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A theorem of Eliashberg and Thurston on foliations and - download pdf or read online

By Carlo Petronio

ISBN-10: 8876422862

ISBN-13: 9788876422867

Those notes originate from a seminar held in Pisa in November and December 1996 together by way of Riccardo Benedetti, Paolo Lisca and me. the purpose of those notes is to offer a close evidence of the subsequent consequence because of Eliashberg and Thurston: THM enable M be a closed orientated 3-manifold and permit F be a cooriented C2-smooth codimension-1 foliation on M. imagine that (M,F) isn't really diffeomorphic to the product foliation on S2xS1. Then arbitrarily as regards to F within the C0 topology there exist a good and a adverse C\infty touch constitution.

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D. (2001) Analysis of relative gene expression data using real-time quantitative PCR and the 2(−delta delta C(T)) method. Methods 25, 402–8. 9. , Magotra, A. , Cannon, B. , and Szafranska, A. E. (2008) Evaluation and validation of total RNA extraction methods for microRNA expression analyses in formalin-fixed, paraffin-embedded tissues. J Mol Diagn 10, 203–11. 10. , and Vandesompele, J. (2008) High-throughput stem-loop RT-qPCR miRNA expression profiling using minute amounts of input RNA. Nucleic Acids Res 36, e143.

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The calculation above assumes that each of the targets have the same (quantitative) PCR efficiency. If this is not true, the Ct values can first be adjusted according to the difference in efficiency (see Note 8), and then compared accordingly. 4. Small RNA isolates should: (1) be free of protein, particularly nucleases; (2) be free of RT-PCR inhibitors (the PCR step is particularly vulnerable, and some targets may be more sensitive to inhibition than others, which can skew data comparisons); and (3) provide clear evidence of the small RNA fraction and ideally the intactness of any larger RNA species.

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A theorem of Eliashberg and Thurston on foliations and contact structures by Carlo Petronio


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