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Mappings with a composite part and with a constant Jacobian

✍ Scribed by R. Peretz

Book ID
104350049
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
242 KB
Volume
11
Category
Article
ISSN
0893-9659

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✦ Synopsis

In this paper, we give a classification for mappings of the form u, vCC[t], p, qEC[x,y],

i.e., mappings with a composite part, that satisfy the Jacobian hypothesis. This is done for those mappings for which a certain "no cancellation" argument can be applied.

The proof is rather technical, and strangely it relies on the study of the rational solutions of the socalled Burger's equation with no viscosity. This is a nonlinear scalar hyperbolic PDE that modelizes the behavior of gas with no viscosity. Originally, it served for street traffic model. geywords--Local structure of maps: etale, Automorphisms, Hyperbolic PDEs.

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On the extremal nature of molecular vibr
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The singularity of the jacobian, recently claimed by Cans to result in the extremal property that infinite values be taken by the partial derivatives of aU the diagonal for;z constants w%h respect to any gi%vven off-diagonai force constant, is shown to be consistent with finite values of all the par