To fabricate quantum dot arrays with programmable periodicity, functionalized DNA origami nanotubes were developed. Selected DNA staple strands were biotin-labeled to form periodic binding sites for streptavidin-conjugated quantum dots. Successful formation of arrays with periods of 43 and 71 nm demonstrates precise, programmable, large-scale nanoparticle patterning; however, limitations in arr...

3-D nonlinear electrostatic plasma wave is periodic along its longitudinal direction. By strictly analyzing a universal equation set of charged particles system, we find that such a longitudinal periodicity has a severe constraint on the transverse shape of a 3-D electrostatic structure. Only few allowed transverse shapes could warrant the longitudinal periodicity. This longitudinal periodicity...

We show the deep connection between two apparently unrelated topics in automata theory and combinatorics on words: the equivalence problem of nite automata and the Fine and Wilf's periodicity theorem. In fact they both refer to the problem of checking whether two congruences agree on a nite set. This also allows us to introduce a notion of periodicity for labelled trees and to derive a periodic...

Given a string x = x[1..n], a repetition of period p in x is a substring ur = x[i..i+rp−1], p = |u|, r ≥ 2, where neither u = x[i..i+p−1] nor x[i..i+(r+1)p−1] is a repetition. The maximum number of repetitions in any string x is well known to be Θ(n logn). A run or maximal periodicity of period p in x is a substring urt = x[i..i+rp+ |t|−1] of x, where ur is a repetition, t is a proper prefix of...

Given an object in a category, we study its orbit algebra with respect to an endofunctor. We show that if the object is periodic, then its orbit algebra modulo nilpotence is a polynomial ring in one variable. This specializes to a result on Ext-algebras of periodic modules over Gorenstein algebras. We also obtain a criterion for an algebra to be of wild representation

We construct periodic families of Poincaré spaces. This gives a partial solution to a question posed by Hodgson in the proceedings of the 1982 Northwestern homotopy theory conference. In producing these families, we formulate a recognition principle for Poincaré duality in the case of finite complexes having one top cell that splits of after a single suspension. We also explain how a Z-equivari...

In the 1980's, remarkable advances were made by Ravenel, Hopkins, Devinatz, and Smith toward a global understanding of stable homotopy theory, showing that some major features arise "chromatically" from an interplay of periodic phenomena arranged in a hierarchy (see [20], [21], [28]). We would like very much to achieve a similar understanding in unstable homotopy theory and shall describe some ...