Search Results for ""

Let F be a finite field with q elements, and let F_s be a field containing F such that [F_s:F]=s. Let chi be a nontrivial multiplicative character of F and chi^'=chi ...

How many times can a shape be completely surrounded by copies of itself without being able to tile the entire plane, i.e., what is the maximum (finite) Heesch number?

In bipolar coordinates, the Helmholtz differential equation is not separable, but Laplace's equation is.

A pyramid with a heptagonal base. The heptagonal pyramid is one of the 257 convex octahedra.

Let X be a continuum (i.e., a compact connected metric space). Then X is hereditarily unicoherent provided that every subcontinuum of X is unicoherent. Any hereditarily ...

For real, nonnegative terms x_n and real p with 0<p<1, the expression lim_(k->infty)x_0+(x_1+(x_2+(...+(x_k)^p)^p)^p)^p converges iff (x_n)^(p^n) is bounded.

If two pairs of opposite polygon vertices of a complete quadrilateral are pairs of harmonic conjugate points, then the third pair of opposite polygon vertices is likewise a ...

The 6-polyiamond illustrated above.

If R is a Noetherian ring, then S=R[X] is also a Noetherian ring.

Let K be an algebraically closed field and let I be an ideal in K(x), where x=(x_1,x_2,...,x_n) is a finite set of indeterminates. Let p in K(x) be such that for any ...