Every two-bridge knot or link is characterized by a rational number p/q, and has a fundamental group which has a simple presentation with only two generators and one relator. The relator has a form that gives rise to a formula for the Alexander polynomial of the knot or link in terms of p and q [15]. Every two-bridge knot or link also has a corresponding “up down” graph in terms of p and q. This graph is analyzed combinatorially to prove several properties of the Alexander polynomial. The number of two-bridge knots and links of a given crossing number are also counted.

Frankfurt (Main), Universiẗat, Diss., 2007.

&quot;Alexander von Humboldt im Netz&quot; ist ein Projekt des Instituts für Romanistik der Universität Potsdam, unter der wissenschaftlichen Leitung von Prof. Dr. Ottmar Ette.<br><br> Die Website verfolgt den Zweck<br><br> - die weltweiten Aktivitäten zu dem großen Forscher und Gelehrten vorzustellen und zu bündeln<br> - mehr Menschen mit dem Denken Alexander von Humboldts vertraut zu machen<br> - einen Überblick über verschiedene Institutionen, Veranstaltungen, Tagungen, Ausstellungen, Projekte, Bibliotheken und vieles mehr zu geben. / &quot;Alexander von Humboldt im Netz&quot; is a project of the Department of Romance Languages and Literature at Potsdam University under the scientific guidance of professor Ottmar Ette.<br><br> is expected to<br><br> - summarize the activities taking place worldwide on Alexander von Humboldt<br> - get a wider public acquainted with Alexander von Humboldts thought<br> - give an overview on different organizations, events, conferences, exhibitions, projects, libraries, and much more related to Alexander von Humboldt

The multivariable Alexander polynomial (MVA) is a classical invariant of knots and links. We give an extension to regular virtual knots which has simple versions of many of the relations known to hold for the classical invariant. By following the previous proofs that the MVA is of finite type we give a new definition for its weight system which can be computed as the determinant of a matrix created from local information. This is an improvement on previous definitions as it is directly computable (not defined recursively) and is computable in polynomial time. We also show that our extension to virtual knots is a finite type invariant of virtual knots. We further explore how the multivariable Alexander polynomial takes local information and packages it together to form a global knot invariant, which leads us to an extension to tangles. To define this invariant we use so-called circuit algebras, an extension of planar algebras which are the `right' setting to discuss virtual knots. Our tangle invariant is a circuit algebra morphism, and so behaves well under tangle operations and gives yet another definition for the Alexander polynomial. The MVA and the single variable Alexander polynomial are known to satisfy a number of relations, each of which has a proof relying on different approaches and techniques. Using our invariant we can give simple computational proofs of many of these relations, as well as an alternate proof that the MVA and our virtual extension are of finite type.

The multivariable Alexander polynomial (MVA) is a classical invariant of knots and links. We give an extension to regular virtual knots which has simple versions of many of the relations known to hold for the classical invariant. By following the previous proofs that the MVA is of finite type we give a new definition for its weight system which can be computed as the determinant of a matrix created from local information. This is an improvement on previous definitions as it is directly computable (not defined recursively) and is computable in polynomial time. We also show that our extension to virtual knots is a finite type invariant of virtual knots. We further explore how the multivariable Alexander polynomial takes local information and packages it together to form a global knot invariant, which leads us to an extension to tangles. To define this invariant we use so-called circuit algebras, an extension of planar algebras which are the `right' setting to discuss virtual knots. Our tangle invariant is a circuit algebra morphism, and so behaves well under tangle operations and gives yet another definition for the Alexander polynomial. The MVA and the single variable Alexander polynomial are known to satisfy a number of relations, each of which has a proof relying on different approaches and techniques. Using our invariant we can give simple computational proofs of many of these relations, as well as an alternate proof that the MVA and our virtual extension are of finite type.

The history of public health has suggested that the progress of societies cannot be understood without understanding community health conditions. The federal government of the United States established the Communicable Disease Center (CDC) in 1946 to assist the states in controlling outbreaks of infectious disease. This coincided with the early days of the Cold War. The concern of some health officials of the time, most notable among them was the CDC’s Chief of Epidemiology, Alexander D. Langmuir, was to address the 1950s threat of “germ warfare,” or bio-terrorism. To do this effectively the CDC established the Epidemic Intelligence Service (EIS) to train field epidemiologists as the first line of defense against biological attack. The role of the Chief EIS Officer was vital to its success. An examination of the Chiefs’ performance from 1951 through 2006 supports this contention.

Thesis (D. Min.)--Trinity International University, 2000. / Abstract. Includes bibliographical references (leaves 266-271).

Zugl.: Hannover, Hochsch. für Musik und Theater, Diss., 2009

Thesis (M.A.)--West Virginia University, 2002. / Title from document title page. Document formatted into pages; contains iii, 99 p. Includes abstract. Includes bibliographical references (p. 93-99).

Thesis (Ph. D.)--University of Chicago. / Includes bibliographical references. Also available on the Internet.