Math Forum / Mathematics / Research / December 2007

Also available as http://math.ucr.edu/home/baez/week260.html
December 24, 2007
This Week's Finds in Mathematical Physics (Week 260)
John Baez

1. If five faces of a distorted cube are cyclic quadrilaterals, then
the sixth is too.
2. If five faces of a distorted cube are quadrilaterals-of-tangents
(QOTs), then the sixth is too,

(I write the mathematical formulas in LATEX format)
$n>=2$ is a natural number,
$H$ is the hyperplane consisting of all vectors in
$R^n$ the sum of

Faculty Position Opportunities
Institute of Statistical Science, Academia Sinica, Taipei
Contingent  upon  administrative  approval,  we  expect  to  have
one  to  two  regular  research  positions  available  in  2008

I'm looking for "nice" surfaces of constant negative Gaussian curvature.
There are quite a few pictures on the web of "minimal surfaces", which
have zero mean curvature. Their Gaussian curvature is generally
negative, but not necessarily constant.

I am looking for an efficient way to encode an n-letter alphabet so
that a stream of random bits will produce an unbiased stream of random
elements of {0,...,n-1}. An easy way to do this is to encode modulo
the next power of 2 greater than (a multiple of) n, then reduce modulo

Let X, Y be affine varieties over an algebraically closed field of
characteristic zero. Assume Y is irreducible. Let  f: X -->Y be a
surjective regular morphism with the property that the fibre over each
point of Y is irreducible, and of the same dimension. I was wondering

Are there any simple results connecting the eigenvalues of a matrix
A
to the eigenvalues of a matrix
AB

The following fact seems very elementary---has anybody heard of it or
anything like it before? Take a cubic in Weierstrass form, say
y2=p(x) where  p is a degree three polynomial. Then any two tangent
conics are either identical or disjoint. It turns out that this works

I am trying to understand the following:
I am trying to understand the set of al solutions to the matrix
equation:
(**)                                                 x^{-1}y^{-1}xy=-

I have just completed a first draft of an expository paper on forcing.
 http://alum.mit.edu/www/tchow/forcing.pdf
This paper grew out of a sci.math.research article that I posted back
in 2001 entitled "Forcing for dummies":

Let
    x0 = 0
    x1 = -1 with probability p
      = 1 with probability 1 - p

Is anybody aware of papers or books
on matheamntical proof of the existence
of some kind of chaos in systems with hysteresis?
Thank you,