Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations

In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given.Comment: 27 page

Effect of period of lactation on milk and quality of butter.

During the month of January, 1897, we completed our third experiment with milk from strippers and fresh cows, for butter making. The test for fresh cows’ milk was taken from four that had been milked for a period of sixty-two days from calving. The strippers, seven in number, had been bred for a period of six and a half months, on an average. Special precautions were taken that the milk in no way could become mixed, as one of our men went night and morning to the barns to see the cows milked, and the milk put in its proper place after it was thoroughly aerated. It was then taken to the creamery and kept until it was separated. Both lots of cows were fed on the following rations: To each cow were given daily: Sheaf oats, 8 pounds; clover hay, 6 pounds; corn, 6 pounds; barley meal, 3 pounds; and sugar butts, 5 pounds

Comparative study of radio pulses from simulated hadron-, electron-, and neutrino-initiated showers in ice in the GeV-PeV range

High energy particle showers produce coherent Cherenkov radio emission in dense, radio-transparent media such as cold ice. Using PYTHIA and GEANT simulation tools, we make a comparative study among electromagnetic (EM) and hadronic showers initiated by single particles and neutrino showers initiated by multiple particles produced at the neutrino-nucleon event vertex. We include all the physics processes and do a complete 3-D simulation up to 100 TeV for all showers and to 1 PeV for electron and neutrino induced showers. We calculate the radio pulses for energies between 100 GeV and 1 PeV and find hadron showers, and consequently neutrino showers, are not as efficient below 1 PeV at producing radio pulses as the electromagnetic showers. The agreement improves as energy increases, however, and by a PeV and above the difference disappears. By looking at the 3-D structure of the showers in time, we show that the hadronic showers are not as compact as the EM showers and hence the radiation is not as coherent as EM shower emission at the same frequency. We show that the ratio of emitted pulse strength to shower tracklength is a function only of a single, coherence parameter, independent of species and energy of initiating particle.Comment: a few comments added, to bo published in PRD Nov. issue, 10 pages, 3 figures in tex file, 3 jpg figures in separate files, and 1 tabl

Direct imaging of a digital-micromirror device for configurable microscopic optical potentials

Programable spatial light modulators (SLMs) have significantly advanced the configurable optical trapping of particles. Typically, these devices are utilized in the Fourier plane of an optical system, but direct imaging of an amplitude pattern can potentially result in increased simplicity and computational speed. Here we demonstrate high-resolution direct imaging of a digital micromirror device (DMD) at high numerical apertures (NA), which we apply to the optical trapping of a Bose-Einstein condensate (BEC). We utilise a (1200 x 1920) pixel DMD and commercially available 0.45 NA microscope objectives, finding that atoms confined in a hybrid optical/magnetic or all-optical potential can be patterned using repulsive blue-detuned (532 nm) light with 630(10) nm full-width at half-maximum (FWHM) resolution, within 5% of the diffraction limit. The result is near arbitrary control of the density the BEC without the need for expensive custom optics. We also introduce the technique of time-averaged DMD potentials, demonstrating the ability to produce multiple grayscale levels with minimal heating of the atomic cloud, by utilising the high switching speed (20 kHz maximum) of the DMD. These techniques will enable the realization and control of diverse optical potentials for superfluid dynamics and atomtronics applications with quantum gases. The performance of this system in a direct imaging configuration has wider application for optical trapping at non-trivial NAs.Comment: 9 page

Spectroscopy of q3qˉ3\rm{q}^3\bar{\rm{q}}^3-States in Quark Model and Baryon-Antibaryon Enhancements

We study the mass spectrum of the $\rm{q}^3\bar{\rm{q}}^3$ mesons both from the quark model with triquark correlations and from common quark model with colormagnetic interactions and with relative S-waves between quarks. Two cluster configurations $(\rm{q}^3)-(\bar{\rm{q}}^3)$ and $(\rm{q}^2\bar{\rm{q}})-(\rm{q}\bar{\rm{q}}^2)$ are considered. In the spectrum we find rather stable states which have the same quantum number with particle resonances which are corresponding to the $p\bar{p}$ enhancement, $p\bar{\Lambda}$ enhancement and $\Lambda\bar{\Lambda}$ enhancement with spin-$\mathbf{0}$ or $\mathbf{1}$. This imply these enhancements are NOT experimental artifacts. The color-spin-flavor structures of $p\bar{p}$, $p\bar{\Lambda}$, and $\Lambda\bar{\Lambda}$ enhancements are revealed. The existence of spin-$\mathbf{1}$ $\Lambda\bar{\Lambda}, p\bar{\Lambda}, p\bar{p}$ enhancements is predicted.Comment: 45 pages, 5 figure

The Generation of Fullerenes

We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes -- fullgen -- and the first program since fullgen to be useful for more than 100 vertices. We also note a programming error in fullgen that caused problems for 136 or more vertices. We tabulate the numbers of fullerenes and IPR fullerenes up to 400 vertices. We also check up to 316 vertices a conjecture of Barnette that cubic planar graphs with maximum face size 6 are hamiltonian and verify that the smallest counterexample to the spiral conjecture has 380 vertices.Comment: 21 pages; added a not

MERLIN observations of relativistic ejections from GRS 1915+105

We present high resolution MERLIN radio images of multiple relativistic ejections from GRS 1915+105 in 1997 October / November. The observations were made at a time of complex radio behaviour, corresponding to multiple optically-thin outbursts and several days of rapid radio flux oscillations. The radio imaging resolved four major ejection events from the system. As previously reported from earlier VLA observations of the source, we observe apparent superluminal motions resulting from intrinsically relativistic motions of the ejecta. However, our measured proper motions are significantly greater than those observed on larger angular scales with the VLA. Under the assumption of an intrinsically symmetric ejection, we can place an upper limit on the distance to GRS 1915+105 of 11.2 +/- 0.8 kpc. Solutions for the velocities unambiguously require a higher intrinsic speed by about 0.1c than that derived from the earlier VLA observations, whilst the angle to the line-of-sight is not found to be significantly different. At a distance of 11 kpc, we obtain solutions of v = 0.98 (-0.05,+0.02)c and theta = 66 +/- 2 degrees. The jet also appears to be curved on a scale which corresponds to a period of around 7 days. We observe significant evolution of the linear polarisation of the approaching component, with large rotations in position angle and a general decrease in fractional polarisation. The power input into the formation of the jet is very large, >10^38 erg/s at 11 kpc for a pair plasma. If the plasma contains a cold proton for each electron, then the mass outflow rate, >10^18 g/sec is comparable to inflow rates previously derived from X-ray spectral fits.Comment: 14 pages, 7 figures. Accepted for publication in MNRA

Life on ice, Antarctica and Mars

The study of the origin of life and the prospects for human exploration of Mars are two themes developed in a new 57-minute film, Life on Ice, Antarctica, and Mars, produced by the InnerSpace Foundation and WHRO Television for broadcast by the Public Broadcasting System (PBS). A brief explanation of the film and how it relates to the future human exploration of space is presented

Effects of weak anchoring on C1 and C2 chevron structures

We present a theoretical study of the effect of weak anchoring on the transition between C1 and C2 chevron structures in smectic C liquid crystals. We employ a continuum theory which allows for variable cone, azimuthal and layer tilt angles. Equilibrium profiles for the director cone and azimuthal angles in the C1 and C2 states are calculated from the standard Euler-Lagrange minimisation of the total energy of the system. By comparing the total energies of the C1 and C2 states we can determine the globally stable chevron profile and calculate the critical temperature for the C1-C2 transition, which depends on anchoring strength and pretilt angle variations