A New Young Diagrammatic Method For Kronecker Products of O(n) and Sp(2m)

A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on representation theory of Brauer algebras. A general procedure for the decomposition of tensor products of representations for O(n) and Sp(2m) is outlined, which is similar to that for U(n) known as the Littlewood rules together with trace contractions from a Brauer algebra and some modification rules given by King.Comment: Latex, 11 pages, no figure

On several families of elliptic curves with arbitrary large Selmer groups

In this paper, we calculate the $\phi (\hat{\phi})-$Selmer groups S^{(\phi)} (E / \Q) and S^{(\hat{\varphi})} (E^{\prime} / \Q) of elliptic curves $y^{2} = x (x + \epsilon p D) (x + \epsilon q D)$ via descent theory (see [S, Chapter X]), in particular, we obtain that the Selmer groups of several families of such elliptic curves can be arbitrary large.Comment: 22 page

In vitro Culture of Several Rice Cultivars

Tissue culture methods have been established to regenerate certain rice (Oryza sativa L) cultivars, but regeneration of the rice cultivars widely grown in Arkansas has not been reported. This study has established an in vitroculture for the rice cultivars \u27Nortai\u27, \u27Starbonnet\u27, \u27Mars\u27, Tebonnet\u27, \u27Newbonnet\u27, and \u27Lemont\u27. Callus was induced in the dark at either 20 or 28 C from dehusked seeds cultured on Murashige and Skoog (MS) medium (Murashige and Skoog, 1962) containing 40 g L^-1 sucrose, 10 g L^1 agar, 0.5, 1.0, or 2.0 mg L^-1 1 2,4-dichlorophenoxyacetic acid (2,4-D) and adjusted to pH 5.7. After four weeks the calli were weighed, transferred onto MS medium containing no 2,4-D, and maintained in a 1 2-h photoperiod (65 uE m^-2 s^-1) at 25 ± 2 C to induce plant regeneration. Callus production was best when cultured on a medium containing 1.0 mg L^-1 2,4-D and incubated at 28 C. Plant regeneration was observed two to four weeks later. The percentage of calli regenerating platlets varied with the cultivar and the callus induction treatment. Callus induction at 20 C on a medium with a 2,4-D level less than 2.0 mg L^-1 enhanced the regenerability of most cultivars. Regenerates were transplanted to soil and grow normally to maturity. This system can be helpful in improving rice cultivars with tissue culture techniques such as somaclonal variant selection and somatic hybridization

Observation of a push force on the end face of a nm fiber taper exerted by outgoing light

There are two different proposals for the momentum of light in a transparent dielectric of refractive index n: Minkowski's version nE/c and Abrahm's version E/(nc), where E and c are the energy and vacuum speed of light, respectively. Despite many tests and debates over nearly a century, momentum of light in a transparent dielectric remains controversial. In this Letter, we report a direct observation of the inward push force on the end face of a free nm fiber taper exerted by the outgoing light. Our results clearly support Abraham momentum. Our experiment also indicates an inward surface pressure on a dielectric exerted by the incident light, different from the commonly recognized pressure due to the specular reflection. Such an inward surface pressure by the incident light may be useful for precise design of the laser-induced inertially-confined fusion.Comment: 9 pages, 3 figures;Accepted for publication as a Letter in Physical Review Letters(CODE: LP11093

Hierarchical fragmentation and collapse signatures in a high-mass starless region

Aims: Understanding the fragmentation and collapse properties of the dense gas during the onset of high-mass star formation. Methods: We observed the massive (~800M_sun) starless gas clump IRDC18310-4 with the Plateau de Bure Interferometer (PdBI) at sub-arcsecond resolution in the 1.07mm continuum andN2H+(3-2) line emission. Results: Zooming from a single-dish low-resolution map to previous 3mm PdBI data, and now the new 1.07mm continuum observations, the sub-structures hierarchically fragment on the increasingly smaller spatial scales. While the fragment separations may still be roughly consistent with pure thermal Jeans fragmentation, the derived core masses are almost two orders of magnitude larger than the typical Jeans mass at the given densities and temperatures. However, the data can be reconciled with models using non-homogeneous initial density structures, turbulence and/or magnetic fields. While most sub-cores remain (far-)infrared dark even at 70mum, we identify weak 70mum emission toward one core with a comparably low luminosity of ~16L_sun, re-enforcing the general youth of the region. The spectral line data always exhibit multiple spectral components toward each core with comparably small line widths for the individual components (in the 0.3 to 1.0km/s regime). Based on single-dish C18O(2-1) data we estimate a low virial-to-gas-mass ratio <=0.25. We discuss that the likely origin of these spectral properties may be the global collapse of the original gas clump that results in multiple spectral components along each line of sight. Even within this dynamic picture the individual collapsing gas cores appear to have very low levels of internal turbulence.Comment: 8 pages, 4 figures, A&A in pres

X-ray Shots of Cyg X-1

X-ray shots of Cyg X-1 in different energy bands and spectral states have been studied with PCA/RXTE observations. The detailed shot structure is obtained by superposing many shots with one millisecond time bin through aligning their peaks with an improved algorithm. In general, the shots are composed of a slow rise and fast decay. The shot structures in the different states are different. The duration of shot in the high state is shorter than that in the low and transition states. The shot profile in the high energy band is more asymmetric and narrower than that in the low energy band. The average hardness of shot is lower than that of steady emission in the transition and low states but higher than that in the high state. The time lags between the shots in higher and lower energy bands have been found in the different states. In transition states, the time lag is the largest among the different states of Cyg X-1, and it is the smallest in the low state. The implications of the observed shot features for shot models are discussed.Comment: Latex, 20 pages, 12 figures(included), to be published in Ap