BBO Discussion Forums: Question and Answer thread - BBO Discussion Forums

Jump to content

  • 3 Pages +
  • 1
  • 2
  • 3
  • You cannot start a new topic
  • You cannot reply to this topic

Question and Answer thread

#41 User is offline   kenberg 

  • PipPipPipPipPipPipPipPip
  • Group: Advanced Members
  • Posts: 6,394
  • Joined: 2004-September-22
  • Location:Northern Maryland

Posted 2011-March-22, 07:39

The generic term is fixed point. Suppose that X is some set, it matters not at all what sort of set. Suppose f is a function such that for each x in the set X, f(x) is also some point of X. In shorthand f:X->X. Then: If f(x)=x then x is called a fixed point for the function f.

For whatever interest it may hold, here is one of the more famous fixed point theorems (called the Brouwer Fixed Point Theorem although the pedigree is maybe more complicated): If X is any closed ball of any (finite) dimension and f: X->X is continuous then f has a fixed point. "Closed" means that the boundary points of X are included in X.

A closed 1-dimensional "ball" is just a closed interval, in 2 dimensions it's a disk, in 3 dimensions it is what you really think of as a ball, and mathematically you can have any number of dimensions.

As for usefulness, it can be in the eye of the beholder. If you take any one theorem from mathematics, by itself it is apt to have little use. As a collective body of knowledge and as a way of dealing with very practical problems, it would be an error to dismiss even the most theoretical mathematics. For a well-known example, the success of the Google search engine was based in part on theorems in linear algebra. See http://www.rose-hulm...ersionFixed.pdf

Similarly, the Brouwer Fixed Point Theorem, and a flock of other fixed point theorems, have been very useful in the right hands, applied to the right problems. Think Nash Equilibrium, see http://en.wikipedia....ash_equilibrium
Ken
1

#42 User is offline   mycroft 

  • Secretary Bird
  • PipPipPipPipPipPipPip
  • Group: Advanced Members
  • Posts: 3,652
  • Joined: 2003-July-12
  • Gender:Male
  • Location:Calgary, Canada

Posted 2011-March-22, 10:08

Ah, good, thanks. I'm glad I was thinking clearly that there was a use for defining a term for that property.

I like the "stupid things you can do with n-dimensional spheres" stuff, too. The worst of those was wrapping my head around "the entire volume of an infinite-dimensional sphere is on its surface" - even with the math that proved it. I've been able to be comfortable with some of "things are different at infinity/infinitesimal", but that one broke my brain for a couple of weeks.

And you don't need to prove to me that there is a use for pure math - I did a degree in cryptography, after all, and had to learn matroid theory the hard way to understand secret sharing schemes (I loved the way that developed in the literature, too: the engineer/applied mathematician/"S" in RSA found a cool development of field theory that allowed for zero-Shannon-information if n-1 people pooled their data, but 100% recovery if one more did (for any people); then they found that they could do "these two people, or any three"; then a mathematician showed that this was a matroid, which exploded the solved space in a very short time: "since it's a matroid, we can do <this>, which means that <this real-world problem> is solvable, and it can be generalized to <that>"; and now the engineering people (like me) were playing catchup).
0

#43 User is offline   gwnn 

  • Csaba the Hutt
  • PipPipPipPipPipPipPipPipPipPip
  • Group: Advanced Members
  • Posts: 11,418
  • Joined: 2006-June-16
  • Gender:Male
  • Location:Enschede, the Netherlands
  • Interests:matching LaTeX delimiters :(

Posted 2011-April-08, 06:53

I have some pdf format books (some of them maybe copyrighted - don't tell anyone). Sometimes I lose track of where I last was. Is there an easy way of doing this or should I just open a text document on the side?
... and I can prove it with my usual, flawless logic.
      George Carlin
0

#44 User is offline   655321 

  • PipPipPipPipPipPipPip
  • Group: Advanced Members
  • Posts: 2,502
  • Joined: 2007-December-22

Posted 2011-April-08, 16:33

View Postgwnn, on 2011-April-08, 06:53, said:

I have some pdf format books (some of them maybe copyrighted - don't tell anyone). Sometimes I lose track of where I last was. Is there an easy way of doing this or should I just open a text document on the side?


Probably eReaders will remember your place - I tried it with Bluefire on the iPad and it works.
That's impossible. No one can give more than one hundred percent. By definition that is the most anyone can give.
0

#45 User is offline   matmat 

  • ded
  • PipPipPipPipPipPipPip
  • Group: Advanced Members
  • Posts: 3,440
  • Joined: 2005-August-11
  • Gender:Male

Posted 2011-April-09, 22:10

If you're using an do*be product to read the pdfs, your version might have a bookmark feature; you do have to save the modified pdf afterward, however.
0

#46 User is offline   Foxx 

  • PipPipPipPip
  • Group: Full Members
  • Posts: 338
  • Joined: 2003-February-15
  • Gender:Male
  • Location:La Jolla, California
  • Interests:Being quick, brown, and foxy; Jumping over lazy dogs

Posted 2011-April-16, 00:30

OK, this is going to sound a little odd, but can anyone identify the kinds of wood shown in this picture:

Attached File(s)

  • Attached File  wood.jpg (33.15K)
    Number of downloads: 22

0

#47 User is offline   matmat 

  • ded
  • PipPipPipPipPipPipPip
  • Group: Advanced Members
  • Posts: 3,440
  • Joined: 2005-August-11
  • Gender:Male

Posted 2011-April-23, 14:53

View PostFoxx, on 2011-April-16, 00:30, said:

OK, this is going to sound a little odd, but can anyone identify the kinds of wood shown in this picture:


For some reason I can't read the attachment :(
0

#48 User is offline   gwnn 

  • Csaba the Hutt
  • PipPipPipPipPipPipPipPipPipPip
  • Group: Advanced Members
  • Posts: 11,418
  • Joined: 2006-June-16
  • Gender:Male
  • Location:Enschede, the Netherlands
  • Interests:matching LaTeX delimiters :(

Posted 2012-March-07, 06:34

I am reading about s-trans-1,3-butadiene. I know what trans-1,3-butadiene means, but what is the s? I am a complete chemistry moron. I would guess it's got something with s orbitals?! Googling didn't bring much joy. It seems they always use "s-trans".
... and I can prove it with my usual, flawless logic.
      George Carlin
0

#49 User is offline   helene_t 

  • The Abbess
  • PipPipPipPipPipPipPipPipPipPip
  • Group: Advanced Members
  • Posts: 12,486
  • Joined: 2004-April-22
  • Gender:Female
  • Location:Leeds (UK)
  • Interests:Every topic that may come up in Scientific American

Posted 2012-March-07, 06:41

s for "single bond". http://www.chem.ucla.../S/s_trans.html
it is amazing to me that over half of declarers in virtually any field would go down in this cold contract. Some things never change, the skill of the "average" bridge player remains well below average. Iandayre
0

#50 User is offline   gwnn 

  • Csaba the Hutt
  • PipPipPipPipPipPipPipPipPipPip
  • Group: Advanced Members
  • Posts: 11,418
  • Joined: 2006-June-16
  • Gender:Male
  • Location:Enschede, the Netherlands
  • Interests:matching LaTeX delimiters :(

Posted 2012-March-07, 06:46

well it is a weird nomenclature but ok, I should have found that! :)
... and I can prove it with my usual, flawless logic.
      George Carlin
0

#51 User is offline   onoway 

  • PipPipPipPipPip
  • Group: Full Members
  • Posts: 936
  • Joined: 2005-August-17

Posted 2012-March-07, 17:43

View PostFoxx, on 2011-April-16, 00:30, said:

OK, this is going to sound a little odd, but can anyone identify the kinds of wood shown in this picture:

If you haven't already done so, you might check out the places that carry veneer wood. This place has very nice photos of veneer wood so maybe you would find a match if you browsed through it
http://www.woodveneer.com/veneer.html There are also other such sites. Good luck.
0

#52 User is offline   mgoetze 

  • PipPipPipPipPipPipPip
  • Group: Advanced Members
  • Posts: 3,445
  • Joined: 2005-January-28
  • Gender:Male
  • Location:Cologne, Germany
  • Interests:Sleeping, Eating

Posted 2012-March-07, 18:57

View Postkenberg, on 2011-March-22, 07:39, said:

If X is any closed ball of any (finite) dimension and f: X->X is continuous then f has a fixed point.

In my mind this statement immediately raised the question of whether this is true for any given topology, but Wikipedia was able to answer that easily so I guess it is off-topic for this thread.
"One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision"
    -- Bertrand Russell
0

#53 User is offline   Cyberyeti 

  • PipPipPipPipPipPipPipPip
  • Group: Advanced Members
  • Posts: 5,872
  • Joined: 2009-July-13
  • Location:England

Posted 2012-March-07, 18:58

View Posthelene_t, on 2012-March-07, 06:41, said:


The s seems to be superfluous. I can see that buta 1,3 diene can be trans or cis, but what's the alternative to "s". I didn't see this terminology in the UK when I was doing chemistry as an undergrad 25-30 years ago.
0

#54 User is offline   gwnn 

  • Csaba the Hutt
  • PipPipPipPipPipPipPipPipPipPip
  • Group: Advanced Members
  • Posts: 11,418
  • Joined: 2006-June-16
  • Gender:Male
  • Location:Enschede, the Netherlands
  • Interests:matching LaTeX delimiters :(

Posted 2012-March-08, 00:41

View PostCyberyeti, on 2012-March-07, 18:58, said:

The s seems to be superfluous. I can see that buta 1,3 diene can be trans or cis, but what's the alternative to "s". I didn't see this terminology in the UK when I was doing chemistry as an undergrad 25-30 years ago.

It is superfluous, but maybe it is neater to have the same term apply for all cis/trans isomers around a single bond? I don't know.
... and I can prove it with my usual, flawless logic.
      George Carlin
0

#55 User is offline   JLOGIC 

  • 2011 Poster of The Year winner
  • PipPipPipPipPipPipPipPip
  • Group: Advanced Members
  • Posts: 6,002
  • Joined: 2010-July-08
  • Gender:Male

Posted 2012-March-08, 01:30

Wolfram Alpha + Quora + Google, you shouldn't need anything else.
0

Share this topic:


  • 3 Pages +
  • 1
  • 2
  • 3
  • You cannot start a new topic
  • You cannot reply to this topic

1 User(s) are reading this topic
0 members, 1 guests, 0 anonymous users