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Brouwer theorem

Some simplifications are possible if equivalence classes of symmorphy transformations can be defined where operations S from the same class transform the space occupied by the object A the same way and differ only in parts of the space where A is not present. Furthermore, using the Brouwer fixed point theorem, a subgroup structure of symmorphy groups Gjph( ) provides a more detailed characterization of molecular shape. These aspects will not be reviewed here. [Pg.169]

Most symmorphy groups hp are rather complicated and their direct use for molecular shape characterization and shape similarity analysis is not a trivial task. Some simplifications are possible using a technique based on the Brouwer fixed point theorem, as described in reference [43]. [Pg.200]

Finally, the theorem asserts the existence of at least one periodic solution. After a bit of algebra, this follows directly from the Brouwer fixed point theorem (see Hastings and Murray). [Pg.54]

A famous result has been given by Brouwer. Consider a smooth map / that takes into itself / -> B. The Brouwer fixed-point theorem states... [Pg.345]


See other pages where Brouwer theorem is mentioned: [Pg.287]    [Pg.287]    [Pg.344]    [Pg.329]    [Pg.345]    [Pg.21]    [Pg.180]    [Pg.303]   
See also in sourсe #XX -- [ Pg.287 ]




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