Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
just another uniqueness musing
#6
Gottfried Wrote:The only idea that remains is, to consider the length of the guessed curve of f°0.5(x) in an interval of f°0.5(x) .. f°2.5(x). (but also... I've never dealt with line-integrals). This length should be minimal if the amplitude of the overlaid mod(1)-function is minimal. But this is just crude guess - should be checked on paper first...

Sounds not bad, but here again the length is infinite, and if you chose f(a) for the shortest length in one interval [a,F(a)] - i.e. a straight line - then in the interval [F(a),F(F(a))] the length is longer then for a better choose in the first interval.
So over which and how many intervals do you want to measure the length without being arbitrary?
Reply


Messages In This Thread
just another uniqueness musing - by Gottfried - 02/11/2009, 12:23 PM
RE: just another uniqueness musing - by bo198214 - 02/11/2009, 03:14 PM
RE: just another uniqueness musing - by tommy1729 - 02/11/2009, 03:42 PM
RE: just another uniqueness musing - by tommy1729 - 02/11/2009, 03:50 PM
RE: just another uniqueness musing - by Gottfried - 02/11/2009, 03:48 PM
RE: just another uniqueness musing - by bo198214 - 02/12/2009, 12:10 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  A conjectured uniqueness criteria for analytic tetration Vladimir Reshetnikov 13 11,516 02/17/2017, 05:21 AM
Last Post: JmsNxn
  Uniqueness of half-iterate of exp(x) ? tommy1729 14 15,374 01/09/2017, 02:41 AM
Last Post: Gottfried
  Removing the branch points in the base: a uniqueness condition? fivexthethird 0 1,581 03/19/2016, 10:44 AM
Last Post: fivexthethird
  [2014] Uniqueness of periodic superfunction tommy1729 0 1,997 11/09/2014, 10:20 PM
Last Post: tommy1729
  almost periodic musing tommy1729 1 2,206 06/17/2014, 12:24 PM
Last Post: tommy1729
  Real-analytic tetration uniqueness criterion? mike3 25 21,856 06/15/2014, 10:17 PM
Last Post: tommy1729
  exp^[1/2](x) uniqueness from 2sinh ? tommy1729 1 2,291 06/03/2014, 09:58 PM
Last Post: tommy1729
  Uniqueness Criterion for Tetration jaydfox 9 11,356 05/01/2014, 10:21 PM
Last Post: tommy1729
  Uniqueness of Ansus' extended sum superfunction bo198214 4 6,786 10/25/2013, 11:27 PM
Last Post: tommy1729
  A question concerning uniqueness JmsNxn 3 5,652 10/06/2011, 04:32 AM
Last Post: sheldonison



Users browsing this thread: 1 Guest(s)