Coupling coefficients of SO(n) and integrals over triplets of Jacobi and Gegenbauer polynomials

The expressions of the coupling coefficients (3j-symbols) for the most degenerate (symmetric) representations of the orthogonal groups SO(n) in a canonical basis (with SO(n) restricted to SO(n-1)) and different semicanonical or tree bases [with SO(n) restricted to SO(n'})\times SO(n''), n'+n''=n] are considered, respectively, in context of the integrals involving triplets of the Gegenbauer and the Jacobi polynomials. Since the directly derived triple-hypergeometric series do not reveal the apparent triangle conditions of the 3j-symbols, they are rearranged, using their relation with the semistretched isofactors of the second kind for the complementary chain Sp(4)\supset SU(2)\times SU(2) and analogy with the stretched 9j coefficients of SU(2), into formulae with more rich limits for summation intervals and obvious triangle conditions. The isofactors of class-one representations of the orthogonal groups or class-two representations of the unitary groups (and, of course, the related integrals involving triplets of the Gegenbauer and the Jacobi polynomials) turn into the double sums in the cases of the canonical SO(n)\supset SO(n-1) or U(n)\supset U(n-1) and semicanonical SO(n)\supset SO(n-2)\times SO(2) chains, as well as into the_4F_3(1) series under more specific conditions. Some ambiguities of the phase choice of the complementary group approach are adjusted, as well as the problems with alternating sign parameter of SO(2) representations in the SO(3)\supset SO(2) and SO(n)\supset SO(n-2)\times SO(2) chains.Comment: 26 pages, corrections of (3.6c) and (3.12); elementary proof of (3.2e) is adde

From Quantum Universal Enveloping Algebras to Quantum Algebras

The ``local'' structure of a quantum group G_q is currently considered to be an infinite-dimensional object: the corresponding quantum universal enveloping algebra U_q(g), which is a Hopf algebra deformation of the universal enveloping algebra of a n-dimensional Lie algebra g=Lie(G). However, we show how, by starting from the generators of the underlying Lie bialgebra (g,\delta), the analyticity in the deformation parameter(s) allows us to determine in a unique way a set of n ``almost primitive'' basic objects in U_q(g), that could be properly called the ``quantum algebra generators''. So, the analytical prolongation (g_q,\Delta) of the Lie bialgebra (g,\delta) is proposed as the appropriate local structure of G_q. Besides, as in this way (g,\delta) and U_q(g) are shown to be in one-to-one correspondence, the classification of quantum groups is reduced to the classification of Lie bialgebras. The su_q(2) and su_q(3) cases are explicitly elaborated.Comment: 16 pages, 0 figures, LaTeX fil

Do geese fully develop brood patches? A histological analysis of lesser snow geese (Chen caerulescens caerulescens) and Ross\u27s geese (C. rossii)

Most birds develop brood patches before incubation; epidermis and dermis in the brood patch region thicken, and the dermal connective tissue becomes increasingly vascularized and infiltrated by leukocytes. However, current dogma states that waterfowl incubate without modifications of skin within the brood patch region. The incubation periods of lesser snow geese (Chen caerulescens caerulescens; hereafter called snow geese) and Ross\u27s geese (C. rossii) are 2-6 days shorter than those of other goose species; only females incubate. Thus, we hypothesized that such short incubation periods would require fully developed brood patches for sufficient heat transfer from incubating parents to eggs. We tested this hypothesis by analyzing the skin histology of abdominal regions of snow and Ross\u27s geese collected at Karrak Lake, Nunavut, Canada. For female snow geese, we found that epidermis and dermis had thickened and vascularization of dermis was 14 times greater, on average, than that observed in males (n=5 pairs). Our results for Ross\u27s geese (n=5 pairs) were more variable, wherein only one of five female Ross\u27s geese fully developed a brood patch. Our results are consistent with three hypotheses about brood patch development and its relationship with different energetic cost-benefit relationships, resulting from differences in embryonic development and body size. © Springer-Verlag 2006

Lesser snow goose helminths show recurring and positive parasite infection-diversity relations

The patterns and mechanisms by which biological diversity is associated with parasite infection risk are important to study because of their potential implications for wildlife population's conservation and management. Almost all research in this area has focused on host species diversity and has neglected parasite diversity, despite evidence that parasites are important drivers of community structure and ecosystem processes. Here, we assessed whether presence or abundance of each of nine helminth species parasitizing lesser snow geese (Chen caerulescens) was associated with indices of parasite diversity (i.e. species richness and Shannon's Diversity Index). We found repeated instances of focal parasite presence and abundance having significant positive co-variation with diversity measures of other parasites. These results occurred both within individual samples and for combinations of all samples. Whereas host condition and parasite facilitation could be drivers of the patterns we observed, other host- or parasite-level effects, such as age or sex class of host or taxon of parasite, were discounted as explanatory variables. Our findings of recurring and positive associations between focal parasite abundance and diversity underscore the importance of moving beyond pairwise species interactions and contexts, and of including the oft-neglected parasite species diversity in infection-diversity studies

Bright Coherent Ultrahigh Harmonics in the keV X-ray Regime from Mid-Infrared Femtosecond Lasers

High-harmonic generation (HHG) traditionally combines ~100 near-infrared laser photons to generate bright, phase-matched, extreme ultraviolet beams when the emission from many atoms adds constructively. Here, we show that by guiding a mid-infrared femtosecond laser in a high-pressure gas, ultrahigh harmonics can be generated, up to orders greater than 5000, that emerge as a bright supercontinuum that spans the entire electromagnetic spectrum from the ultraviolet to more than 1.6 kilo–electron volts, allowing, in principle, the generation of pulses as short as 2.5 attoseconds. The multiatmosphere gas pressures required for bright, phase-matched emission also support laser beam self-confinement, further enhancing the x-ray yield. Finally, the x-ray beam exhibits high spatial coherence, even though at high gas density the recolliding electrons responsible for HHG encounter other atoms during the emission process.The experimental work was funded by a National Security Science and Engineering Faculty Fellowship, and the NSF Center for EUV Science and Technology. A.G., A.J.-B., M.M.M., H.C.K. and A. Becker acknowledge support for theory from the U.S. Air Force Office of Scientific Research (grant no. FA9550-10-1-0561); A. Baltuška acknowledges support from Austrian Science Fund (FWF, grant no. U33-16) and the Austrian Research Promotion Agency (FFG, Project 820831 UPLIT); and C.H.-G. and L.P. acknowledge support from Junta de Castilla y León, Spanish MINECO (CSD2007-00013 and FIS2009-09522), and from Centro de Láseres Pulsados, CLPU. T.P., M.-C.C., A. Bahabad, M.M.M. and H.C.K. have filed for a patent on “Method for phase-matched generation of coherent soft and hard X-rays using IR lasers,” U.S. patent application 61171783 (2008)

On the Implementation of the Canonical Quantum Simplicity Constraint

In this paper, we are going to discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional General Relativity and Supergravity developed in our companion papers. Since the canonical quadratic simplicity constraint operators have been shown to be anomalous in any dimension D>2, non-standard methods have to be employed to avoid inconsistencies in the quantum theory. We show that one can choose a subset of quadratic simplicity constraint operators which are non-anomalous among themselves and allow for a natural unitary map of the spin networks in the kernel of these simplicity constraint operators to the SU(2)-based Ashtekar-Lewandowski Hilbert space in D=3. The linear constraint operators on the other hand are non-anomalous by themselves, however their solution space will be shown to differ in D=3 from the expected Ashtekar-Lewandowski Hilbert space. We comment on possible strategies to make a connection to the quadratic theory. Also, we comment on the relation of our proposals to existing work in the spin foam literature and how these works could be used in the canonical theory. We emphasise that many ideas developed in this paper are certainly incomplete and should be considered as suggestions for possible starting points for more satisfactory treatments in the future.Comment: 30 pages, 2 figures. v2: Journal version. Comparison to existing approaches added. Discussion extended. References added. Sign error in equation (2.15) corrected. Minor clarifications and correction

The Drinfeld double gl(n) \oplus t_n

The two isomorphic Borel subalgebras of gl(n), realized on upper and lower triangular matrices, allow us to consider the gl(n) \opus t_n algebra as a self-dual Drinfeld double. Compatibility conditions impose the choice of an orthonormal basis in the Cartan subalgebra and fix the basis of gl(n). A natural Lie bialgebra structure on gl(n) is obtained, that offers a new perspective for its standard quantum deformation.Comment: 8 page

Ground-gamma band mixing and odd-even staggering in heavy deformed nuclei

It is proposed that the odd-even staggering (OES) in the $\gamma$- bands of heavy deformed nuclei can be reasonably characterized by a discrete approximation of the fourth derivative of the odd-even energy difference as a function of angular momentum $L$. This quantity exhibits a well developed staggering pattern (zigzagging behavior with alternating signs) in rare earth nuclei and actinides with long $\gamma$- bands ($L\geq 10$). It is shown that the OES can be interpreted reasonably as the result of the interaction of the $\gamma$ band with the ground band in the framework of a Vector Boson Model with SU(3) dynamical symmetry. The model energy expression reproduces successfully the staggering pattern in all considered nuclei up to $L=12-13$. The general behavior of the OES effect in rotational regions is studied in terms of the ground--$\gamma$ band-mixing interaction, showing that strong OES effect occurs in regions with strong ground--$\gamma$ band-mixing interaction. The approach used allows a detailed comparison of the OES in $\gamma$ bands with the other kinds of staggering effects in nuclei and diatomic molecules.Comment: 25 pages, 11 postscript figure

Constraining the Evolution of Zz Ceti

We report our analysis of the stability of pulsation periods in the DAV star (pulsating hydrogen atmosphere white dwarf) ZZ Ceti, also called R548. On the basis of observations that span 31 years, we conclude that the period 213.13 s observed in ZZ Ceti drifts at a rate dP/dt ≤ (5:5 ± 1:9) x 10-15 s s-1, after correcting for proper motion. Our results are consistent with previous Ṗ values for this mode and an improvement over them because of the larger time base. The characteristic stability timescale implied for the pulsation period is ⎸P / Ṗ ⎸=⎹≥ 1:2 Gyr, comparable to the theoretical cooling timescale for the star. Our current stability limit for the period 213.13 s is only slightly less than the present measurement for another DAV, G117-B15A, for the period 215.2 s, establishing this mode in ZZ Ceti as the second most stable optical clock known, comparable to atomic clocks and more stable than most pulsars. Constraining the cooling rate of ZZ Ceti aids theoretical evolutionary models and white dwarf cosmochronology. The drift rate of this clock is small enough that we can set interesting limits on reflex motion due to planetary companions

Ground-γ\gamma band coupling in heavy deformed nuclei and SU(3) contraction limit

We derive analytic expressions for the energies and $B(E2)$-transition probabilities in the states of the ground and $\gamma$ bands of heavy deformed nuclei within a collective Vector-Boson Model with SU(3) dynamical symmetry. On this basis we examine the analytic behavior of the SU(3) energy splitting and the B(E2) interband transition ratios in the SU(3) contraction limits of the model. The theoretical analyses outline physically reasonable ways in which the ground-$\gamma$ band coupling vanishes. The experimental data on the lowest collective states of even-even rare earth nuclei and actinides strongly support the theoretical results. They suggest that a transition from the ground-$\gamma$ band coupling scheme to a scheme in which the ground band is situated in a separate irreducible representation of SU(3) should be realized towards the midshell regions. We propose that generally the SU(3) group contraction process should play an important role for such a kind of transitions in any collective band coupling scheme in heavy deformed nuclei.Comment: 24 pages (LaTeX), 7 figures (12 postscript files