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Please use this new version of Motion 27 Re: KISS-decorations

P-1788,

Please use this new version in discussions, and
for posting to the web page.  I apologize for
any confusion.

Baker

On 6/29/2011 6:14 AM, Marco Nehmeier wrote:

Am 29.06.2011 07:56, schrieb John Pryce:

Marco, Jürgen, P1788

On 28 Jun 2011, at 21:13, Jürgen Wolff von Gudenberg wrote:

we have prepared a third motion on decorations that clearly follows the KISS principle. Perhaps it is too simple, but we are convinced that it works better than the two current approaches. We only have 4 different decorations and one
linear order.
We are eager to read your comments.
Perhaps we can prolong the discussion time again? but there is not much discussion(!)


Thank you. I like the push back towards simplicity. Arnold has more-or-less completed his new FTDIA proof and has sent me a part for checking. I think we both want to revert from the present 7-decoration idea, and get rid of boundedness.
Yes, please chairman, can we extend the discussion period?

That said, I have some criticisms.

1. Theorem 1 on p2 is surely well known to be false.
Let f(x)=x for real x. Define F: IR -> IR by
F(xx) = Entire if 0 not in xx, and xx otherwise.
Then for any xx, and x in xx, we have f(x) in F(xx), so F
is an interval extension of f.
But xx=[1,2], yy=[0,2] give F(xx)=Entire, F(yy)=[0,2], so
isotonicity fails.

2. Theorem 2 (1st part) is carelessly stated, in fact meaningless as
written IMO.
It's not "For every interval extension F ...", but "For the
particular interval *function* F that results from applying straight-
forward interval computation ..., F(xx) encloses the range of f
over xx" -- or better, "... encloses the range over xx of the point
function defined by the expression f."

3. And surely Theorem 2 (2nd part) needs some continuity assumption,
because of the effect of taking the hull. I think it's false for
f(x)=1/x with xx=[-1,1]. And for sign(x) with xx=[0,0.5].

Further, and I trust more constructive, remarks to follow.

John




Dear John, P1788,

thank you for the quick comments.
You where right with your criticism.
We have changed the sections 1.2 and 1.4 according to your advice.

Please find attached the new version 1.2 of our motion (draft).

Best regards

Jürgen and Marco




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Ralph Baker Kearfott,   rbk@xxxxxxxxxxxxx   (337) 482-5346 (fax)
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Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
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Attachment: positionpaper.pdf
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