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Search Results: 1 - 6 of 6 matches for " Alisauskas "
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The multiple sum formulas for 9j and 12j coefficients of SU(2) and $u_q$(2)
Sigitas Alisauskas
Physics , 1999, DOI: 10.1063/1.1312198
Abstract: Seven different triple sum formulas for $9j$ coefficients of the quantum algebra $u_q(2)$ are derived, using for these purposes the usual expansion of $q$-$9j$ coefficients in terms of $q$-$6j$ coefficients and recent summation formula of twisted $q$-factorial series (resembling the very well-poised basic hypergeometric $_5\phi_4$ series) as a $q$-generalization of Dougall's summation formula of the very well-poised hypergeometric $_4F_3(-1)$ series. This way for $q=1$ the new proof of the known triple sum formula is proposed, as well as six new triple sum formulas for $9j$ coefficients of the SU(2) group, in the angular momentum theory. The mutual rearrangement possibilities of the derived triple sum formulas by means of the Chu--Vandermonde summation formulas are considered and applied to derive several versions of double sum formulas for the stretched $q$-$9j$ coefficients, which give new rearrangement and summation formulas of special Kamp\'e de F\'eriet functions and their $q$-generalizations. Several fourfold sum formulas [with each sum of the $_5F_4(1)$ or $_5\phi_4$ type] for the $12j$ coefficients of the second kind (without braiding) of the SU(2) and $u_q(2)$ are proposed, as well as expressions with five sums [of the $_4F_3(1)$ and $_3F_2(1)$ or $_4\phi_3$ and $_3\phi_2$ type] for the $12j$ coefficients of the first kind (with braiding) instead of the usual expansion in terms of $q$-$6j$ coefficients. Stretched and doubly stretched $q$-$12j$ coefficients [as triple, double or single sums, related to composed or separate hypergeometric $_4F_3(1)$ and $_5F_4(1)$ or $_4\phi_3$ and $_5\phi_4$ series, respectively] are considered.
6j-symbols for symmetric representations of SO(n) as the double series
S. Alisauskas
Mathematics , 2002, DOI: 10.1088/0305-4470/35/48/303
Abstract: The corrected triple sum expression of Ali\v{s}auskas (1987) for the recoupling (Racah) coefficients (6j-symbols) of the symmetric (most degenerate) representations of the orthogonal groups SO(n) (previously derived from the fourfold sum expression of Ali\v{s}auskas also related to result of Horme\ss and Junker 1999) is rearranged into three new different double sum expressions (related to the hypergeometric Kamp\'e de F\'eriet type series) and a new triple sum expression with preferable summation condition. The Regge type symmetry of special 6j-symbols of the orthogonal groups SO(n) in terms of special Kamp\'e de F\'eriet $F_{1:3}^{1:4}$ series is revealed. The recoupling coefficients for antisymmetric representations of symplectic group Sp(2n) are derived using their relation with the recoupling coefficients of the formal orthogonal group SO(-2n).
Integrals involving triplets of Jacobi and Gegenbauer polynomials and some 3j-symbols of SO(n), SU(n) and Sp(4)
S. Alisauskas
Mathematics , 2005,
Abstract: The coupling coefficients (3j-symbols) for the symmetric (most degenerate) irreducible representations of the orthogonal groups SO(n) in a canonical basis and different semicanonical (tree) bases [with SO(n) restricted to SO(n')\times SO(n''), n'+n''=n] are expressed in terms of the integrals involving triplets of the Gegenbauer and the Jacobi polynomials. The derived usual triple-hypergeometric series (which do not reveal the apparent triangle conditions of the 3j-symbols) are rearranged (in contrast with math-ph/0201048) directly [without using their relation with the semistretched isofactors of the second kind for the complementary chain Sp(4)\supset SU(2)\times SU(2)] into formulas with more rich limits for summation intervals and obvious triangle conditions. The isofactors for the class-one representations of the orthogonal groups and for the class-two representations of the unitary groups (and, of course, the related integrals) 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. Expressions for the most general isofactors of SO(n) for coupling of the two symmetric irreps in the canonical basis are also derived.
Breeding dispersal by Ross's geese in the Queen Maud Gulf metapopulation
Drake, k. L.,Alisauskas, R. T.
Animal Biodiversity and Conservation , 2004,
Abstract: We estimated rates of breeding philopatry and complementary dispersal within the Queen Maud Gulf metapopulation of Ross's Geese (Chen rossii) using multistate modeling of neckband observations at five breeding colonies, 1999-2003. Probability of philopatry was female-biased, but varied among colonies. Probabilies of annual movement among breeding colonies ranged 0.02 to 0.14 for females and 0.12 to 0.38 for males and was substantially higher than expected. These estimates (1) underscore the potential for dispersal to alter breeding distribution, (2) demonstrates that the influence of immigration on colony-specific rates of population growth is nontrivial, and (3) provides behavioral evidence for extensive gene flow among subpopulations. Sex differences in apparent survival estimated from multistate models likely resulted from a combination of higher rates of neckband loss by males compared to females, and higher rates of permanent emigration by males from our study area.
Multistate modeling of brood amalgamation in White-winged Scoters Melanitta fusca deglandi
Traylor, J. J.,Alisauskas, R. T.,Kehoe, F.
Animal Biodiversity and Conservation , 2004,
Abstract: Female waterfowl may lose or abandon offspring shortly after hatch often resulting in the phenomena of post–hatch brood amalgamation (PHBA; Eadie et al., 1988). Potential fitness implications of this behavior has generated considerable debate (Eadie et al., 1988; P ys , 1995; Savard et al., 1998) about physiological or ecological costs and benefits to ducklings in amalgamated broods. Several researchers have proposed that PHBA is a result of, but is not limited to, accidental mixing (i.e., accidental mixing hypothesis), initial brood size at hatch (i.e., brood size and success hypotheses), or maternal female condition at hatch (i.e., energetic stress hypothesis) (Eadie et al., 1988; Bustnes & Erikstad, 1991; P ys , 1995). We studied PHBA in July and August, 2000–2001, in a population of White–winged Scoters on Redberry Lake, Saskatchewan, (52° 00' N, 107° 10' W), a 4,500 ha federal bird sanctuary and World Biosphere Reserve. Ducklings (n = 265 in 2000 and n = 399 in 2001) were captured in nests at hatch, given a uniquely– colored nape marker for individual identification, and re–observed during daily observation sessions. We were interested primarily in movement probabilities during the first two weeks after hatch, when most travel by ducklings occurs, and after which duckling survival was constant (Traylor, 2003). We used multistate modeling (Brownie et al., 1993) in Program MARK (White & Burnham, 1999) to test hypotheses concerning PHBA. We estimated probabilities of (1) staying with putative mothers and natal siblings, , or (2) movement to a foster brood followed by adoption by a foster mother and conspecific non–siblings, . We tested hypotheses about relationships between and hatch date, brood size at hatch, female condition at hatch and size, duckling condition and size at hatch, and weather within one week of hatching. An average of 37.7% and 9.6% of ducklings moved to foster broods in 2000 and 2001, respectively. PHBA was highest the first four days of duckling age in 2000 and the first ten days in 2001. Duckling movement to foster broods in 2000 was a function of hatch date ( = –1.24, 95% CL: –2.33, –0.15), female condition ( = –0.83, 95% CL: –1.52, –0.14), and female size ( = –1.26, 95% CL: –2.21, –0.32). In 2001, duckling movement probability was related to hatch date ( = 0.33, 95% CL: –0.07, 0.72), initial brood size ( = –0.69, 95% CL: –1.12, –0.25), female condition at hatch ( = 0.35, 95% CL: –0.08, 0.78), female size ( = –0.32, 95% CL: –0.74, 0.10), duckling condition ( = –0.54, 95% CL: –0.99, –0.10), and weather ( = 1.14, 95% CL: 0.63, 1.64
Components of population growth rate for White-winged Scoters in Saskatchewan, Canada
Alisauskas, R. T.,Traylor, J.,Swoboda, C. J.,Kehoe, F. P.
Animal Biodiversity and Conservation , 2004,
Abstract: Breeding range and abundance of White-winged Scoters (Melanitta fusca deglandi) have declined in northwestern North America. Hypotheses proposed to account for this trend are that survival and/or recruitment of females had declined. Thus, we used a reverse-time capture-recapture approach to directly estimate survival, seniority and capture probabilities for females of breeding age at Redberry Lake, Saskatchewan, Canada for 1975-1980 and 2000-2003. We also estimated population size of breeding females for 1975-1985 and 2000-2003 using capture-recapture data. Initially, this local population was in serious decline [95%CL(landa75-80) = 0.89 ± 0.09], but has since stabilized and may be slowly increasing [95%CL(landa00-03)=1.07±0.11]. This reversal in trajectory apparently resulted from increased recruitment rather than increased apparent survival. Importantly, recent recruitment of adult females appeared to be driven solely by immigration of adult females with no detectable in situ recruitment, suggesting a hypothesis that the local population is being rescued by females produced elsewhere.
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