We show improved approximation guarantees for the traveling salesman problem on cubic graphs, and cubic bipartite graphs. For cubic bipartite graphs with n nodes, we improve on recent results of Karp and Ravi (2014) by giving a simple “local improvement” algorithm that finds a tour of length at most 5/4n − 2. For 2-connected cubic graphs, we show that the techniques of Mömke and Svensson (2011)...

We define and study a family of cubic surfaces in the projectivized tangent bundle over a four dimensional projective space associated to the root system D 5. The 27 lines are rational over the base and we determine the classifying map to the moduli space of marked cubic surfaces. This map has degree two and we use it to get short proofs for some results on the Chow group of the moduli space of...

Stearic acid (SA) is highly soluble in structurally diverse solvents. SA/solvent packing within a (24.8 A)3 cubic volume explains the stoichiometry of SA solubility at multiple temperatures in multiple solvents. In the absence of solvent, the cubic volume contains 25 molecules at van der Waals distances from each other. At 55 degrees C, SA occupied half the cubic volume in saturated solution of...