General Conditions for Lepton Flavour Violation at Tree- and 1-Loop Level

In this work, we compile the necessary and sufficient conditions a theory has to fulfill in order to ensure general lepton flavour conservation, in the spirit of the Glashow-Weinberg criteria for the absence of flavour-changing neutral currents. At tree-level, interactions involving electrically neutral and doubly charged bosons are investigated. We also investigate flavour changes at 1-loop level. In all cases we find that the essential theoretical requirements can be reduced to a few basic conditions on the particle content and the coupling matrices. For 1-loop diagrams, we also investigate how exactly a GIM-suppression can occur that will strongly reduce the rates of lepton flavour violating effects even if they are in principle present in a certain theory. In all chapters, we apply our criteria to several models which can in general induce lepton flavour violation, e.g. LR-symmetric models or the MSSM. In the end we give a summarizing table of the obtained results, thereby demonstrating the applicability of our criteria to a large class of models beyond the Standard Model.Comment: 31 pages, 2 figure

Mathematical programs with equilibrium constraints: automatic reformulation and solution via constrained optimization

Constrained optimization has been extensively used to solve many large scale deterministic problems arising in economics, including, for example, square systems of equations and nonlinear programs. A separate set of models have been generated more recently, using complementarity to model various phenomenon, particularly in general equilibria. The unifying framework of mathematical programs with equilibrium constraints (MPEC) has been postulated for problems that combine facets of optimization and complementarity. This paper briefly reviews some methods available to solve these problems and described a new suite of tools for working with MPEC models. Computational results demonstrating the potential of this tool are given that automatically construct and solve a variety of different nonlinear programming reformulations of MPEC problems.\ud \ud This material is based on research partially supported by the National Science Foundation Grant CCR-9972372, the Air Force Office of Scientific Research Grant F49620-01-1-0040, Microsoft Corporation and the Guggenheim Foundation

Non-principal ultrafilters, program extraction and higher order reverse mathematics

We investigate the strength of the existence of a non-principal ultrafilter over fragments of higher order arithmetic. Let U be the statement that a non-principal ultrafilter exists and let ACA_0^{\omega} be the higher order extension of ACA_0. We show that ACA_0^{\omega}+U is \Pi^1_2-conservative over ACA_0^{\omega} and thus that ACA_0^{\omega}+\U is conservative over PA. Moreover, we provide a program extraction method and show that from a proof of a strictly \Pi^1_2 statement \forall f \exists g A(f,g) in ACA_0^{\omega}+U a realizing term in G\"odel's system T can be extracted. This means that one can extract a term t, such that A(f,t(f))

TEXAS FIELD CROPS: ESTIMATION WITH CURVATURE

Some implications of theory are easily maintained in econometric estimation, but computational costs of maintaining curvature properties (sufficient for existence of an optimal solution) have often proved prohibitive. They also have been violated frequently by unrestricted econometric estimates. A computationally manageable procedure for maintaining and testing curvature is used here to obtain estimates of product supplies and input demands for Texas field crops consistent with the theory of the competitive industry. The curvature properties are tested along with several technology restrictions.Crop Production/Industries,

Topological phase states of the SU(3) QCD

We consider the topologically nontrivial phase states and the corresponding topological defects in the SU(3) d-dimensional quantum chromodynamics (QCD). The homotopy groups for topological classes of such defects are calculated explicitly. We have shown that the three nontrivial groups are pi_3 SU(3)=Z, pi_5 SU(3)=Z, and pi_6 SU(3)=Z_6 if 3 < d < 6. The latter result means that we are dealing exactly with six topologically different phase states. The topological invariants for d=3,5,6 are described in detail.Comment: LATEX2e, 5 page