Wigner 6j symbols for SU(N): Symbols with at least two quark-lines

We study a class of SU(N) Wigner 6j symbols involving two fundamental representations, and derive explicit formulae for all 6j symbols in this class. Our formulae express the 6j symbols in terms of the dimensions of the involved representations, and they are thereby functions of N. We view these explicit formulae as a first step towards efficiently decomposing SU(N) color structures in terms of group invariants.Comment: 39 pages, 1 figur

Oral Motor and Gesture Abilities Independently Associated With Preschool Language Skill:Longitudinal and Concurrent Relationships at 21 Months and 3-4 Years

Purpose Early motor abilities (gesture, oral motor, and gross/fine skills) are related to language abilities, and this is not due to an association with cognitive or symbolic abilities: Oral motor skills are uniquely associated with language abilities at 21 months of age. It is important to determine whether this motor-language relationship continues beyond the earliest stage of language development to understand language acquisition better and better predict which children may have lasting language difficulties. Method In this longitudinal study, we assessed language comprehension and production, oral motor skill, gross/fine motor skill, and meaningless manual gesture at ages 3 years (N = 89) and 4 years (N = 71), comparing the contribution of motor skill and earlier (at 21 months of age) language ability. We also examined covariates: nonverbal cognitive ability, socioeconomic status, and stimulation in the home as measured on the Home Screening Questionnaire. Results Motor abilities continue to have a significant relationship with language abilities independent of other factors in the preschool years. Meaningless manual gesture ability, gross/fine motor skill, and oral motor skill were still associated with language skill at 3 years of age; these relationships are not explained by the contribution of cognitive abilities or earlier language abilities. Conclusions Relationships between early motor skill and language development persist into preschool years and are not explained by other cognitive or home factors, nor by a relationship with earlier language ability. This finding should lead to a better understanding of the origins of language abilities

Using pi_2(1670) -> b_1(1235) pi to Constrain Hadronic Models

We show that current analyses of experimental data indicate that the strong decay mode pi_2 -> b_1 pi is anomalously small. Non-relativistic quark models with spin-1 quark pair creation, such as ^3P_0, ^3S_1 and ^3D_1 models, as well as instanton and lowest order one-boson (in this case pi) emission models, can accommodate the analyses of experimental data, because of a quark-spin selection rule. Models and effects that violate this selection rule, such as higher order one-boson emission models, as well as mixing with other Fock states, may be constrained by the small pi_2 -> b_1 pi decay. This can provide a viability check on newly proposed decay mechanisms. We show that for mesons made up of a heavy quark and anti-quark, the selection rule is exact to all orders of Quantum Chromodynamics (QCD) perturbation theory.Comment: 11 pages, LaTeX, 3 encapsulated Postscript figures, small change

The mechanical properties of amniotic membrane influence its effect as a biomaterial for ocular surface repair

The human amniotic membrane (AM) is a tissue of fetal origin and has proven to be clinically useful as a biomaterial in the management of various ocular surface disorders including corneal stem cell transplantation. However, its success rate displays a degree of clinical unpredictability. We suggest that the measured variability inAMstiffness offers an explanation for the poor clinical reproducibility when it is used as a substrate for stem cell expansion and transplantation. Corneal epithelial stem cells were expanded upon AM samples possessing different mechanical stiffness. To investigate further the importance of biological substrate stiffness on cell phenotype we replaced AM with type I collagen gels of known stiffness. Substrate stiffness was measured using shear rheometry and surface topography was characterized using scanning electron microscopy and atomic force microscopy. The differentiation status of epithelial cells was examined using RT-PCR, immunohistochemistry and Western blotting. The level of corneal stem cell differentiation was increased in cells expanded upon AM with a high dynamic elastic shear modulus and cell expansion on type I collagen gels confirmed that the level of corneal epithelial stem cell differentiation was related to the substrate’s mechanical properties. In this paper we provide evidence to show that the preparatory method of AM for clinical use can affect its mechanical properties and that these measured differences can influence the level of differentiation within expanded corneal epithelial stem cells

A large-scale survey for variable stars in M33

We have started a survey of M 33 in order to find variable stars and Cepheids in particular. We have obtained more than 30 epochs of g'r'i' data with the CFHT and the one-square-degree camera MegaCam. We present first results from this survey, including the search for variable objects and a basic characterization of the various groups of variable stars.Comment: To appear in the proceedings of the "Nonlinear stellar hydrodynamics", conference in honor of Robert Buchler's 65th birthday, July 2007, Pari

Further empirical evidence for the non-linearity of the period-luminosity relations as seen in the Large Magellanic Cloud Cepheids

(abridged) Recent studies, using OGLE data for LMC Cepheids in the optical, strongly suggest that the period-luminosity (PL) relation for the Large Magellanic Cloud (LMC) Cepheids shows a break or non-linearity at a period of 10 days. In this paper we apply statistical tests, the chi-square test and the F-test, to the Cepheid data from the MACHO project to test for a non-linearity of the V- and R-band PL relations at 10 days, and extend these tests to the near infrared (JHK-band) PL relations with 2MASS data. We correct the extinction for these data by applying an extinction map towards the LMC. The statistical test we use, the F-test, is able to take account of small numbers of data points and the nature of that data on either side of the period cut at 10 days. With our data, the results we obtained imply that the VRJH-band PL relations are non-linear around a period of 10 days, while the K-band PL relation is (marginally) consistent with a single-line regression. The choice of a period of 10 days, around which this non-linearity occurs, is consistent with the results obtained when this "break" period is estimated from the data. Long period Cepheids are supplemented from the literature to increase our sample size. The photometry of these long period Cepheids is compared with our data and no trend with period is found. Our main results remain unchanged when we supplement our dataset with these long period Cepheids. By examining our data at maximum light, we also suggest arguments why errors in reddening are unlikely to be responsible for our results. The non-linearity of the mean V-band PL relation as seen in both of the OGLE and MACHO data, using different extinction maps, suggests that this non-linearity is real.Comment: 18 pages, 10 tables, 7 figures. MNRAS accepte

The contribution of microlensing surveys to the distance scale

In the early nineties several teams started large scale systematic surveys of the Magellanic Clouds and the Galactic Bulge to search for microlensing effects. As a by product, these groups have created enormous time-series databases of photometric measurements of stars with a temporal sampling duration and accuracy which are unprecedented. They provide the opportunity to test the accuracy of primary distance indicators, such as Cepheids, RRLyrae stars, the detached eclipsing binaries, or the luminosity of the red clump. We will review the contribution of the microlensing surveys to the understanding of the physics of the primary distance indicators, recent differential studies and direct distance determinations to the Magellanic Clouds and the Galactic Bulge.Comment: Invited review article to appear in: `Post-Hipparcos Cosmic Candles', A. Heck & F. Caputo (Eds), Kluwer Academic Publ., Dordrecht, in press. 21 pages; uses Kluwer's crckapb.sty LaTeX style file, enclose

Small Dwarf Galaxies Within Larger Dwarfs: Why Some Are Luminous While Most Go Dark

We consider the possibility that the Magellanic Clouds were the largest members of a group of dwarf galaxies that entered the Milky Way (MW) halo at late times. Seven of the eleven brightest satellites of the MW may have been part of this system. The proximity of some dwarfs to the plane of the orbit of the Large Magellanic Cloud (LMC) has been used to argue that they formed from tidal debris from the LMC and Small Magellanic Cloud (SMC). Instead, they may owe to the tidal breakup of the Magellanic Group. This can explain the association of many of the dwarf galaxies in the Local Group with the LMC system. It provides a mechanism for lighting up dwarf galaxies and reproduces the bright end of the cumulative circular velocity distribution of the satellites in the MW without invoking a stripping scenario for the subhalos to match the satellite distribution expected according to CDM theory. Finally, our model predicts that other isolated dwarfs will be found to have companions. Evidence for this prediction is provided by nearby, recently discovered dwarf associations.Comment: ApJ Letters in pres

A first-overtone RR Lyrae star with cyclic period changes

A detailed light curve analysis is presented for a first-overtone RR Lyrae star, MACHO* J050918.712-695015.31, based on MACHO and OGLE-III observations. As a foreground object of the Large Magellanic Cloud, it gives an extraordinary opportunity to study an almost continuous, 12-year long dataset of a relatively bright (V~15.0 mag) RRc star with rapid period change. Cyclic period modulation is suggested by the O-C method, where the cycle length is about 8 years. With the available unique dataset, we could draw strong limits on other light curve changes that may be associated to the period modulation. We could exclude both multiple periodicity and amplitude modulation unambiguously. Any theoretical model should reproduce the observed lack of photometric modulations. Simple arguments are also given for possible hydromagnetic effects.Comment: 6 pages, 6 figures, accepted for publication in MNRA

1 m long multilayer-coated deformable piezoelectric bimorph mirror for adjustable focusing of high-energy X-rays

The Diamond Light Source (DLS) beamline I15-1 measures atomic pair distribution functions (PDF) using scattering of 40-80 keV X-rays. A unique focusing element was needed to condense these X-rays from an initial large cross section (11.0 mm H × 4.2 mm V) into a required spot size of FWHM ≈680 μm (H) × 20 μm (V) at a variable position between the sample and the detector. The large numerical aperture is achieved by coating a silicon substrate over 1 m long with three multilayer stripes of Bragg angle 4.2 mrad. One stripe selects X-rays of each energy 40.0, 65.4, and 76.6 keV. Sixteen piezoelectric bimorph actuators attached to the sides of the mirror substrate adjusted the reflecting surface’s shape. Focal spots of vertical width < 15 μm were obtained at three positions over a 0.92 m range, with fast, easy switching from one focal position to another. Minimized root mean square slope errors were close to 0.5 μrad after subtraction of a uniform curvature. Reflectivity curves taken along each stripe showed consistent high peaks with generally small angular variation of peak positions. This is the first application of a 1 m long multilayercoated bimorph mirror at a synchrotron beamline. Data collected with its help on a slice of a lithium ion battery’s cathode are presented