A universal solution

The phenomenon of an implicit function which solves a large set of second order partial differential equations obtainable from a variational principle is explicated by the introduction of a class of universal solutions to the equations derivable from an arbitrary Lagrangian which is homogeneous of weight one in the field derivatives. This result is extended to many fields. The imposition of Lorentz invariance makes such Lagrangians unique, and equivalent to the Companion Lagrangians introduced in [baker].Comment: arxiv version is already officia

Character varieties of once-punctured torus bundles with tunnel number one

We determine the PSL_2(C) and SL_2(C) character varieties of the once-punctured torus bundles with tunnel number one, i.e. the once-punctured torus bundles that arise from filling one boundary component of the Whitehead link exterior. In particular, we determine `natural' models for these algebraic sets, identify them up to birational equivalence with smooth models, and compute the genera of the canonical components. This enables us to compare dilatations of the monodromies of these bundles with these genera. We also determine the minimal polynomials for the trace fields of these manifolds. Additionally we study the action of the symmetries of these manifolds upon their character varieties, identify the characters of their lens space fillings, and compute the twisted Alexander polynomials for their representations to SL_2(C).Comment: 49 pages, 6 figure

Confronting The Challenge Of Information Literacy

Confronting the challenges to any academic institution posed by the revolution in information resources since the appearance of the Internet can be a daunting task. Providing the financial and human resources required to provide reliable and secure access can alone be a major hurdle. The specialized equipment needed to effectively incorporate the new resources into student learning environments present an additional burden. The need to collaboratively manage the systems and adapt staffing patterns to the new resources can challenge the skills of the best administrators. The patterns of information seeking behavior exhibited by students in today\u27s richly diverse information environment can frustrate the assumptions that both faculty and librarian have long held about the research process. For those colleges who have made significant strides in addressing these challenges the last one may be the most important from a pedagogical perspective

A Rubric of Shared Leadership: “Revolutions are no trifles”

In a letter reflecting back on the heady times of revolt against the tyranny of England, John Adams makes the observation that “revolutions are no trifles.”1 Adams and other founders of the new republic knew full well the seriousness of declaring independence and setting out on a new course of governance for the colonies. While that is true on the macro level of geo-politics it is also true on the micro level of organizational culture. Embarking on a dramatic change in social structure, whether great or small, ought not to be taken lightly. Thorough planning and careful execution are important ingredients in successful revolutions. However, the essential ingredient is leadership that is passionate about the change

A note on the concordance of fibered knots

Either fibered knots supporting the tight contact structure are unique in their smooth concordance class or there exists a fibered counterexample to the Slice-Ribbon Conjecture.Comment: Accepted for publication by the Journal of Topolog