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.

We introduce a notion of tangential Alexander polynomials for plane curves and study the relation with θ-Alexander polynomial. As an application, we use these polynomials to study a non-reduced degeneration Ct, → D0 + jL. We show that there exists a certain surjectivity of the fundamental groups and divisibility among their Alexander polynomials.

WINTER 2015 87 The Internet has been strongly gaining prominence as a news medium; in 2012, it overtook the TV as the most used news source for people under 30 in the United States (Kohut 2013). In addition, it has significantly changed the way in which many people find and consume news. Multiple publishers are now reachable more easily than ever before. Social bookmarking sites present us with...

We show that for the Kauffman bracket skein module over the field of rational functions in variable A, the module of a connected sum of 3-manifolds is the tensor product of modules of the individual manifolds.

We determine all Riemannian manifolds for which the tangent sphere bundles, equipped with the Sasaki metric, are local or global Riemannian product manifolds.

The extended Alexander group of an oriented virtual link l of d components is defined. From its abelianization a sequence of polynomial invariants ∆i(u1, . . . , ud, v), i = 0, 1, . . . , is obtained. When l is a classical link, ∆i reduces to the well-known ith Alexander polynomial of the link in the d variables u1v, . . . , udv; in particular, ∆0 vanishes.

Let S be a proper partial geometry pg(s, t, 2), and let G be an abelian group of automorphisms of S acting regularly on the points of S. Then either t ≡ 2 (mod s+1) or S is a pg(5, 5, 2) isomorphic to the partial geometry of van Lint and Schrijver [11]. This result is a new step towards the classification of partial geometries with an abelian Singer group and further provides an interesting cha...