Thesis (Ph. D.)--University of Virginia. / "Private edition, distributed by the University of Virginia Library, University, Virginia.

Thesis (Ph. D.)--John Hopkins University. / Reprinted from the Transactions of the American mathematical society, v. 6, no. 4, October, 1905. Biography.

Thesis--Universität Bern, 1904.

Thesis (Ph. D.)--John Hopkins University. / Reprinted from the Transactions of the American mathematical society, v. 6, no. 4, October, 1905. Biography.

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An (n, k) configuration is a set of n “points” and n “lines” such that each point lies on k lines and each line contains k points. Motivated by the geometric definition of a group law on non-singular cubic curves, we define the concept of group embeddability of (n, k) configuration C as a mapping g of C into an abelian group G such that a set of k points {P1 , P2 , ..., Pk } are collinear in the configuration C if and only if ∑ g (Pi ) = 0 in the group G. Here we classify the set of all (n, 3) configurations for n ≤ 11 as well as some other notable configurations which can be embedded into abelian groups. Here we use the notation introduced by Branko Grünbaum [2]. The following theorems are proved in this thesis: n (n, 3) 7 Fano Plane 8 (8, 3) group Z2 × Z2 × Z2 Z3 × Z3 9 Of the three configurations, two are embeddable in groups. 10 Of the 10 configurations, five are embeddable in groups. 11 Of the 31 configurations, 9 have group embeddings. But for the first three examples (n = 7, 8 and the Pappus configuration), all other embeddability theorems proved here are new. In doing so we develop several different techniques for finding a group embedding or proving that no such embedding exists. Some ideas in this thesis were inspired by the late Professor N. S. Mendelsohn. For example, group embeddings can be thought of as extensions of configurations to Mendelsohn Triple Systems (see [8], [10]). In fact, configurations naturally give rise to partial quasigroups and adding the “missing triples” including the so-called "tangential relations" are the essential ideas behind the Mendelsohn triple Systems [8].

An (n, k) configuration is a set of n “points” and n “lines” such that each point lies on k lines and each line contains k points. Motivated by the geometric definition of a group law on non-singular cubic curves, we define the concept of group embeddability of (n, k) configuration C as a mapping g of C into an abelian group G such that a set of k points {P1 , P2 , ..., Pk } are collinear in the configuration C if and only if ∑ g (Pi ) = 0 in the group G. Here we classify the set of all (n, 3) configurations for n ≤ 11 as well as some other notable configurations which can be embedded into abelian groups. Here we use the notation introduced by Branko Grünbaum [2]. The following theorems are proved in this thesis: n (n, 3) 7 Fano Plane 8 (8, 3) group Z2 × Z2 × Z2 Z3 × Z3 9 Of the three configurations, two are embeddable in groups. 10 Of the 10 configurations, five are embeddable in groups. 11 Of the 31 configurations, 9 have group embeddings. But for the first three examples (n = 7, 8 and the Pappus configuration), all other embeddability theorems proved here are new. In doing so we develop several different techniques for finding a group embedding or proving that no such embedding exists. Some ideas in this thesis were inspired by the late Professor N. S. Mendelsohn. For example, group embeddings can be thought of as extensions of configurations to Mendelsohn Triple Systems (see [8], [10]). In fact, configurations naturally give rise to partial quasigroups and adding the “missing triples” including the so-called "tangential relations" are the essential ideas behind the Mendelsohn triple Systems [8].

A wide range of libraries are available for a developer to choose from when building a software system, but once the library is chosen, the developer must determine which version of the library to use. Is there some characteristic that can identify the correct version of a library to use? Even if a library compiles correctly, there could be a better version of that library that will provide superior performance. In particular, the developer would prefer to avoid poor con figurations: that is sets of libraries that perform poorly, or not at all. This paper describes a methodology by which the sub-performing version of a library can be identifi ed from the behavior observed from diff erent con figuration of libraries. These are measured by time, static and dynamic analysis of the results of executing the test suite in a project. During the course of these runs, different configurations of the libraries are substituted in and the results collected to be analyzed. The results of this analysis shows that there is no quick way to identify a sub performing library. However this library can be determined through concentrated eff orts to collect and analyze time-based data.

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (leaves 87-88).

A wide range of libraries are available for a developer to choose from when building a software system, but once the library is chosen, the developer must determine which version of the library to use. Is there some characteristic that can identify the correct version of a library to use? Even if a library compiles correctly, there could be a better version of that library that will provide superior performance. In particular, the developer would prefer to avoid poor con figurations: that is sets of libraries that perform poorly, or not at all. This paper describes a methodology by which the sub-performing version of a library can be identifi ed from the behavior observed from diff erent con figuration of libraries. These are measured by time, static and dynamic analysis of the results of executing the test suite in a project. During the course of these runs, different configurations of the libraries are substituted in and the results collected to be analyzed. The results of this analysis shows that there is no quick way to identify a sub performing library. However this library can be determined through concentrated eff orts to collect and analyze time-based data.