| 41. | The Paneitz operator appears in extremal problems for the Moser & ndash; Trudinger inequality in dimension four as well
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| 42. | "' Extremal graph theory "'is a branch of the graphs which satisfy a certain property.
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| 43. | Results on the truncated moment problem have numerous applications to extremal problems, optimisation and limit theorems in probability theory.
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| 44. | His research interests are ocean and shelf circulation, 4D data assimilation, extremal analysis and applied time series analysis.
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| 45. | They are in fact extremal with respect to the number of cycles whose length is the girth of the graph.
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| 46. | Note that a state is a pure state if and only if it is extremal in the convex set of states.
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| 47. | It is also of interest to study the extremal numbers of triangular cells in arrangements that may not necessarily be simplicial.
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| 48. | Namely, there is an upper bound for the entropy of a systolically extremal surface, in terms of its systole.
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| 49. | If a group has a central series, then there are two central series whose terms are extremal in certain senses.
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| 50. | The potentials generating the extremal solution separately because it is much more than the degenerate state of the nonextremal counterpart .)
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