5 papers
A note on the quality of simultaneous Diophantine approximations obtained by the LLL algorithm
Machiel van Frankenhuijsen, Edward K. Voskanian
In 1982, A. K. Lenstra, H. W. Lenstra, and L. Lovász introduced the first polynomial-time method to factor a nonzero polynomial into irreducible factors. This…
Diffraction measures and patterns of the complex dimensions of self-similar fractal strings. I. The lattice case
Michel L. Lapidus, Machiel van Frankenhuijsen, Edward K. Voskanian
We give a generalization of Lagarias' formula for diffraction by ideal crystals, and we apply it to the lattice case, in preparation for addressing the problem of quasicrystals and…
The Fractal Dimension of Product Sets
Machiel van Frankenhuijsen, Clayton Moore Williams
Using ultraproduct techniques we define a nonstandard Minkowski dimension which exists for all bounded sets and which has the property that That…
Quasiperiodic patterns of the complex dimensions of nonlattice self-similar strings, via the LLL algorithm
Michel L. Lapidus, Machiel van Frankenhuijsen, Edward K. Voskanian
The Lattice String Approximation algorithm (or LSA algorithm) of M. L. Lapidus and M. van Frankenhuijsen is a procedure that approximates the complex dimensions of a nonlattice sel…
Minkowski Measurability and Exact Fractal Tube Formulas for p-Adic Self-Similar Strings
Michel L. Lapidus, Lu Hung, Machiel van Frankenhuijsen
The theory of p-adic fractal strings and their complex dimensions was developed by the first two authors in [17, 18, 19], particularly in the self-similar case, in parallel with it…