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Journal articles on the topic 'Identités de Macdonald'

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Published: 4 June 2021

Last updated: 4 February 2022

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1

Nishino, Akinori, Yasushi Komori, Hideaki Ujino, and Miki Wadati. "Symmetrization of Nonsymmetric Macdonald Polynomials and Macdonald's Inner Product Identities." Studies in Applied Mathematics 108, no. 4 (May 2002): 399–425. http://dx.doi.org/10.1111/1467-9590.01431.

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2

Cooper, Shaun. "A new proof of the Macdonald identities for An−1." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 62, no. 3 (June 1997): 345–60. http://dx.doi.org/10.1017/s1446788700001051.

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AbstractA new, elementary proof of the Macdonald identities for An−1 using induction on n is given. Specifically, the Macdonald identity for An is deduced by multiplying the Macdonald identity for An−1 and n Jacobi triple product identities together.

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3

Stokman, Jasper V. "Generalized Cherednik-Macdonald identities." Mathematical Research Letters 15, no. 4 (2008): 745–60. http://dx.doi.org/10.4310/mrl.2008.v15.n4.a12.

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4

Sein, Layla. "Muslim Identities." American Journal of Islam and Society 24, no. 1 (January 1, 2007): 147–50. http://dx.doi.org/10.35632/ajis.v24i1.1581.

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The AMSS 35th Annual Conference, held from 27-29 October 2006 andcosponsored by Hartford Seminary’s Macdonald Center for the Study ofIslam and Christian-Muslim Relations, analyzed “Muslim Identities: ShiftingBoundaries and Dialogues.” Welcoming and introductory remarks werepresented by Seminary President Dr. Heidi Hadsell, Program Chair Dr. JaneI. Smith (co-director, Macdonald Center for the Study of Islam andChristian-Muslim Relations), and AMSS President Dr. Rafik Beekun.Many regular participants mentioned how they look forward to the collegialatmosphere. In fact, as the majority of presenters were Ph.D. candidates,Program Chair Smith stated that “often at academic meetings like thisone, younger scholars listen while the more experienced ones dominate theconversation. … This conference displayed a seriousness of interchangeamong the participants and an appreciation of the contributions of everyone.”Friday’s three panel sessions explored the engagement of Muslim discoursesand institutions with democracy and political transitions in Iran, ...

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5

Etingof, Pavel, and Alexander Kirillov. "On Cherednik-Macdonald-Mehta identities." Electronic Research Announcements of the American Mathematical Society 4, no. 7 (June 11, 1998): 43–47. http://dx.doi.org/10.1090/s1079-6762-98-00045-6.

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6

Stanton, Dennis. "Sign Variations of the Macdonald Identities." SIAM Journal on Mathematical Analysis 17, no. 6 (November 1986): 1454–60. http://dx.doi.org/10.1137/0517103.

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7

Vsemirnov, M. A. "Macdonald identities and multidimensional theta-functions." Journal of Mathematical Sciences 96, no. 5 (October 1999): 3486–92. http://dx.doi.org/10.1007/bf02175826.

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8

Westbury, Bruce W. "Universal characters from the MacDonald identities." Advances in Mathematics 202, no. 1 (May 2006): 50–63. http://dx.doi.org/10.1016/j.aim.2005.03.013.

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9

Olshanski, Grigori. "Interpolation Macdonald polynomials and Cauchy-type identities." Journal of Combinatorial Theory, Series A 162 (February 2019): 65–117. http://dx.doi.org/10.1016/j.jcta.2018.09.007.

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10

TOH, PEE CHOON. "GENERALIZED mth ORDER JACOBI THETA FUNCTIONS AND THE MACDONALD IDENTITIES." International Journal of Number Theory 04, no. 03 (June 2008): 461–74. http://dx.doi.org/10.1142/s1793042108001456.

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We describe an mth order generalization of Jacobi's theta functions and use these functions to construct classes of theta function identities in multiple variables. These identities are equivalent to the Macdonald identities for the seven infinite families of irreducible affine root systems. They are also equivalent to some elliptic determinant evaluations proven recently by Rosengren and Schlosser.

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11

Parman, Susan. ": Inside European Identities: Ethnography in Western Europe . Sharon MacDonald." American Anthropologist 96, no. 3 (September 1994): 743–44. http://dx.doi.org/10.1525/aa.1994.96.3.02a00470.

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12

COOK, WILLIAM J., HAISHENG LI, and KAILASH C. MISRA. "A RECURRENCE RELATION FOR CHARACTERS OF HIGHEST WEIGHT INTEGRABLE MODULES FOR AFFINE LIE ALGEBRAS." Communications in Contemporary Mathematics 09, no. 02 (April 2007): 121–33. http://dx.doi.org/10.1142/s0219199707002368.

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Using certain results for the vertex operator algebras associated with affine Lie algebras, we obtain recurrence relations for the characters of integrable highest weight irreducible modules for an affine Lie algebra. As an application we show that in the simply-laced level 1 case, these recurrence relations give the known characters, whose principal specializations naturally give rise to some multisum Macdonald identities.

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13

Rosengren, Hjalmar, and Michael Schlosser. "Elliptic determinant evaluations and the Macdonald identities for affine root systems." Compositio Mathematica 142, no. 04 (July 2006): 937–61. http://dx.doi.org/10.1112/s0010437x0600203x.

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14

Milne, S. C. "An elementary proof of the Macdonald identities for A(1)l." Advances in Mathematics 57, no. 1 (July 1985): 34–70. http://dx.doi.org/10.1016/0001-8708(85)90105-7.

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15

Weiler, P. "Review: MacDonald's Party: Labour Identities and Crisis, 1922-1931 * David Howell: MacDonald's Party: Labour Identities and Crisis, 1922-1931." Twentieth Century British History 15, no. 1 (January 1, 2004): 111–13. http://dx.doi.org/10.1093/tcbh/15.1.111.

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16

Tanner, D. "MacDonald's Party: Labour Identities and Crisis, 1922-1932." English Historical Review 119, no. 480 (February 1, 2004): 153–55. http://dx.doi.org/10.1093/ehr/119.480.153.

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17

Bazlov, Yu. "The homology of graded infinite-dimensional Lie algebras in connection with Macdonald identities." Journal of Mathematical Sciences 96, no. 5 (October 1999): 3447–54. http://dx.doi.org/10.1007/bf02175822.

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18

Leibenzon, Z. L. "Simple proof of Macdonald's identities for the series a." Functional Analysis and Its Applications 25, no. 3 (1991): 180–83. http://dx.doi.org/10.1007/bf01085487.

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19

Bringmann, Kathrin, Corina Calinescu, Amanda Folsom, and Susie Kimport. "Graded dimensions of principal subspaces and modular Andrews–Gordon-type series." Communications in Contemporary Mathematics 16, no. 04 (July 14, 2014): 1350050. http://dx.doi.org/10.1142/s0219199713500508.

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Our results in this paper are threefold: First, we establish the modular properties of the graded dimensions of principal subspaces of level one standard modules for [Formula: see text], and of principal subspaces of certain higher level standard modules for [Formula: see text]. Second, we establish the modular properties of families of q-series that appear in identities due to Warnaar and Zudilin, which generalize Macdonald's [Formula: see text] identities and the Rogers–Ramanujan identities. Third, we formulate a number of conjectures regarding the modularity of series of this type related to AN-1 root systems.

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20

Zelditch, Steve. "Macdonald?s Identities and the Large N Limit of YM 2 on the Cylinder." Communications in Mathematical Physics 245, no. 3 (March 1, 2004): 611–26. http://dx.doi.org/10.1007/s00220-003-1027-x.

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21

Haglund, J., J. Morse, and M. Zabrocki. "A Compositional Shuffle Conjecture Specifying Touch Points of the Dyck Path." Canadian Journal of Mathematics 64, no. 4 (August 1, 2012): 822–44. http://dx.doi.org/10.4153/cjm-2011-078-4.

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Abstract We introduce a q, t-enumeration of Dyck paths that are forced to touch the main diagonal at specific points and forbidden to touch elsewhere and conjecture that it describes the action of the Macdonald theory ∇ operator applied to a Hall–Littlewood polynomial. Our conjecture refines several earlier conjectures concerning the space of diagonal harmonics including the “shuffle conjecture” (Duke J. Math. 126 (2005), pp. 195 − 232) for ∇ en[X]. We bring to light that certain generalized Hall–Littlewood polynomials indexed by compositions are the building blocks for the algebraic combinatorial theory of q, t-Catalan sequences, and we prove a number of identities involving these functions.

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22

Ansari, Alireza, and Shiva Eshaghi. "Macdonald's identities and integral representations of products of Airy functions." Integral Transforms and Special Functions 31, no. 9 (March 9, 2020): 744–57. http://dx.doi.org/10.1080/10652469.2020.1737529.

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23

VORONIN, VASILY. "SPECIAL AND EXCEPTIONAL JORDAN DIALGEBRAS." Journal of Algebra and Its Applications 11, no. 02 (April 2012): 1250029. http://dx.doi.org/10.1142/s0219498811005531.

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In this paper, we study the class of Jordan dialgebras (also called quasi-Jordan algebras). We develop an approach for reducing problems on dialgebras to the case of ordinary algebras. It is shown that straightforward generalizations of the classical Cohn's, Shirshov's, and Macdonald's Theorems do not hold for dialgebras. However, we prove dialgebraic analogues of these statements. Also, we study multilinear special identities which hold in all special Jordan algebras and do not hold in all Jordan algebras. We find a natural correspondence between special identities for ordinary algebras and dialgebras.

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24

Lashkevich, Michael, and Yaroslav Pugai. "Form factors in sinh- and sine-Gordon models, deformed Virasoro algebra, Macdonald polynomials and resonance identities." Nuclear Physics B 877, no. 2 (December 2013): 538–73. http://dx.doi.org/10.1016/j.nuclphysb.2013.10.013.

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25

Viswanath, S. "AFFINE HALL-LITTLEWOOD FUNCTIONS FOR AFormula AND SOME CONSTANT TERM IDENTITIES OF CHEREDNIK-MACDONALD-MEHTA TYPE." Quarterly Journal of Mathematics 62, no. 1 (November 2, 2009): 223–33. http://dx.doi.org/10.1093/qmath/hap035.

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26

Sthanumoorthy, N., and M. Tamba. "A note on a generalization of Macdonald’s identities forA l andB l." Proceedings of the Indian Academy of Sciences - Section A 104, no. 2 (May 1994): 377–83. http://dx.doi.org/10.1007/bf02863417.

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27

Bonelli, Diego. "Manufacturing urban identities: The emergence of Auckland’s and Wellington’s ‘character’ in New Zealand tourism film." Journal of New Zealand & Pacific Studies 9, no. 1 (June 1, 2021): 43–58. http://dx.doi.org/10.1386/nzps_00047_1.

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Since its inception, New Zealand film production has often been characterized by a strong focus on the promotion and marketing of local scenic locations. However, over the last few decades and simultaneously with New Zealand’s rapidly increasing urbanization rates, urban narratives have gained prominence in the cinematic representation of the country, gradually becoming important aspects of national tourism marketing campaigns. This article first provides an overview of New Zealand tourism film’s dynamics of production and recurring themes and narratives from the early twentieth century to the 1960s. It then focuses on Toehold on a Harbour and This Auckland – tourism films produced by the government-led New Zealand National Film Unit and released respectively in 1967 and 1966 – and identifies a turning point in the manufacturing of local urban narratives and in New Zealand urban tourism marketing. My critical and textual analysis of these two case studies notably relies on the examination of archival documents related to their production and on an interview with This Auckland’s director Hugh Macdonald. It ultimately shows how the emergence of ‘cities with a character’ as a tourism marketing tool was in fact a carefully planned, articulated and years-long government-driven strategy.

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28

Allchin, Arthur Macdonald. "National Identity." Grundtvig-Studier 44, no. 1 (January 1, 1993): 9–15. http://dx.doi.org/10.7146/grs.v44i1.16094.

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National identitet og internationalt fællesskabAf Arthur Macdonald AllchinI sin redegørelse inddrager Allchin personligt farvede betragtninger over, hvad han som englænder har lært ved at stifte bekendtskab med Grundtvig og hans betydning for Danmark i historie og nutid. I fortsættelsen skitserer Allchin, hvordan vigtige perspektiver hos Grundtvig først bliver anskuet i deres virkelige rækkevidde, nr. deres aktuelle relevans langt ud over Danmarks grænser bliver taget med i betragtning.Alt for ofte har det været således, at 'national identitet' er blevet anskuet som et sæt af værdier, der ligger i strid med det pågældende lands plads i det internationale fællesskab. For Grundtvig var det ikke således. Selv om han undertiden kunne give anledning til nationalistiske forestillinger og også. siden hen er blevet brugt i samme retning, var Grundtvigs egentlige overbevisning knyttet til, at han forstod sig selv og sin virksomhed inden for danskhedens rammer og p. samme tid understregede Danmarks plads i universalhistorien. Således var han alt andet end isolationist.Grundtvigs forståelse af national identitet bygger på tre ting: et folk, der bebor et afgrænset geografisk omr.de, som endvidere har et modersmål og en digtning, og som endelig har en fælles historisk arv.De indsigter, der rummes heri, har på afgørende punkter relevans i lyset af dagens internationale situation. Men netop ved at gennemføre en afbalanceret vurdering af Grundtvigs tanker, kan vi opnå et frugtbart grundlag for bestræbelser, der rækker fra kultur- og samfundspolitik til undervisning, fra kirkeliv og teologi til bestræbelserne p. at virkeligg.re en højere grad af fællesskab mellem kristenhedens kirkesamfund.Med denne omfattende målsætning som sin ledetråd udtrykker Allchin for sit eget vedkommende taknemmelighed over at kunne deltage i et samarbejde med kolleger fra Det teologiske Fakultet ved Aarhus Universitet og i særdeleshed Center for Grundtvig Studier.

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29

PITTS, STEPHANIE. "Musical Identities edited by R. MacDonald, D. Hargreaves & D. Miell. Oxford: Oxford University Press, 2002. 250 pp, £24.50, paperback." British Journal of Music Education 20, no. 1 (March 2003): 101–15. http://dx.doi.org/10.1017/s0265051702245301.

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30

DUBBS, ALEXANDER, and ALAN EDELMAN. "THE BETA-MANOVA ENSEMBLE WITH GENERAL COVARIANCE." Random Matrices: Theory and Applications 03, no. 01 (January 2014): 1450002. http://dx.doi.org/10.1142/s2010326314500026.

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We consider adding arbitrary covariance to the β-Jacobi random matrix model. We recall that for β = 1 the Jacobi random matrix model may be thought of as the eigenvalues, λi, of YtY(XTX + YtY)-1 where X and Y are matrices whose elements are i.i.d. standard normals. Equivalently we can take the generalized cosine singular values of (Y, X), ci, and use [Formula: see text]. When β = 1 we add covariance by considering YtY(YtY + ΩXtXΩ)-1, for a positive definite diagonal matrix Ω. Equivalently, and preferably, we consider the generalized singular value decomposition (gsvd) of (Y, XΩ). We refer to Ω = I as the Jacobi case and the general Ω case as the MANOVA case. In this paper, we provide a matrix model for the general β-MANOVA ensemble. In particular, we provide an algorithm for the numerical sampling of eigenvalues or generalized cosine singular values. The β-MANOVA algorithm uses the β-Wishart algorithm of Forrester and Dubbs–Edelman–Koev–Venkataramana as a subroutine, perhaps making β-MANOVA the first "second-order" continuous-β random matrix algorithm. Our proofs make use of a conjecture of MacDonald (proven by Baker and Forrester), a theorem of Kaneko, and many identities from Forrester's Log-Gases and Random Matrices. We supply numerical evidence that our theorems are correct.

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31

egan, vincent. "musical identities. edited by raymond macdonald, david hargreaves and dorothy miell. oxford: oxford university press, 2002. 224 pp. isbn 0-19-850932-4 (pb)." Popular Music 24, no. 3 (October 2005): 462–63. http://dx.doi.org/10.1017/s0261143005240655.

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32

Williams, Colin H. "Book Reviews : Inside European identities. Ethnography in western Europe. Edited by S. Macdonald. Providence and Oxford: Berg Publishers. 1993. viii + 247 pp. £30.00 cloth. ISBN 0 85496 723." Ecumene 3, no. 1 (January 1996): 101–3. http://dx.doi.org/10.1177/147447409600300112.

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33

Meethan, Kevin. "Sharon Macdonald, Reimagining Culture: Histories, Identities and the Gaelic Renaissance, Oxford: Berg, 1997, £34.99 (£14.99 pbk), xx+298 pp. (ISBN 1-85973-980-6 hbk; 1-85973-985-7 pbk)." Sociology 33, no. 4 (November 1999): 835–65. http://dx.doi.org/10.1017/s0038038599360533.

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34

Parish, Helen. "MURIEL MCCLENDON,JOSEPH WARD, MICHAEL MACDONALD (EDS.), Protestant Identities: Religion, Society and Self-fashioning in Post-Reformation England. Cambridge University Press, Cambridge 2000, xiii + 372 pp. ISBN 08047 3611 1. £40.00." Nederlands Archief voor Kerkgeschiedenis / Dutch Review of Church History 81, no. 2 (2001): 239–41. http://dx.doi.org/10.1163/002820301x00419.

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35

Ritschel, Daniel. "David Howell. MacDonald's Party: Labour Identities and Crisis, 1922–1931. New York: Oxford University Press. 2002. Pp. xii, 452. $85.00. ISBN 0-19-820304-7." Albion 36, no. 2 (2004): 357–59. http://dx.doi.org/10.2307/4054269.

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36

Atwood, Craig D. "Protestant Identities: Religion, Society, and Self-Fashioning in Post-Reformation England. Edited by Muriel C. McClendon, Joseph P. Ward, and MacDonald Michael. Stanford, Calif.: Stanford University Press, 1999. xvi + 371 pp. $55.00 cloth." Church History 71, no. 4 (December 2002): 900–902. http://dx.doi.org/10.1017/s000964070009661x.

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37

CAMERON, EWEN A. "Reimagining Culture: Histories, Identities and the Gaelic Renaissance. By Sharon Macdonald. Pp. xix, 297. ISBN 1 85973 980 6 cloth; 1 85973 985 7 paper. Oxford and New York: Berg. 1997. £39.99. Pb. £14.99." Scottish Historical Review 78, no. 2 (October 1999): 289. http://dx.doi.org/10.3366/shr.1999.78.2.289.

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38

Breslow, Marvin A. "Muriel C. McClendon, Joseph P. Ward, and Michael MacDonald, eds. Protestant Identities: Religion, Society, and Self-Fashioning in Post-Reformation England. Stanford, Calif.: Stanford University Press. 1999. Pp. xi, 372. $55.00. ISBN 0-8047-3611-1." Albion 33, no. 02 (2001): 292–94. http://dx.doi.org/10.1017/s0095139000067284.

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39

Sommerville, Johann P. "Protestant identities. Religion, society, and self-fashioning in post-Reformation England. Edited by Muriel C. McClendon, Joseph P. Ward and Michael MacDonald. Pp. xiii+374 incl. 3 figs. Stanford, Ca: Stanford University Press, 1999. £35 ($55). 08047 3611 1." Journal of Ecclesiastical History 53, no. 3 (July 2002): 545–650. http://dx.doi.org/10.1017/s0022046902824769.

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40

Morgan, John. "Protestant Identities: Religion, Society, and Self-Fashioning in Post-Reformation England, edited by Muriel C. McClendon, Joseph P. Ward, and Michael MacDonaldProtestant Identities: Religion, Society, and Self-Fashioning in Post-Reformation England, edited by Muriel C. McClendon, Joseph P. Ward, and Michael MacDonald. Stanford, California, Stanford University Press, 1999. xiii, 372 pp. $55.00 U.S. (cloth)." Canadian Journal of History 36, no. 2 (August 2001): 349–51. http://dx.doi.org/10.3138/cjh.36.2.349.

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41

KITLV, Redactie. "Book Reviews." Bijdragen tot de taal-, land- en volkenkunde / Journal of the Humanities and Social Sciences of Southeast Asia 163, no. 4 (2008): 559–621. http://dx.doi.org/10.1163/22134379-90003696.

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Benedict Anderson; Under three flags; Anarchism and the anticolonial imagination (Greg Bankoff) Leakthina Chau-Pech Ollier, Tim Winter (eds); Expressions of Cambodia; The politics of tradition, identity and change (David Chandler) Ying Shing Anthony Chung; A descriptive grammar of Merei (Vanuatu) (Alexandre François) Yasuyuki Matsumoto; Financial fragility and instability in Indonesia (David C. Cole) Mason C. Hoadley; Public administration; Indonesian norms versus Western forms (Jan Kees van Donge) Samuel S. Dhoraisingam; Peranakan Indians of Singapore and Melaka (Joseph M. Fernando) Vatthana Pholsena; Post-war Laos; The politics of culture, history and identity (Volker Grabowksy) Gert Oostindie; De parels en de kroon; Het koningshuis en de koloniën (Hans Hägerdal) Jean-Luc Maurer; Les Javanais du Caillou; Des affres de l’exil aux aléas de l’intégration; Sociologie historique de la communauté indonésienne de Nouvelle-Calédonie (Menno Hecker) Richard Stubbs; Rethinking Asia’s economic miracle; The political economy of war, prosperity and crisis (David Henley) Herman Th. Verstappen; Zwerftocht door een wereld in beweging (Sjoerd R. Jaarsma) Klokke, A.H. (ed. and transl.); Fishing, hunting and headhunting in the former culture of the Ngaju Dayak in Central Kalimantan; Notes from the manuscripts of the Ngaju Dayak authors Numan Kunum and Ison Birim; from the Legacy of Dr. H. Schaerer; With a recent additional chapter on hunting by Katuah Mia (Monica Janowski) Ian Proudfoot; Old Muslim calendars of Southeast Asia (Nico J.G. Kaptein) Garry Rodan; Transparency and authoritarian rule in Southeast Asia (Soe Tjen Marching) Greg Fealy, Virginia Hooker (eds); Voices of Islam in Southeast Asia; A contemporary sourcebook (Dick van der Meij) Eko Endarmoko; Tesaurus Bahasa Indonesia (Don van Minde) Charles J.-H. Macdonald; Uncultural behavior; An anthropological investigation of suicide in the southern Philippines (Raul Pertierra) Odd Arne Westad, Sophie Quinn-Judge (eds); The Third Indochina War; Conflict between China, Vietnam and Cambodia, 1972-79 (Vatthana Pholsena) B. Bouman; Ieder voor zich en de Republiek voor ons allen; De logistiek achter de Indonesische Revolutie 1945-1950 (Harry A. Poeze) Michel Gilquin; The Muslims of Thailand (Nathan Porath) Tom Boellstorff; The gay archipelago; Sexuality and nation in Indonesia (Raquel Reyes) Kathleen M. Adams; Art as politics; Re-crafting identities, tourism, and power in Tana Toraja, Indonesia (Dik Roth) Aris Ananta, Evi Nurvidya Arifin, Leo Suryadinata; Emerging democracy in Indonesia (Henk Schulte Nordholt) Casper Schuring; Abdulgani; 70 jaar nationalist van het eerste uur (Nico G. Schulte Nordholt) Geoff Wade (ed. and transl.); Southeast Asia in the Ming Shi-lu; An open access resource (Heather Sutherland) Alexander Horstmann, Reed L. Wadley (eds); Centering the margin; Agency and narrative in Southeast Asian Borderlands (Nicholas Tapp) Marieke Brand, Henk Schulte Nordholt, Fridus Steijlen (eds); Indië verteld; Herinneringen, 1930-1950 (Jean Gelman Taylor) Tin Maung Maung Than; State dominance in Myanmar; The political economy of industrialization (Sean Turnell) Henk Schulte Nordholt, Ireen Hoogenboom (eds); Indonesian transitions (Robert Wessing) In: Bijdragen tot de Taal-, Land- en Volkenkunde no. 163 (20075), no: 4, Leiden

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42

Jensen-Tracy, S., S. Kenaley, G. Hudler, T. Harrington, and C. Logue. "First Report of the Oak Wilt Fungus, Ceratocystis fagacearum, in New York State." Plant Disease 93, no. 4 (April 2009): 428. http://dx.doi.org/10.1094/pdis-93-4-0428b.

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Ceratocystis fagacearum (T.W. Bretz) J. Hunt is considered to be the most destructive vascular pathogen of oaks (Fagaceae: Quercus spp.) in the eastern, north-central, and south-central United States. (1,2,4). All red oak species (subgenus Quercus: section Lobatae) are highly susceptible to C. fagacearum, and infected trees typically die within 3 months of first symptom expression. However, members of the white oak group (subgenus Quercus: section Quercus) are moderately to highly resistant to C. fagacearum and rarely die from oak wilt (1,3). In early August of 2008, we received branch samples taken from wilting red oaks (Q. rubra L.) growing in a residential neighborhood in Scotia, NY (Schenectady County). The endoconidial state of the oak wilt fungus, Thielaviopsis quercina (B.W. Henry) A.E. Paulin, T.C. Harr. & McNew, was consistently isolated from the xylem in the branches. The cultures were identified based on hyphal and conidial morphology on acidified potato dextrose agar (aPDA) as well as sequences of the internal transcribed spacer (ITS) (GenBank Accession No. FJ347031) and large subunit (LSU) (GenBank Accession No. FJ347030) regions of nuclear ribosomal DNA (rDNA). The nucleotide identities for the ITS and LSU sequences were a precise match, 99 and 100%, to rDNA sequences (GenBank Accession Nos. AF043598 and AF222483, respectively) of other isolates of C. fagacearum. According to the homeowners at the site, 12 red oaks have died during the last 3 years, and each tree died within one growing season after oak wilt-like symptoms were noted. In a brief survey of nearby properties in late August of 2008, we found 12 additional trees that were either expressing crown symptoms of oak wilt (e.g., premature leaf casting, bronzing of leaf margins, and water-soaked leaves) or were standing dead and within close proximity (5 to 10 m) to symptomatic trees. Branch samples from four of the symptomatic trees revealed limited (spotted) or no vascular discoloration; however, C. fagacearum was isolated from each suspect tree on aPDA. Remnants of gray mycelial mats and associated pressure cushions were observed beneath the bark of one standing dead oak. The sweet fruit-like odor characteristic of the oak wilt fungus was immediately evident once the bark overlying the mats was removed. Prior to this discovery, the Susquehanna River in north-central Pennsylvania was considered to be the northeastern limit for oak wilt occurrence in the United States (2,4). To our knowledge, this is the first report of the fungus from New York and expands the known range of C. fagacearum to the northeast by at least 300 km, supporting the hypothesis that the range of this fungus continues to expand via animal vectors and/or human activities (2). An isolate of C. fagacearum from New York has been deposited at the Centraalbureau voor Schimmelcultures (CBS 123913). References: (1) D. N. Appel. Ann. Rev. Phytopathol. 33:103, 1995. (2) J. Juzwik et al. Ann. Rev. Phytopathol. 46:13, 2008. (3) W. L. MacDonald et al. European oaks-susceptible to oak wilt? Page 131 in: Shade Tree Wilt Diseases. C. L. Ash, ed. The American Phytopathological Society, St. Paul, MN, 2001. (4) USDA Forest Service. Oak Wilt Distribution. Northeast Area, State and Private Forestry, St. Paul, MN. Online publication, 2005.

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Pétréolle, Mathias. "A Nekrasov-Okounkov type formula for affine $\widetilde{C}$." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings, 27th..., Proceedings (January 1, 2015). http://dx.doi.org/10.46298/dmtcs.2498.

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International audience In 2008, Han rediscovered an expansion of powers of Dedekind $\eta$ function due to Nekrasov and Okounkov by using Macdonald's identity in type $\widetilde{A}$. In this paper, we obtain new combinatorial expansions of powers of $\eta$, in terms of partition hook lengths, by using Macdonald's identity in type $\widetilde{C}$ and a new bijection. As applications, we derive a symplectic hook formula and a relation between Macdonald's identities in types $\widetilde{C}$, $\widetilde{B}$, and $\widetilde{BC}$. En 2008, Han a redécouvert un développement des puissances de la fonction $\eta$ de Dedekind, dû à Nekrasov et Okounkov, en utilisant l’identité de Macdonald en type $\widetilde{A}$. Dans cet article, nous obtenons un nouveau développement combinatoire des puissances de $\eta$, en termes de longueurs d’équerres de partitions, en utilisant l’identité de Macdonald en type $\widetilde{C}$ ainsi qu’une nouvelle bijection. Plusieurs applications en sont déduites, comme un analogue symplectique de la formule des équerres, ou une relation entre les identités de Macdonald en types $\widetilde{C}$, $\widetilde{B}$, et $\widetilde{BC}$.

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Jones, Miles Eli, and Luc Lapointe. "Pieri rules for Schur functions in superspace." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings, 27th..., Proceedings (January 1, 2015). http://dx.doi.org/10.46298/dmtcs.2497.

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International audience The Schur functions in superspace $s_\Lambda$ and $\overline{s}_\Lambda$ are the limits $q=t= 0$ and $q=t=\infty$ respectively of the Macdonald polynomials in superspace. We present the elementary properties of the bases $s_\Lambda$ and $\overline{s}_\Lambda$ (which happen to be essentially dual) such as Pieri rules, dualities, monomial expansions, tableaux generating functions, and Cauchy identities. Les fonctions de Schur dans le superespace $s_\Lambda$ et $\overline{s}_\Lambda$ sont les limites $q=t= 0$ et $q=t=\infty$ respectivement des polynômes de Macdonald dans le superespace. Nous présentons les propriétés élémentaires des bases $s_\Lambda$ et $\overline{s}_\Lambda$ (qui sont essentiellement duales l'une de l'autre) tels que les règles de Pieri, la dualité, le développement en fonctions monomiales, les fonctions génératrices de tableaux et les identités de Cauchy.

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Sahi, Siddhartha, and Jasper Stokman. "Some Remarks on Non-Symmetric Interpolation Macdonald Polynomials." International Mathematics Research Notices, November 8, 2019. http://dx.doi.org/10.1093/imrn/rnz229.

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Abstract We provide elementary identities relating the three known types of non-symmetric interpolation Macdonald polynomials. In addition we derive a duality for non-symmetric interpolation Macdonald polynomials. We consider some applications of these results, in particular to binomial formulas involving non-symmetric interpolation Macdonald polynomials.

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46

Milas, Antun. "Virasoro Algebra, Dedekind ?-function and Specialized Macdonald Identities." Transformation Groups 9, no. 3 (July 2004). http://dx.doi.org/10.1007/s00031-004-7014-2.

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Lee, Chul-hee, Eric M. Rains, and S. Ole Warnaar. "An Elliptic Hypergeometric Function Approach to Branching Rules." Symmetry, Integrability and Geometry: Methods and Applications, December 23, 2020. http://dx.doi.org/10.3842/sigma.2020.142.

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We prove Macdonald-type deformations of a number of well-known classical branching rules by employing identities for elliptic hypergeometric integrals and series. We also propose some conjectural branching rules and allied conjectures exhibiting a novel type of vanishing behaviour involving partitions with empty 2-cores.

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Bhatnagar, Gaurav. "In Praise of an Elementary Identity of Euler." Electronic Journal of Combinatorics 18, no. 2 (June 11, 2011). http://dx.doi.org/10.37236/2009.

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We survey the applications of an elementary identity used by Euler in one of his proofs of the Pentagonal Number Theorem. Using a suitably reformulated version of this identity that we call Euler's Telescoping Lemma, we give alternate proofs of all the key summation theorems for terminating Hypergeometric Series and Basic Hypergeometric Series, including the terminating Binomial Theorem, the Chu–Vandermonde sum, the Pfaff–Saalschütz sum, and their $q$-analogues. We also give a proof of Jackson's $q$-analog of Dougall's sum, the sum of a terminating, balanced, very-well-poised $_8\phi_7$ sum. Our proofs are conceptually the same as those obtained by the WZ method, but done without using a computer. We survey identities for Generalized Hypergeometric Series given by Macdonald, and prove several identities for $q$-analogs of Fibonacci numbers and polynomials and Pell numbers that have appeared in combinatorial contexts. Some of these identities appear to be new.

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Pérez-Colodrero, Consuelo. "MacDonald, R., Hargreaves , D. J., y Miell, D. (Eds.) (2017). "Handbook of Musical Identities"." Revista Electrónica Complutense de Investigación en Educación Musical - RECIEM 14 (October 23, 2017). http://dx.doi.org/10.5209/reciem.56569.

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Haglund, J. "A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version)." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AO,..., Proceedings (January 1, 2011). http://dx.doi.org/10.46298/dmtcs.2924.

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International audience A special case of Haiman's identity [Invent. Math. 149 (2002), pp. 371–407] for the character of the quotient ring of diagonal coinvariants under the diagonal action of the symmetric group yields a formula for the bigraded Hilbert series as a sum of rational functions in $q,t$. In this paper we show how a summation identity of Garsia and Zabrocki for Macdonald polynomial Pieri coefficients can be used to transform Haiman's formula for the Hilbert series into an explicit polynomial in $q,t$ with integer coefficients. We also provide an equivalent formula for the Hilbert series as the constant term in a multivariate Laurent series. Un cas spécial de l'identité de Haiman [Invent. Math. \textbf149 (2002), pp. 371–407] pour le caractère de l'anneau quotient des coinvariants diagonaux sous l'action du groupe symétrique fournit une formule pour la série de Hilbert bigraduée comme somme de fonctions rationnelles en q,t. Dans cet article nous montrons comment une identité de sommation de Garsia et Zabrocki pour les coefficients de Pieri des polynômes de Macdonald peut être utilisée pour transformer la formule de Haiman pour la série de Hilbert en un polynôme explicite en q,t à coefficients entiers. Nous présentons également une formule équivalente pour la série de Hilbert comme terme constant d'une série de Laurent multivariée.

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