Habilitationsschrift--Bonn. / Bibliography: p. 81.

Thesis (Ph. D.)--University of North Texas, May, 2009. / Title from title page display. Includes bibliographical references.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2004. / Includes bibliographical references (p. 99-102).

A test case is a set of input data and expected output, designed to verify whether the system under test satisfies all requirements and works correctly. An effective test case reveals a fault when the actual output differs from the expected output (i.e., the test case fails). The effectiveness of test cases is estimated using quality metrics, such as code coverage, size, and historical fault detection. Prior studies have shown that previously failing test cases are highly likely to fail again in the next releases; therefore, they are ranked higher. However, in practice, a failing test case may not be exactly the same as a previously failed test case, but quite similar. In this thesis, I have defined a metric that estimates test case quality using its similarity to the previously failing test cases. Moreover, I have evaluated the effectiveness of the proposed test quality metric through detailed empirical study. / February 2016

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<p>Perfect codes and minimal distance of a code have great importance in the study of theoryof codes. The perfect codes are classified generally and in particular for the Lee metric.However, there are very few perfect codes in the Lee metric. The Lee metric hasnice properties because of its definition over the ring of integers residue modulo q. It isconjectured that there are no perfect codes in this metric for q > 3, where q is a primenumber.The minimal distance comes into play when it comes to detection and correction oferror patterns in a code. A few bounds on the number of codewords and minimal distanceof a code are discussed. Some examples for the codes are constructed and their minimaldistance is calculated. The bounds are illustrated with the help of the results obtained.</p>

In this paper we study properties of metric spaces. We consider the collection of all nonempty closed subsets, Cl(X), of a metric space (X,d) and topologies on C.(X) induced by d. In particular, we investigate the Hausdorff topology and the Wijsman topology. Necessary and sufficient conditions are given for when a particular pseudo-metric is a metric in the Wijsman topology. The metric properties of the two topologies are compared and contrasted to show which also hold in the respective topologies. We then look at the metric space R-n, and build two residual sets. One residual set is the collection of uncountable, closed subsets of R-n and the other residual set is the collection of closed subsets of R-n having n-dimensional Lebesgue measure zero. We conclude with the intersection of these two sets being a residual set representing the collection of uncountable, closed subsets of R-n having n-dimensional Lebesgue measure zero.

<p>This thesis is about complex convexity. We compare it with other notions of convexity such as ordinary convexity, linear convexity, hyperconvexity and pseudoconvexity. We also do detailed study about ℂ-convex Hartogs domains, which leads to a definition of ℂ-convex functions of class <i>C</i>¹. The study of Hartogs domains also leads to characterization theorem of bounded ℂ-convex domains with <i>C</i>¹ boundary that satisfies the interior ball condition. Both the method and the theorem is quite analogous with the known characterization of bounded ℂ-convex domains with <i>C</i>² boundary. We also show an exhaustion theorem for bounded ℂ-convex domains with <i>C</i>² boundary. This theorem is later applied, giving a generalization of a theorem of L. Lempert concerning the relation between the Carathéodory and Kobayashi metrics.</p>

This thesis is about complex convexity. We compare it with other notions of convexity such as ordinary convexity, linear convexity, hyperconvexity and pseudoconvexity. We also do detailed study about ℂ-convex Hartogs domains, which leads to a definition of ℂ-convex functions of class C1. The study of Hartogs domains also leads to characterization theorem of bounded ℂ-convex domains with C1 boundary that satisfies the interior ball condition. Both the method and the theorem is quite analogous with the known characterization of bounded ℂ-convex domains with C2 boundary. We also show an exhaustion theorem for bounded ℂ-convex domains with C2 boundary. This theorem is later applied, giving a generalization of a theorem of L. Lempert concerning the relation between the Carathéodory and Kobayashi metrics.