Hyperk\"ahler Arnold Conjecture and its Generalizations

We generalize and refine the hyperk\"ahler Arnold conjecture, which was originally established, in the non-degenerate case, for three-dimensional time by Hohloch, Noetzel and Salamon by means of hyperk\"ahler Floer theory. In particular, we prove the conjecture in the case where the time manifold is a multidimensional torus and also establish the degenerate version of the conjecture. Our method relies on Morse theory for generating functions and a finite-dimensional reduction along the lines of the Conley-Zehnder proof of the Arnold conjecture for the torus.Comment: 13 page

Collective Chord Behavior in Large Flexible Diaphragms

The seismic behavior of large low-rise buildings with rigid walls and flexible diaphragms will be dominated more by the diaphragm’s seismic response than by the very stiff vertical walls. For practitioners, estimating the stiffness of large flexible diaphragms is important for computing building setbacks from property lines and adjacent structures as well as evaluating structural integrity under seismic loads. In addition, researchers attempting to accurately model a building’s dynamic behavior need to assemble an accurate diaphragm stiffness prediction. The traditional diaphragm chord model consists of a single continuous line of axial resistance at the diaphragm boundaries; however, as this paper will demonstrate a collective series of structural members distributed across the diaphragm will function intentionally or unintentionally as a collective chord, adding significant flexural stiffness and reducing chord forces. In seismically active areas, masonry and concrete wall anchorage forces utilize code-mandated continuous cross-ties within the diaphragm, and often these cross-ties are sufficiently strong and stiff to unintentionally develop collective chord behavior whether in steel or in wood diaphragm systems. While neglecting this embedded collective chord behavior results in conservative chord and diaphragm drift designs, researchers or practitioners trying to predict seismic response of these buildings will potentially underestimate the true seismic response

Number of Spin II States of Identical Particles

In this paper we study the enumeration of number (denoted as ${D_I}$) of spin $I$ states for fermions in a single-$j$ shell and bosons with spin $l$. We show that $D_I$ can be enumerated by the reduction from SU$(n+1)$ to SO(3). New regularities of $D_I$ are discerned.Comment: 3 pages, no figures. to be publishe

Activities of \gamma-ray emitting isotopes in rainwater from Greater Sudbury, Canada following the Fukushima incident

We report the activity measured in rainwater samples collected in the Greater Sudbury area of eastern Canada on 3, 16, 20, and 26 April 2011. The samples were gamma-ray counted in a germanium detector and the isotopes 131I and 137Cs, produced by the fission of 235U, and 134Cs, produced by neutron capture on 133Cs, were observed at elevated levels compared to a reference sample of ice-water. These elevated activities are ascribed to the accident at the Fukushima Dai-ichi nuclear reactor complex in Japan that followed the 11 March earthquake and tsunami. The activity levels observed at no time presented health concerns.Comment: 4 pages, 8 figure

Extending the Ehresmann-Schein-Nambooripad Theorem

We extend the `join-premorphisms' part of the Ehresmann-Schein-Nambooripad Theorem to the case of two-sided restriction semigroups and inductive categories, following on from a result of Lawson (1991) for the `morphisms' part. However, it is so-called `meet-premorphisms' which have proved useful in recent years in the study of partial actions. We therefore obtain an Ehresmann-Schein-Nambooripad-type theorem for meet-premorphisms in the case of two-sided restriction semigroups and inductive categories. As a corollary, we obtain such a theorem in the inverse case.Comment: 23 pages; final section on Szendrei expansions removed; further reordering of materia

LOCAL VARIABILITY IN THE ORBIT OF SATURN'S F RING

This work was supported by the Science and Technology Facilities Council (grant number ST/F007566/1)

Companion problems in quasispin and isospin

We note that the same mathematical results apply to problems involving quasispin and isospin, but the problems per se are different. In the quasispin case, one deals with a system of identical fermions (e.g. neutrons) and address the problem of how many seniority conserving interactions there are. In the isospin case, one deals with a system of both neutrons and protons and the problem in question is the number of neutron-proton pairs with a given total angular momentum. Other companion problems are also discussed.Comment: 12 pages, Latex; some additions in section II and a brief summary at the en