A Classification of Minimal Sets of Torus Homeomorphisms

We provide a classification of minimal sets of homeomorphisms of the two-torus, in terms of the structure of their complement. We show that this structure is exactly one of the following types: (1) a disjoint union of topological disks, or (2) a disjoint union of essential annuli and topological disks, or (3) a disjoint union of one doubly essential component and bounded topological disks. Periodic bounded disks can only occur in type 3. This result provides a framework for more detailed investigations, and additional information on the torus homeomorphism allows to draw further conclusions. In the non-wandering case, the classification can be significantly strengthened and we obtain that a minimal set other than the whole torus is either a periodic orbit, or the orbit of a periodic circloid, or the extension of a Cantor set. Further special cases are given by torus homeomorphisms homotopic to an Anosov, in which types 1 and 2 cannot occur, and the same holds for homeomorphisms homotopic to the identity with a rotation set which has non-empty interior. If a non-wandering torus homeomorphism has a unique and totally irrational rotation vector, then any minimal set other than the whole torus has to be the extension of a Cantor set.Comment: Published in Mathematische Zeitschrift, June 2013, Volume 274, Issue 1-2, pp 405-42

Thermodynamic study of interactions between ZnO and ZnO binding peptides using isothermal titration calorimetry

Whilst material specific peptide binding sequences have been identified using a combination of combinato-rial methods and computational modelling tools, a deep molecular level understanding of the fundamental principles through which these interactions occur and in some instances modify the morphology of inorganic materials is far from being fully realized. Understanding the thermodynamic changes that occur during peptide-inorganic interactions and correlating these to structural modifications of the inorganic materials could be the key to achieving and mastering con-trol over material formation processes. This study is a detailed investigation applying isothermal titration calorimetry (ITC) to directly probe thermodynamic changes that occur during interaction of ZnO binding peptides (ZnO-BPs) and ZnO. The ZnO-BPs used are reported sequences G-12 (GLHVMHKVAPPR), GT-16 (GLHVMHKVAPPR-GGGC) and alanine mutants of G-12 (G-12A6, G-12A11 and G-12A12) whose interaction with ZnO during solution synthesis studies have been extensively investigated. The interactions of the ZnO-BPs with ZnO yielded biphasic isotherms comprising both an endo-thermic and an exothermic event. Qualitative differences were observed in the isothermal profiles of the different pep-tides and ZnO particles studied. Measured ΔG values were between -6 and -8.5 kcal/mol and high adsorption affinity val-ues indicated the occurrence of favourable ZnO-BP-ZnO interactions. ITC has great potential in its use to understand peptide-inorganic interactions and with continued development, the knowledge gained may be instrumental for simplifi-cation of selection processes of organic molecules for the advancement of material synthesis and design

Analytic topology

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