proteins, notably of proteins carrying out regulatory functions.
Systems theory also deals with the question as to what extent a system is closed or open to its environment and how exchanges between system and environment take place.
We also asked to what extent the system would change their behaviour, as participants trialled the system and should have a good idea of the potential effects of such system on their driving behaviour.
Programming on Channel One, Floriana Fossato, who worked on media projects in Moscow in the aughts and now studies Russian television at University College London, said, showed "people surviving a cruel but, to a certain extent, necessary system".
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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