| 11. | Bump functions are often used as mollifiers, as smooth cutoff functions, and to form smooth partitions of unity.
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| 12. | A Hausdorff space X \, is paracompact if and only if it every open cover admits a subordinate partition of unity.
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| 13. | Add an open with closure in to produce a cover of and let be a partition of unity subordinate to this cover.
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| 14. | Existence, however, requires using the change of variables formula, the inverse function theorem ( locally ) and a partition of unity argument.
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| 15. | In addition, MIGFEM is another IGA code which is implemented in Matlab and supports Partition of Unity enrichment IGA for 2D and 3D fracture.
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| 16. | To prove the second formula take a partition of unity ? " i " supported in coordinate charts covering the support of ?.
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| 17. | This quantity is well-defined; that is, it does not depend on the choice of the coordinate charts, nor the partition of unity.
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| 18. | *PM : existence of partitions of unity, id = 9780 new !-- WP guess : existence of partitions of unity-- Status:
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| 19. | *PM : existence of partitions of unity, id = 9780 new !-- WP guess : existence of partitions of unity-- Status:
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| 20. | I had a feeling that a partition of unity type argument ( e . g ., Urson's lemma ) doesn't quite work.
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