Based on the work of Pinkall, characterizations of spherical curves are given whose corresponding Hopf cylinders are isothermic surfaces in the threedimensional sphere. Comparing these characterizations with results of Langer and Singer about elastic spherical curves we determine all isothermic Willmore Hopf tori.

We confirm a conjecture of Littlewood: there exist seven infinite circular cylinders of unit radius which mutually touch each other. In fact, we exhibit two such sets of cylinders. Our approach is algebraic and uses symbolic and numerical computational techniques. We consider a system of polynomial equations describing the position of the axes of the cylinders in the 3 dimensional space. To hav...

We show that the cylinder Z(1) := B(1) × R2(n−1) embeds symplectically into B(R)× R2(n−2) if R > √ 3.

The enumeration of perfect matchings of graphs is equivalent to the dimer problem which has applications in statistical physics. A graph G is said to be n-rotation symmetric if the cyclic group of order n is a subgroup of the automorphism group of G. Jockusch (Perfect matchings and perfect squares, J. Combin. Theory Ser. A, 67(1994), 100-115) and Kuperberg (An exploration of the permanent-deter...

A fixed 2-dimensional projection of a 3-dimensional Brownian motion is almost surely neighborhood recurrent; is this simultaneously true of all the 2-dimensional projections with probability one? Equivalently: 3-dimensional Brownian motion hits any infinite cylinder with probability one; does it hit all cylinders? This papers shows that the answer is no. Brownian motion in three dimensions avoi...

Hollow circular cylinders of single crystal copper are subjected to externally applied explosive loads that cause the collapse of the cylinder. Then numerical simulations are performed to understand the deformation process that leads to localized deformation and tensile cracking, observed in partially collapsed cylinders of fcc single crystals. The results of experiments and numerical simulatio...