@article{EvansHyde2022,
  author    = {Evans, Myfanwy E. and Hyde, Stephen T.},
  title     = {Symmetric Tangling of Honeycomb Networks},
  series = {Symmetry},
  volume    = {14},
  journal   = {Symmetry},
  edition   = {9},
  publisher = {MDPI},
  address   = {Basel, Schweiz},
  issn      = {2073-8994},
  doi       = {10.3390/sym14091805},
  pages     = {1 -- 13},
  year      = {2022},
  abstract  = {Symmetric, elegantly entangled structures are a curious mathematical construction that has found their way into the heart of the chemistry lab and the toolbox of constructive geometry. Of particular interest are those structures—knots, links and weavings—which are composed locally of simple twisted strands and are globally symmetric. This paper considers the symmetric tangling of multiple 2-periodic honeycomb networks. We do this using a constructive methodology borrowing elements of graph theory, low-dimensional topology and geometry. The result is a wide-ranging enumeration of symmetric tangled honeycomb networks, providing a foundation for their exploration in both the chemistry lab and the geometers toolbox.},
  language  = {en}
}
@misc{EvansHyde2022,
  author    = {Evans, Myfanwy E. and Hyde, Stephen T.},
  title     = {Symmetric Tangling of Honeycomb Networks},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1282},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-57084},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-570842},
  pages     = {13},
  year      = {2022},
  abstract  = {Symmetric, elegantly entangled structures are a curious mathematical construction that has found their way into the heart of the chemistry lab and the toolbox of constructive geometry. Of particular interest are those structures—knots, links and weavings—which are composed locally of simple twisted strands and are globally symmetric. This paper considers the symmetric tangling of multiple 2-periodic honeycomb networks. We do this using a constructive methodology borrowing elements of graph theory, low-dimensional topology and geometry. The result is a wide-ranging enumeration of symmetric tangled honeycomb networks, providing a foundation for their exploration in both the chemistry lab and the geometers toolbox.},
  language  = {en}
}
@article{BeckusPinchover2020,
  author    = {Beckus, Siegfried and Pinchover, Yehuda},
  title     = {Shnol-type theorem for the Agmon ground state},
  series = {Journal of spectral theory},
  volume    = {10},
  journal   = {Journal of spectral theory},
  number    = {2},
  publisher = {EMS Publishing House},
  address   = {Z{\"u}rich},
  issn      = {1664-039X},
  doi       = {10.4171/JST/296},
  pages     = {355 -- 377},
  year      = {2020},
  abstract  = {LetH be a Schrodinger operator defined on a noncompact Riemannianmanifold Omega, and let W is an element of L-infinity (Omega; R). Suppose that the operator H + W is critical in Omega, and let phi be the corresponding Agmon ground state. We prove that if u is a generalized eigenfunction ofH satisfying vertical bar u vertical bar <= C-phi in Omega for some constant C > 0, then the corresponding eigenvalue is in the spectrum of H. The conclusion also holds true if for some K is an element of Omega the operator H admits a positive solution in (Omega) over bar = Omega \ K, and vertical bar u vertical bar <= C psi in (Omega) over bar for some constant C > 0, where psi is a positive solution of minimal growth in a neighborhood of infinity in Omega. Under natural assumptions, this result holds also in the context of infinite graphs, and Dirichlet forms.},
  language  = {en}
}
@article{BeckusEliaz2021,
  author    = {Beckus, Siegfried and Eliaz, Latif},
  title     = {Eigenfunctions growth of R-limits on graphs},
  series = {Journal of spectral theory / European Mathematical Society},
  volume    = {11},
  journal   = {Journal of spectral theory / European Mathematical Society},
  number    = {4},
  publisher = {EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut f{\"u}r Mathematik, Technische Universit{\"a}t},
  address   = {Berlin},
  issn      = {1664-039X},
  doi       = {10.4171/JST/389},
  pages     = {1895 -- 1933},
  year      = {2021},
  abstract  = {A characterization of the essential spectrum of Schrodinger operators on infinite graphs is derived involving the concept of R-limits. This concept, which was introduced previously for operators on N and Z(d) as "right-limits," captures the behaviour of the operator at infinity. For graphs with sub-exponential growth rate, we show that each point in sigma(ss)(H) corresponds to a bounded generalized eigenfunction of a corresponding R-limit of H. If, additionally, the graph is of uniform sub-exponential growth, also the converse inclusion holds.},
  language  = {en}
}