We find new facet-defining inequalities for the linear ordering polytope generalizing the well-known Möbius ladder inequalities. Our starting point is to observe that the natural derivation of the Möbius ladder inequalities as {0, 1 2 }-cuts produces triangulations of the Möbius band and of the corresponding (closed) surface, the projective plane. In that sense, Möbius ladder inequalities have ...

We study steady states of Stefan-type problems in the plane with the Gibbs-Thomson correction involving general anisotropic energy density function. By a local analysis we prove the global result showing that the solution is the Wulff shape. The key element is a stability result which enables us to approximate singular models by regulars ones. keywords: Stefan-type problems, singular interfacia...

spear-like martensite thermally formed in the same alloy in several respects such as in shape, lattice invariant shear, habit plane and orientation relationship, even though both have the same crystal structure and lattice parameters. The lattice invariant strain of the martensite was found to be stacking faults on the basal plane, and a defectless region was observed at the middle of the marte...

We use intermediate symplectic characters to give a proof and variations of Hopkins' conjecture, now proved by Hopkins Lai, on the number shifted plane partitions double staircase shape with bounded entries. In fact, we prove some character identities involving characters, find generating functions for such partitions. The key ingredients are bialternant formula which interpolates between those...