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September 15, 2006
O P - S F N E T Volume 13, Number 5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Editors:
Diego Dominici dominicd@newpaltz.edu
Martin Muldoon muldoon@yorku.ca
The Electronic News Net of the SIAM Activity Group
on Orthogonal Polynomials and Special Functions
Please send contributions to: poly@siam.org
Subscribe by mailing to: poly-request@siam.org
or to: listproc@nist.gov
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Today's Topics:
1. Workshop on Applications of Macdonald Polynomials
2. New book on Painleve Transcendents
3. New book on Number Theory in the Spirit of Ramanujan
4. Sum of even terms in E_q(q^{1/2}) indeed related
to root system E_8
5. 2007 SIAM Prizes - Open Calls for Nominations
6. Preprints in arXiv.org
7. About the Activity Group
8. Submitting contributions to OP-SF NET
Calendar of Events:
2006
September 15-19: International Conference on Numerical
Analysis and Applied Mathematics 2006 (ICNAAM 2006)
Hersonnisos, Crete, Greece 13.3 #1
http://www.icnaam.org/
November 6-11: Harmonic Analysis and Applications, Sousse, Tunisia
http://ichaa.50webs.com/ 13.3 #2
2007
July 2-6: The 9th Conference on Orthogonal Polynomials, Special
Functions and Applications, Marseille, France
http://www.cirm.univ-mrs.fr/web.ang/liste_rencontre/Rencontres2007/
Valent07/Valent07.html
July 9-13: International Conference on SCIentific Computation and
Differential Equations, Saint-Malo, France
http://scicade07.irisa.fr/
July 16-20: ICIAM 2007 - 6th International Congress on Industrial
and Applied Mathematics, Zurich, Switzerland
http://www.iciam07.ch 13.4 #2
September 9-14: Applications of Macdonald Polynomials, Banff
International Research Station, Banff, Alberta, Canada
www.pims.math.ca/birs/birspages.php?task=displayevent&event_id=07w5048
13.5 #1
Topic #1 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: OP-SF NET Editors
Subject: Workshop on Applications of Macdonald Polynomials
A workshop "Applications of Macdonald Polynomials" will be held at the
Banff International Research Station, Alberta, Canada during 9-14
September 2007. The Organizers are Francois Bergeron (Université du
Quebec a Montréal), Jim Haglund (University of Pennsylvania) and Jeff
Remmel (Univ. of California at San Diego).
From the Workshop web site:
The study of Macdonald polynomials is one of the most active current
areas of research in Algebraic Combinatorics. It exhibits natural ties
with many area of mathematics: Algebraic Geometry, Representation
Theory, Special Function Theory, etc., and raises new exciting questions
in all of these subjects. The techniques involved in this study are also
wide ranging, going from the uses of Double Affine Hecke Algebras to the
study of Hilbert Schemes, passing through the study of deep
combinatorial statistics on tableaux. For example, in the mid 90's
Cherednik showed that nonsymmetric Macdonald polynomials are intimately
tied up with the representation theory of Double Affine Hecke Algebras,
and resolved the ``Macdonald constant term-conjectures" for arbitrary
root systems. These conjectures were a focal point of research in
Algebraic Combinatorics throughout the 1980's. Another example is the
work of Haiman, who showed that there are deep connections between
algebraic geometry, the representation theory of the space of diagonal
harmonics, and the the theory of Macdonald polynomials. He was awarded
the 2004 Moore AMS prize for this work. Haiman subsequently extended his
methods to prove a long-standing conjecture for the character of
diagonal harmonics as an analytic expression involving a sum of rational
functions in two parameters q,t. A related result was obtained by Iain
Gordon, who using Cherednik's approach proved an analogue of Haiman's
result on the dimension of diagonal harmonics for other root systems. In
addition Lapointe and Morse have introduced a generalization of Schur
functions called k-Schur functions which have many unexpected
connections to geometry and Macdonald polynomial theory.
For more information. see:
http://www.pims.math.ca/birs/birspages.php?task=displayevent&event_id=07w5048
Topic #2 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: OP-SF NET Editors
Subject: New book on Painleve Transcendents
From: http://www.ams.org/bookstore
Painleve Transcendents: The Riemann-Hilbert Approach,
Athanassios S. Fokas, Cambridge University, United Kingdom, Alexander R.
Its, Indiana State University, Indianapolis, IN, Andrei A. Kapaev,
Steklov Mathematical Institute, St. Petersburg, Russia, and Victor Yu.
Novokshenov, Russian Academy of Sciences, Ufa, Russia
Mathematical Surveys and Monographs
2006; approx. 560 pp; hardcover
Volume: 128
ISBN-10: 0-8218-3651-X
ISBN-13: 978-0-8218-3651-4
List Price: US$109
Member Price: US$87
Order Code: SURV/128
Expected publication date is November 2, 2006.
At the turn of the twentieth century, the French mathematician Paul
Painleve and his students classified second order nonlinear ordinary
differential equations with the property that the location of possible
branch points and essential singularities of their solutions does not
depend on initial conditions. It turned out that there are only six such
equations (up to natural equivalence), which later became known as
Painleve I-VI.
Although these equations were initially obtained answering a strictly
mathematical question, they appeared later in an astonishing (and
growing) range of applications, including, e.g., statistical physics,
fluid mechanics, random matrices, and orthogonal polynomials. Actually,
it is now becoming clear that the Painleve transcendents (i.e., the
solutions of the Painleve equations) play the same role in nonlinear
mathematical physics that the classical special functions, such as Airy
and Bessel functions, play in linear physics.
The explicit formulas relating the asymptotic behaviour of the classical
special functions at different critical points, play a crucial role in
the applications of these functions. It is shown in this book, that even
though the six Painleve equations are nonlinear, it is still possible,
using a new technique called the Riemann-Hilbert formalism, to obtain
analogous explicit formulas for the Painleve transcendents. This
striking fact, apparently unknown to Painleve and his contemporaries, is
the key ingredient for the remarkable applicability of these "nonlinear
special functions".
The book describes in detail the Riemann-Hilbert method and emphasizes
its close connection to classical monodromy theory of linear equations
as well as to modern theory of integrable systems. In addition, the book
contains an ample collection of material concerning the asymptotics of
the Painleve functions and their various applications, which makes it a
good reference source for everyone working in the theory and
applications of Painleve equations and related areas.
Readership: Graduate students and research mathematicians interested in
special functions, in particular, Painleve transcendents.
Table of Contents
* Introduction. Painleve transcendents as nonlinear special functions
Part 1. Riemannian-Hilbert problem, isomonodromy method and special
functions
* Systems of linear ordinary differential equations with rational
coefficients. Elements of the general theory
* Monodromy theory and special functions
* Inverse monodromy problem and Riemann-Hilbert factorization
* Isomonodromy deformations. The Painleve equations
* The isomonodromy method
* Bäcklund transformations
Part 2. Asymptotics of the Painleve II transcendent. A case study
* Asymptotic solutions of the second Painleve equation in the complex
plane. Direct monodromy problem approach
* Asymptotic solutions of the second Painleve equation in the complex
plane. Inverse monodromy problem approach
* PII asymptotics on the canonical six-rays. The purely imaginary case
* PII asymptotics on the canonical six-rays. Real-valued case
* PII quasi-linear Stokes phenomenon
Part 3. Asymptotics of the third Painleve transcendent
* PIII equation, an overview
* Sine-Gordon reduction of PIII
* Canonical four-rays. Real-valued solutions of SG-PIII
* Canonical four-rays. Singular solutions of the SG-PIII
* Asymptotics in the complex plane of the SG-PIII transcendent
* Proof of Theorem 3.4
* The Birkhoff-Grothendieck theorem with a parameter
* Bibliography
* Subject index
Topic #3 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: OP-SF NET Editors
Subject: New book on Number Theory in the Spirit of Ramanujan
Bruce C. Berndt
Number Theory in the Spirit of Ramanujan
Student Mathematical Library, Vol 34
American Mathematical Society, 2006, 187 pp.
ISBN: 0-8218-4178-5; List US$35 (AMS Member US$28)
From the web site
http://www.ams.org/bookstore
Ramanujan is recognized as one of the great number theorists of the
twentieth century. Here now is the first book to provide an introduction
to his work in number theory. Most of Ramanujan's work in number theory
arose out of $q$-series and theta functions. This book provides an
introduction to these two important subjects and to some of the topics
in number theory that are inextricably intertwined with them, including
the theory of partitions, sums of squares and triangular numbers, and
the Ramanujan tau function. The majority of the results discussed here
are originally due to Ramanujan or were rediscovered by him. Ramanujan
did not leave us proofs of the thousands of theorems he recorded in his
notebooks, and so it cannot be claimed that many of the proofs given in
this book are those found by Ramanujan. However, they are all in the
spirit of his mathematics.
The subjects examined in this book have a rich history dating back to
Euler and Jacobi, and they continue to be focal points of contemporary
mathematical research. Therefore, at the end of each of the seven
chapters, Berndt discusses the results established in the chapter and
places them in both historical and contemporary contexts. The book is
suitable for advanced undergraduates and beginning graduate students
interested in number theory.
Topic #4 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: Tom Koornwinder
Subject: Sum of even terms in E_q(q^{1/2}) indeed related
to root system E_8
In OP-SF NET 13.4, Topic #9 I wrote:
>In the preprint
>http://www.arxiv.org/abs/hep-th/0404120
>Werner Nahm,
>Conformal field theory and torsion elements of the Bloch group,
>Contribution to Les Houches Lecture Notes, March 2003,
>the Introduction mentions the conjectured identity
>
>\sum_{n=0}^\infty \frac{q^{2n^2}}{(q;q)_{2n} =
>\sum_{m_1,\ldots,m_8=0}^\infty
>\frac{q^{mCm}}{(q;q)_{m_1}\ldots(q;q){m_8}}
>
>where C is the inverse of the Cartan matrix of the exceptional Lie
>algebra E_8.
>The formula has been checked to high order by computer algebra.
>Note that the left-hand side is the sum of the even degree terms
>in the power series of E_q(z)=(-z;q)_\infty for z=q.
First of all, the last q above must be q^{1/2}. Furthermore, Hjalmar
Rosengren communicated to me that W. Nahm's conjectured formula already
occurs with proof as formula (8) in the paper
S. Warnaar & P.A. Pearce, Exceptional structure of the dilute $A_3$
model: $E_8$ and $E_7$ Rogers-Ramanujan identities, J. Phys. A 27
(1994), L891-L897.
In order to match the Warnaar-Pearce formula with Nahm's formula, it
still has to be shown that
(q;q)_\infty \sum_{n=0}^\infty \frac{q^{2n^2}}{(q;q)_{2n} =
\sum_{n=-\infty}^\infty (q^{12 n^2+n} - q^{12 n^2+7n+1}),
which might have been a relatively easy exercise in the book by
Gasper & Rahman.
Topic #5 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: J. M. Littleton
Subject: 2007 SIAM Prizes - Open Calls for Nominations
The following SIAM prizes will be awarded in 2007 and currently have
open calls for nominations. Calls for nominations can be found at
www.siam.org/prizes/nominations.php.
* SIAM/ACM PRIZE IN CSE
Nominations due Sept. 30
To be presented at the SIAM Conference on Computational Science and
Engineering (CSE07), Feb 19-23, 2007.
* JURGEN MOSER LECTURE
Nominations due Oct. 2
* J. D. CRAWFORD PRIZE
Nominations due Oct. 15
Both to be presented at the SIAM Conference on Applications of Dynamical
Systems (DS07), May 28-June 1, 2007.
Please address inquiries to:
J. M. Littleton
SIAM
E-mail: littleton@siam.org
Telephone: +1-215-382-9800 ext. 303
Fax: +1-215-386-7999
Topic #6 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: OP-SF NET Editors
Subject: Preprints in arXiv.org
The following preprints related to the fields of orthogonal polynomials
and special functions were posted or cross-listed to one of the
subcategories of arXiv.org during July and August 2006. See
especially:
http://front.math.ucdavis.edu/math.CA
http://front.math.ucdavis.edu/math.CO
http://front.math.ucdavis.edu/math.QA
http://xxx.lanl.gov/archive/solv-int
http://arxiv.org/abs/math.CA/0607250
Title: Properties of generalized univariate hypergeometric functions
Authors: Fokko J. van de Bult, Eric M. Rains, Jasper V. Stokman
Comments: 46 pages
Subj-class: Classical Analysis and ODEs
http://arxiv.org/abs/math.CA/0607093
Title: Limits of elliptic hypergeometric integrals
Authors: Eric M. Rains
Comments: 40 pages LaTeX
Subj-class: Classical Analysis and ODEs
http://arxiv.org/abs/nlin.SI/0607065
Title: Hypergeometric Solutions to the q-Painlev\'e Equation of Type
$(A_1+A_1')^{(1)}$
Authors: Taro Hamamoto, Kenji Kajiwara, Nicholas S. Witte
Comments: 17 pages
Subj-class: Exactly Solvable and Integrable Systems; Classical Analysis
and ODEs
http://arxiv.org/abs/math.NT/0607733
Title: On Nyman, Beurling and Baez-Duarte's Hilbert space reformulation
of the Riemann hypothesis
Authors: Bhaskar Bagchi
Comments: 10 pages
Subj-class: Number Theory; Classical Analysis and ODEs
http://arxiv.org/abs/math.FA/0607711
Title: Analytic approximation of rational matrix functions
Authors: V.V. Peller, V.I. Vasyunin
Subj-class: Functional Analysis; Classical Analysis and ODEs; Complex
Variables
MSC-class: 47B35
http://arxiv.org/abs/math.CA/0607694
Title: Inequalities related to the error function
Authors: Omran Kouba
Comments: 12 pages
Subj-class: Classical Analysis and ODEs; Probability
http://arxiv.org/abs/math.CA/0607650
Title: On a new unified integral
Authors: Mridula Garg, Shweta Mittal
Comments: 3 pages
Subj-class: Classical Analysis and ODEs
MSC-class: 33C20; 33C47; 33C60
http://arxiv.org/abs/math.CA/0607649
Title: Operator calculus approach to solving analytic systems
Authors: Ph. Feinsilver, R. Schott
Comments: 3 figures (Maple worksheets)
Subj-class: Classical Analysis and ODEs; Functional Analysis
http://arxiv.org/abs/math.CA/0607555
Title: Meromorphic Solutions of Linear Differential Systems, Painleve
type functions
Authors: Lev Sakhnovich
Subj-class: Classical Analysis and ODEs; Functional Analysis
MSC-class: 34M05; 34M55; 47B38
http://arxiv.org/abs/math.CA/0607471
Title: Zeros of the Macdonald function of complex order
Authors: Erasmo M. Ferreira, Javier Sesma
Comments: 13 pages, 3 figures
Subj-class: Classical Analysis and ODEs
MSC-class: 33C10
http://arxiv.org/abs/math.CV/0607416
Title: Polya-Schur master theorems for circular domains and their
boundaries
Authors: Julius Borcea, Petter Brändén, Boris Shapiro
Comments: 17 pages
Subj-class: Complex Variables; Classical Analysis and ODEs
MSC-class: 47D03; 26C10; 30C15; 30D15; 32A60; 47B38
http://arxiv.org/abs/math.CO/0607359
Title: The Abel Lemma and the q-Gosper Algorithm
Authors: Vincent Y. B. Chen, William Y. C. Chen, Nancy S. S. Gu
Comments: 17 pages
Subj-class: Combinatorics; Classical Analysis and ODEs
http://arxiv.org/abs/math.CA/0607122
Title: A new multivariable 6-psi-6 summation formula
Authors: Michael Schlosser
Comments: 16 pages
Subj-class: Classical Analysis and ODEs
MSC-class: 33D15
http://arxiv.org/abs/math.CA/0608742
Title: Multilateral inversion of A_r, C_r and D_r basic hypergeometric
series
Authors: Michael J. Schlosser
Comments: 24 pages
Subj-class: Classical Analysis and ODEs; Combinatorics
MSC-class: 33D67 (Primary) 15A09, 33D15 (Secondary)
http://arxiv.org/abs/math.CA/0608026
Title: Curious extensions of Ramanujan's 1-psi-1 summation formula
Authors: Victor J. W. Guo, Michael J. Schlosser
Comments: 12 pages
Subj-class: Classical Analysis and ODEs
MSC-class: 33D15 (Primary) 05A19, 33D99 (Secondary)
http://arxiv.org/abs/hep-ph/0607006
Title: Hypergeometric representation of a four-loop vacuum bubble
Authors: Ervin Bejdakic, York Schroder
Comments: 5 pages, to appear in the proceedings of the conference "Loops
and Legs", Eisenach, 2006
http://arxiv.org/abs/math.CA/0607823
Title: An Intertwining Operator for the Group B2
Authors: Charles F. Dunkl
Comments: 27 pages
Subj-class: Classical Analysis and ODEs
MSC-class: 33C80, 33C20 (Primary); 33C70, 43A80 (Secondary)
http://arxiv.org/abs/math.CV/0607773
Title: Dessins d'enfants and differential equations
Authors: Finnur Larusson, Timur Sadykov
Comments: 11 pages
Subj-class: Complex Variables; Algebraic Geometry; Combinatorics
MSC-class: 32S40; 05C05, 14H30, 32G34, 34M15, 34M50
http://arxiv.org/abs/hep-ph/0607300
Title: Evaluating Two-Loop massive Operator Matrix Elements with
Mellin-Barnes Integrals
Authors: I. Bierenbaum, J. Blümlein, S. Klein
Comments: 6 pages, 3 figures, 1 style file, to appear in the Proceedings
of "Loops and Legs in Quantum Field Theory 2006", Eisenach, April,
2006
http://arxiv.org/abs/math/0607202
Title: Some more identities of the Rogers-Ramanujan type
Authors: Douglas Bowman, James Mc Laughlin
Comments: 24 pages. Updated in response to comments concerning one of
the identities
Subj-class: Number Theory; Combinatorics
MSC-class: 33D15; 05A17; 05A19; 11B65; 11P81; 33F10
http://arxiv.org/abs/math.RT/0608301
Title: On the evaluation of some Selberg-like integrals
Authors: B. Binegar
Subj-class: Representation Theory
MSC-class: 33D70,05E05,32M15
http://arxiv.org/abs/math/0608410
Title: On optimal truncation of divergent series solutions of nonlinear
differential systems; Berry smoothing
Authors: O. Costin, M. D. Kruskal
Subj-class: Classical Analysis and ODEs
MSC-class: 34M40,34M30,34M37,34M40,34E05
Journal-ref: Proc. R. Soc. Lond. A 455, 1931-1956 (1999)
http://arxiv.org/abs/math.CV/0608297
Title: Sums of entire functions having only real zeros
Authors: Steven R. Adams, David A. Cardon
Comments: 10 pages
Subj-class: Complex Variables
MSC-class: 30C15
http://arxiv.org/abs/math-ph/0608023
Title: sl(2,R) Symmetry and solvable multiboson systems
Authors: Tomasz Golinski, Maciej Horowski, Anatol Odzijewicz, Aneta
Slizewska
Comments: 23 pages, 1 figure
Subj-class: Mathematical Physics
MSC-class: 81V80; 17B15; 47L90; 47N50
http://arxiv.org/abs/math-ph/0607007
Title: Skew-orthogonal polynomials, differential systems and random
matrix theory
Authors: Saugata Ghosh
Comments: 22 pages
Subj-class: Mathematical Physics
http://arxiv.org/abs/math-ph/0607022
Title: New connection formulae for the q-orthogonal polynomials via a
series expansion of the q-exponential
Authors: R. Chakrabarti, R. Jagannathan, S. S. Naina Mohammed
Comments: 14 pages
Subj-class: Mathematical Physics; Quantum Algebra
http://arxiv.org/abs/math-ph/0607043
Title: Universality of a double scaling limit near singular edge points
in random matrix models
Authors: T. Claeys, M. Vanlessen
Comments: 32 pages, 3 figures
Subj-class: Mathematical Physics
MSC-class: 15A52; 33E17; 35Q15
http://arxiv.org/abs/cond-mat/0607243
Title: Energy correlations for a random matrix model of disordered
bosons
Authors: T. Lueck, H.-J. Sommers, M.R. Zirnbauer
Comments: 20 pages, 3 figures
Subj-class: Mesoscopic Systems and Quantum Hall Effect; Disordered
Systems and Neural Networks; Mathematical Physics
http://arxiv.org/abs/math.CO/0607138
Title: Dyson's new symmetry and generalized Rogers-Ramanujan identities
Authors: Cilanne Boulet
Subj-class: Combinatorics
MSC-class: 05A17; 11P81
http://arxiv.org/abs/math.NT/0607199
Title: On the mean values of Dirichlet $L$-functions
Authors: H. M. Bui, J. P. Keating
Subj-class: Number Theory
http://arxiv.org/abs/math.NT/0607782
Title: Equivalence of Riesz and Baez-Duarte criterion for the Riemann
Hypothesis
Authors: J.Cislo, M.Wolf
Subj-class: Number Theory
MSC-class: 11M26
http://arxiv.org/abs/math.CO/0607514
Title: On asymptotics, Stirling numbers, Gamma function and polylogs
Authors: Daniel B. Gruenberg
Comments: 24 pages, to appear in Results for Mathematics
Subj-class: Combinatorics; Number Theory
MSC-class: 05A10; 11A07; 30B10
http://arxiv.org/abs/math.GM/0607095
Title: Chebyshev Partition function: A connection between Statistical
Physics and Riemann Hypothesis
Authors: Jose Javier garcia Moreta
Comments: 5 pages research paper, an approach to solve Riemann
Hypothesis by means of Statistical Physics
Subj-class: General Mathematics; Number Theory
MSC-class: 11.xx 45.xx 46.xx
http://arxiv.org/abs/math-ph/0608015
Title: Sturm-Liouville Problem in Quantum Calculus
Authors: Ahmed Fitouhi, Akram Nemri, Meniar Haddad
Comments: 16 pages
Subj-class: Mathematical Physics
MSC-class: 33D60, 26D15, 33D05, 33D15, 33D90
http://arxiv.org/abs/math-ph/0608040
Title: The evanescent waves in geometrical optics and the mixed
hyperbolic-elliptic type systems
Authors: Enrico De Micheli, Giovanni Alberto Viano
Comments: 30 pages, 3 figures
Subj-class: Mathematical Physics; Optics
MSC-class: 78A05; 35M10; 34M40
Journal-ref: Appl. Anal. 85 (2006), 181-204
http://arxiv.org/abs/quant-ph/0608099
Title: Uniform semiclassical approximations of the nonlinear
Schroedinger equation by a Painleve mapping
Authors: D. Witthaut, H. J. Korsch
http://arxiv.org/abs/math-ph/0607011
Title: General Relativity and Quantum Mechanics: Towards a
Generalization of the Lambert W Function
Authors: Tony C. Scott, Robert B. Mann, Roberto E. Martinez
Comments: A generalization of the Lambert W function is presented: it
was found as a consequence of a previously unknown link between Gravity
Theory and the Schroedinger wave equation in lower dimensions (1+1).
This paper is related to physics/0607081 which presents analytical
solutions to a special case of the quantum 3-body problem
Subj-class: Mathematical Physics
MSC-class: 33E30; 83C80; 81V55
Journal-ref: AAECC (Applicable Algebra in Engineering, Communication and
Computing), vol. 16, no. 6, (2006)
Topic #7 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: OP-SF NET Editors
Subject: About the Activity Group
The SIAM Activity Group on Orthogonal Polynomials and Special Functions
consists of a broad set of mathematicians, both pure and applied. The
Group also includes engineers and scientists, students as well as
experts. We have around 140 members scattered about in more than 20
countries. Whatever your specialty might be, we welcome your
participation in this classical, and yet modern, topic. Our WWW home
page is:
http://math.nist.gov/opsf/
This is a convenient point of entry to all the services provided by the
Group. Our Webmaster is Bonita Saunders (bonita.saunders@nist.gov).
The Activity Group sponsors OP-SF NET, which is transmitted periodically
by SIAM. It is provided as a free public service; membership in SIAM
is not required. The OP-SF Net Editors are Diego Dominici
(dominicd@newpaltz.edu) and Martin Muldoon (muldoon@yorku.ca).
To receive the OP-SF NET, send your name and email address to
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Back issues can be obtained at the WWW addresses:
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For several years the Activity Group sponsored a printed Newsletter,
most recently edited by Rafael Yanez. Back issues are accessible at:
http://www.mathematik.uni-kassel.de/~koepf/siam.html
Given the widespread availability of email and the Internet, the need for
the printed Newsletter has decreased. Discussions are underway concerning
whether an annual printed Newsletter or Annual Report should be
instituted.
SIAM has several categories of membership, including low-cost categories
for students and residents of developing countries. For current
information on SIAM and Activity Group membership, contact:
Society for Industrial and Applied Mathematics
3600 University City Science Center
Philadelphia, PA 19104-2688 USA
phone: +1-215-382-9800
email: service@siam.org
WWW : http://www.siam.org
http://www.siam.org/membership/outreachmem.htm
Finally, the Activity Group operates an email discussion group, called
OP-SF Talk. To subscribe, send the email message
subscribe opsftalk Your Name
to listproc@nist.gov. To contribute an item to the discussion, send
email to opsftalk@nist.gov. The archive of all messages is accessible
at:
http://math.nist.gov/opsftalk/archive
Topic #8 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: OP-SF NET Editors
Subject: Submitting contributions to OP-SF NET
To contribute a news item to OP-SF NET, send email to poly@siam.org
with a copy to one of the OP-SF Editors or
.
Contributions to OP-SF NET 13.6 should be sent by November 1, 2006.
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OP-SF NET is a forum of the SIAM Activity Group on
Special Functions and Orthogonal Polynomials.
We disseminate your contributions on anything of interest to the
special functions and orthogonal polynomials community. This
includes announcements of conferences, forthcoming books, new
software, electronic archives, research questions, job openings.
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Send submissions to: poly@siam.org
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The elected Officers of the Activity Group (2005-2007) are:
Peter A. Clarkson, Chair
Daniel W. Lozier, Vice Chair
Javier Segura, Secretary
Peter A. McCoy, Program Director
The appointed officers are:
Diego Dominici, OP-SF NET co-editor
Martin Muldoon, OP-SF NET co-editor
Bonita Saunders, Webmaster
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September 15, 2006
O P - S F N E T Volume 13, Number 5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Editors:
Diego Dominici dominicd@newpaltz.edu
Martin Muldoon muldoon@yorku.ca
The Electronic News Net of the SIAM Activity Group
on Orthogonal Polynomials and Special Functions
Please send contributions to: poly@siam.org
Subscribe by mailing to: poly-request@siam.org
or to: listproc@nist.gov
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Today's Topics:
1. Workshop on Applications of Macdonald Polynomials
2. New book on Painleve Transcendents
3. New book on Number Theory in the Spirit of Ramanujan
4. Sum of even terms in E_q(q^{1/2}) indeed related
to root system E_8
5. 2007 SIAM Prizes - Open Calls for Nominations
6. Preprints in arXiv.org
7. About the Activity Group
8. Submitting contributions to OP-SF NET
Calendar of Events:
2006
September 15-19: International Conference on Numerical
Analysis and Applied Mathematics 2006 (ICNAAM 2006)
Hersonnisos, Crete, Greece 13.3 #1
http://www.icnaam.org/
November 6-11: Harmonic Analysis and Applications, Sousse, Tunisia
http://ichaa.50webs.com/ 13.3 #2
2007
July 2-6: The 9th Conference on Orthogonal Polynomials, Special
Functions and Applications, Marseille, France
http://www.cirm.univ-mrs.fr/web.ang/liste_rencontre/Rencontres2007/
Valent07/Valent07.html
July 9-13: International Conference on SCIentific Computation and
Differential Equations, Saint-Malo, France
http://scicade07.irisa.fr/
July 16-20: ICIAM 2007 - 6th International Congress on Industrial
and Applied Mathematics, Zurich, Switzerland
http://www.iciam07.ch 13.4 #2
September 9-14: Applications of Macdonald Polynomials, Banff
International Research Station, Banff, Alberta, Canada
www.pims.math.ca/birs/birspages.php?task=displayevent&event_id=07w5048
13.5 #1
Topic #1 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: OP-SF NET Editors
Subject: Workshop on Applications of Macdonald Polynomials
A workshop "Applications of Macdonald Polynomials" will be held at the
Banff International Research Station, Alberta, Canada during 9-14
September 2007. The Organizers are Francois Bergeron (Université du
Quebec a Montréal), Jim Haglund (University of Pennsylvania) and Jeff
Remmel (Univ. of California at San Diego).
From the Workshop web site:
The study of Macdonald polynomials is one of the most active current
areas of research in Algebraic Combinatorics. It exhibits natural ties
with many area of mathematics: Algebraic Geometry, Representation
Theory, Special Function Theory, etc., and raises new exciting questions
in all of these subjects. The techniques involved in this study are also
wide ranging, going from the uses of Double Affine Hecke Algebras to the
study of Hilbert Schemes, passing through the study of deep
combinatorial statistics on tableaux. For example, in the mid 90's
Cherednik showed that nonsymmetric Macdonald polynomials are intimately
tied up with the representation theory of Double Affine Hecke Algebras,
and resolved the ``Macdonald constant term-conjectures" for arbitrary
root systems. These conjectures were a focal point of research in
Algebraic Combinatorics throughout the 1980's. Another example is the
work of Haiman, who showed that there are deep connections between
algebraic geometry, the representation theory of the space of diagonal
harmonics, and the the theory of Macdonald polynomials. He was awarded
the 2004 Moore AMS prize for this work. Haiman subsequently extended his
methods to prove a long-standing conjecture for the character of
diagonal harmonics as an analytic expression involving a sum of rational
functions in two parameters q,t. A related result was obtained by Iain
Gordon, who using Cherednik's approach proved an analogue of Haiman's
result on the dimension of diagonal harmonics for other root systems. In
addition Lapointe and Morse have introduced a generalization of Schur
functions called k-Schur functions which have many unexpected
connections to geometry and Macdonald polynomial theory.
For more information. see:
http://www.pims.math.ca/birs/birspages.php?task=displayevent&event_id=07w5048
Topic #2 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: OP-SF NET Editors
Subject: New book on Painleve Transcendents
From: http://www.ams.org/bookstore
Painleve Transcendents: The Riemann-Hilbert Approach,
Athanassios S. Fokas, Cambridge University, United Kingdom, Alexander R.
Its, Indiana State University, Indianapolis, IN, Andrei A. Kapaev,
Steklov Mathematical Institute, St. Petersburg, Russia, and Victor Yu.
Novokshenov, Russian Academy of Sciences, Ufa, Russia
Mathematical Surveys and Monographs
2006; approx. 560 pp; hardcover
Volume: 128
ISBN-10: 0-8218-3651-X
ISBN-13: 978-0-8218-3651-4
List Price: US$109
Member Price: US$87
Order Code: SURV/128
Expected publication date is November 2, 2006.
At the turn of the twentieth century, the French mathematician Paul
Painleve and his students classified second order nonlinear ordinary
differential equations with the property that the location of possible
branch points and essential singularities of their solutions does not
depend on initial conditions. It turned out that there are only six such
equations (up to natural equivalence), which later became known as
Painleve I-VI.
Although these equations were initially obtained answering a strictly
mathematical question, they appeared later in an astonishing (and
growing) range of applications, including, e.g., statistical physics,
fluid mechanics, random matrices, and orthogonal polynomials. Actually,
it is now becoming clear that the Painleve transcendents (i.e., the
solutions of the Painleve equations) play the same role in nonlinear
mathematical physics that the classical special functions, such as Airy
and Bessel functions, play in linear physics.
The explicit formulas relating the asymptotic behaviour of the classical
special functions at different critical points, play a crucial role in
the applications of these functions. It is shown in this book, that even
though the six Painleve equations are nonlinear, it is still possible,
using a new technique called the Riemann-Hilbert formalism, to obtain
analogous explicit formulas for the Painleve transcendents. This
striking fact, apparently unknown to Painleve and his contemporaries, is
the key ingredient for the remarkable applicability of these "nonlinear
special functions".
The book describes in detail the Riemann-Hilbert method and emphasizes
its close connection to classical monodromy theory of linear equations
as well as to modern theory of integrable systems. In addition, the book
contains an ample collection of material concerning the asymptotics of
the Painleve functions and their various applications, which makes it a
good reference source for everyone working in the theory and
applications of Painleve equations and related areas.
Readership: Graduate students and research mathematicians interested in
special functions, in particular, Painleve transcendents.
Table of Contents
* Introduction. Painleve transcendents as nonlinear special functions
Part 1. Riemannian-Hilbert problem, isomonodromy method and special
functions
* Systems of linear ordinary differential equations with rational
coefficients. Elements of the general theory
* Monodromy theory and special functions
* Inverse monodromy problem and Riemann-Hilbert factorization
* Isomonodromy deformations. The Painleve equations
* The isomonodromy method
* Bäcklund transformations
Part 2. Asymptotics of the Painleve II transcendent. A case study
* Asymptotic solutions of the second Painleve equation in the complex
plane. Direct monodromy problem approach
* Asymptotic solutions of the second Painleve equation in the complex
plane. Inverse monodromy problem approach
* PII asymptotics on the canonical six-rays. The purely imaginary case
* PII asymptotics on the canonical six-rays. Real-valued case
* PII quasi-linear Stokes phenomenon
Part 3. Asymptotics of the third Painleve transcendent
* PIII equation, an overview
* Sine-Gordon reduction of PIII
* Canonical four-rays. Real-valued solutions of SG-PIII
* Canonical four-rays. Singular solutions of the SG-PIII
* Asymptotics in the complex plane of the SG-PIII transcendent
* Proof of Theorem 3.4
* The Birkhoff-Grothendieck theorem with a parameter
* Bibliography
* Subject index
Topic #3 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: OP-SF NET Editors
Subject: New book on Number Theory in the Spirit of Ramanujan
Bruce C. Berndt
Number Theory in the Spirit of Ramanujan
Student Mathematical Library, Vol 34
American Mathematical Society, 2006, 187 pp.
ISBN: 0-8218-4178-5; List US$35 (AMS Member US$28)
From the web site
http://www.ams.org/bookstore
Ramanujan is recognized as one of the great number theorists of the
twentieth century. Here now is the first book to provide an introduction
to his work in number theory. Most of Ramanujan's work in number theory
arose out of $q$-series and theta functions. This book provides an
introduction to these two important subjects and to some of the topics
in number theory that are inextricably intertwined with them, including
the theory of partitions, sums of squares and triangular numbers, and
the Ramanujan tau function. The majority of the results discussed here
are originally due to Ramanujan or were rediscovered by him. Ramanujan
did not leave us proofs of the thousands of theorems he recorded in his
notebooks, and so it cannot be claimed that many of the proofs given in
this book are those found by Ramanujan. However, they are all in the
spirit of his mathematics.
The subjects examined in this book have a rich history dating back to
Euler and Jacobi, and they continue to be focal points of contemporary
mathematical research. Therefore, at the end of each of the seven
chapters, Berndt discusses the results established in the chapter and
places them in both historical and contemporary contexts. The book is
suitable for advanced undergraduates and beginning graduate students
interested in number theory.
Topic #4 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: Tom Koornwinder
Subject: Sum of even terms in E_q(q^{1/2}) indeed related
to root system E_8
In OP-SF NET 13.4, Topic #9 I wrote:
> In the preprint
> http://www.arxiv.org/abs/hep-th/0404120
> Werner Nahm,
> Conformal field theory and torsion elements of the Bloch group,
> Contribution to Les Houches Lecture Notes, March 2003,
> the Introduction mentions the conjectured identity
>
> \sum_{n=0}^\infty \frac{q^{2n^2}}{(q;q)_{2n} =
> \sum_{m_1,\ldots,m_8=0}^\infty
> \frac{q^{mCm}}{(q;q)_{m_1}\ldots(q;q){m_8}}
>
> where C is the inverse of the Cartan matrix of the exceptional Lie
> algebra E_8.
> The formula has been checked to high order by computer algebra.
> Note that the left-hand side is the sum of the even degree terms
> in the power series of E_q(z)=(-z;q)_\infty for z=q.
First of all, the last q above must be q^{1/2}. Furthermore, Hjalmar
Rosengren communicated to me that W. Nahm's conjectured formula already
occurs with proof as formula (8) in the paper
S. Warnaar & P.A. Pearce, Exceptional structure of the dilute $A_3$
model: $E_8$ and $E_7$ Rogers-Ramanujan identities, J. Phys. A 27
(1994), L891-L897.
In order to match the Warnaar-Pearce formula with Nahm's formula, it
still has to be shown that
(q;q)_\infty \sum_{n=0}^\infty \frac{q^{2n^2}}{(q;q)_{2n} =
\sum_{n=-\infty}^\infty (q^{12 n^2+n} - q^{12 n^2+7n+1}),
which might have been a relatively easy exercise in the book by
Gasper & Rahman.
Topic #5 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: J. M. Littleton
Subject: 2007 SIAM Prizes - Open Calls for Nominations
The following SIAM prizes will be awarded in 2007 and currently have
open calls for nominations. Calls for nominations can be found at
www.siam.org/prizes/nominations.php.
* SIAM/ACM PRIZE IN CSE
Nominations due Sept. 30
To be presented at the SIAM Conference on Computational Science and
Engineering (CSE07), Feb 19-23, 2007.
* JURGEN MOSER LECTURE
Nominations due Oct. 2
* J. D. CRAWFORD PRIZE
Nominations due Oct. 15
Both to be presented at the SIAM Conference on Applications of Dynamical
Systems (DS07), May 28-June 1, 2007.
Please address inquiries to:
J. M. Littleton
SIAM
E-mail: littleton@siam.org
Telephone: +1-215-382-9800 ext. 303
Fax: +1-215-386-7999
Topic #6 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: OP-SF NET Editors
Subject: Preprints in arXiv.org
The following preprints related to the fields of orthogonal polynomials
and special functions were posted or cross-listed to one of the
subcategories of arXiv.org during July and August 2006. See
especially:
http://front.math.ucdavis.edu/math.CA
http://front.math.ucdavis.edu/math.CO
http://front.math.ucdavis.edu/math.QA
http://xxx.lanl.gov/archive/solv-int
http://arxiv.org/abs/math.CA/0607250
Title: Properties of generalized univariate hypergeometric functions
Authors: Fokko J. van de Bult, Eric M. Rains, Jasper V. Stokman
Comments: 46 pages
Subj-class: Classical Analysis and ODEs
http://arxiv.org/abs/math.CA/0607093
Title: Limits of elliptic hypergeometric integrals
Authors: Eric M. Rains
Comments: 40 pages LaTeX
Subj-class: Classical Analysis and ODEs
http://arxiv.org/abs/nlin.SI/0607065
Title: Hypergeometric Solutions to the q-Painlev\'e Equation of Type
$(A_1+A_1')^{(1)}$
Authors: Taro Hamamoto, Kenji Kajiwara, Nicholas S. Witte
Comments: 17 pages
Subj-class: Exactly Solvable and Integrable Systems; Classical Analysis
and ODEs
http://arxiv.org/abs/math.NT/0607733
Title: On Nyman, Beurling and Baez-Duarte's Hilbert space reformulation
of the Riemann hypothesis
Authors: Bhaskar Bagchi
Comments: 10 pages
Subj-class: Number Theory; Classical Analysis and ODEs
http://arxiv.org/abs/math.FA/0607711
Title: Analytic approximation of rational matrix functions
Authors: V.V. Peller, V.I. Vasyunin
Subj-class: Functional Analysis; Classical Analysis and ODEs; Complex
Variables
MSC-class: 47B35
http://arxiv.org/abs/math.CA/0607694
Title: Inequalities related to the error function
Authors: Omran Kouba
Comments: 12 pages
Subj-class: Classical Analysis and ODEs; Probability
http://arxiv.org/abs/math.CA/0607650
Title: On a new unified integral
Authors: Mridula Garg, Shweta Mittal
Comments: 3 pages
Subj-class: Classical Analysis and ODEs
MSC-class: 33C20; 33C47; 33C60
http://arxiv.org/abs/math.CA/0607649
Title: Operator calculus approach to solving analytic systems
Authors: Ph. Feinsilver, R. Schott
Comments: 3 figures (Maple worksheets)
Subj-class: Classical Analysis and ODEs; Functional Analysis
http://arxiv.org/abs/math.CA/0607555
Title: Meromorphic Solutions of Linear Differential Systems, Painleve
type functions
Authors: Lev Sakhnovich
Subj-class: Classical Analysis and ODEs; Functional Analysis
MSC-class: 34M05; 34M55; 47B38
http://arxiv.org/abs/math.CA/0607471
Title: Zeros of the Macdonald function of complex order
Authors: Erasmo M. Ferreira, Javier Sesma
Comments: 13 pages, 3 figures
Subj-class: Classical Analysis and ODEs
MSC-class: 33C10
http://arxiv.org/abs/math.CV/0607416
Title: Polya-Schur master theorems for circular domains and their
boundaries
Authors: Julius Borcea, Petter Brändén, Boris Shapiro
Comments: 17 pages
Subj-class: Complex Variables; Classical Analysis and ODEs
MSC-class: 47D03; 26C10; 30C15; 30D15; 32A60; 47B38
http://arxiv.org/abs/math.CO/0607359
Title: The Abel Lemma and the q-Gosper Algorithm
Authors: Vincent Y. B. Chen, William Y. C. Chen, Nancy S. S. Gu
Comments: 17 pages
Subj-class: Combinatorics; Classical Analysis and ODEs
http://arxiv.org/abs/math.CA/0607122
Title: A new multivariable 6-psi-6 summation formula
Authors: Michael Schlosser
Comments: 16 pages
Subj-class: Classical Analysis and ODEs
MSC-class: 33D15
http://arxiv.org/abs/math.CA/0608742
Title: Multilateral inversion of A_r, C_r and D_r basic hypergeometric
series
Authors: Michael J. Schlosser
Comments: 24 pages
Subj-class: Classical Analysis and ODEs; Combinatorics
MSC-class: 33D67 (Primary) 15A09, 33D15 (Secondary)
http://arxiv.org/abs/math.CA/0608026
Title: Curious extensions of Ramanujan's 1-psi-1 summation formula
Authors: Victor J. W. Guo, Michael J. Schlosser
Comments: 12 pages
Subj-class: Classical Analysis and ODEs
MSC-class: 33D15 (Primary) 05A19, 33D99 (Secondary)
http://arxiv.org/abs/hep-ph/0607006
Title: Hypergeometric representation of a four-loop vacuum bubble
Authors: Ervin Bejdakic, York Schroder
Comments: 5 pages, to appear in the proceedings of the conference "Loops
and Legs", Eisenach, 2006
http://arxiv.org/abs/math.CA/0607823
Title: An Intertwining Operator for the Group B2
Authors: Charles F. Dunkl
Comments: 27 pages
Subj-class: Classical Analysis and ODEs
MSC-class: 33C80, 33C20 (Primary); 33C70, 43A80 (Secondary)
http://arxiv.org/abs/math.CV/0607773
Title: Dessins d'enfants and differential equations
Authors: Finnur Larusson, Timur Sadykov
Comments: 11 pages
Subj-class: Complex Variables; Algebraic Geometry; Combinatorics
MSC-class: 32S40; 05C05, 14H30, 32G34, 34M15, 34M50
http://arxiv.org/abs/hep-ph/0607300
Title: Evaluating Two-Loop massive Operator Matrix Elements with
Mellin-Barnes Integrals
Authors: I. Bierenbaum, J. Blümlein, S. Klein
Comments: 6 pages, 3 figures, 1 style file, to appear in the Proceedings
of "Loops and Legs in Quantum Field Theory 2006", Eisenach, April,
2006
http://arxiv.org/abs/math/0607202
Title: Some more identities of the Rogers-Ramanujan type
Authors: Douglas Bowman, James Mc Laughlin
Comments: 24 pages. Updated in response to comments concerning one of
the identities
Subj-class: Number Theory; Combinatorics
MSC-class: 33D15; 05A17; 05A19; 11B65; 11P81; 33F10
http://arxiv.org/abs/math.RT/0608301
Title: On the evaluation of some Selberg-like integrals
Authors: B. Binegar
Subj-class: Representation Theory
MSC-class: 33D70,05E05,32M15
http://arxiv.org/abs/math/0608410
Title: On optimal truncation of divergent series solutions of nonlinear
differential systems; Berry smoothing
Authors: O. Costin, M. D. Kruskal
Subj-class: Classical Analysis and ODEs
MSC-class: 34M40,34M30,34M37,34M40,34E05
Journal-ref: Proc. R. Soc. Lond. A 455, 1931-1956 (1999)
http://arxiv.org/abs/math.CV/0608297
Title: Sums of entire functions having only real zeros
Authors: Steven R. Adams, David A. Cardon
Comments: 10 pages
Subj-class: Complex Variables
MSC-class: 30C15
http://arxiv.org/abs/math-ph/0608023
Title: sl(2,R) Symmetry and solvable multiboson systems
Authors: Tomasz Golinski, Maciej Horowski, Anatol Odzijewicz, Aneta
Slizewska
Comments: 23 pages, 1 figure
Subj-class: Mathematical Physics
MSC-class: 81V80; 17B15; 47L90; 47N50
http://arxiv.org/abs/math-ph/0607007
Title: Skew-orthogonal polynomials, differential systems and random
matrix theory
Authors: Saugata Ghosh
Comments: 22 pages
Subj-class: Mathematical Physics
http://arxiv.org/abs/math-ph/0607022
Title: New connection formulae for the q-orthogonal polynomials via a
series expansion of the q-exponential
Authors: R. Chakrabarti, R. Jagannathan, S. S. Naina Mohammed
Comments: 14 pages
Subj-class: Mathematical Physics; Quantum Algebra
http://arxiv.org/abs/math-ph/0607043
Title: Universality of a double scaling limit near singular edge points
in random matrix models
Authors: T. Claeys, M. Vanlessen
Comments: 32 pages, 3 figures
Subj-class: Mathematical Physics
MSC-class: 15A52; 33E17; 35Q15
http://arxiv.org/abs/cond-mat/0607243
Title: Energy correlations for a random matrix model of disordered
bosons
Authors: T. Lueck, H.-J. Sommers, M.R. Zirnbauer
Comments: 20 pages, 3 figures
Subj-class: Mesoscopic Systems and Quantum Hall Effect; Disordered
Systems and Neural Networks; Mathematical Physics
http://arxiv.org/abs/math.CO/0607138
Title: Dyson's new symmetry and generalized Rogers-Ramanujan identities
Authors: Cilanne Boulet
Subj-class: Combinatorics
MSC-class: 05A17; 11P81
http://arxiv.org/abs/math.NT/0607199
Title: On the mean values of Dirichlet $L$-functions
Authors: H. M. Bui, J. P. Keating
Subj-class: Number Theory
http://arxiv.org/abs/math.NT/0607782
Title: Equivalence of Riesz and Baez-Duarte criterion for the Riemann
Hypothesis
Authors: J.Cislo, M.Wolf
Subj-class: Number Theory
MSC-class: 11M26
http://arxiv.org/abs/math.CO/0607514
Title: On asymptotics, Stirling numbers, Gamma function and polylogs
Authors: Daniel B. Gruenberg
Comments: 24 pages, to appear in Results for Mathematics
Subj-class: Combinatorics; Number Theory
MSC-class: 05A10; 11A07; 30B10
http://arxiv.org/abs/math.GM/0607095
Title: Chebyshev Partition function: A connection between Statistical
Physics and Riemann Hypothesis
Authors: Jose Javier garcia Moreta
Comments: 5 pages research paper, an approach to solve Riemann
Hypothesis by means of Statistical Physics
Subj-class: General Mathematics; Number Theory
MSC-class: 11.xx 45.xx 46.xx
http://arxiv.org/abs/math-ph/0608015
Title: Sturm-Liouville Problem in Quantum Calculus
Authors: Ahmed Fitouhi, Akram Nemri, Meniar Haddad
Comments: 16 pages
Subj-class: Mathematical Physics
MSC-class: 33D60, 26D15, 33D05, 33D15, 33D90
http://arxiv.org/abs/math-ph/0608040
Title: The evanescent waves in geometrical optics and the mixed
hyperbolic-elliptic type systems
Authors: Enrico De Micheli, Giovanni Alberto Viano
Comments: 30 pages, 3 figures
Subj-class: Mathematical Physics; Optics
MSC-class: 78A05; 35M10; 34M40
Journal-ref: Appl. Anal. 85 (2006), 181-204
http://arxiv.org/abs/quant-ph/0608099
Title: Uniform semiclassical approximations of the nonlinear
Schroedinger equation by a Painleve mapping
Authors: D. Witthaut, H. J. Korsch
http://arxiv.org/abs/math-ph/0607011
Title: General Relativity and Quantum Mechanics: Towards a
Generalization of the Lambert W Function
Authors: Tony C. Scott, Robert B. Mann, Roberto E. Martinez
Comments: A generalization of the Lambert W function is presented: it
was found as a consequence of a previously unknown link between Gravity
Theory and the Schroedinger wave equation in lower dimensions (1+1).
This paper is related to physics/0607081 which presents analytical
solutions to a special case of the quantum 3-body problem
Subj-class: Mathematical Physics
MSC-class: 33E30; 83C80; 81V55
Journal-ref: AAECC (Applicable Algebra in Engineering, Communication and
Computing), vol. 16, no. 6, (2006)
Topic #7 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: OP-SF NET Editors
Subject: About the Activity Group
The SIAM Activity Group on Orthogonal Polynomials and Special Functions
consists of a broad set of mathematicians, both pure and applied. The
Group also includes engineers and scientists, students as well as
experts. We have around 140 members scattered about in more than 20
countries. Whatever your specialty might be, we welcome your
participation in this classical, and yet modern, topic. Our WWW home
page is:
http://math.nist.gov/opsf/
This is a convenient point of entry to all the services provided by the
Group. Our Webmaster is Bonita Saunders (bonita.saunders@nist.gov).
The Activity Group sponsors OP-SF NET, which is transmitted periodically
by SIAM. It is provided as a free public service; membership in SIAM
is not required. The OP-SF Net Editors are Diego Dominici
(dominicd@newpaltz.edu) and Martin Muldoon (muldoon@yorku.ca).
To receive the OP-SF NET, send your name and email address to
poly-request@siam.org.
Back issues can be obtained at the WWW addresses:
http://staff.science.uva.nl/~thk/opsfnet
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http://math.nist.gov/opsfnet/archive
For several years the Activity Group sponsored a printed Newsletter,
most recently edited by Rafael Yanez. Back issues are accessible at:
http://www.mathematik.uni-kassel.de/~koepf/siam.html
Given the widespread availability of email and the Internet, the need for
the printed Newsletter has decreased. Discussions are underway concerning
whether an annual printed Newsletter or Annual Report should be
instituted.
SIAM has several categories of membership, including low-cost categories
for students and residents of developing countries. For current
information on SIAM and Activity Group membership, contact:
Society for Industrial and Applied Mathematics
3600 University City Science Center
Philadelphia, PA 19104-2688 USA
phone: +1-215-382-9800
email: service@siam.org
WWW : http://www.siam.org
http://www.siam.org/membership/outreachmem.htm
Finally, the Activity Group operates an email discussion group, called
OP-SF Talk. To subscribe, send the email message
subscribe opsftalk Your Name
to listproc@nist.gov. To contribute an item to the discussion, send
email to opsftalk@nist.gov. The archive of all messages is accessible
at:
http://math.nist.gov/opsftalk/archive
Topic #8 ---------- OP-SF NET 13.5 ---------- September 15, 2006
~~~~~~~~~~~~~~
From: OP-SF NET Editors
Subject: Submitting contributions to OP-SF NET
To contribute a news item to OP-SF NET, send email to poly@siam.org
with a copy to one of the OP-SF Editors or
.
Contributions to OP-SF NET 13.6 should be sent by November 1, 2006.
o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o
OP-SF NET is a forum of the SIAM Activity Group on
Special Functions and Orthogonal Polynomials.
We disseminate your contributions on anything of interest to the
special functions and orthogonal polynomials community. This
includes announcements of conferences, forthcoming books, new
software, electronic archives, research questions, job openings.
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Send submissions to: poly@siam.org
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Back issues can be obtained at the WWW addresses:
http://staff.science.uva.nl/~thk/opsfnet
http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html
http://math.nist.gov/opsfnet/archive
WWW home page of this Activity Group:
http://math.nist.gov/opsf/
Information on joining SIAM
and this activity group: service@siam.org
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The elected Officers of the Activity Group (2005-2007) are:
Peter A. Clarkson, Chair
Daniel W. Lozier, Vice Chair
Javier Segura, Secretary
Peter A. McCoy, Program Director
The appointed officers are:
Diego Dominici, OP-SF NET co-editor
Martin Muldoon, OP-SF NET co-editor
Bonita Saunders, Webmaster
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