Thesis (doctoral)--Eberhard-Karls-Universität in Tübingen, 1920.

The purpose of this paper is to define an integral for real-valued functions which are defined on a field of sets and to demonstrate several properties of such an integral.

We present a detailed method for proving shear-free perfect fluid theorems in General Relativity. This method uses the (1+3)-covariant formalism to establish the consistency of the Einstein gravitational field equations under the barotropic shear-free perfect fluid condition. Using a Mathematica package xTensor, we were able to prove the following cases: the case where the pressure is constant, the acceleration vector is parallel to the vorticity, the components of a rescaled acceleration vector field orthogonal to the vorticity are basic and the case where the dot product of the rescaled acceleration vector field and the unit vorticity vector is basic, leading to the existence of a Killing vector along the vorticity

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Several conjectured and proven generalizations of the Brouwer Fixed Point Theorem are examined, the plane fixed point problem in particular. The difficulties in proving this important conjecture are discussed. It is shown that it is true when strong additional assumptions are made. Canonical examples are produced which demonstrate the differences between this result and other generalized fixed point theorems.

Several conjectured and proven generalizations of the Brouwer Fixed Point Theorem are examined, the plane fixed point problem in particular. The difficulties in proving this important conjecture are discussed. It is shown that it is true when strong additional assumptions are made. Canonical examples are produced which demonstrate the differences between this result and other generalized fixed point theorems.

This document presents a systematic investigation of the geometric index theory of Dirac operators coupled superconnections. A local version of the index theorem for Dirac operators coupled to superconnection is proved, and extended to families. An [eta]-invariant is defined, and it is shown to satisfy an APS-like theorem. A geometric determinant line bundle with section, metric, and connection is associated to a family of Dirac operators coupled to superconnections, and its holonomy is calculated in terms of the [eta]-invariant. / text

M. Tech. Information Networks / This dissertation reports on the development of an algorithm based on e-commerce matchmaking to select students. The student selection is an important strategic decision making task for the management of higher educational institutions and human resource departments of corporate organizations. The selection task has proven to be tedious mainly because of the decision process, the fundamental assumptions made and the level of accuracy achieved. The decision error that results from inaccurate student selection process is one source of skill mismatch. This work therefore seeks to improve the student selection accuracy using matchmaking approach. In doing so, e-commerce matchmaking method is applied to student selection and offered as an effective way of integrating cognitive and noncognitive skills to improve the selection accuracy. The efficacy of the matchmaking algorithm is demonstrated through a prototype implementation of the algorithm and specifically applied to university student selection.

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