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Crucially, the committee's report recognises the multifaceted nature of the problem and notes that without a coherent innovation policy to address many distinct problems, the UK will continue to miss out on its own opportunities.
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Convex optimization theory [1, 2] has provided in the last decades a powerful framework to solve optimization problems in many distinct areas.
It is reasonable to guess that for dimΩ≥2 above problem possesses infinitely many distinct solutions since this is proved to be true for ODE.
As is the case with all Olympiad problems, there are often many distinct ways to solve them, and correct complete solutions are maximally rewarded irrespective of the elegance or complexity of the proof.
For instance, "Given a graph G and a fixed value (k > 0), how many distinct k-cores are there for G?" is not a trivial problem and it empirically depends on the density of the graph.
A problem for this view is that any one token instantiates indefinitely many distinct shapes or patterns, i.e. many different expressions.
Father Judge moved in many distinct circles.
These are two distinct problems.
There are three distinct problems here.
There are really two distinct problems here.
So they solve two distinct problems of building websites.
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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