Parasitic twins, a specific type of conjoined twins [6], occur when one twin ceases development during gestation [7] and becomes vestigial to the fully formed dominant twin, called the autositic twin. The underdeveloped twin is called parasitic because it is only partially formed, is not functional, or is wholly dependent on the autositic twin. In most cases, the phenotype of parasitic twins is...

Parasitic twins, a specific type of conjoined twins [6], occur when one twin ceases development during gestation [7] and becomes vestigial to the fully formed dominant twin, called the autositic twin. The underdeveloped twin is called parasitic because it is only partially formed, is not functional, or is wholly dependent on the autositic twin. In most cases, the phenotype of parasitic twins is...

Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of complex flag varieties are characterized by inequalities parameterized by similar non-vanishing products in the cohomology of “smaller” flag varieties. We consider the type A partial flag variety and find that its cohomology exhibits a Horn recursion on a certain deformation of the cup...

It is proven that up to possible surface terms, the only non-vanishing momentum-dependent amplitudes for the self-dual N=2 string in R 2,2 are the tree-level two and three-point functions, and the only non-vanishing momentum-independent amplitudes are the one-loop partition function and the tree-level two and four-point functions. The calculations are performed using the topological prescriptio...

Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of flag varieties G/P are characterized by inequalities parameterized by similar non-vanishing products in the cohomology of ”smaller” flag varieties. We consider the partial flag variety SLn/P and find that H (SLn/P ) exhibits Horn recursion on a certain deformation of the cup product. W...

We give conceptual proofs of some well known results concerning compact non-positively curved locally symmetric spaces. We discuss vanishing and non-vanishing of Pontrjagin numbers and Euler characteristics for these locally symmetric spaces. We also establish vanishing results for StiefelWhitney numbers of (finite covers of) the Gromov-Thurston examples of negatively curved manifolds. We menti...