Walter Van Assche
Address:
Department of Mathematics
Section of Analysis
Celestijnenlaan 200 B box 2400
B-3001 Heverlee
BELGIUM
tel: +32-16-327051
fax: +32-16-327998
Email: walter@wis.kuleuven.be
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I am full professor of mathematics at the department of mathematics of the University of Leuven (KU Leuven). I am currently the head of the department of mathematics and I am a member of the
section of Analysis.Up to September 30, 2000 I was a Research
Director (onderzoeksdirecteur) of the
Belgian National Fund for Scientific
Research, now Research Foundation - Flanders (FWO).
I am an editor of the Journal
of Approximation Theory
I am on the editorial board of the Journal of Difference
Equations and Applications
I am on the editorial board of the Proceedings of the American
Mathematical Society
Research
Teaching
Upcoming Events
- Dick Askey's 80th birthday, Madison, Wisconsin, USA,
December 6-7, 2013. (done)
- International Symposium on Orthogonality, Quadrature and Related Topics,
in memory of Pablo González Vera, Puerto de la Cruz, Tenerife, 20-24 January, 2014. (done)
- Constructive Functions 2014,
in honor of Ed Saff's 70th birhday, Vanderbilt University, Nashville, TN, 26-30 May, 2014. (done)
- Symmetries and Integrability of Difference Equations (SIDE-11),
Bangalore, India, 16-20 June 2014. (done)
- workshop: Exceptional orthogonal polynomials and exact solutions
in Mathematical Physics, Segovia, Spain, 7-12 September 2014. (done)
- workshop: Recent advances in
orthogonal polynomials, University of Kent, September 18, 2014. (done)
- International conference on Orthogonal Polynomials,
Integrable Systems and their Applications, on the occasion of Mourad Ismail's 70th birthday, Shanghai Jiao Tong University and Shaoxing University, China, October 25-29, 2014. (done)
- International Conference on Applied Mathematics,
in honor of Roderick Wong's 70th birthday, City University of Hong Kong, 1-5 December 2014. (done)
- Foundations of Computational Mathematics,
(including workshops on Approximation Theory, Random Matrices, and Special Functions and Orthogonal Polynomials), Montevideo, Uruguay,
11-20 December 2014. (done)
- International conference on Orthogonal Polynomials
and q-series, celebrating the 70th birthday of Mourad Ismail, Orlando, Florida, USA, May 10-12, 2015.
- 13th International Symposium on Orthogonal Polynomials, Special
Functions and Applications (OPSFA13), NIST Gaithersburg, MD, USA, June 1-5, 2015.
- V Iberoamerican workshop on Orthogonal Polynomials,
Mexico City, June 8-12, 2015.
- AMS-EMS-SPM International meeting,
with a special session on Orthogonal Polynomials and Integrable Systems, Porto, Portugal, 10-13 June, 2015.
- Orthogonal and Multiple Orthogonal Polynomials,
Oaxaca, Mexico, August 9-14, 2015.
- International symposium The real world is complex, in honor of
Christian Berg, Copenhagen, Denmark, 26-28 August, 2015.
Ph. D. Students
- Ann Sinap: Berekeningsaspecten van orthogonale
matrixveeltermen (computational aspects of orthogonal matrix
polynomials); March 3, 1995.
- Rudi Maelbrancke: Linear and spatial data structures: new
techniques for analysis and optimization (advisors: H. Olivié and W. Van Assche); March 11, 1996.
- Michael Leuschel: Advanced techniques for logic program
specialisation (Advisors: D. De Schreye and W. Van Assche); May 27,
1997.
- Lieve Delbeke: Wavelet based estimators for the Hurst
parameter of a self-similar process; June 12, 1998.
- Erwin Simons: An efficient multi-domain approach to
large-eddy simulation of incompressible turbulent flows in complex
geometries (advisors: M. Manna and W. Van Assche; prepared at von
Karman Institute),
October 10, 2000.
- Els Coussement: Multiple orthogonal polynomials
associated with modified Bessel functions, July 4, 2002
- Jonathan Coussement: Integrable systems of Toda type related
to orthogonal functions, February 23, 2005
- Hans Van de Vyver: Runge-Kutta type methods for periodic
initial value problems, March 15, 2006
- Christophe Smet: The Hermite-Padé approximation technique for proving irrationality
of certain numbers, September 22, 2009
- Lies Boelen: Discrete Painlevé equations and
orthogonal polynomials, May 28, 2010
- François
Ndayiragije: Multiple Charlier and Meixner polynomials,
July 10, 2012
- Maciej
Haneczok: Nearest neighbor recurrence relations for multiple
orthogonal polynomials, October 9, 2014
- Stijn Tóth: Asymptotics for rational solutions
of Painlevé equations
- Eric Niyikiza: Exceptional orthogonal polynomials and applications in mathematical phyisics
Recent Publications
Books:
ˇ
Orthogonal
Polynomials and Special Functions: Computation and Applications, Lecture
Notes in Mathematics 1883 (F. Marcellán, W. Van Assche)
ˇ
Laredo
Lectures on Orthogonal Polynomials and Special Functions, Nova Science
Publishers (R. Álvarez-Nodarse, F. Marcellán, W. Van Assche)
ˇ
Orthogonal
Polynomials and Special Functions: Leuven 2002, Lecture Notes in
Mathematics 1817 (E. Koelink, W. Van Assche)
ˇ
Asymptotics
for Orthogonal Polynomials, Lecture Notes in Mathematics 1265
ˇ
Difference Equations,
Special Functions and Orthogonal Polynomials, proceedings of the
international conference, Munich, Germany 25-30 July 2005, World Scientific,
2007 (S. Elaydi, J. Cushing, R. Lasser, A. Ruffing, V. Papageorgiou, W. Van
Assche)
ˇ
I wrote two
chapters in Mourad Ismail’s book: Classical
and Quantum Orthogonal Polynomials in One Variable, Encyclopedia of
Mathematics and its Applications 98, Cambridge University Press, 2005. These
are Chapter 22 (The Riemann-Hilbert Problem) and Chapter 23 (Multiple
Orthogonal Polynomials).
Papers:
- On 2D discrete Schrödinger operators associated with multiple orthogonal
polynomials (with Alexander Aptekarev and Maxim Derevyagin), J. Phys. A: Math. Theor. 48 (2015), 065201 (16 pp.)
doi:10.1088/1751-8113/48/6/065201
- Discrete integrable systems generated by Hermite-Padé approximants
(with Alexander Aptekarev and Maxim Derevyagin)
- Mehler-Heine asymptotics for multiple orthogonal polynomials
- Ratio asymptotics for multiple orthogonal polynomials
- Hyperelliptic uniformization of algebraic curves of the third order
(with A.I. Aptekarev and D.N. Toulyakov), J. Comput. Appl. Math.
doi:10.1016/j.cam.2014.11.048
- Computing recurrence coefficients of multiple orthogonal polynomials
(with Galina Filipuk and Maciej Haneczok), Numer. Algorithms
doi:10.1007/s11075-015-9959-8
- Orthogonal polynomials for Minkowski's question mark function
(with Zoé Dresse), J. Comput. Appl. Math.
doi:10.1016/j.cam.2014.07.013
- Multiple orthogonal polynomials associated with an exponential cubic weight
(with Galina Filipuk and Lun Zhang), J. Approx. Theory. 190 (2015), 1-25
doi:10.1016/j.jat.2014.06.006
- A family of nonlinear difference equations:
existence, uniqueness, and asymptotic behavior of
positive solutions (with Saud M. Alsulami, József Szabados and Paul Nevai), J. Approx. Theory.
doi:10.1016/j.jat.2014.04.012
- Zero distribution of polynomials satisfying a differential-difference equation
(with Diego Dominici), Analysis and Applications 12 (2014), no. 6, 635-666.
doi:10.1142/S0219530514500390
- Variations of Stieltjes-Wigert and q-Laguerre polynomials and their recurrence
coefficients (with Lies Boelen), J. Approx. Theory
doi:10.1016/j.jat.2014.06.012
- Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians
(with François Ndayiragije), J. Phys. A: Math. Theor. 46 (2013), 505201 (17 pp).
doi:10.1088/1751-8113/46/50/505201
- Chapter 15: Gauss-type quadrature, in
“Walter Gautschi, Volume 2: Selected Works with Commentaries”, C. Brezinski and A. Sameh (eds.), Birkhäuser Basel, 2014,
pp. 35-49. doi:10.1007/978-1-4614-7049-6_5
- The generalized Krawtchouk polynomials and the fifth Painlevé equation
(with Lies Boelen, Galina Filipuk, Christophe Smet and Lun Zhang), J. Difference Equations Appl. 19, no. 9 (2013), 1437-1451.
doi:10.1080/10236198.2012.755522
- Ladder operators and differential equations for
multiple orthogonal polynomials
(with Galina Filipuk and Lun Zhang), J. Phys. A: Math. Theor. 46 (2013), 205204 (24 pp).
doi:10.1088/1751-8113/46/20/205204
- Life and work (so far) of Paco Marcellán
(with Manuel Alfaro), Recent Advantages in Orthogonal Polynomials, Special Functions, and Their Applications
(J. Arvesú and G. López Lagomasino, eds.), Contemporary Mathematics 578 (2012), 1-18.
doi:10.1090/conm/578/11476
- Interlacing properties of zeros of multiple orthogonal polynomials
(with Maciej Haneczok), J. Math. Anal. Appl. 389 (2012), 429-438.
doi:10.1016/j.jmaa.2011.11.077
- Asymptotics for the ratio and the zeros of multiple Charlier polynomials
(with François Ndayiragije), J. Approx. Theory 164 (2012), 823-840; reprinted in J. Approx. Theory 170 (2013), 3-20
(Proceedings of OPSFA-11).
doi:10.1016/j.jat.2012.03.005
- Recurrence coefficients of generalized Charlier polynomials and the fifth Painlevé equation
(with Galina Filipuk), Proc. Amer. Math. Soc. 141, nr. 2 (2013), 551-562.
doi:10.1090/S0002-9939-2012-11468-6
- Recurrence coefficients of a new generalization of the Meixner polynomials
(with Galina Filipuk), SIGMA Symmetry Integrability Geom. Methods Appl. 7 (2011), 068, 11 pages.
doi:10.3842/SIGMA.2011.068
- Nearest neighbor recurrence relations for multiple orthogonal polynomials,
J. Approx. Theory 163 (2011), 1427-1448.
doi:10.1016/j.jat.2011.05.003
- The recurrence coefficients of semi-classical Laguerre polynomials and the fourth
Painlevé equation
(with Galina Filipuk and Lun Zhang), J. Phys. A: Math. Theor. 45, number 20 (2012), 205201 (13 pp).
doi:10.1088/1751-8113/45/20/205201
- Orthogonal polynomials on a bi-lattice
(with Christophe Smet), Constr. Approx. 36, nr. 2 (2012), 215-242.
doi:10.1007/s00365-011-9145-8
- Recurrence coefficients of generalized Meixner polynomials
and Painlevé equations
(with Lies Boelen and Galina Filipuk), J. Phys. A: Math. Theor. 44, number 3 (2011), 035202 (19 pp.)
doi:10.1088/1751-8113/44/3/035202
- Hermite-Padé rational approximation to irrational numbers
Comput. Methods Funct. Theory 10 (2010), nr. 2, 585-602.
- Orthogonal
polynomials and approximation theory: some open problems in "Recent Trends in Orthogonal Polynomials
and Approximation Theory" (eds. J. Arvesú, F. Marcellán, A. Martínez-Finkelshtein), Contemporary Mathematics
507, (2010), 287-298
- Discrete Painlevé
equations for recurrence coefficients of semiclassical Laguerre
polynomials (with Lies Boelen), Proc. Amer. Math. Soc. 138, no. 4 (2010), 1317-1331.
- Irrationality proof of a
q-extension of ζ(2) using little q-Jacobi polynomials
(with Christophe Smet), Acta Arithmetica 138, nr. 2 (2009), 165-178.
- Mellin transforms for
multiple Jacobi-Pińeiro polynomials (with Christophe Smet), J. Approx. Theory 162 (2010), 782-806.
- q-Discrete Painlevé equations for recurrence
coefficients of modified q-Freud
orthogonal polynomials (with Lies Boelen and Christophe Smet), J.
Difference Equations Appl.
16, no. 1 (2010), 37-53.
- Asymptotics of
Hermite-Padé rational approximants for two analytic functions with
separated pairs of branch points (case of genus 0) (with A.I.
Aptekarev and AB.J. Kuijlaars), Internat. Math. Research Papers 2008
(2008), rpm007-128.
- Leonhard Euler and a q-analogue
of the logarithm (with Erik Koelink), Proc. Amer. Math. Soc. 137 (2009),
1663-1676.
- Padé and Hermite-Padé
approximation and orthogonality, Surveys in Approximation Theory 2
(2006), 61-91.
- Multiple orthogonal
polynomials on the unit circle (with Judit Mínguez Ceniceros), Constr.
Approx. 28 (2008), 173-197.
- Asymptotic zero distribution
for a class of multiple orthogonal polynomials (with E. Coussement and
J. Coussement), Trans. Amer. Math. Soc. 360 (2008), 5571-5588.
- Rakhmanov’s theorem for
orthogonal matrix polynomials on the unit circle, J. Approx. Theory 146
(2007), 227-242
- Irrationality of z_{q}(1) and z_{q}(2) (with K.
Postelmans), J. Number Theory 126 (2007), 119-154.
- Chapter 22: The Riemann Hilbert Problem, in “Classical
and Quantum Orthogonal Polynomials in One Variable”, M.E.H. Ismail,
Cambridge University Press, 2005.
- Chapter 23: Multiple Orthogonal Polynomials,
in “Classical
and Quantum Orthogonal Polynomials in One Variable”, M.E.H. Ismail,
Cambridge University Press, 2005.
- Varying weights for
orthogonal polynomials with monotonically varying recurrence coefficients
(with A.I. Aptekarev and J.S. Geronimo), J. Approx. Theory 150
(2008), 214-238.
- Differential
equations for multiple orthgonal polynomials with respect to classical
weights: raising and lowering operators (with J. Coussement), J. Phys.
A: Math. Gen. 39 (2006), 3311-3318.
- Discrete Painlevé
equations for recurrence coefficients of orthogonal polynomials,
Proceedings of the international conference on Difference Equations,
Special Functions and Orthogonal Polynomials, World Scientific, 2007, pp.
687-725.
- Type II Hermite-Padé
approximation to the exponential function (with A.B.J. Kuijlaars, H.
Stahl, F. Wielonsky), J. Comput. Appl. Math. 207 (2007), 227-244.
- WKB and turning point
theory for second-order difference equations (with J.S. Geronimo and
O. Bruno), Operator Theory: Advances and Applications 154 (2004),
101-138.
- Analytic number theory
and approximation, Coimbra Lecture Notes on Orthogonal Polynomials
(A.P. Foulquié Moreno et al, eds.), Nova Science Publishers, 2007, pp.
211-243.
- A continuum
limit of the relativistic Toda lattice: asymptotic theory of discrete
Laurent orthogonal polynomials with varying recurrence coefficients
(with J. Coussement), J. Phys. A: Math. Gen. 38 (2005), 3337-3366
- Generalizations of orthogonal polynomials (with A. Bultheel, A. Cuyt, M. Van
Barel, B. Verdonk), J. Comput. Appl. Math. 179 (2005), 57-95.
- An extension of the Toda lattice: a
direct and inverse spectral transform connected with orthogonal rational
functions, (with J.
Coussement), Inverse Problems 20 (2004), 297-318.
- Multiple little q-Jacobi
polynomials (with K.
Postelmans), J. Comput. Appl. Math. 178 (2005), 361-375.
- Gauss quadrature for multiple orthogonal
polynomials (with J.
Coussement), J. Comput. Appl. Math. 178 (2005), 131-145.
- Quadratic Hermite-Padé approximation
to the exponential function: a Riemann-Hilbert approach (with A.B.J. Kuijlaars and F.
Wielonsky), Constr. Approx.
21 (2005), 351-412.
- Asymptotique des approximants de
Hermite-Padé quadratiques de la fonction exponentielle et problčmes de
Riemann-Hilbert
(with A. Kuijlaars, H. Stahl and F. Wielonsky), C. R. Acad. Sci. Paris, Ser. I 336 (2003),
893-896.
- Multiple
Wilson and Jacobi-Pińeiro polynomials (with B. Beckermann and J. Coussement), J.
Approx. Theory 132 (2005), 155-181.
- Scalar and matrix Riemann-Hilbert
approach to the strong asymptotics of Padé approximants and complex
orthogonal polynomials with varying weight (with A. I. Aptekarev), J. Approx. Theory 129
(2004), 129-166.
- Analysis of non-linear recurrence
relations for the recurrence coefficients of generalized Charlier
polynomials (with M.
Foupouagnigni), J. Nonlinear Math. Phys. 10 Supplement 2 (2003), 231-237.
- Difference equations for multiple
Charlier and Meixner polynomials in New Progress in Difference Equations (S. Elaydi et al.,
eds.), Taylor & Francis, London, 2003, pp. 547-555.
- Szegö quadrature and frequency
analysis (with L.
Daruis, O. Njĺstad), ETNA 19 (2005), 48-57.
- Para-orthogonal polynomials in
frequency analysis
(with L. Daruis, O. Njĺstad), Rocky Mountain J. Math. 33 No. 2
(2003), 629-645.
- Direct and inverse spectral transform
for the relativistic Toda lattice and the connection with Laurent
orthogonal polynomials (with J. Coussement and A.B.J. Kuijlaars), Inverse Problems 18 (2002),
923-942.
- Blumenthal's theorem for Laurent
orthogonal polynomials (with A. Sri Ranga), J. Approx. Theory 117 (2002), 255-278.
- The Riemann-Hilbert approach to strong
asymptotics for orthogonal polynomials on [-1,1] (with A.B.J. Kuijlaars, K.T-R McLaughlin,
and M. Vanlessen), Adv. Math. 188 (2004), 337-398.
- Strong asymptotics for relativistic
Hermite polynomials
(with W. Gawronski), Rocky Mountain J. Math. 33 No. 2 (2003),
489-524.
- Some discrete multiple orthogonal
polynomials (with J.
Arvesú and J. Coussement), J. Comput. Appl. Math.153 (2003), 19-45.
- Asymptotics of multiple orthogonal
polynomials associated with the modified Bessel functions of the first
kind (with E.
Coussement), J. Comput. Appl. Math. 153 (2003), 141-149.
- Multiple orthogonal polynomials
associated with the modified Bessel functions of the first kind (with E. Coussement), Construct.
Approx. 19 (2003), 237-263.
- Multiple orthogonal polynomials for
classical weights
(with A.I. Aptekarev and A. Branquinho), Trans. Amer. Math. Soc. 355 (2003),
3887-3914.
- Riemann-Hilbert problems for multiple
orthogonal polynomials (with J.S. Geronimo and A.B.J. Kuijlaars), in Special
Functions 2000: Current Perspectives and Future Directions (J. Bustoz
et al., eds.), NATO Science Series II. Mathematics, Physics and Chemistry 30,
Kluwer, Dordrecht, 2001, pp. 23-59.
- Some classical multiple orthogonal
polynomials (with E.
Coussement), J. Comput. Appl. Math. 127 (2001), 317-347
- Little q-Legendre polynomials
and irrationality of certain Lambert series, The Ramanujan Journal 5 (2001),
295-310.
- Entropic integrals of hypersperical
harmonics and spatial entropy of D-dimensional central potentials, (with R. J. Yáńez, R. González-Férez
and J. S. Dehesa), J. Math. Phys. 40 (1999), 5675-5686.
- Functionals of Gegenbauer polynomials
and D-dimensional hydrogenic momentum expectation values, (with R. J. Yáńez, R. González-Férez
and J. S. Dehesa), J. Math. Phys. 41 (2000), 6600-6613.
- Information entropy of Gegenbauer
polynomials, (with
V. S. Buyarov, P. López-Artés, A. Martínez-Finkelshtein), J. Phys. A,
Math. Gen. 33 (2000), 6549-6560.
- Nonsymmetric linear difference
equations for multiple orthogonal polynomials, proceedings of SIDEIII (Symmetry and
Integrability of Difference Equations), CRM Proceedings and Lecture Notes 25,
Amer. Math. Soc., 2000, pp. 391-405.
- Lamé differential equations and
electrostatics,
(with Dimitar K. Dimitrov), Proc. Amer. Math. Soc. 128 (2000),
3621-3628 (see also the erratum)
- Zero distribution of orthogonal
polynomials with asymptotically periodic varying recurrence coefficients, proceedings of Self-Similar
Systems, Dubna, Russia, 1998, pp. 392-402.
- Multiple orthogonal polynomials,
irrationality and transcendence, in Continued Fractions: from analytic number theory to
constructive approximation, Contemporary Mathematics 236, Amer.
Math. Soc., 1999, pp. 325-342
- Spectral representation of certain
finite birth and death processes, (with P. R. Parthasarathy and R. B. Lenin), The
Math. Scientist 24 (1999), 105-112
- Multiple orthogonal polynomials
associated with Macdonald functions, (with S.B. Yakubovich), Integral Transforms
and Special Functions 9 (2000), 229-244
- Asymptotics for polynomials
satisfying a certain twin limit periodic recurrence relation, (with E.X.L. de Andrade and A. Sri
Ranga), Methods and Applications of Analysis 6 (1999), 535-548
- The asymptotic zero distribution of
orthogonal polynomials with varying recurrence coefficients (with A. B .J. Kuijlaars), J.
Approx. Theory 99 (1999), 167-197
- A birth and death process related to
the Rogers-Ramanujan continued fraction (with P. R. Parthasarathy, R. B. Lenin and W.
Schoutens), J. Math. Anal. Appl. 224 (1998), 297-315
- Asymptotic behavior of the continued
fraction coefficients of a class of Stieltjes transforms including the
Binet function (with
W. B. Jones), Orthogonal Functions, Moment Theory and Continued
Fractions (W.B. Jones, A. Sri Ranga, eds.), Marcel Dekker, 1998, pp.
257-274
- Extremal polynomials on discrete sets (with A. B. J. Kuijlaars), Proc.
London Math. Soc. (3) 79 (1999), 191-221
- Approximation theory and analytic
number theory, Special
Functions and Differential Equations (K. Srinivasa Rao et al., eds.),
Allied Publishers, New Delhi, 1998, pp. 336-355.
- Perturbation of orthogonal
polynomials on an arc of the unit circle, II, (with L. Golinskii, P. Nevai and F.
Pinter), J. Approx. Theory 96 (1999), 1-33.
- A contact problem in elasticity
related to weighted polynomials on the real line (with A.B.J. Kuijlaars), Rend. Circ. Mat. Palermo,
serie II, 52 (supplemento), volume II (1998), 575-587
- A problem of Totik on fast decreasing
polynomials (with A.B.J.
Kuijlaars), Constr.
Approx. 14 (1998), 97-112
- A wavelet based estimator for the
parameter of self-similarity of fractional Brownian motion (with Lieve Delbeke)
- A wavelet based estimator for the
parameter of self-similarity of fractional Brownian motion (with Lieve Delbeke),
Aportaciones Matematicas (a short version of the previous paper)
- Information entropy of classical
orthogonal polynomials and their application to the harmonic oscillator
and Coulomb potentials(with J.S. Dehesa and R.J. Yanez), Methods Appl. Anal. 4 (1997),
91-110
- Compact Jacobi matrices: from
Stieltjes to Krein and M(a,b), Ann. Fac. Sci. Toulouse, numéro special Stieltjes (1996), 195-215
- Perturbation of orthogonal
polynomials on an arc of the unit circle (with L. Golinskii and P. Nevai), J. Approx.
Theory 83 (1995), 392-422
- Upward extension of the Jacobi matrix
for orthogonal polynomials (with A. Ronveaux), J. Approx. Theory 86 (1996), 335-357
- Orthogonal polynomials in the complex
plane and on the real line, Special Functions, q-Series and Related Topics (M.E.H. Ismail
et al., eds.), Fields Institute Communications 14 (1997), 211-245
- The impact of Stieltjes' work on
continued fractions and orthogonal polynomials: additional remarks (with G. Valent), J. Comput. Appl.
Math. 65 (1995), 419-447
- Orthogonal matrix polynomials and
applications (with
A. Sinap), J. Comput. Appl. Math. 66 (1996), 27-52
- Entropy of orthogonal polynomials
with Freud weights and information entropies of the harmonic oscillator (with J.S. Dehesa and R.J. Yanez) J.
Math. Phys. 36 (1995), 4106-4118
- Orthogonal polynomials and Laurent
polynomials related to the Hahn-Exton q-Bessel function (with H.T. Koelink), Constr. Approx.
11 (1995), 477-512
- and some more of which I don't have electronic versions.
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