Math Forum / Mathematics / Research / January 2007

Let p be a polynomial of degree m over a finite field F. Let A be its
companion matrix.
Does anyone know if the solutions of p(A^k)=0 have been characterized?
If p is primitive, it looks like there are exactly m solutions (based

Dear Colleagues
I have a question from theory of integral transforms and
would appreciate some guidance w.r.t. that.
Imagine we have a transform of the complex-valued function f(z)

In a message dated 1/29/2007 10:36:44 P.M. Pacific Standard Time,  
zaslav@math.binghamton.edu writes:
I wonder  why you list the hypercube's main name as "measure polytope".
I'm a  working mathematical geometer and I never saw that name until I

i have a task:
Given: many rectangular shapes with the same measurements (length and
width) and many smaller size rectangular shapes, that are given like
this: a(1), b(1), k(1); ...; a(n), b(n), k(n) here a(i) - is shape

has someone an idea which helps me to solve the following problem?
Given is a cube in R^K
        Q = { x is element of R^K | 0 <= x <= 1 }
and a grid (not necessary equidistant) of points within Q.

Dear Group,
this seems like a simple problem, but I cannot find any results
anywhere.
P_n(X) = X*(X-1)*...*(X-n+1) = a_0+a_1*X+...+X^n,

I am interested in references about the folowing shape:
Cut the flexible garden pipe  radially at some place so that cut is a
perfect circle. Hold one end motionless. Twist another by 180 degrees.
Glue back to the other end. Is this topologically a knot with k=1?

Is the field of ration functions of a (real or complex) variety functorial in the variety?
I have a smooth manifold with a smooth bundle over it, each fiber of which is isomorphic to the same variety (a real Grassmannian, if that's relevant). What I want to know is if I consider ...

Want to know integer general integer solution (x,y,z).
Kent Holing

let s_1, ..., s_k be nxn permutation matrices such that s_ij =
s_i(s_j)^{-1} has no fixed point. let a_1,...,a_k
be integers.
consider the matrix A = a_1s_1+...+a_ks_k.

A thread from last May (2006), subject "Definition for UFD", posed the
question whether or not an alternate definition for a UFD was the same as
the usual definition. For easy reference, here's the original post:
==================================================

I have a large sparse matrix A (symmetric, positive definite with
approx 20M rows/columns and 200M nonzeros) which has upper+lower
bandwidth about 1000, and I want to solve a single equation of the form
Ax=b.

If you have "n choose k" numbers and you want to know whether they
could be constructed as the maximal minor determinants of a single n by
k matrix, you can check this using the Plucker Relations.
(Equivalently, the Plucker relations determine which elements of an

Do you have any idea to compute the fredholm index of the following differential operator defined on
H^s(W)  ,the sobolev space on an open bounded set of R^2:
x^3*U_x+y^3*U_y
Note that the above is the derivation of U along the vector field (x^3,y^3),this vector field has a unique

As far as I can tell, the rotations that you can do to the platonic
solids that leave them looking the same is rotating about either the
center of a face or a vertex. For a cube, you can rotate each face by
either 1/4 rotation, 1/2 rotation, or 3/4 rotation. If you rotate by