Mathematicians have long thought of symmetry in terms of actions of groups, but group actions have proven too restrictive in some cases to give an interesting picture of the symmetry of some mathematical objects, e.g. some noncommutative algebras. It is generally agreed that the right generalizations of group actions to solve this problem are actions of Hopf algebras, the study of which has exploded in the years since the publication of Sweedler's Hopf algebras in 1969. Different varieties of Hopf algebras have been useful in many fields of mathematics. For instance, in his "Quantum Groups" paper, Vladimir Drinfel'd introduced quasitriangular Hopf algebras, a class of Hopf algebras whose modules each provide a solution to the quantum Yang-Baxter equation. Solutions of this equation are a source of knot and link invariants and in physics, determine if a one-dimensional quantum system is integrable. Drinfel'd also introduced the Drinfel'd double construction, which produces for each finite-dimensional Hopf algebra a quasitriangular one in which the original embeds. This thesis is motivated by work of Susan Montgomery and Hans-Jürgen Schneider on actions of the Taft (Hopf) algebras T_n(q) and extending such actions to the Drinfel'd double D(T_n(q)). In 2001, Montgomery and Schneider classified all non-trivial actions of T_n(q) on an n-dimensional associative algebra A. It turns out that A must be isomorphic to the group algebra of grouplike elements kG(T_n(q)). They further determined that each such action extends uniquely to an action of the Drinfel'd double D(T_n(q)) on A, effectively showing that each action has a unique compatible coaction. We generalize Montgomery and Schneider's results to Hopf algebras related to the Taft algebras: the Sweedler (Hopf) algebra, bosonizations of 1-dimensional quantum linear spaces, generalized Taft algebras, and the Frobenius-Lusztig kernel u_q(sl_2). For each Hopf algebra H, we determine 1. whether there are non-trivial actions of H on A, 2. the possible H-actions on A, and 3. the possible D(H)-actions on A extending an H-action and how many there are. / Mathematics

abstract: Historians often characterize first ladies in the Progressive Era as representatives of the last vestiges of Victorian womanhood in an increasingly modern society. This dissertation argues that first ladies negotiated an image of themselves that fulfilled both traditional and modern notions of womanhood. In crafting these images, first ladies constructed images of their celebrity selves that were uniquely modern. Thus, images of first ladies in the Progressive Era show them as modest and feminine but also autonomous, intelligent, and capable. Using the historian Charles Ponce de Leon's research on modern human-interest journalism, I contend that first ladies in the Progressive Era worked with the modern press in a symbiotic relationship. This relationship allowed the press exclusive access to what was, ostensibly, the first lady's private, and therefore authentic, self. By purporting to reveal parts of their private lives in the press, first ladies showed themselves as down-to-earth despite their success and fulfilled by their domestic pursuits despite their compelling public lives. By offering the press exclusive access to their lives, first ladies secured the opportunity to shape specific images of themselves to appeal, as broadly as possible, to their husbands and parties' constituents and the American public. First ladies in the Progressive Era thus acted as political figures by using both public and private, or what historian Catherine Allgor terms, "unofficial spaces" to support and reflect their husbands and parties' political agendas. In examining representations of first ladies in popular magazines and newspapers from 1901 to 1921 in tandem with letters, memoirs, and other personal papers from these women, a clear pattern emerges. Despite personal differences, first ladies in the Progressive Era represented themselves according to a specific formula in the modern press. The images, constructed by first ladies in this time period, reflect shifts in economic, social, and political life in Progressive Era America, which called for women to be independent and intelligent yet still maintain their femininity and domesticity. / Dissertation/Thesis / Ph.D. History 2011

American Foreign Policy at the outset of the Twentieth century evolved from a realist to an idealist position as the United States transitioned to an imperial power. This ideal framework was formed in the crucible of China during the Spheres of Influence and the Open Door. The US had to play delicate game of helping China to maintain their territorial, and administrative integrity while at the same time protecting their newly acquired overseas interests against more established imperial actors. While there were many missteps, and failures during this transition perhaps the most the important result was the change toward the approach of US foreign policy. Not only did the United States have to balance realist geo-political goals, but it had to define what an imperial United States looked like. In a sense the United States was starting from scratch, processing to a completely different game and in order to be successful it had evolve.

A series of para-substituted acetophenones bearing a furanyl or a thiophenyl moiety show a large Stokes-shift, which is a function of various solvent properties. Photophysical properties such as emission lifetime of the compounds have been determined using time-correlated-single photon counting to secure the intrinsic fluorescence behaviour. The solvent dependent position of the UV/Vis emission band [small nu, Greek, tilde]max,em of the compounds has been measured in 26 various solvents. The influence of the solvent on [small nu, Greek, tilde]max,em is of very complex nature and mathematically analysed by multiple square linear solvation energy (LSE)-correlation analysis using Catalán's four-solvent parameter set. Solvent acidity has a strong influence on the bathochromic shift of 2,5-disubstituted furan derivatives compared to the non-5-substituted furan and thiophene derivatives, which show a contrary behaviour. Therefore, the 5-cyanofuranyl-substituted acetophenone derivative is useful as a probe for measuring environmental properties by fluorescence spectroscopy. / Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

A series of para-substituted acetophenones bearing a furanyl or a thiophenyl moiety show a large Stokes-shift, which is a function of various solvent properties. Photophysical properties such as emission lifetime of the compounds have been determined using time-correlated-single photon counting to secure the intrinsic fluorescence behaviour. The solvent dependent position of the UV/Vis emission band [small nu, Greek, tilde]max,em of the compounds has been measured in 26 various solvents. The influence of the solvent on [small nu, Greek, tilde]max,em is of very complex nature and mathematically analysed by multiple square linear solvation energy (LSE)-correlation analysis using Catalán's four-solvent parameter set. Solvent acidity has a strong influence on the bathochromic shift of 2,5-disubstituted furan derivatives compared to the non-5-substituted furan and thiophene derivatives, which show a contrary behaviour. Therefore, the 5-cyanofuranyl-substituted acetophenone derivative is useful as a probe for measuring environmental properties by fluorescence spectroscopy. / Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

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Bibliographische Beschreibung und Referat Mais, Silvio Synthese von N-Benzhydryl-anilinen und Untersuchungen zu Struktur- Eigenschafts-Zusammenhaengen hinsichtlich der Photoleitung in Polymermatrizen Technische Universitaet Chemnitz-Zwickau, Fakultaet fuer Naturwissenschaften, Dissertation, 1995, 134 Seiten Es erfolgen zum gegenwaertigen Kenntnisstand der Elektrophotographie kurze Abrisse bezueglich Wirkungsweise, Messprinzipien, Theorie der Photoleitfaehigkeit und Struktur-Eigenschafts-Zusammenhaengen. Synthesen von N-Benzhydryl-anilinen und substituierten N,N'-Dibenzhydryl-4,4'-diamino-biphenyle werden vorgestellt und diskutiert. Im Mittelpunkt steht die Substituentenvariation von Akzeptoren bis Donatoren. Vergleichende elektrophotographische Empfindlichkeitsmessungen dieser Verbindungen in polymeren Bindemittelschichten zeigen eine Abhaengigkeit der Photoleitung von der Substitution, welche sich mit den entsprechenden Hammett- Konstanten beschreiben laesst. NMR-Untersuchungen belegen die Abhaengigkeiten der chemischen Verschiebungen und Kopplungskonstanten bestimmter 1H-, 13C- und 15N-Kerne von der Substituentenvariation, welche sich ebenfalls mit grosser Korrelationsguete durch Hammett- oder Taft-Konstanten linear beschreiben lassen. Die elektrophotographische Empfindlichkeit der untersuchten Schichtsysteme laesst sich durch Farbstoffsensibilisierung und Erhoehung der Photoleiterkonzentration in praktisch interessierender Groessenordnungen steigern.

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This thesis discusses the history of the closed shop as a form of union security and the changes that arose with the passage of the Taft-Hartley Law in 1947 which declared the closed shop illegal and morally reprehensible.

In dieser Arbeit wird die Synthese neuartiger 5-monosubstituierter Barbituratfarbstoffe mit elektronenziehenden Substituenten in 5-Position beschrieben. Durch diese Funktionalisierung entstehen schaltbare Farbstoffe mit einer farblosen Ketoform und einer farbigen Enolform. Die Einflüsse verschieden stark elektronenziehender Substituenten sowie unterschiedlich großer konjugierter π-Systeme auf die Keto-Enol-Tautomerie wurden untersucht. Dies erfolgt einerseits mittels Röntgeneinkristallstrukturanalysen der Festkörper und andererseits mit solvatochromen Untersuchungen in Lösung. Durch die Keto-Enol-Tautomerie der Barbituratfarbstoffe wird die Wasserstoffbrücken¬bindungssequenz beim Übergang zwischen Keto- und Enol-Form verändert. Es wurde gezeigt, dass durch Zugabe von Rezeptoren mit komplementärer Wasserstoffbrückenbindungssequenz zur Enol-Form das tautomere Gleichgewicht der Barbitursäuren hin zur Enol-Form verschoben werden kann. Um hierzu verlässliche Aussagen zu erhalten wurden vergleichende Experimente mit N,N´-dialkylierten Barbituratfarbstoffen durchgeführt. Aufgrund der Synthesestrategie der Barbituratfarbstoffe, welche ausgehend von Barbituratanionen über nukleophile aromatische Substitutionsreaktionen hergestellt wurden, war es zweckmäßig die Nukleophilieparameter der Barbituratanionen zu ermitteln. Dazu wurde der Ansatz von Mayr gewählt und die Nukleophilie von vier Barbituratanionen bestimmt. Weiterhin konnte in dieser Arbeit die Charakterisierung von ionischen Flüssigkeiten nach der 4-Parameter-Gleichung von Catalán umgesetzt werden. Dabei gelang es erstmal für eine vielzahl verschiedener ionischer Flüssigkeiten die Polarisierbarkeit und Dipolarität getrennt voneinander mit Hilfe zweier solvatochromer Farbstoffe zu ermitteln.