We derive the first and second variation formula for the Greens function poles value of Paneitz operator on the standard three sphere. In particular it is shown that the first variation vanishes and the second variation is nonpositively definite. Mor
eover, the second variation vanishes only at the direction of conformal deformation. We also introduce a new invariant of the Paneitz operator and illustrate its close relation with the second eigenvalue and Sobolev inequality of Paneitz operator.
We report the timing and spatial resolution from the Muon Telescope Detector (MTD) installed in the STAR experiment at RHIC. Cosmic ray muons traversing the STAR detector have an average transverse momentum of 6 GeV/c. Due to their very small multipl
e scattering, these cosmic muons provide an ideal tool to calibrate the detectors and measure their timing and spatial resolution. The values obtained were ~100 ps and ~1-2 cm, respectively. These values are comparable to those obtained from cosmic-ray bench tests and test beams.
Ultrafast nanocrystallography has the potential to revolutionize biology by enabling structural elucidation of proteins for which it is possible to grow crystals with 10 or fewer unit cells on the side. The success of nanocrystallography depends on r
obust orientation-determination procedures that allow us to average diffraction data from multiple nanocrystals to produce a three dimensional (3D) diffraction data volume with a high signal-to-noise ratio. Such a 3D diffraction volume can then be phased using standard crystallographic techniques. Indexing algorithms used in crystallography enable orientation determination of diffraction data from a single crystal when a relatively large number of reflections are recorded. Here we show that it is possible to obtain the exact lattice geometry from a smaller number of measurements than standard approaches using a basis pursuit solver.
