We construct an Alexander-type invariant for oriented doodles from a deformation of the Tits representation twin group and Chebyshev polynomials second kind. Like Alexander polynomial, our vanishes on unlinked with more than one component. also include values several doodles.

hellenism is a part of iran’s historical period. this era starts with the devastating onslaught of alexander, the macedonian warlord. our historical sources introduce alexander with a collection of mythic-historical features which make us visualize the real alexander with an ambiguous image. the conflicting viewpoints of eastern and western historical works in pre-islamic periods can be the rea...

What does it mean for a molecule to generate force? A good way to think about the force generated by a molecular machine is that force is one of the products of the cyclic, fuelconsuming chemical reaction. If the chemical reaction is favorable it will go forward even against a moderate load force. But if the force is too high, then it will inhibit the reaction, just like a high concentration of...

1 Department of Pediatrics and Adolescent Medicine, University Hospital Erlangen, Friedrich Alexander University ErlangenNuremberg, Erlangen, Germany, 2 Medical Clinic II, Waldkrankenhaus, Erlangen, Germany, 3 Medical Clinic III for Rheumatology and Immunology, University Hospital Erlangen, Friedrich Alexander University Erlangen-Nuremberg, Erlangen, Germany, 4 Institute of Pathology, Friedrich...

We develop a dimer model for the Alexander polynomial of a knot. This recovers Kauffman's state sum model for the Alexander polynomial using the language of dimers. By providing some additional structure we are able to extend this model to give a state sum formula for the twisted Alexander polynomial of a knot depending on a representation of the knot group.