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-------- Original Message -------- Subject: OP-SF Net Volume 7 #1 Date: Wed, 19 Jan 2000 09:06:02 -0500 (EST) From: mailer@siam.org o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o January 15, 2000 O P - S F N E T Volume 7, Number 1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Editor: 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 o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o Today's Topics 1. From the Editor 2. Research Perspectives 3. NATO ASI and Conference: "Special Functions 2000" 4. Conference on Reproducing Kernel Hilbert Spaces 5. Krawtchouk Conference 6. Session on Adaptive Quadrature and Cubature Formulae 7. Dalian Symposium on Analysis, Combinatorics and Computing 8. Reports on OPSFA-Patras 9. Report on AMADE Conference in Minsk 10. Report on Benin Workshop 11. Askey issues of Methods and Applications of Analysis 12. Changes at Methods and Applications of Analysis 13. Review Of "Special Functions" by Andrews, Askey and Roy 14. Doron Zeilberger's Maple Packages and Programs 15. Question on Schrodinger equations 16. SIAM Student Paper Prizes 17. OP-SF preprints in xxx archive 18. Changes of Address, WWW Pages, etc 19. Subscribing to OP-SF NET 20. Obtaining back issues of OP-SF NET and submitting contributions to OP-SF NET and Newsletter Calendar of Events: 2000 March 27-31: Workshop on Quantum Groups, Morelia, Mexico 6.5 #3 April 14-18: Workshop on Orthogonal Polynomials, Approximation and Harmonic Analysis, Inzell, Germany 6.6 #2 April 16-21: Conference on Reproducing Kernel Hilbert Spaces, Krakow, Poland 7.1 #4 May 11-13: VIII International Krawtchouk Conference, Kiev, Ukraine 7.1 #5 May 17-20: Symposium on Trends in Approximation Theory, Nashville, Tennessee, USA 6.5 #4 May 29 - June 9: Special Functions 2000: Current Perspective and Future Directions, Tempe, Arizona, USA 6.5 #2, 7.1 #3 July 3-7: Alhambra 2000, a Joint Mathematical European-Arabic Conference 6.4 #7 July 10-14: SIAM Annual Meeting in Puerto Rico See: http://www.siam.org/meetings/an00/index.htm July 17-22: I Colloquium on Lie Theory and Applications, Vigo, Spain 6.4 #8 July 19-26: Third World Congress of Nonlinear Analysts, Catania, Italy (including session on "Adaptive quadrature and cubature formulae". 7.1 #6 July 24-28: Summer School "Orthogonal Polynomials and Special Functions", Laredo, Spain. 6.6 #3 August 5-8: International Symposium on Analysis, Combinatorics and Computing, Dalian, China 7.1 #7 August 14-18: International Symposium on Applied Mathematics, Dalian, China 6.5 #5 Topic #1 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: OP-SF NET Editor <muldoon@yorku.ca> Subject: From the Editor The year 2000 promises to be a busy one with respect to conferences and workshops in our area. The NATO ASI and conference in Tempe, Arizona, USA form May 29 to June 9 promises to be a major event but here are several other workshops and conference in various parts of the world with at least tangential interest for members of our Activity Group. Don't forget to submit information on any relevant events which are not listed here. Included here are reports on some 1999 events. I especially enjoyed Bill Connett's report from OPSFA-Patras. Topic #2 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: Walter Van Assche <walter@wis.kuleuven.ac.be> Subject: Research Perspectives As a follow-up of the Honk Kong panel discussion, the SIAM activity group will maintain a list of "research perspectives" on the web. The activity group homepage will soon contain a link to a list of possible directions in research relevant for (young) people interested in our field. This link will be coordinated by Walter Van Assche. Please send possible suggestions and items for inclusions to walter@wis.kuleuven.ac.be . Topic #3 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: Sergei Suslov <sks@asu.edu> Subject: NATO Advanced Study Institute and International Conference: "Special Functions 2000" [This is an updated version of the announcement in OP-SF NET 6.5, Topic #2. We emphasize the early deadline February 21, 2000 for application for financial support. The application form is at the website: http://math.la.asu.edu/~sf2000/index.html The reason for the deadline is that the organizers have to submit a list of participants to NATO at an early date in order to get funding. Applications are especially welcome from graduate students and young researchers.] NATO Advanced Study Institute: "Special Functions 2000" Arizona State University Tempe, Arizona, USA May 29 to June 9, 2000 Objective of the ASI: to summarize results in special functions and their diverse applications obtained over the last three decades and to discuss future directions. Topics: Orthogonal polynomials and special functions in one and several variables, asymptotics, continued fractions, applications to number theory, combinatorics and mathematical physics, integrable systems, harmonic analysis and quantum groups, Painleve classification, and others. Lecturers: G. Andrews, Pennsylvania State University, USA R. Askey, University of Wisconsin, Madison, USA P. Deift, Courant Institute, USA C. Dunkl, University of Virginia, USA A. Grunbaum, University of California, Berkeley, USA M.E.H. Ismail, University of South Florida, Tampa, USA A. Its, Indiana University - Purdue University, Indianapolis, USA E. Koelink, Technische Universiteit Delft, The Netherlands T. Koornwinder, KdV Institute, University of Amsterdam, The Netherlands I. Macdonald, Queen Mary College, London, England (not confirmed) S. Milne, The Ohio State University, USA O. Njastad, Norwegian University of Science & Technology, Norway M. Rahman, Carleton University, Ottawa, Canada V. Spiridonov, Joint Institute of Nuclear Research, Dubna, Russia D. Stanton, University of Minnesota, USA S. K. Suslov, Arizona State University, USA N. Temme, CWI, Amsterdam, The Netherlands V. N. Tolstoi, Moscow State University, Russia L. Vinet, McGill University, Montreal, Canada A. Zhedanov, Donetsk Institute for Physics and Technology, Ukraine International Organizing Committee: Sergei Suslov, Arizona State University, USA (Director from NATO country) Vyacheslav Spiridonov, Joint Institute for Nuclear Research, Dubna, Russia (Director from Partner country) Tom Koornwinder, KdV Institute, University of Amsterdam, The Netherlands Luc Vinet, McGill University, Montreal, Canada Local Organizing Committee: Joaquin Bustoz, Arizona State University (Chair) Mourad Ismail, University of South Florida Sergei Suslov, Arizona State University Sponsors: NATO Scientific and Environmental Affairs Division, Arizona State University, Wolfram Research, and Centre de Recherches Mathematiques, Universite de Montreal Address: Advanced Study Institute SF2000 Arizona State University Department of Mathematics Box 871804 Tempe, AZ 85287-1804 U.S.A. E-mail: sf2000@math.la.asu.edu Fax: 1-480-965-8119 Webpage: http://math.la.asu.edu/~sf2000/index.html Application form is available on the webpage. Young researchers and graduate students from NATO and Partner Countries are especially encouraged to apply. Applications for financial support must be received no later then February 21, 2000. Decision will be made by February 28, 2000. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% International conference: "Special Functions 2000: Current Perspective and Future Directions" May 29 to June 9, 2000 Arizona State University Tempe, Arizona, USA This conference will run concurrently with a NATO ASI and will be supported by the National Science Foundation and Arizona State University. Young researchers and graduate students from the US, Latin American countries and Eastern European countries are encouraged to apply for contributed presentations and/or financial support to the address: Special Functions 2000 Arizona State University Department of Mathematics Box 871804 Tempe, AZ 85287-1804 U.S.A. E-mail: sf2000@math.la.asu.edu Fax: 1-480-965-8119 Web page: http://math.la.asu.edu/~sf2000/index.html Application form is available on the webpage. Application deadline is February 21, 2000. Decision will be made by February 28, 2000. Topic #4 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: Franek Szafraniec <fhszafra@im.uj.edu.pl> Subject: Conference on Reproducing Kernel Hilbert Spaces The long maturing idea of organizing a conference in Krakow to commemorate the 90th anniversary of introducing the reproducing kernel property by Stanislaw Zaremba has become a reality. Now I can announce the conference is going to be in April 2000, from the 16th till the 21st . The aim is to gather people who work in areas to which RKHS pertains like function theory, differential equations, operator theory or probability, so to mention some of them (even so abstract domain as operator algebras is not free of it: the famous GNS construction can be viewed as an application of this property). The first announcement will appear towards the end of January 2000 and will be distributed by email. You can express your interest by sending an email to rkhs2000@im.uj.edu.pl Franek Szafraniec E-mail: fhszafra@im.uj.edu.pl, [also umszafra@cyf-kr.edu.pl or fhszafra@impan.gov.pl]. Topic #5 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: Charles Dunkl <cfd5z@virginia.edu> Subject: Krawtchouk Conference The VIII International Conference devoted to the memory of Academician M. Krawtchouk (or Kravchuk) (1892-1942) will be held May 11-13, 2000, in Kyiv (Kiev), Ukraine. It is sponsored by the National Technical University of Ukraine (KPI), the Institute of Mathematics of the Ukrainian National Academy of Sciences, the National Taras Shevchenko University, and the National Dragomanov Pedagogical University. Programme sections: (1) differential and integral equations, their applications (2) algebra, geometry, mathematical and numerical analysis (3) history of probability and mathematical statistics, (4) history, methods of teaching of mathematics Contact person: Prof. Nina Virchenko (KPI) Tel: +380 44 441 14 41 e-mail: syta@imath.kyiv.ua random@imath.kyiv.ua (there is a $50 registration fee for foreign attendees), abstract deadline is 1 March 2000. Conference Web page: http://www.isir.minsk.by/~zelenkov/physmath/kr_polyn/conf8.html Topic #6 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: Sever Dragomir <sever@matilda.vu.edu.au> Subject: Organising a Session "Adaptive quadrature and cubature formulae" I have been appointed to organize a session within the "Third Congress of Nonlinear Analysts" which will be held during July 19-26, 2000 in Catania, Sicily, Italy, on the topic "Adaptive quadrature and cubature formulae". In addition to the classical approach for adaptive quadrature and cubature formulae which will be welcome in that section, we would like to encourage the following topics in Theory of Inequalities which are related to Numerical Integration: - Ostrowski Type Inequalities - Hermite -Hadamard Type Inequalities - Gruss type inequalities - Trapezoid, Midpoint, Lobatto, Newton-Cotes Type (Rules and) Inequalities - Integral Inequalities of Iyengar, Mahajani, Fink, etc... type where the integrals are estimated in terms of Polynomials, Series etc... - Any other integral inequality which might be of help in approximating Riemann, Riemann-Stieltjes, Lebesgue or other integrals (Bochner, Denjoy, Perron, Henstock etc...) If you are interested to participate, please let me know before the 20th of December and I will be able to post you the corresponding documents to register. For information on The Third World Congress of Nonlinear Analysts (WCNA-2000) please consult the web site: http://www.fit.edu/AcadRes/math/wcna/wcna2000.htm Sever S. Dragomir Topic #7 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: Li Zhongkai <lizk@mail.cnu.edu.cn> Subject: International Symposium on Analysis, Combinatorics and Computing First Announcement: International Symposium on Analysis, Combinatorics and Computing, Dalian, P. R. China, August 5-8, 2000 Objective The purpose of this conference is to provide a forum for an exchange of ideas among experts in the various topics listed below, and to disseminate information on recent advances made in these areas. Session Topics 1. Special Functions and its Applications 2. Combinatorics and its Applications 3. Approximation Theory and Numerical Analysis 4. Harmonic and Wavelet Analysis Sponsored by Dalian University of Technology Organizing Committee Chairman: Leetsch C. Hsu (Xu, Lizhi) (Dalian, PRC) Members: Tian-Xiao He (Illinois, USA) Zhongkai Li (Beijing, PRC) Jun Wang (Dalian, PRC) Sining Zheng (Dalian, PRC) Academic Committee Richard Askey (Madison, USA) Paul L. Butzer (Aachen, Germany) Guochen Feng (Changchun, PRC) Leetsch C. Hsu (Dalian, PRC) Peter Shiue (Las Vegas, USA) Lewis Solomon (Madison, USA) Zhexian Wan (Beijing, PRC) Renhong Wang (Dalian, PRC) Registration fee (including the official fee for the conference and the fee for a reception banquet, daily breakfast, lunch and dinner, but not the room fee. Each participant should pay his room fee separately.) US$250 before May 31, 2000 US$300 after May 31, 2000 Call for Talks and Registration The organizing committee encourages early registration and submission of original technical and unpublished papers related to the above session topics. Those who reply to the organizers by e-mail or post-mail before February 15, 2000, will receive directly the second announcement, in which the official forms for registration and accommodation are included. Replies after this date will also be accepted. Abstracts of contributed talks must be received by June 30, 2000. Invited Speakers: Richard Askey (USA) Paul L. Butzer (Germany) Mourad Ismail (USA) Peter Shiue (USA) Lewis Solomon (USA) Please contact one of the members of the organizing committee if you are interested in this symposium or have any questions: Jun Wang Department of Applied Mathematics Dalian University of Technology Dalian 116024, P. R. CHINA Email: junwang@dlut.edu.cn Fax: 86-411-4708360 Sining Zheng Department of Applied Mathematics Dalian University of Technology Dalian 116024, P. R. CHINA Email:snzheng@dlut.edu.cn Fax: 86-411-4708360 Zhongkai Li Department of Mathematics Capital Normal University Beijing 100037, P. R. CHINA Email: lizk@mail.cnu.edu.cn Tel. 86-10-68462115 Tian-Xiao He Department of Mathematics Illinois Wesleyan University Illinois, USA Email: the@sun.iwu.edu Tel: 309-556-3089 Remarks: 1. This conference will be held at the Dalian University of Technology, Dalian, China, from August 5 to 8, 2000. For information about the University and the City of Dalian, please visit the following web sites: http://www.dlut.edu.cn http://www.china-dalian.com/100 2. If you are interested in or wish to participate in the conference, please let us know your following information as soon as possible, which are necessary for you to go through your Chinese visa: (1) Full name (First) (Last) (2) Citizenship (3) Date of birth (month, day, and year) (4) City and country of birth (5) Passport number (6) Correspondence address Topic #8 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: OP-SF NET Editor <muldoon@yorku.ca> Subject: Reports on OPSFA-Patras The Fifth International Symposium on Orthogonal Polynomials, Special Functions and their Applications (OPSFA, for short), was held in Patras, Greece, September 20 - 24, 1999. This was a conference in a European series including Bar-Le-Duc (1984), Segovia (1986), Erice (1990), Granada (1991, VII SPOA), Evian (1992), Delft (1994, Stieltjes centenary) and Seville (1997, VIII SPOA); it certainly lived up to reputation of that series for the excellence of the program and organization. The Symposium was dedicated to Professor Ted Chihara in honour of his many contributions to the subject of Orthogonal Polynomials. In fact the opening ceremony consisted of a presentation to Chihara, a talk on his work by Walter Van Assche and a characteristically modest lecture by Ted entitled "Orthogonal Polynomials - a view from the wings". There was a very full programme of plenary and contributed talks. The main events were held in a new building at the magnificently located University of Patras, the participants being bussed from nearby hotels to the sessions and to the extensive program of social events. Though Thursday was announced as a "Greek evening" (with respect to food and entertainment) but it was quickly observed by the participants that every evening could be so characterized. The local organizers themselves set a great example for singing and dancing and succeeded in drawing all participants. The proceedings of the Symposium will appear as a special volume of the JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. The proceedings volume is expected to include a report on a session for open problems which concluded the symposium. The next meeting in the European series on Orthogonal Polynomials will be held in Italy in 2001, possibly in late June though the location and exact dates have not been determined. The contact person is Andrea Laforgia (laforgia@dma.uniroma3.it). Here are reports from two other participants: Marcel de Bruin and Bill Connett. Report from Marcel de Bruin <M.G.deBruin@its.tudelft.nl> September 20--24, 1999, the city of Patra (Greece, approximately 200 kilometers West from Athens), hosted the "Fifth International Symposium on Orthogonal Polynomials, Special Functions and their Applications". The local organizing committee consisting of Evangelos Ifantis, Chrysoula Kokologiannaki and Panayiotis Siafarikas succeeded, with the aid of Eugenia N. Petropoulou and Kiriaki Vlachou to set a standard of both scientific and social level that will be difficult to better. On one hand the scientific program with plenary lectures in the morning, followed by research seminars in parallel sessions and the social program on the other hand showed unexpected talents of many a participant. Central was the guided visit to the ancient city of Olympia: history looked over our shoulders to see how the mathematicians of today shape the history of tomorrow. And each day the recurrent happening of the evening meal that should be called a `social gathering'. There it became clear that not only mathematics linked the participants together, but also the intricacies of the `links and braids' of the steps of the Greek dance. Greek music united many and succeeded in loosening up a community that is usually considered `stuffy' by the outside world. Other documents will give an account of the main mathematical achievements. I can only say that this was a superbly organised conference and conclude this with a well meant $E\upsilon\chi\alpha\rho\iota\sigma\tau\omega\ \pi o\lambda\upsilon$ From: William Connett <connett@arch.umsl.edu> The Fifth International Symposium on Orthogonal Polynomials, Special Functions and their Applications which took place in Patras Greece from September 20 to 24, 1999, is the most recent of a series of primarily european conferences focused on these questions. It is inspiring to see how the fields of orthogonal polynomials and special functions have grown since the first of these series of meetings in Bar-Le-Duc in 1984. Over 160 people appeared in the provincial University of Patras in the middle of the semester to participate in one of the most intense scientific meetings I have ever attended. With representatives from thirty-two countries in attendance, it was truly one of the most cosmopolitan meetings, it has ever been my pleasure to attend. A field of mathematics that once was the special interest of a few specialists in Northern Europe, is now flourishing in Spain, Italy, Portugal, and Greece. It was also heartening to see that the large number of mathematicians from the Maghreb in attendance. If Ferdinand Braudel was writing his great book "La Mediterranee et la Monde Mediteraneen..." today, he would have to a chapter on the study of orthogonal polynomials as one of the great unifying trans-cultural themes of the Mediterranean basin. There were talks from 9:00 am to 1:30 pm, a two hour break for lunch, and then more talks from 3:30 to 7:00 pm every day. After the talks, the very energetic organizers took us off to visit some great ruin, and then about the time I was longing for bed, we would begin dinner around 10:00 pm. After dinner the bouzouki music began and there was general dancing led by our Greek colleagues who are stronger human beings than I. We would go to bed at 1:00 am, and then start over the next day. By the fourth day of the conference there were middle aged mathematicians asleep leaning against trees all over the lovely campus. The most impressive single event in the social program was our visit to Olympus, where Walter van Assche was challenged to a foot race in the Olympic stadium by his student Els Coussement. Age triumphed over beauty! Walter was rewarded for his olympian efforts with the presentation of the traditional wreath of laurels on the last day of the conference. The conference was honoring the work of Ted Chihara, and the opening session of the conference was presented by Walter van Assche who gave an overview of Chihara's many accomplishments. Then Professor Chihara responded with his typical modesty, and gave a very personal, and delightful interpretation of the developments in orthogonal polynomials over the last half century. There were eight other plenary lectures, and over one hundred research seminars, so it will be impossible to give anything but a very personal, selective, and impressionistic description of the many fine papers. The plenary lecture that I was most interested in was Lance Littlejohn's presentation of his and Norrie Everitt's progress on the "Erice Conjecture". These results are part of the effort to develop a complete theory of multivariate orthogonal polynomials that are the eigenfunctions of differential operators. Walter Gautschi gave a magisterial overview of the problems that occur when polynomials are used for quadrature when there is a pole near the interval of integration. The lecture of Arno Kuijlaars was a personal revelation, since I knew very little about the asymptotics of polynomials orthogonal with respect to Freud weights, and Kuijlaars' elegant presentation brought this corner alive to me. I must be even more selective in discussing the research seminars. Nico Temme continued his efforts to fill in my vast ignorance about asymptotics with a very clear talk about obtaining the asymptotics for polynomials in the Askey scheme as limits of the asymptotics of other polynomials in that scheme that we already understand. Kathy Driver gave a provocative and delightful report on what the zeros of the ultraspherical polynomials do when the parameter is less than minus one half. Wojciech Mlotkowski reported on some joint work with Ryszard Szwarc. They have found a new and very clever way to prove the non-negativity of the linearization coefficients for polynomials supported on discrete measures. And finally, the last talk on the last day of the conference, when the participants were near mental and physical exhaustion, the members of the organizing committee (Ifantis, Kokologiannaki, and Siafarikas) presented a very nice sufficient condition for the support of the orthogonality measure of a family of polynomials to be the entire interval. I was tired. They must have been near collapse. What a display of "paidea". I came to Greece not knowing what to expect. I was awed by the science, the land, and the people. To paraphrase Alan Bates's line at the end of that famous movie, "Panos, Chrysoula, Teach me to dance!" Topic #9 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: Sergei Rogosin <rogosin@mmf.bsu.unibel.by> Subject: Report on AMADE Conference in Minsk The international conference "Analytic Methods of Analysis and Differential Equations" (AMADE) took place September 14-18, 1999 in Minsk, Belarus. It was organized by the Belarusian State University, the Belarusian National Academy of Sciences together with Moscow State University and the Computer Center of the Russian Academy of Sciences. It was held at the Olympic Sport Center "Staiki" which is situated 10 km from Minsk, the capital of Belarus. More than 320 mathematicians confirmed their interest in the Conference. Abstracts of their reports were published in "Abstracts of AMADE". 165 scientists from Algeria, Australia, Belarus, France, Germany, Great Britain, Italy, Japan, Korea, Lithuania, Poland, Portugal, Russia, Spain, Ukraine and USA took part in AMADE. There were 18 plenary invited lectures and 93 sectional talks on various modern problems of integral transforms, special functions, differential equations, operator theory, approximation and fractional calculus. Plenary invited lectures were given by the following mathematicians: Burenkov, V.I. (Great Britain): Extension theorems for spaces of differentiable functions defined on strongly degenerated domains. Gaishun, I.V. (Belarus): Canonical forms of linear nonstationary system of equations and their applications. Glaeske, H.-J. (Germany), together with Saigo, M. (Japan): On a hybrid Laguerre Fourier transforms. Grebennikov, E.A. (Russia), together with Kozak, D., and Yakubyak, M. (Poland): KAM-theory and stability of homographic solutions of Hamiltonian systems of cosmic dynamics. Gromak, V.I. (Belarus): Isodromic deformation of linear systems and of p-type equations. Karapetyants, N.K.(Russia): On a fredholmness of a class of Hankel operators. Kilbas, A.A. (Belarus): Integral and differential equations of fractional order. Theory and applications. Korzyuk, V.I. (Belarus): Conjugation problems for differential equations with integro-differential conditions. Kun Soo Chang (Korea): Analytic Fourier-Feynman transform and convolution of functionals on abstract Wiener space. Laurinchikas, A. (Lithuania) - The Lerch zeta function. Lebedev, A.V., together with Antonevich, A.B. and Bakhtin, V.I. (Belarus): Variational principle for spectral radius. Love, E.R. (Australia): Fourier-style expansions in series of general Legendre functions. Marichev, O.I., together with Trott, M. and Adamchik, V.S. (USA): The mathematical functions in Mathematica. Mitjushev, V.V. (Poland), together with Adler, P. (France): Boundary value problems in a class of doubly periodic functions and their applications in porous media. Nakhushev, A.M., together with Nakhusheva, V.A. (Russia): On some differential equations of fractional order and their applications. Rogosin, S.V.(Belarus), together with Reissig, M.(Germany): Complex Hele-Shaw model with linear and nonlinear kinetic undercooling regularization. Saitoh, S.(Japan): Various integral operators induced by integral transforms. Yurchuk, N.I.(Belarus): Regularization by nonlocal conditions of the incorrect problems for the differential operator equations. The 93 sectional talks were distributed as follows: Integral Transforms and Special Functions (14); Ordinary Differential equations (13); Partial Differential Equations (13); Different Aspects of Function Theory (12); Applications of Differential Equations and Function Theory (15); Integral and Functional Equations and Applications (13); Operator Theory (13). It is hoped that the Proceedings of AMADE will be published in "Proceedings of Institute of Mathematics" of the Belarusian National Academy of Sciences. Some of the reports will be published in a special issue of "Integral Transforms and Special Functions", dedicated to Professor Anatolii Platonovich Prudnikov (Russia) who was one of the main founders of AMADE. Though his sudden death on January 10, 1999 was a big tragedy, participants at the Conference honored his memory in their reports. Topic #10 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: Andre Ronveaux <Andre.Ronveaux@fundp.ac.be> Subject: Report on Benin Workshop The FIRST INTERNATIONAL WORKSHOP ON CONTEMPORARY PROBLEMS IN MATHEMATICAL PHYSICS was held in Cotonou, Republique de BENIN from Oct 31st to Nov 7th, 1999. About 100 participants from Africa, Europe and North America attended this Workshop organized by the IMSP (Institut de Mathematiques et Sciences Physiques in Porto-Novo,BENIN). Presentations included invited 50-minute plenary talks (21), and 20-minute communications (36). The following topics were covered in parallel sessions: Coherent states, wavelets and geometric methods in theoretical physics. Quantum field theory, atomic and molecular physics, Operator theory and orthogonal polynomials. Being involved only in the last topic I can say that the Operator theory part was devoted mainly to PDE and Integral operators, presented more or less in the French tradition (Sobolev spaces,numerical approximations etc...) but sometimes applied to African needs. For instance, regulation of dams on the Senegal river and transport problems in the Oueme river (Benin) motivated sophisticated simulations with control theory coupled with fluid mechanics. Three Lectures on Classical Orthogonal Polynomials (available on request) were given by the author of this report, and other communications dealt with some semi-classical families (generalized Charlier and Meixner), Laguerre-Freud equations, Laguerre-Hahn class and numerical integration. During the last day participants also had the opportunity to attend an International Conference on Interuniversity Cooperation, under the auspices of UNESCO. We appreciated the efforts of the organizers to ensure the comfort of all participants, and the relaxing outdoor discussions between lectures among wonderful trees and flowers. Several banquets, receptions and excursions also succeeded in creating a friendly ambience for which we are indebted to the organizers. The proceedings will be published by World Scientific (Editors: J.Govaerts, N.M.Hounkonnou and W.A.Lester,Jr) and the second Workshop is already planned, again in Cotonou, in November 2001. Topic #11 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: OP-SF NET Editor <muldoon@yorku.ca> Subject: Special issues of Methods and Applications of Analysis in honour of Richard Askey Richard Askey turned 65 in June 1998 and, some time before that, Mourad Ismail and Dennis Stanton started to solicit articles for a special issue of "Methods and Application of Analysis" in his honour. Dick had been on the Editorial Board of the journal since its inception and had been for 20 years on the Editorial Board of SIAM Journal on Mathematical Analysis for 20 years before that. As the Special Issue Editors explain in a tribute to Askey (Vol 6, no 1, March 1999), the response was overwhelming and so far the articles received and accepted have filled nos 1 and 2 and others are just now appearing in no 3. Topic #12 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: OP-SF NET Editor <muldoon@yorku.ca> Subject: Changes at Methods and Applications of Analysis The journal "Methods and Applications of Analysis" has new Editors-in-Chief, Zhouping Xin (Courant Institute and Chinese University of Hong Kong) and Shing-Tung Yau (Harvard University) replacing the founding Editors-in-Chief, Roderick Wong and Robert Miura. Roderick and Robert deserve the heartfelt thanks of the OP and SF community for their service in providing such an excellent journal for the publication of work in our areas and related parts of mathematics. In particular, Roderick Wong took on and continued this work at the same time as he moved to the City University of Hong Kong and undertook heavy administrative responsibilities. Information on the journal is maintained at the web site: http://www.intlpress.com/journals/maa/index.html Topic #13 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: Wolfram Koepf Subject: Review Of "Special Functions" by Andrews, Askey and Roy [This item appeared in our printed Newsletter, October, 1999.] Special Functions By George E. Andrews, Richard Askey, Ranjan Roy Encyclopedia of Mathematics and its Applications Vol. 71. Cambridge University Press, Cambridge, 1999. US$ 85.00, xvi, 664 pp., ISBN 0-521-62321-9. This book covers a wealth of material on special functions, notably knowledge which was developed by Richard Askey and his co-authors during the several decades of his contributions to this subject, but also material which connects special functions with combinatorial questions collected by George Andrews. These two researchers are well-known for their efforts to support and demand the use of hypergeometric functions in their respective fields, hence hypergeometric functions and q-hypergeometric functions (basic hypergeometric functions) play a prominent role in the book under review. The book covers 12 chapters and 6 appendices. Furthermore, it contains a rich collection of 444 (!) exercises that are distributed among the different chapters. Here are the details: Chapter 1: The Gamma and Beta Functions. In this chapter the usual material about the Gamma and Beta functions is covered. Moreover, results for the logarithmic derivative psi(x)=Gamma'(x)/Gamma(x) of the Gamma function and for the Hurwitz and Riemann zeta function are developed; in particular, several integral representations are given. The Gamma function is characterized by the Bohr-Mollerup theorem, and finally the p-adic Gamma function is introduced. Chapter 2: The Hypergeometric Functions. The generalized hypergeometric function is introduced, and elementary examples are given. Euler's integral representation, and the usual summation theorems (Gauss, Chu-Vandermonde, Pfaff-Saalschutz, Dixon) come next. Then the hypergeometric differential equation is treated from the Riemannian point of view that analytic functions are determined to a large extent by their singularities. Next, Barnes type integrals, contiguous relations, and continued fractions of ratios of hypergeometric functions are covered. The Jacobi polynomials as specific hypergeometric polynomials are introduced. Finally, dilogarithms, binomial sums, and fractional integration by parts are treated. Chapter 3: Hypergeometric Transformations and Identities. This chapter starts with quadratic transformations. Then elliptic integrals are considered as hypergeometric functions, and arithmetic-geometric mean sequences are introduced. Next, transformations for balanced series, Whipple's transformation and Dougall's formula are given. Integral analogs of hypergeometric sums lead to the Wilson polynomials. The Riemannian point of view is reconsidered in connection with quadratic transformations. Gosper's algorithm on indefinite hypergeometric summation is given, and the Wilf-Zeilberger method for proving hypergeometric identities is compared with Pfaff's method, and the question of how these methods are related to contiguous relations is analyzed. Chapter 4: Bessel Functions and Confluent Hypergeometric Functions. Here, the confluent hypergeometric function is introduced. Then a Barnes type integral is given. As special cases, the Whittaker and the Bessel functions are covered. Recurrence equations, integral representations, and asymptotic expansions are treated. A two-dimensional Fourier transform leads to a generating function of the Bessel functions. Addition theorems and integrals of Bessel functions come next. Finally zeros and monotonicity properties of Bessel functions are discussed. Chapter 5: Orthogonal Polynomials. The elementary properties of general orthogonal polynomials are derived. Next, Gauss quadrature is examined. Then zeros of orthogonal polynomials are discussed, and the connection of orthogonal polynomials with continued fractions is treated. After Parseval's formula, the moment-generating function is introduced. Chapter 6: Special Orthogonal Polynomials. Under this heading comes a discussion of the classical hypergeometric type orthogonal polynomials. The Hermite, Laguerre and Jacobi polynomials and their properties are discussed in detail. Then linearization coefficients are considered, and combinatorial interpretations of the classical systems are given. The Wilson polynomials and their properties come next. Finally a q-generalization of the ultraspherical polynomials is deduced. Chapter 7: Topics in Orthogonal Polynomials. Connection coefficients are introduced, and for the classical systems these coefficients are explicitly determined. Nonnegativity results for hypergeometric functions and positive polynomial sums come next. In particular, the Askey-Gasper inequality which was used by de Branges in his proof of the Bieberbach conjecture [1] is deduced using results about connection coefficients. Theorems by Vietoris and Turan are covered. Finally, Apery's irrationality proof of zeta(3) is given. Chapter 8: The Selberg Integral and Its Applications. Here, Selberg's and Aomoto's integrals and extensions of these formulas are given. A two-dimensional electrostatic problem studied by Stieltjes connects the zeros of the Jacobi polynomials with Selberg's integral in an interesting way. Siegel's inequality, which is a refinement of the arithmetic-geometric mean inequality, is studied next, and a connection to the Laguerre polynomials is considered. Applications of Selberg's integral to constant-term identities and nearly-poised _3F_2 identities are given. The Hasse-Davenport relation and a finite-field analog of Selberg's integral finish this chapter. Chapter 9: Spherical Harmonics. Harmonic polynomials and the Laplace equation in three dimensions provide an introduction to the topic of this chapter. Then the harmonic polynomials of degree k and their orthogonality are studied. Their addition theorem yields an addition theorem for ultraspherical polynomials which was used by Weinstein [3] in his proof of the Bieberbach conjecture. It is shown that Fourier transforms of higher order are still expressible in terms of Bessel functions. Next, finite-dimensional representations of compact groups are studied. Finally, Koornwinder's product formula for Jacobi polynomials is given. Chapter 10: Introduction to q-series. In this chapter, the theory of q-hypergeometric series (basic hypergeometric series) is motivated by considering non-commutative q-algebra, related with the rule yx=qxy. Using this approach, the definition of the q-binomial coefficients and their connection with the standard binomial coefficients are straightforward. The q-integral is defined, and the q-binomial theorem is proved by two different approaches both based on recurrence equations. The q-Gamma function, and Jacobi's triple product identity are next. Ramanujan's summation formula is used to give results about the representations of numbers as sums of squares. Elliptic and theta functions are covered, and q-beta integrals are used to find a q-analog of the Wilson polynomials. Finally, the basic hypergeometric series is studied. Basic hypergeometric identities, the q-ultraspherical polynomials and the Mellin transform finish this chapter. Chapter 11: Partitions. Partitions are defined, and the connection of partition analysis with q-series is studied. Generating functions, and other results on partitions are obtained by this method. Next, graphical methods are discussed, and congruence properties of partitions are covered. Chapter 12: Bailey Chains. Rogers's second proof of the Rogers-Ramanujan identities is given. Then, Bailey's lemma and Watson's transformation formula are treated. Finally, some applications are given. Appendices on Infinite Products, Summability and Fractional Integration, Asymptotic Expansions, Euler-Maclaurin Summation Formula, Lagrange Inversion Formula, and Series Solutions of Differential Equation follow, and a bibliography, an index, a subject index and a symbol index complete the book. To begin with these last items: For a book of this size, the subject index is rather small (3 pages). Hence, obviously not every subject can be found here. Just to mention a few, one finds neither "addition theorem", nor "Bieberbach conjecture", nor "irrationality of zeta(3)", nor "indicial equation" (notation defined on p. 640 in Appendix F, and used on p. 74). Many other topics cannot be found in the subject index either. In my opinion, a book covering such a wealth of information needs a better index. Similarly, the bibliography (on purpose) contains only the articles that are explicitly mentioned in the text, and by no means covers the topic of the book encyclopedically. Another minor irritation is the fact that the notations [x] (e.g. on pp. 203, 314) and lfloor x rfloor (e.g. on pp. 279, 340) for the greatest integer in x are used synonymously, but only the latter is defined on p 15. On the other hand, the material is written in an excellent manner, and it gives the reader very interesting insights to special functions. On many occasions, theorems are proved by several alternative methods. This gives the reader a much better feeling for what is going on, indicating that Special Functions is not a topic which can be taught deductively. Furthermore, the book contains very few typos. But a book of this size covers thousands of formulas, and by Murphy's law, a few of them should be incorrect. I tried to find such misprints, in particular in the sections 3.11 and 3.12 about summation methods, since there I could use my Maple software for purposes of detection [2]. Not surprisingly, this search was successful: Formula (3.11.10) is incorrect by a factor -n; both identities in the middle of p. 175 are incorrect restatements of the corresponding contiguous relations (3.11.12) and (3.11.15) on p. 173; furthermore, in formula (3.12.1) the upper parameter z+n-1 should read z+n+1. (I would like to thank George Andrews for sending me the corrected formula.) In spite of these minor shortcomings, I recommend this book warmly as a rich source of information to everybody who is interested in Special Functions. References [1] de Branges, L.: A proof of the Bieberbach conjecture. Acta Math. 154, 1985, 137--152. [2] Koepf, Wolfram: Hypergeometric Summation. An Algorithmic Approach to Summation and Special Function Identities. Vieweg, Braunschweig/Wiesbaden, 1998. [3] Weinstein, L.: The Bieberbach conjecture. Int. Math. Res. Not. 5, 1991, 61--64. Topic #14 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: Tom Koornwinder <thk@wins.uva.nl> Subject: Doron Zeilberger's Maple Packages and Programs The following is from the web site: http://www.math.temple.edu/~zeilberg/programs.html EKHAD, a Maple package for proving binomial coefficients and other types of identities. To use it, download it as EKHAD, go into Maple, type `read EKHAD:`, and follow the instructions given there. Version of Feb. 25, 1999. This new version benefited from a GREAT SUGGESTION of Frederic CHYZAK (whom we thank so much!), and now is roughly four times as fast. It may not work on very early versions of Maple, in which case you still use the Old Version of EKHAD. qEKHAD, a Maple package for proving q-binomial coefficients (a.k.a. basic-hypergeometric, and q-) identities. To use it, download it as qEKHAD, go into Maple, type `read qEKHAD:`, and follow the instructions given there. Version of July 20, 1999. The new version implements the above suggestion of Frederic CHYZAK, but the speed-up is not so dramatic. If you have a very early versions of Maple, you may need the Old Version of qEKHAD. Topic #15 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: Ernst Davidovich Krupnikov <ernst@neic.nsk.su> Subject: Question on Schrodinger equations What are all the Schrodinger equations that have exact solutions expressible in terms of the Kampe de Feriet function? Topic #16 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: Allison Bogardo <bogardo@siam.org> Subject: SIAM Student Paper Prizes SIAM Student Paper Prizes The annual SIAM Student Paper Prizes will be awarded during the 2000 SIAM Annual Meeting, July 10-14, at the Westin Rio Mar Beach Resort in Rio Grande, Puerto Rico. If you are a student or know of a student who would like to take part in the competition, here are the details: The authors of the three best papers in applied and computational mathematics written by students and submitted to SIAM will receive a $1,000 cash prize and a framed calligraphed certificate as well as gratis registration for the meeting. There is no provision for travel expenses associated with the prize. Papers must be singly authored and not previously published or submitted for publication to be eligible for consideration. To qualify, authors must be students in good standing who have not received their PhDs at the time of submission. In submitting their work for publication, authors are asked to consider SIAM journals. However, student paper prize winners are not guaranteed publication in any SIAM journal; all papers submitted to SIAM journals are subject to the same refereeing process and standards. Submissions must be received in the SIAM office before February 15, 2000. Submissions, which must be in English, can be sent by regular mail or fax. Each submission must include (1) an extended abstract NOT LONGER THAN 5 PAGES (including bibliography); (2) the complete paper, which will be used solely for clarification of any questions; (3) a statement by the student's faculty advisor that the paper has been prepared by the author indicated and that the author is a student in good standing; (4) a letter by the student's faculty advisor describing and evaluating the paper's contribution; and (5) a short biography of the student. Submissions will be judged on originality, significance, and quality of exposition. The winners will be notified by April 15, 2000. Please direct your submission and any questions you may have to A. Bogardo at SIAM, 3600 University City Science Center, Philadelphia, PA 19104-2688; telephone (215) 382-9800; e-mail to bogardo@siam.org. Topic #17 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: OP-SF NET Editor <muldoon@yorku.ca> Subject: OP-SF preprints in xxx archive The following preprints related to the field of orthogonal polynomials and special functions were recently posted or cross-listed to one of the subcategories of the xxx archives. See: 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 E-print math.QA/0001033 Title: Askey-Wilson polynomials: an affine Hecke algebraic approach Authors: Masatoshi Noumi, Jasper V. Stokman Categories: QA Quantum Algebra (CA Classical Analysis; RT Representation Theory) Math Subject Class: 33D45, 33D80 Comments: 35 pages Abstract: We study Askey-Wilson type polynomials using representation theory of the double affine Hecke algebra. In particular, we prove bi-orthogonality relations for non-symmetric and anti-symmetric Askey-Wilson polynomials with respect to a complex measure. We give duality properties of the non-symmetric Askey-Wilson polynomials, and we show how the non-symmetric Askey-Wilson polynomials can be created from Sahi's intertwiners. The diagonal terms associated to the bi-orthogonality relations (which replace the notion of quadratic norm evaluations for orthogonal polynomials) are expressed in terms of residues of the complex weight function using intertwining properties of the non-symmetric Askey-Wilson transform under the action of the double affine Hecke algebra. We evaluate the constant term, which is essentially the well-known Askey-Wilson integral, using shift operators. We furthermore show how these results reduce to well-known properties of the symmetric Askey-Wilson polynomials, as were originally derived by Askey and Wilson using basic hypergeometric series theory. From: Jasper V. Stokman <stokman@math.jussieu.fr> Date: Thu 6 Jan 2000 11:49:54 GMT E-print math.CA/9912149 Title: A remark on perturbations of sine and cosine sums Author: Mihail N. Kolountzakis Categories: CA Classical Analysis Math Subject Class: 42A05 Comments: 2 pages Abstract: Consider a collection $\lambda_1<...<\lambda_N$ of distinct positive integers and the quantities $$ M_1 = M_1(\lambda_1,...,\lambda_N) = \max_{0\le x \le 2\pi} |\sum_{j=1}^N \sin{\lambda_j x}| $$ and $$ M_2 = M_2(\lambda_1,...,\lambda_N) = - \min_{0\le x \le 2\pi} \sum_{j=1} \cos{\lambda_j x}. $$ Prompted by a discussion with G. Benke we prove that collections of frequencies $\lambda_j$ which have $M_1 = o(N)$ or $M_2 = o(N)$ are unstable, in the sense that one can perturb the $\lambda_j$ by one each and get $M_1 \ge c N$ and $M_2 \ge c N$. From: Mihail N. Kolountzakis <kolount@itia.math.uch.gr> Date: Sat 18 Dec 1999 10:39:21 GMT E-print math.CA/9912140 Title: The Askey-Wilson function transform scheme Authors: Erik Koelink, Jasper V. Stokman Categories: CA Classical Analysis (QA Quantum Algebra) Math Subject Class: 33D15, 33D45 (Primary) 33D80 (Secondary) Comments: 17 pages, 2 figures, AMS-TeX Some formulas corrected, reference updated Abstract: In this paper we present an addition to Askey's scheme of q-hypergeometric orthogonal polynomials involving classes of q-special functions which do not consist of polynomials only. The special functions are q-analogues of the Jacobi and Bessel function, and are Askey-Wilson functions, big q-Jacobi functions and little q-Jacobi functions and the corresponding q-Bessel functions. The generalised orthogonality relations and the second order q-difference equations for these families are given. Limit transitions between these families are discussed. The quantum group theoretic interpretations are discussed shortly. From: Erik Koelink <koelink@twi.tudelft.nl> Date: Fri 17 Dec 1999 14:52:03 GMT Revised: Thu 23 Dec 1999 13:57:36 GMT E-print math.CA/9912113 Title: On the q-convolution on the line Author: Giovanna Carnovale Categories: CA Classical Analysis (QA Quantum Algebra) Math Subject Class: 33D80; 33D15; 42A85 (primary); 17B37 (secondary) Report number: 33/99 Abstract: I continue the investigation of a q-analogue of the convolution on the line started in a joint work with Koornwinder and based on a formal definition due to Kempf and Majid. Two different ways of approximating functions by means of the convolution and convolution of delta functions are introduced. A new family of functions that forms an increasing chain of algebras depending on a parameter s > 0 is constructed. The value of the parameter for which the mentioned algebras are well behaved, commutative and unital is found. In particular a privileged algebra of functions belonging to the above family is shown to be the quotient of an algebra studied in the previous article modulo the kernel of a q-analogue of the Fourier transform. This result has an analytic interpretation in terms of analytic functions whose q-moments have a particular behaviour. The same result makes it possible to extend results on invertibility of the q-Fourier transform due to Koornwinder. A few results on invertibility of functions with respect to the q-convolution are also obtained and they are related to solving certain simple linear q-difference equations with polynomial coefficients. From: carnoval <carnoval@math.jussieu.fr> Date: Wed 15 Dec 1999 09:38:09 GMT E-print math-ph/9912020 Title: One Dimensional Regularizations of the Coulomb Potential with Application to Atoms in Strong Magnetic Fields Authors: Raymond Brummelhuis, Mary Beth Ruskai, Elisabeth Werner Categories: MP Mathematical Physics (CA Classical Analysis) Math Subject Class: 81V45, 33E20 Journal reference: Differential Equations and Mathematical Physics, ed. by G. Weinstein and R. Weikard, pp. 43-51 (International Press, 2000) Comments: 9 pages, Proceedings of a conference on Differential Equations and Mathematical Physics at University of Alabama Birmingham (March 1998) Abstract: We consider one-dimensional regularizations of the Coulomb potential formed by taking a two-dimensional expectation of the Coulomb potential with respect to the Landau states. It is well-known that such functions arises naturally in the study of atoms in strong magnetic fields. For many-electron atoms consideration of the Pauli principle requires convex combinations of such potentials and interactions in which the regularizations also contain a 2^{-1/2} rescaling. We summarize the results of a comprehensive study of these functions including recursion relations, tight bounds, convexity properties, and connections with confluent hypergeometric functions. We also report briefly on their application in one-dimensional models of many-electrons atoms in strong magnetic fields. From: Mary Beth Ruskai <bruskai@cs.uml.edu> Date: Tue 28 Dec 1999 06:40:19 GMT E-print math.PR/9912170 Title: Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions Authors: P. Biane, J. Pitman, M. Yor Categories: PR Probability Theory (CA Classical Analysis) Math Subject Class: 11M06; 60J65; 60E07 Report number: DMA-99-30 Comments: LaTeX; 40 pages; review paper Abstract: This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these probability laws, and some approximations of Riemann's zeta function which are related to these laws. From: Biane <philippe.biane@ens.fr> Date: Tue 21 Dec 1999 11:18:04 GMT E-print math.QA/9911163 Title: Fourier transforms on the quantum SU(1,1) group Authors: Erik Koelink, Jasper Stokman, Mizan Rahman (appendix) Categories: QA Quantum Algebra (CA Classical Analysis) Math Subject Class: 17B37, 33D55, 33D80 (Primary) 43A32, 43A90, 46L89, 47B15 (Secondary) Comments: 77 pages, 1 figure Abstract: The main goal is to interpret the Askey-Wilson function and the corresponding transform pair on the quantum SU(1,1) group. A weight on the C^*-algebra of continuous functions vanishing at infinity on the quantum SU(1,1) group is studied, which is left and right invariant in a weak sense with respect to a product defined using Wall functions. The Haar weight restricted to certain subalgebras are explicitly determined in terms of an infinitely supported Jackson integral and in terms of an infinitely supported Askey-Wilson type measure. For the evaluation the spectral analysis of explicit unbounded doubly infinite Jacobi matrices and some new summation formulas for basic hypergeometric series are needed. The spherical functions are calculated in terms of Askey-Wilson functions and big q-Jacobi functions. The corresponding spherical Fourier transforms are identified with special cases of the big q-Jacobi function transform and of the Askey-Wilson function transform. From: Erik Koelink <koelink@twi.tudelft.nl> Date: Mon 22 Nov 1999 11:05:06 GMT E-print math.CO/9912093 Title: Riemann-Hilbert problem and the discrete Bessel kernel Author: Alexei Borodin Categories: CO Combinatorics (MP Mathematical Physics) Comments: AMSTeX, 17 pages Abstract: We use discrete analogs of Riemann-Hilbert problem's methods to derive the discrete Bessel kernel which describes the poissonized Plancherel measures for symmetric groups. To do this we define a discrete analog of 2 by 2 Riemann-Hilbert problems of special type. We also give an example, explicitly solvable in terms of classical special functions, when a discrete Riemann-Hilbert problem converges in a certain scaling limit to a conventional one; the example originates from the representation theory of the infinite symmetric group. From: Alexei Borodin <borodine@math.upenn.edu> Date: Sun 12 Dec 1999 17:46:39 GMT E-print math.CO/9912052 Title: Restricted permutations, continued fractions, and Chebyshev polynomials Authors: T. Mansour, A. Vainshtein Categories: CO Combinatorics Abstract: Let f_n^r(k) be the number of 132-avoiding permutations on n letters that contain exactly r occurrences of 12... k, and let F_r(x;k) and F(x,y;k) be the generating functions defined by $F_r(x;k)=\sum_{n\gs0} f_n^r(k)x^n$ and $F(x,y;k)=\sum_{r\gs0}F_r(x;k)y^r$. We find an explicit expression for F(x,y;k) in the form of a continued fraction. This allows us to express F_r(x;k) for $1\ls r\ls k$ via Chebyshev polynomials of the second kind. From: Toufik Mansour <tmansur@study.haifa.ac.il> Date: Mon 6 Dec 1999 22:55:37 GMT E-print math.QA/9912094 Title: Ubiquity of Kostka polynomials Author: Anatol N. Kirillov Categories: QA Quantum Algebra (CO Combinatorics) Comments: LaTeX, 60 pages, some typos corrected, and new exercises added Abstract: We report about results revolving around Kostka-Foulkes and parabolic Kostka polynomials and their connections with Representation Theory and Combinatorics. It appears (see Section 7) that the set of all parabolic Kostka polynomials forms a semigroup, which we call Liskova semigroup. We show that polynomials frequently appearing in Representation Theory and Combinatorics belong to the Liskova semigroup. Among such polynomials we study rectangular q-Catalan numbers; generalized exponents polynomials; principal specializations of the internal product of Schur functions; generalized q-Gaussian polynomials; parabolic Kostant partition function and its q-analog; certain generating functions on the set of transportation matrices. In each case we apply rigged configurations technique to obtain some interesting information about Kostka-Foulkes polynomials, Kostant partition function, MacMahon, Gelfand-Tsetlin and Chan-Robbins polytopes. We study also some properties of l-restricted generalized exponents and the stable behaviour of certain Kostka-Foulkes polynomials. From: Anatol N. Kirillov <kirillov@math.nagoya-u.ac.jp> Date: Sun 12 Dec 1999 15:08:55 GMT Revised: Mon 27 Dec 1999 06:48:47 GMT E-print math.AG/9911030 Title: Rational Hypergeometric Functions Authors: Eduardo Cattani, Alicia Dickenstein, Bernd Sturmfels Categories: AG Algebraic Geometry (CO Combinatorics) Report number: MSRI 1999-051 Comments: LaTeX, 26 pages Abstract: Multivariate hypergeometric functions associated with toric varieties were introduced by Gel'fand, Kapranov and Zelevinsky. Singularities of such functions are discriminants, that is, divisors projectively dual to torus orbit closures. We show that most of these potential denominators never appear in rational hypergeometric functions. We conjecture that the denominator of any rational hypergeometric function is a product of resultants, that is, a product of special discriminants arising from Cayley configurations. This conjecture is proved for toric hypersurfaces and for toric varieties of dimension at most three. Toric residues are applied to show that every toric resultant appears in the denominator of some rational hypergeometric function. From: Eduardo Cattani <cattani@math.umass.edu> Date: Thu 4 Nov 1999 22:23:38 GMT nlin.SI/0001001 From: Dmitri Scherbin <sdm@pool-7.ru> Date: Thu, 6 Jan 2000 22:32:36 GMT (16kb) Fermionic representation for basic hypergeometric functions related to Schur polynomials Authors: A.Yu.Orlov, D.M.Scherbin Subj-class: Exactly Solvable and Integrable Systems We present the fermionic representation for the q-deformed hypergeometric functions related to Schur polynomials. For q=1 it is known that these hypergeometric functions are related to zonal spherical polynomials for GL(N,C)/U(N) symmetric space. Multivariable hypergeometric functions appear to be tau-functions of the KP and of the two-dimensional Toda lattice hierarchies. The variables of the hypergeometric functions are the higher times of those hierarchies. The discrete Toda lattice variable shifts parameters of hypergeometric functions. math-ph/0001003 From: Aleksandar Mikovic <amikovic@ualg.pt> Date: Mon, 3 Jan 2000 12:22:33 GMT (9kb) Matrix Factorization for an SO(2) Spinning Top and Related Problems Authors: Aleksandar Mikovic Comments: 11 pages, Latex Subj-class: Mathematical Physics; Exactly Solvable and Integrable Systems We study the matrix factorization problem associated with an SO(2) spinning top by using the algebro-geometric approach. We derive the explicit expressions in terms of Riemann theta functions and discus some related problems including a non-compact extension and the case when the Lax matrix contains higher-order powers of the spectral parameter. solv-int/9912006 From: Dimitri Kusnezov <dimitri@nst.physics.yale.edu> Date: Mon, 6 Dec 1999 20:00:52 GMT (158kb) Group Theoretical Properties and Band Structure of the Lame Hamiltonian Authors: Hui Li, Dimitri Kusnezov, Francesco Iachello Comments: 21 pages Revtex + 6 eps + 2 jpg figures Subj-class: Exactly Solvable and Integrable Systems We study the group theoretical properties of the Lame equation and its relation to su(1,1) and su(2). We compute the band structure, dispersion relation and transfer matrix and discuss the dynamical symmetry limits. Topic #18 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: OP-SF NET Editor <muldoon@yorku.ca> Subject: Changes of Address, WWW Pages, etc The URL of Margit Roesler's home page has changed to http://pckoenig7.mathematik.tu-muenchen.de/~roesler/ Dr. Semyon Yakubovich (Technishe Universiteit Eindhoven, Netherlands) has been appointed as a Visiting Associate Professor at the University of Porto (Portugal) starting February 2000. His address will be: Departamento de Matematica Pura Faculdade de Ciencias Universidade do Porto Praca a gomes Teixeira 4099-002 Porto Portugal Luc Vinet has been appointed Vice-Principal (Academic) at McGill University, Montreal, Canada. His e-mail address is: Vinet@vps.mcgill.ca Topic #19 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: OP-SF NET Editor <muldoon@yorku.ca> Subject: Subscribing to OP-SF NET There are two ways to subscribe to OP-SF NET: 1. 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Topic #20 ------------ OP-SF NET 7.1 ----------- January 15, 2000 ~~~~~~~~~~~~~ From: OP-SF NET Editor <muldoon@yorku.ca> Subject: Obtaining back issues of OP-SF NET and submitting contributions to OP-SF NET and Newsletter Back issues of OP-SF NET can be obtained from WWW: http://turing.wins.uva.nl/~thk/opsfnet/ or WWW: http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html Contributions to the OP-SF NET 7.2 should reach the email address poly@siam.org before March 1, 2000. The Activity Group also sponsors a (printed) Newsletter edited by Renato Alvarez-Nodarse and Rafael Yanez. The deadline for submissions to be included in the February 2000 issue is January 15, 2000 and for the June 2000 issue it is May 15, 2000. Please send your Newsletter contributions directly to the Editors: Renato Alvarez-Nodarse Departamento de Analisis Matematico Universidad de Sevilla Apdo. Postal 1160, Sevilla E-41080 Spain fax: +34-95-455-7972 e-mail: renato@gandalf.ugr.es ran@cica.es Rafael J. 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