The existence of universal unfoldings of certain germs of meromorphic connections is established. This is used to prove a general construction theorem for Frobenius manifolds. It includes semisimple Frobenius manifolds as a particular case. Another special case starts with variations of Hodge structures. This case is used to compare two constructions of Frobenius manifolds, the one in singulari...

We introduce the operation of forming the tensor product in the theory of analytic Frobenius manifolds. Building on the results for formal Frobenius manifolds which we extend to the additional structures of Euler fields and flat identities, we prove that the tensor product of pointed germs of Frobenius manifolds exists. Furthermore, we define the notion of a tensor product diagram of Frobenius ...

One of the most important reactions of the URCA that lead to the cooling of a neutron star, is neutron beta-decay ( ). In this research, the energy spectra and wave functions of massive fermions taking into account the Anomalous Magnetic Moment (AMM) in the presence of a strong changed magnetic field are calculated. For this purpose, the Dirac-Pauli equation for charged and neutral fermions is ...

Interrelated inequalities involving doubly stochastic matrices are presented. For example, if B is an n by n doubly stochasti c matrix, x any nonnega tive vector and y = Bx, the n XIX,· •• ,x" :0:::; YIY" •• y ... Also, if A is an n by n nonnegotive matrix and D and E are positive diagonal matrices such that B = DAE is doubly s tochasti c, the n det DE ;:::: p(A) ... , where p (A) is the Perron...

We explore several variations of the notion of purity for the action of Frobenius on schemes defined over finite fields. In particular, we study how these notions are preserved under certain natural operations like quotients for principal bundles and also geometric quotients for reductive group actions. We then apply these results to study the cohomology of quiver moduli. We prove that a natura...

This dissertation provides an introduction to the ideas employed in topological quantum field theory. We illustrate how the field began by considering knot invariants of three-manifolds and demonstrating the consequences of defining such a theory axiomatically. The ideas of category theory are introduced and we show that what we are actually concerned with are symmetric monoidal functors from t...