We describe the global dynamics of some pointwise periodic piecewise linear maps in plane that exhibit interesting dynamic features. For each these we find a first integral. integrals set values are discrete, thus quantized. Furthermore, level sets bounded whose interior is formed by finite number open tiles certain regular or uniform tessellations. The action on invariant described geometrical...

In [4] has been proved the bijectivity of a natural mapping Φ from words on a totally ordered alphabet onto multisets of primitive necklaces (circular words) on this alphabet. This mapping has many enumerative applications; among them, the fact that the number of permutations in a given conjugation class and with a given descent set is equal to the scalar product of two representations naturall...

We consider a model of static cosmic string loops in type IIB string theory, where the strings wrap cycles within the internal space. The strings are not topologically stabilised, however the presence of a lifting potential traps the windings giving rise to kinky cycloops. We find that PBH formation occurs at early times in a small window, whilst at late times we observe the formation of dark m...

This paper creates a simple Gray code for fixed-density binary necklaces and Lyndon words. The Gray code is simultaneously a left-shift Gray code and a 2-transposition Gray code and is cyclic with these properties. It also has the advantage of using canonical representations (lexicographically minimum rotations) yielding the first known Gray code for Lyndon words ordered by density. This work s...

Studying the problem of quasi-commuting quantum minors, Leclerc and Zelevinsky [3] introduced the notion of weakly separated sets in [n] := {1, . . . , n}. They raised conjectures on the purity, with respect to this weakly separation relation, of certain set-systems. In particular, a conjecture on the purity of the whole Boolean cube 2; equivalently: on the max-clique purity of the graph on 2 w...

It is well established that in a salt-free environment and under good or Θ-solvent conditions, the electrostatic interaction between the monomers of a single polyelectrolyte chain induces a rod-like conformation. In the pressence of of a small amount of salt, if the ions are homogeneously distributed such that their interaction with the chain is limited to screen the elctrostatic interactions, ...

Stories take hundreds of different forms and serve many functions. They can be as energetic as an entire life story or as simple as directions to a favorite beach. Technological developments challenge and change storytelling processes. The invention of writing changed the story from an orally recounted form, mediated by the storyteller, to a recorded version which was technologically reproducib...

We study Bose-Hubbard models in a family of diamond necklace lattices with $n$ central sites. The single-particle spectrum these presents compact localized states (CLSs) that occupy the up and down sites each diamond. By performing an appropriate basis rotation, fragmentation many-boson Hilbert space becomes apparent adjacency graph Hamiltonian, showing disconnected sub-sectors wide range dimen...

A (continuous) necklace is simply an interval of the real line colored measurably with some number of colors. A well-known application of the Borsuk-Ulam theorem asserts that every k-colored necklace can be fairly split by at most k cuts (from the resulting pieces one can form two collections, each capturing the same measure of every color). Here we prove that for every k ≥ 1 there is a measura...