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Ij Ch. 9

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Into the Jungle Chapter 9: In Cold Blood: The Tale of the Icefish

1) How did the fish antifreeze originate? The fish antifreeze originated from an ancestral trypsinogen gene. The team at the University of Illinois came to this conclusion when they found shocking similarities between the antifreeze glycoproteins (AFGPs) and a trypsinogen gene. These similarities were between the AFGP exon and the sequence of the trypsinogen gene, between the 3’ end of the AFGP gene and trypsinogen, as well as between the two introns. All these similarities between the AFGP gene and trypsinogen gene were at least 90 percent identical. Not only that, but it was also found that the trypsinogen gene’s nine base pair segment encoded, by repeated duplication, tripeptide (Thr-Ala-Ala) repeats in the AFGP gene; which are the building blocks of AFGPs (Carroll, 178). Basically, the fish antifreeze originated from a gene that already existed.

2) What is a fossil gene? A fossil gene, or more commonly known as pseudogene, is a gene that is present but is inactive or “abandoned” (Carroll, 179). In the case of the icefish ancestors, the remaining alpha-globin gene is the fossil gene.

3) How do icefish obtain their oxygen? What might happen to icefish if the waters around the Antarctic became warmer? Icefish obtain their oxygen due to their cardiovascular system. Large gills and scaleless skin with large capillaries allow the icefish to “increase [their] absorption of oxygen from the environment” (Carroll, 180). They also have larger hearts and blood volumes to assist them in pumping the blood more efficiently throughout their body. If the waters around the Antarctic became warmer, the icefish would not survive. This is due to the fact that they do not have red blood cells, which allows them to thrive in cold environments and not freeze. The absence of red blood cells also reduces...

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Euler-Lagrange Partial Di Erential Equations

...arXiv:math.DG/0207039 v1 3 Jul 2002 Exterior Differential Systems and Euler-Lagrange Partial Differential Equations Robert Bryant Phillip Griffiths July 3, 2002 Daniel Grossman ii Contents Preface Introduction 1 Lagrangians and Poincar´-Cartan Forms e 1.1 Lagrangians and Contact Geometry . . . . . . . . . 1.2 The Euler-Lagrange System . . . . . . . . . . . . . . 1.2.1 Variation of a Legendre Submanifold . . . . . 1.2.2 Calculation of the Euler-Lagrange System . . 1.2.3 The Inverse Problem . . . . . . . . . . . . . . 1.3 Noether’s Theorem . . . . . . . . . . . . . . . . . . . 1.4 Hypersurfaces in Euclidean Space . . . . . . . . . . . 1.4.1 The Contact Manifold over En+1 . . . . . . . 1.4.2 Euclidean-invariant Euler-Lagrange Systems . 1.4.3 Conservation Laws for Minimal Hypersurfaces 2 The 2.1 2.2 2.3 2.4 2.5 Geometry of Poincar´-Cartan Forms e The Equivalence Problem for n = 2 . . . . . . . Neo-Classical Poincar´-Cartan Forms . . . . . . e Digression on Affine Geometry of Hypersurfaces The Equivalence Problem for n ≥ 3 . . . . . . . The Prescribed Mean Curvature System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v vii 1 1 7 7 8 10 14 21 21 24 27......

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