Hamiltonian G-Spaces with Regular Momenta

Let G be a compact connected non-Abelian Lie group and let (P, w, G, J) be a Hamiltonian G-space. Call this space a G-space with regular momenta if J(P) ⊂ g*reg, here g*reg⊂g* denotes the regular points of the co-adjoint action of G. Here problems involving a G-space with regular momenta are reduced to problems in an associated lower dimensional Hamiltonian T-space, where T ⊂ G is a maximal torus. For example two such G-spaces are shown to be equivalent if and only if they have equivalent associated T-spaces. We also give a new construction of a normal form due to Marle (1983), for integrable G-spaces with regular momenta. We show that this construction, which is a kind of non-Abelian generalization of action-angle coordinates, can be reduced to constructing conventional action-angle coordinates in the associated T-space. In particular the normal form applies globally if the action-angle coordinates can be constructed globally. We illustrate our results in concrete examples from mechanics, including the rigid body. We also indicate applications to Hamiltonian perturbation theory

Pseudogroups via pseudoactions: Unifying local, global, and infinitesimal symmetry

A multiplicatively closed, horizontal foliation on a Lie groupoid may be viewed as a "pseudoaction" on the base manifold $M$. A pseudoaction generates a pseudogroup of transformations of $M$ in the same way an ordinary Lie group action generates a transformation group. Infinitesimalizing a pseudoaction, one obtains the action of a Lie algebra on $M$, possibly twisted. A global converse to Lie's third theorem proven here states that every twisted Lie algebra action is integrated by a pseudoaction. When the twisted Lie algebra action is complete it integrates to a twisted Lie group action, according to a generalization of Palais' global integrability theorem.Comment: 31 pages; minor revision

Gargoyles on Glatfelter Hall

When one walks around the campus of Gettysburg College, Glatfelter Hall towers above them, as one of the College’s most commanding edifices. One takes notice of the arched doorways, sunken windows, and the giant bell tower whose occupant chimes on the hour. What one may not notice are the eyes watching from the brownstone; faces and creatures at home in the stone, surveying your every move. Grotesques and gargoyles sit in the moldings, on the window sills and at the junction where roof and wall meet, hidden from the eye that does not have the compulsion to look. These architectural ornaments are not noticed outright because they tend to blend in with the stonework on the building. However, once you have seen them, you never cease to feel their eyes upon you. [excerpt] Course Information: Course Title: HIST 300: Historical Method Academic Term: Spring 2006 Course Instructor: Dr. Michael J. Birkner \u2772 Hidden in Plain Sight is a collection of student papers on objects that are hidden in plain sight around the Gettysburg College campus. Topics range from the Glatfelter Hall gargoyles to the statue of Eisenhower and from historical markers to athletic accomplishments. You can download the paper in pdf format and click View Photo to see the image in greater detail.https://cupola.gettysburg.edu/hiddenpapers/1001/thumbnail.jp

‘Dominant ethnicity’ and the ‘ethnic-civic’ dichotomy in the work of A. D. Smith

This article considers the way in which the work of Anthony Smith has helped to structure debates surrounding the role of ethnicity in present-day nations. Two major lines of enquiry are evident here. First, the contemporary role of dominant ethnic groups within 'their' nations and second, the interplay between ethnic and civic elements in nationalist argument. The two processes are related, but maintain elements of distinctiveness. Smith's major contribution to the dominant ethnicity debate has been to disembed ethnicity from the ideologically-charged and/or anglo-centric discourse of ethnic relations and to place it in historical context, thereby opening up space for dominant group ethnicity to be considered as a distinct phenomenon. This said, Smith's work does not adequately account for the vicissitudes of dominant ethnicity in the contemporary West. Building on the classical works of Hans Kohn and Friedrich Meinecke, Anthony Smith has also made a seminal contribution to the debate on civic and ethnic forms of national identity and nationalist ideology. As well as freeing this debate from the strong normative overtones which it has often carried, he has continued to insist that the terms civic and ethnic should be treated as an ideal-typical distinction rather than a scheme of classification

The influence of 6 weeks of maximal eccentric plantarflexor training on muscle-tendon mechanics

Resistance training can influence muscle-tendon properties including strength, flexibility, stretch tolerance and muscle-tendon stiffness; however the specific influence of eccentric-only training is unknown. Therefore, the aims of the present study were to examine the effects of a 6-week maximal eccentric resistance training programme on isometric plantarflexor moment (MVC), dorsiflexion range of motion (ROM), stretch tolerance (peak passive moment), muscle and tendon stiffness and running economy. Thirteen recreationally active men (age = 20.0 ± 0.9 yr, mass = 75.9 ± 8.5 kg, height = 1.8 ± 0.1 m) volunteered for the study after giving written informed consent; ethical approval was granted from the University of Northampton. Training was performed twice weekly for six weeks and consisted of 5 sets of 12 repetitions of 3-s maximal eccentric contractions at 10°•s-1 from 20° plantarflexion to 10° dorsiflexion. Maximal isometric plantarflexor moment, dorsiflexion ROM, stretch tolerance, and muscle, tendon and muscle-tendon unit (MTU) stiffness were measured using isokinetic dynamometry, real-time ultrasound and 3D motion analyses before and after the training. Running economy (VO2) was determined at a running speed equating to 70%VO2max using online gas analysis. Repeated measures t-tests were used to determine significant differences between pre- and post-training data, significance accepted at p0.05). Analysis of ultrasound data revealed a significant decrease in muscle stiffness (20.6%; p0.05). While the training-induced increase in plantarflexor strength was expected, the substantial increases in ROM, stretch tolerance and tendon stiffness, and the reduction in passive muscle stiffness, were important and novel findings. Interestingly, when measured during passive stretch, MTU stiffness remained unchanged while tendon stiffness increased and muscle stiffness decreased. These disparate findings have clear implications for testing methodologies, and indicate that imaging techniques must be utilised in order to examine the effects of interventions on specific tissues. As the training clearly enhanced the capacity of the muscle to tolerate both tissue loading and deformation, which are commonly associated with muscle strain injury, these data have clear implications for both muscular performance and injury risk