Math @ Duke

Papers Published
 PerezArancibia, C; Shipman, SP; Turc, C; Venakides, S, Domain Decomposition for QuasiPeriodic Scattering by Layered Media via Robust BoundaryIntegral Equations at All Frequencies,
Communications in Computational Physics, vol. 26 no. 1
(July, 2019),
pp. 265310, Global Science Press [doi]
 Aristotelous, AC; Crawford, JM; Edwards, GS; Kiehart, DP; Venakides, S, Mathematical models of dorsal closure.,
Progress in Biophysics and Molecular Biology, vol. 137
(September, 2018),
pp. 111131 [doi] [abs]
 Venakides, S; Komineas, S; Melcher, C, Traveling domain walls in chiral ferromagnets,
Nonlinearity
(June, 2018), London Mathematical Society
 PerezArancibia, C; Shipman, S; Turc, C; Venakides, S, DDM solutions of quasiperiodic transmission problems in layered
media via robust boundary integral equations at all frequencies,
Communications in Computational Physics
(May, 2018), Global Science Press
 Bruno, OP; Shipman, SP; Turc, C; Stephanos, V, Threedimensional quasiperiodic shifted Green function throughout the spectrum, including Wood anomalies.,
Proceedings. Mathematical, Physical, and Engineering Sciences, vol. 473 no. 2207
(November, 2017),
pp. 20170242, The Royal Society [doi] [abs]
 Kiehart, DP; Crawford, JM; Aristotelous, A; Venakides, S; Edwards, GS, Cell Sheet Morphogenesis: Dorsal Closure in Drosophila melanogaster as a Model System.,
Annual Review of Cell and Developmental Biology, vol. 33
(October, 2017),
pp. 169202 [doi] [abs]
 Sergey Belov and Stephanos Venakides, Smooth parametric dependence of asymptotics of the semiclassical focusing NLS,
Analysis & PDE, vol. 8 no. 2
(April, 2015),
pp. 257288 [doi] [abs]
 Komineas, S; Shipman, SP; Venakides, S, Continuous and discontinuous dark solitons in polariton condensates,
Physical Review B, vol. 91 no. 13
(April, 2015), American Physical Society (APS), ISSN 10980121 [doi] [abs]
 Belov, S; Venakides, S, Smooth parametric dependence of asymptotics of the semiclassical focusing NLS,
Analysis & Pde, vol. 8 no. 2
(January, 2015),
pp. 257288, Mathematical Sciences Publishers [1211.7111v2], [doi] [abs]
 Oscar P. Bruno, Stephen P. Shipman, Catalin Turc, Stephanos Venakides, Efficient Evaluation of Doubly Periodic Green Functions in 3D Scattering, Including Wood Anomaly Frequencies,
ArXiv>Mathematics > Analysis of PDEs
(July 4, 2013) [arXiv:1307.1176] [abs]
 Jackson, AD; Huang, D; Gauthier, DJ; Venakides, S, Destructive impact of imperfect beam collimation in extraordinary optical transmission.,
Journal of the Optical Society of America A, vol. 30 no. 6
(June, 2013),
pp. 12811290, ISSN 10847529 (doi: 10.1364/JOSAA.30.001281..) [doi] [abs]
 Shipman, SP; Venakides, S, An exactly solvable model for nonlinear resonant scattering,
Nonlinearity, vol. 25 no. 9
(September, 2012),
pp. 24732501, IOP Publishing, ISSN 09517715 (doi:10.1088/09517715/25/9/2473.) [doi] [abs]
 Tovbis, A; Venakides, S, Semiclassical limit of the scattering transform for the focusing nonlinear Schrödinger equation,
International Mathematics Research Notices, vol. 2012 no. 10
(May, 2012),
pp. 22122271, Oxford University Press (OUP), ISSN 10737928 (doi:10.1093/imrn/rnr092.) [doi] [abs]
 Tovbis, A; Venakides, S, Nonlinear steepest descent asymptotics for semiclassical limit of Integrable systems: Continuation in the parameter space,
Communications in Mathematical Physics, vol. 295 no. 1
(2010),
pp. 139160, Springer Nature, ISSN 00103616 [doi] [abs]
 Layton, AT; Toyama, Y; Yang, GQ; Edwards, GS; Kiehart, DP; Venakides, S, Drosophila morphogenesis: tissue force laws and the modeling of dorsal closure.,
Hfsp Journal, vol. 3 no. 6
(December, 2009),
pp. 441460, HFSP [20514134], [doi] [abs]
 Lefew, WR; Venakides, S; Gauthier, DJ, Accurate description of optical precursors and their relation to weakfield coherent optical transients,
Physical Review A, vol. 79 no. 6
(June, 2009),
pp. 063842, American Physical Society (APS), ISSN 10502947 [doi] [abs]
 Tovbis, A; Venakides, S, Determinant form of the complex phase function of the steepest descent analysis of RiemannHilbert problems and its application to the focusing nonlinear schrödinger equation,
International Mathematics Research Notices, vol. 2009 no. 11
(February, 2009),
pp. 20562080, Oxford University Press (OUP), ISSN 10737928 [doi] [abs]
 Tovbis, A; Venakides, S, Determinant form of modulation equations for the semiclassical focusing
Nonlinear Schr\" odinger equation
(2009) [abs]
 Ptitsyna, N; Shipman, SP; Venakides, S, Fano resonance of waves in periodic slabs,
Mathematical Methods in Electromagnetic Theory, Mmet, Conference Proceedings
(September, 2008),
pp. 7378 [doi] [abs]
 Tovbis, A; Venakides, S; Zhou, X, Semiclassical Focusing Nonlinear Schrodinger equation in the pure radiation case: RiemannHilbert Problem approach, edited by Baik, J; Kriecherbauer, T; Li, LC; McLaughlin, KDT; Tomei, C,
Surveys on Discrete and Computational Geometry: Twenty Years Later, vol. 458
(2008),
pp. 117144, AMER MATHEMATICAL SOC, ISBN 9780821842409
 Tovbis, A; Venakides, S; Zhou, X, Semiclassical focusing nonlinear schrödinger equation i: Inverse scattering map and its evolution for radiative initial data,
International Mathematics Research Notices, vol. 2007 no. Article ID rnm094,
54 pages.
doi:10.
(December, 2007), Oxford University Press (OUP), ISSN 10737928 [doi] [abs]
 Buckingham, R; Venakides, S, Longtime asymptotics of the nonlinear Schrödinger equation shock problem,
Communications on Pure and Applied Mathematics, vol. 60 no. 9
(2007),
pp. 13491414, WILEY, ISSN 00103640 [MR2337507], [doi] [abs]
 Peralta, XG; Toyama, Y; Hutson, MS; Montague, R; Venakides, S; Kiehart
and, DP; Edwards, GS, Resiliency, coordination, and synchronization of dorsal closure during Drosophila
morphogenesis,
Biophysical Journal, vol. 92 no. 7
(April, 2007),
pp. 25832596, ISSN 00063495 [17218455], [doi] [abs]
 Peralta, XG; Toyama, Y; Hutson, MS; Montague, R; Venakides, S; Kiehart, DP; Edwards, GS, Upregulation of forces and morphogenic asymmetries in dorsal closure during Drosophila development.,
Biophysical Journal, vol. 92 no. 7
(April, 2007),
pp. 25832596, ISSN 00063495 [17218455], [doi] [abs]
 Buckingham, R; Tovbis, A; Venakides, S; Zhou, X, The semiclassical focusing nonlinear Schrodinger equation,
in "Recent Advances in Nonlinear Partial Differentila Equations and Applications'', Proceedings of Symposia in Applied Mathematics, edited by Bonilla, LL; Carpio, A; Vega, JM; Venakides, S,
Recent Advances in Nonlinear Partial Differential Equations and Applications, vol. 65
(2007),
pp. 4780, AMER MATHEMATICAL SOC, ISBN 9780821842119
 Tovbis, A; Venakides, S; Zhou, X, On the longtime limit of semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation: Pure radiation case,
Communications on Pure and Applied Mathematics, vol. 59 no. 10
(2006),
pp. 13791432, WILEY, ISSN 00103640 [MR2248894], [doi] [abs]
 Shipman, SP; Venakides, S, Resonant transmission near nonrobust periodic slab modes.,
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 71 no. 2 Pt 2
(2005),
pp. 026611, ISSN 15393755 [15783445], [doi] [abs]
 Peralta, XG; Toyama, Y; Wells, A; Tokutake, Y; Hutson, MS; Venakides, S; Kiehart, DP; Edwards, GS, Force regulation during dorsal closure in Drosophila,
Molecular Biology of the Cell, vol. 15
(November, 2004),
pp. 403A403A, AMER SOC CELL BIOLOGY
 Tovbis, A; Venakides, S; Zhou, X, On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation,
Communications on Pure and Applied Mathematics, vol. 57 no. 7
(2004),
pp. 877985, WILEY, ISSN 00103640 [MR2044068 (2005c:35269)], [doi] [abs]
 Lipton, RP; Shipman, SP; Venakides, S, Optimization of Resonances in Photonic Crystal Slabs,
Smart Structures and Materials 2005: Active Materials: Behavior and Mechanics, vol. 5184
(December, 2003),
pp. 168177, SPIE [doi] [abs]
 Shipman, SP; Venakides, S, Resonance and bound states in photonic crystal slabs,
Siam Journal on Applied Mathematics, vol. 64 no. 1
(2003),
pp. 322342, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361399 [doi] [abs]
 Hutson, MS; Tokutake, Y; Chang, MS; Bloor, JW; Venakides, S; Kiehart, DP; Edwards, GS, Forces for morphogenesis investigated with laser microsurgery and quantitative modeling.,
Science (New York, N.Y.), vol. 300 no. 5616
(April, 2003),
pp. 145149 [12574496], [doi] [abs]
 Hutson, S; Tokutake, Y; Chang, M; Bloor, JW; Venakides, S; Kiehart, DP; Edwards, GS, Measuring the forces that drive morphogenesis: Lasermicrosurgery and quantitative modeling applied to dorsal closure in Drosophila,
Molecular Biology of the Cell, vol. 13
(November, 2002),
pp. 476A476A, American Society for Cell Biology
 Haider, MA; Shipman, SP; Venakides, S, Boundaryintegral calculations of twodimensional electromagnetic scattering in infinite photonic crystal slabs: Channel defects and resonances,
Siam Journal on Applied Mathematics, vol. 62 no. 6
(July, 2002),
pp. 21292148, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 El, GA; Krylov, AL; Venakides, S, Unified approach to KdV modulations,
Communications on Pure and Applied Mathematics, vol. 54 no. 10
(October, 2001),
pp. 12431270, WILEY [doi] [abs]
 Deift, P; Kriecherbauer, T; McLaughlin, KR; Venakides, S; Zhou, X, A riemannHilbert approach to asymptotic questions for orthogonal polynomials,
Journal of Computational and Applied Mathematics, vol. 133 no. 12
(August, 2001),
pp. 4763, Elsevier BV, ISSN 03770427 [doi] [abs]
 El, GA; Krylov, AL; Molchanov, SA; Venakides, S, Soliton turbulence as a thermodynamic limit of stochastic soliton lattices,
Physica D: Nonlinear Phenomena, vol. 152153
(May, 2001),
pp. 653664, Elsevier BV [doi] [abs]
 Georgieva, A; Kriecherbauer, T; Venakides, S, 1:2 resonance mediated second harmonic generation in a 1D nonlinear discrete periodic medium,
Siam Journal on Applied Mathematics, vol. 61 no. 5
(January, 2001),
pp. 18021815, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Tovbis, A; Venakides, S, The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases,
Physica D: Nonlinear Phenomena, vol. 146 no. 14
(November, 2000),
pp. 150164, Elsevier BV [doi] [abs]
 Venakides, S; Haider, MA; Papanicolaou, V, Boundary integral calculations of twodimensional electromagnetic scattering by photonic crystal FabryPerot structures,
Siam Journal on Applied Mathematics, vol. 60 no. 5
(May, 2000),
pp. 16861706, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Reed, D; Venakides, S, Studying the asymptotics of Selbergtype integrals, edited by Spigler, R,
Applied and Industrial Mathematics, Venice 2, 1998
(January, 2000),
pp. 187198, SPRINGER, ISBN 0792361520
 VENAKIDES, S, Boundary integral calculations of twodimensional electromagnetic scattering by photonic crystal FabriPeror structures,
Siam J. Appl. Math., vol. 60
(2000),
pp. 16861706 [doi]
 Beaky, MM; Burk, JB; Everitt, HO; Haider, MA; Venakides, S, Twodimensional photonic crystal fabryperot resonators with lossy dielectrics,
Ieee Transactions on Microwave Theory and Techniques, vol. 47 no. 11
(December, 1999),
pp. 20852091, Institute of Electrical and Electronics Engineers (IEEE), ISSN 00189480 [doi] [abs]
 Filip, AM; Venakides, S, Existence and modulation of traveling waves in particle chains,
Communications on Pure and Applied Mathematics, vol. 52 no. 6
(June, 1999),
pp. 693735 [abs]
 Cheng, PJ; Venakides, S; Zhou, X, Longtime asymptotics for the pure radiation solution of the sineGordon equation,
Communications in Partial Differential Equations, vol. 24 no. 78
(January, 1999),
pp. 11951262, Informa UK Limited [doi]
 Georgieva, A; Kriecherbauer, T; Venakides, S, Wave Propagation and Resonance in a OneDimensional Nonlinear Discrete Periodic Medium,
Siam Journal on Applied Mathematics, vol. 60 no. 1
(January, 1999),
pp. 272294, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Deift, P; Kriecherbauer, T; McLaughlin, KTR; Venakides, S; Zhou, X, Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory,
Communications on Pure and Applied Mathematics, vol. 52 no. 11
(January, 1999),
pp. 13351425, WILEY [doi] [abs]
 Deift, P; Kriecherbauer, T; Mclaughlin, KTR; Venakides, S; Zhou, X, Strong asymptotics of orthogonal polynomials with respect to exponential weights,
Communications on Pure and Applied Mathematics, vol. 52 no. 12
(January, 1999),
pp. 14911552 [doi] [abs]
 Deift, P; Venakides, S; Zhou, X, An extension of the steepest descent method for RiemannHilbert problems: the small dispersion limit of the Kortewegde Vries (KdV) equation.,
Proceedings of the National Academy of Sciences of the United States of America, vol. 95 no. 2
(January, 1998),
pp. 450454, ISSN 00278424 [11038618], [doi] [abs]
 McDonald, MA; Venakides, S, Renormalization of the τfunctions for integrable systems: A model problem,
Communications on Pure and Applied Mathematics, vol. 51 no. 8
(January, 1998),
pp. 937966, WILEY [doi] [abs]
 Deift, P; Kriecherbauer, T; McLaughlin, KTR; Venakides, S; Zhou, X, Asymptotics for Polynomials Orthogonal with Respect to Varying Exponential Weights,
International Mathematics Research Notices no. 16
(December, 1997),
pp. X782
 Deift, P; Venakides, S; Zhou, X, New Results in Small Dispersion KdV by an Extension of the Steepest Descent Method for RiemannHilbert Problems,
International Mathematics Research Notices no. 6
(December, 1997),
pp. 284299
 Bonilla, LL; Kindelan, M; Moscoso, M; Venakides, S, Periodic generation and propagation of traveling fronts in dc voltage biased semiconductor superlattices,
Siam Journal on Applied Mathematics, vol. 57 no. 6
(January, 1997),
pp. 15881614, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Deift, P; Venakides, S; Zhou, X, New results in small dispersion kdV by an extension of the steepest descent method for RiemannHilbert problems,
International Mathematics Research Notices no. 6
(January, 1997),
pp. 285299, DUKE UNIV PRESS
 Deift, P; Kriecherbauer, T; McLaughlin, KTR; Venakides, S; Zhou, X, Asymptotics for polynomials orthogonal with respect to varying exponential weights,
International Mathematics Research Notices no. 16
(1997),
pp. 759782, Oxford University Press (OUP): Policy B  Oxford Open Option A
 Deift, P; Kriecherbauer, T; Venakides, S, Forced lattice vibrations: Part I,
Communications on Pure and Applied Mathematics, vol. 48 no. 11
(January, 1995),
pp. 11871249, WILEY [doi] [abs]
 Deift, P; Kriecherbauer, T; Venakides, S, Forced lattice vibrations: Part II,
Communications on Pure and Applied Mathematics, vol. 48 no. 11
(January, 1995),
pp. 12511298, WILEY [doi] [abs]
 Bonilla, LL; Higuera, FJ; Venakides, S, The Gunn Effect: Instability of the Steady State and Stability of the Solitary Wave in Long Extrinsic Semiconductors,
Siam Journal on Applied Mathematics, vol. 54 no. 6
(December, 1994),
pp. 15211541, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Deift, P; Venakides, S; Zhou, X, The collisionless shock region for the long‐time behavior of solutions of the KdV equation,
Communications on Pure and Applied Mathematics, vol. 47 no. 2
(January, 1994),
pp. 199206, WILEY [doi] [abs]
 Zhang, T; Venakides, S, Periodic limit of inverse scattering,
Communications on Pure and Applied Mathematics, vol. 46 no. 6
(July, 1993),
pp. 819865, WILEY [doi] [abs]
 Venakides, S; Deift, P; Oba, R, The toda shock problem,
Communications on Pure and Applied Mathematics, vol. 44 no. 89
(January, 1991),
pp. 11711242, WILEY [doi]
 VENAKIDES, S, THE KORTEWEGDEVRIES EQUATION WITH SMALL DISPERSION  HIGHERORDER LAX LEVERMORE THEORY, edited by SPIGLER, R,
Applied and Industrial Mathematics, vol. 56
(January, 1991),
pp. 255262, KLUWER ACADEMIC PUBL, ISBN 0792305213
 Reed, MC; Venakides, S; Blum, JJ, Approximate traveling waves in linear reactionhyperbolic equations,
Siam Journal on Applied Mathematics, vol. 50 no. 1
(January, 1990),
pp. 167180, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Venakides, S, The korteweg‐de vries equation with small dispersion: Higher order lax‐levermore theory,
Communications on Pure and Applied Mathematics, vol. 43 no. 3
(January, 1990),
pp. 335361, WILEY [doi]
 Venakides, S, The continuum limit of theta functions,
Communications on Pure and Applied Mathematics, vol. 42 no. 6
(January, 1989),
pp. 711728, WILEY [doi]
 VENAKIDES, S, THE SMALL DISPERSION LIMIT OF THE KORTEWEGDEVRIES EQUATION, edited by DAFERMOS, CM; LADAS, G; PAPANICOLAOU, G,
Differential Equations //, vol. 118
(January, 1989),
pp. 725737, Marcel Dekker, ISBN 0824780779
 Venakides, S, The infinite period limit of the inverse formalism for periodic potentials,
Communications on Pure and Applied Mathematics, vol. 41 no. 1
(January, 1988),
pp. 317, WILEY [doi]
 Venakides, S, The Zero Dispersion Limit of the KortewegDevries Equation with Periodic Initial Data,
Transactions of the American Mathematical Society, vol. 301 no. 1
(May, 1987),
pp. 189226, American Mathematical Society [doi]
 Venakides, S, The zero dispersion limit of the kortewegde vries equation with periodic initial data,
Transactions of the American Mathematical Society, vol. 301 no. 1
(January, 1987),
pp. 189226, American Mathematical Society (AMS) [doi] [abs]
 Venakides, S, Long time asymptotics of the kortewegde vries equation,
Transactions of the American Mathematical Society, vol. 293 no. 1
(January, 1986),
pp. 411419, American Mathematical Society (AMS) [doi] [abs]
 Venakides, S, Long Time Asymptotics of the Kortewegde Vries Equation,
Transactions of the American Mathematical Society, vol. 293 no. 1
(January, 1986),
pp. 411411, JSTOR [doi]
 Venakides, S, The generation of modulated wavetrains in the solution of the Korteweg—de vries equation,
Communications on Pure and Applied Mathematics, vol. 38 no. 6
(January, 1985),
pp. 883909, WILEY [doi]
 Venakides, S, The zero dispersion limit of the korteweg‐de vries equation for initial potentials with non‐trivial reflection coefficient,
Communications on Pure and Applied Mathematics, vol. 38 no. 2
(January, 1985),
pp. 125155, WILEY [doi] [abs]
 El, G.A.; Krylov, A.L.; Molchanov, S.A.; Venakides,
S., Soliton turbulence as a thermodynamic
limit of stochastic soliton lattices. In Advances in nonlinear mathematics and science.,
Physica D 152/153 (2001), 653664
 S. Venakides, M. Haider, V. Papanicolaou, Boundary Integral Calculations of 2d Electromagnetic Scattering by Photonic Crystal FabryPerot Structures,
SIAM J. Appl. Math. vol. 60/5, (2000), pp. 16361706
 A. Georgieva, T. Kriecherbauer, Stephanos Venakides, Wave Propagation and Resonance in a 1d Nonlinear Discrete Periodic Medium,
SIAM J. Appl. Math., vol. 60/1, (1999), pp. 272294
 P. Deift, T. Kriecherbauer, K. TR McLaughlin,S. Venakides, X. Zhou, Strong Asymptotics of Orhtogonal Polynomials with Respect to Exponential Weights,
CPAM, vol.52 (1999) 14911552.
 M. McDonald, S. Venakides, Renormalization of the Tau Function for Integrable Systems: A Model Problem,
CPAM, Vol 51, 1998, 937966.
 P. Deift, S. Venakides, X. Zhou, An Extension of the Method of Steepest Descent for RiemannHilbert Problems: The Small Dispersion Limit of the Kortewegde Vries (KdV) Equation,
Proc. Ntl. Acad. Sc. USA, vol. 95, Jan 1998, 450454.
 P. Deift, S. Venakides, X. Zhou, New Results in the SmallDispersion KdV by an Extension of the Method of Steepest Descent for RiemannHilbert Problems,
IMRN, 1997, N0. 6, 285299.
 P. Deift, T. Kriecherbauer, K. TR McLaughlin,S. Venakides, X. Zhou, Asymptotics of Polynomials Orthogonal with Respect to Varying Exponential Weights,
IMRN, 1997 No 16, pp. 759782
 P. Deift, T. Kriecherbauer, S. Venakides, Forced Lattice Vibrations Part II,
Comm. Pure Appl. Math. 48, 1995, 12511298.
 P. Deift, T. Kriecherbauer, S. Venakides, Forced Lattice Vibrations Part I,
Comm. Pure Appl. Math. 48,1995, 11871250.
 L. L. Bonilla, F. Higuera, S. Venakides, The Stability of the Steady State of the Gunn Oscillator,
SIAM J. Appl. Math. vol. 54, No 6, (1994), pp. 15211541.
 P. Deift, S. Venakides, X. Zhou, The Collisionless Shock Region for the Long Time Behavior of the Solutions of the KdV Equation,
CPAM. vol. 47, (1994), pp. 199206.
 P. D. Lax, C. D. Levermore, S. Venakides, The Generation and Propagation of Oscillations in Dispersive IVP's and their Limiting Behavior,
Important Developments in Soliton Theory 19801990}, T. Fokas and V.E. Zakharov eds., SpringerVerlag, Berlin (1992).
 S. Venakides, The solution of completely integrable systems in the continuum limit of the spectral data,
IMA Proceedings, vol. 2, (1986) pp. 337356..
 S. Venakides, The zerodispersion limit of the Kortewegde Vries equation with nontrivial reflection coefficient,
Comm. Pure and Appl. Math. 38, pp. 125155, 1985.
Papers Accepted
 Komineas, S; Shipman, SP; Venakides, S, Lossless polariton solitons,
Physica D: Nonlinear Phenomena, vol. 316
(February, 2016),
pp. 4356, Elsevier BV [doi] [abs]
Preprints
 Stavros Komineas, Stephen P. Shipman, Stephanos Venakides, Lossless Polariton Solitons,
arXiv
(2014) [arXiv:1409.4067] [abs]


dept@math.duke.edu
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Mathematics Department
Duke University, Box 90320
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