Irreducible Specht modules are signed Young modules

Recently Donkin defined signed Young modules as a simultaneous generalization of Young and twisted Young modules for the symmetric group. We show that in odd characteristic, if a Specht module $S^\lambda$ is irreducible, then $S^\lambda$ is a signed Young module. Thus the set of irreducible Specht modules coincides with the set of irreducible signed Young modules. This provides evidence for our conjecture that the signed Young modules are precisely the class of indecomposable self-dual modules with Specht filtrations. The theorem is false in characteristic two.Comment: to appear Journal of Algebr

Crossover Behavior in Burst Avalanches of Fiber Bundles: Signature of Imminent Failure

Bundles of many fibers, with statistically distributed thresholds for breakdown of individual fibers and where the load carried by a bursting fiber is equally distributed among the surviving members, are considered. During the breakdown process, avalanches consisting of simultaneous rupture of several fibers occur, with a distribution D(Delta) of the magnitude Delta of such avalanches. We show that there is, for certain threshold distributions, a crossover behavior of D(Delta) between two power laws D(Delta) proportional to Delta^(-xi), with xi=3/2 or xi=5/2. The latter is known to be the generic behavior, and we give the condition for which the D(Delta) proportional to Delta^(-3/2) behavior is seen. This crossover is a signal of imminent catastrophic failure in the fiber bundle. We find the same crossover behavior in the fuse model.Comment: 4 pages, 4 figure

Evidence for Superfluidity in a Resonantly Interacting Fermi Gas

We observe collective oscillations of a trapped, degenerate Fermi gas of $^6$Li atoms at a magnetic field just above a Feshbach resonance, where the two-body physics does not support a bound state. The gas exhibits a radial breathing mode at a frequency of 2837(05) Hz, in excellent agreement with the frequency of $\nu_H\equiv\sqrt{10\nu_x\nu_y/3}=2830(20)$ Hz predicted for a {\em hydrodynamic} Fermi gas with unitarity limited interactions. The measured damping times and frequencies are inconsistent with predictions for both the collisionless mean field regime and for collisional hydrodynamics. These observations provide the first evidence for superfluid hydrodynamics in a resonantly interacting Fermi gas.Comment: 5 pages, ReVTeX4, 2 eps figs. Resubmitted to PRL in response to referees' comments. Title and abstract changed. Corrected error in Table 1, atom numbers for 0.33 TF and 0.5 TF data were interchanged. Corrected typo in ref 3. Added new figure of damping time versus temperatur

The Influence of Setting on Supreme Court Religious Expression Decisions

The First Amendment prohibits any establishment of religion, a dicta that has been applied in an apparently inconsistent manner by the Supreme Court when called upon to evaluate various forms of verbal and nonverbal religious communication. Court decisions have approved religious prayers and displays in government settings. When such exercises and displays were introduced to the public school academic setting, the Court chose to disallow the practice. An examination of judicial opinions reveals that justices recognize three factors inherent to the academic setting which justify the apparently contradictory decisions. Because of the captive nature of the audience, the presence of peer pressure, and the unpredictability of pedagogical influences, the Supreme Court has significantly restricted religious communication in K-12 public schools