Subject: NA Digest, V. 94, # 2 NA Digest Sunday, January 9, 1994 Volume 94 : Issue 2 Today's Editor: Cleve Moler The MathWorks, Inc. moler@mathworks.com Today's Topics: Scientific American January Cover Story Change of Address for Charles Tong PhD Abstracts in Numerical Mathematics Help Needed for Coupled PDE and ODE System Two Canadian Conferences IPNet: Network in Inverse and Ill-Posed Problems Washington/Baltimore Seminar List Scientific Computation and Differential Equations Positions at University of Zuerich Position at Argonne National Laboratory Position at University of New South Wales Electronic Transactions on Numerical Analysis Contents, SIAM Math Analysis Submissions for NA Digest: Mail to na.digest@na-net.ornl.gov. Information about NA-NET: Mail to na.help@na-net.ornl.gov. ------------------------------------------------------- From: Joseph Traub Date: Mon, 3 Jan 94 09:10:45 EST Subject: Scientific American January Cover Story The cover story in the January 1994 issue of Scientific American is "Breaking Intractability" by Traub and Wozniakowski. It is shown that some computationally intractable problems can be solved if one settles for a good solution on the average. Examples of such problems are high dimensional integration and approximation. The current method of choice for computing high dimensional integrals is Monte Carlo. Preliminary results of software testing by a PhD student, Spassimir Paskov, indicates that deterministic methods are superior to Monte Carlo. This testing has been primarily on real-world problems, of dimension as high as 360, from finance. We would be grateful to be send other high dimensonal integration or approximation problems from diverse applications. ------------------------------ From: Charles Tong Date: Tue, 4 Jan 1994 16:04:21 +0800 Subject: Change of Address for Charles Tong Effective immediately, my address is : Charles Tong Dept. of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong e-mail : matong@uxmail.ust.hk or na.tong@na-net.ornl.gov ------------------------------ From: Tom Coleman Date: Fri, 7 Jan 94 12:37:39 -0500 Subject: PhD Abstracts in Numerical Mathematics The SIGNUM Newsletter, a quarterly publication of the ACM Special Interest Group on Numerical Mathematics, publishes one-paragraph abstracts of recent Ph.D. theses in numerical mathematics. (A recent Ph.D. thesis should have been completed within the last year.) If you (or your student) qualifies then you can submit a one-paragraph abstract, along with the student's name, advisor's name, and thesis approval date to: coleman@cs.cornell.edu ------------------------------ From: Deepti Date: Fri, 07 Jan 94 16:39:31 EST Subject: Help Needed for Coupled PDE and ODE System I'm looking for a fortran software package/code that can solve a system of PDEs and ODEs. The PDE is a parabolic PDE in one space dimension with known initial and boundary conditions at x=0.1 and x=1. par(u)/par(t) = par(par(u)/par(x))/par(x) - f(g(x),m(x),g(x=1),m(x=1)) where f is a function . m(x) = (u/x + a) where a is a constant g(x) is the solution of the initial value 2nd order ODE: 2 2 g" + ( m(x) - n(n+1)/x )g = 0 where n is known and the initial conditons are given x=0.1 : g(x) = 0 g'(x) = 0 The reason I have not been able to use a standard package to solve this is because the boundary conditions for the ODE for g(x) are not known. Any help in solving this system of DE's will be greatly appreciated. Thanx in advance... Deepti ------------------------------ From: Edmund West Date: Mon, 3 Jan 1994 11:59:44 -0500 (EST) Subject: Two Canadian Conferences Preliminary Information about SS '94 Supercomputing Symposium '94 Canada's Eighth Annual High Performance Computing Conference and Exhibition June 6-8, 1994 Sponsored by: Supercomputing Canada (Super*Can) Hosted by: University of Toronto * Conference Plans: The symposium is concerned with all aspects of high performance computing. World class invited speakers and informative technical sessions will expose attendees to the latest developments in this field. There will also be an exhibition of vendor products. Presentations will be made that describe the hardware, software, programming tools and techniques, applications, networks and experiences related to high performance computing. Topics will include, but are not limited to: o vector computing technology o parallel computing technology o workstation clusters o parallel programming techniques o distributed computing o languages for high performance computing o experiences with high performance computers o applications of high performance computing technology to solve problems in government, academia and industry o networking and communications o scientific data visualization o compiler and operating system issues * Deadlines: Call for Papers distributed: January 5, 1994 Registration materials distributed: January 21, 1994 Abstract submissions due: February 14, 1994 Notification of acceptance: March 14, 1994 Camera-ready papers due: May 6, 1994 Early registration: May 6, 1994 * Conference Social Scene o Ice-breaker Reception (Sunday evening, June 5, 1994) o Conference Banquet (Monday evening, June 6, 1994) o Special Entertainment For more information contact the Conference Chairman: Dr. Edmund West 4 Bancroft Avenue, Room 202 University of Toronto Toronto, Ontario M5S 1A1 416-978-4085 * yedwest@utirc.utoronto.ca [ftp info at ftp.utirc.utoronto.ca in /pub/SS94] Some participants in Supercomputing Symposium '94 may also be interested in the CFD 94 conference, being held in Toronto on the Thursday and Friday (June 2 and 3) immediately preceeding SS '94. CONFERENCE ANNOUNCEMENT: CFD 94 CFD 94 is the annual meeting of the Computational Fluid Dynamics Society of Canada. The objectives of CFD 94 are to bring together researchers and practitioners in computational fluid dynamics (CFD) and to promote this methodology. CFD-94 addresses all aspects of CFD including, but not restricted to, acoustics, aerodynamics, astrophysics, automotive engineering, biomedicine, hypersonics, industrial engineering, new CFD algorithms, process engineering, transport in porous media, and weather prediction. Individuals, companies, vendors and government research labs are invited to submit scientific presentations. CFD-oriented companies and consultants are encouraged to participate in CFD-94 with exhibits of hardware, software and applications. Abstract submission deadline: 14 January 1994 Preregistration deadline: 30 April 1994 For further information, contact either: Prof. C. Ross Ethier email: ethier@me.utoronto.ca voice: (416) 978-6728 fax: (416) 978-7753 Prof. James J. Gottlieb email: gottlieb@bach.utias.utoronto.ca voice: (416) 667-7740 fax: (416) 667-7799 ------------------------------ From: lamm@mth.msu.edu (Patricia K Lamm) Date: Wed, 5 Jan 94 11:50:47 EST Subject: IPNet: Network in Inverse and Ill-Posed Problems I wish to announce the formation of the IPNet, an electronic network for researchers working in the areas of Inverse and/or Ill-Posed Problems. The goal of IPNet is to - promote communication between scientists interested in these research areas - to generate a regular newsletter called the 'IPNet Digest' for announcements and scientific queries of general interest - provide a central site for obtaining current e-mail addresses and affiliations of those working in these areas. For automated subscription to the IPNet, send an e-mail message to the address ipnet-request@math.msu.edu with the following in the BODY of the message: subscribe lastname firstname institution You should supply the information in the brackets < > without typing the brackets. The subject line of your message is ignored. For more help, for examples of how to subscribe, or information on automated mailing lists, change-of-address, archived files, etc., send an e-mail message to ipnet-request@math.msu.edu with the following in the BODY of the message: help E-mail addresses for the IPNet: ipnet-request@math.msu.edu - automated subscribe, unsubscribe, help, mailing lists, archive info., etc., as described above. ipnet-digest@math.msu.edu - for submissions to the IPNet Digest ipnet-owner@math.msu.edu - for comments/questions needing human response ------------------------------ From: Kosmo Tatalias Date: Wed, 5 Jan 94 10:21:21 EST Subject: Washington/Baltimore Seminar List ANNOUNCING REVIVAL OF DIGEST LISTING WASHINGTON/BALTIMORE AREA SEMINARS IN MATHEMATICS AND COMPUTER SCIENCE Michael Mascagni and I are attempting to revive his weekly digest listing (non-commercial) mathematics and computer science talks and seminars in the Washington-Baltimore area. If you would like to be on the distribution list, please send an e-mail message including your name, preferred e-mail address, and telephone number to: tatalias@gsisun.gsi.nic.ddn.mil . If you would like to have any seminars listed in the first digest, please send me e-mail by January 14 giving the name of the speaker, speaker's affiliation, title of talk, date, time, location, sponsor's name, e-mail address and telephone, and if possible a short abstract of the talk. Only e-mail and ASCII files on PC diskette will be accepted for inclusion in the digest. The first new digest of seminars should be distributed by late January. Kosmo Tatalias Government Systems Inc 14200 Park Meadow Drive, Suite 200 Chantilly, VA 22021 (703) 802-8519 ------------------------------ From: Robert Skeel Date: Wed, 5 Jan 1994 12:35:12 -0600 Subject: Scientific Computation and Differential Equations First Announcement SciCADE 95 International Conference on Scientific Computation and Differential Equations Stanford, California, March 28--April 1, 1995 This meeting will feature current research in scientific computing with an emphasis on the numerical solution of differential equations in science and engineering, particularly ordinary differential equations. The meeting will close with a celebration of the sixtieth birthday of C. William Gear. Watch for the second announcement also here in the NA Digest. Alternatively, send a message to scicade@sccm.stanford.edu with enquiries and for future mailings. Organizing committee: Gene Golub (Stanford), Linda Petzold (Minnesota), Robert Skeel (Illinois), Andrew Stuart (Stanford). ------------------------------ From: Rolf Jeltsch Date: Mon, 3 Jan 94 17:42:57 +0100 Subject: Positions at University of Zuerich Applications are invited for two positions as Professor of Mathematics at the University of Zuerich, one in Analysis and one in Numerical Analysis. Applicants are expected to be active in research and to be willing to participate in teaching at all levels. Applications, including CV and list of publications, should be sent to Professor G. Rasche, Dekan der Philosophischen Fakultaet II, Universitaet Zuerich-Irchel, Winterthurerstrasse 190, CH-8057 Zuerich, Switzerland, to arrive by 15th February 1994. Winterthurerstrasse 190 CH-8057 Zuerich, Switzerland. Teaching Assistant Positions The Seminar for Applied Mathematics will have two open positions starting April 1st, 1994. These are teaching assistant positions where the successful candidate is supposed to work towards his PhD in addition to his regular teaching. One position is funded through a project. The successful candidate should develop and analyse algorithms to solve time dependent convection dominated partial differential equations using massively parallel computers. The other Ph.D. topic will be in one of the research areas treated currently at the Seminar for Applied Mathematics. The main research directions of the Seminar are numerics in partial differential equations, especially hyperbolic nonlinear conservation laws with applications in fluid mechanics, Navier-Stokes equations, inverse problems and approximation theory. For further information contact Prof. Dr. Rolf Jeltsch Semianr fur Angewandte Mathematik ETH Zurich CH-8092 Zurich Switzerland Phone +41-1-632 3452 FAX +41-1-252 3401 e-mail jeltsch@sam.math.ethz.ch Applications, with a Curriculum Vitae, should be sent to the above address before January 31, 1994. ------------------------------ From: M. K. Kwong" Date: Thu, 6 Jan 1994 21:48:40 -0600 (CST) Subject: Position at Argonne National Laboratory Postdoctoral Position Mathematics and Computer Science Division Argonne National Laboratory Argonne National Laboratory invites outstanding candidates to apply for a postdoctoral research position in the Mathematics and Computer Science Division. Candidates should have a Ph.D. in mathematics, computer science, or a related area. Candidates must have extensive experience and knowledge in image and signal processing. A good knowledge of wavelet theory, parallel programming and algorithms, computer architecture and computer systems is desirable. The successful candidate will participate in an advanced large-scale image processing project within the Mathematics and Computer Science Division. This program brings together computer scientists, mathematicians, and image processing experts at Argonne National Laboratory and other institutions to develop algorithms and software environment for large-scale image processing on scalable parallel computers. The Mathematics and Computer Science Division supports an excellent computational environment that includes access to high-performance scientific workstations, a scientific visualization laboratory, and state-of-the-art parallel computers (including the IBM SP-1 and the Intel Touchstone DELTA). Argonne is located in the southwestern Chicago suburbs, offering the advantages of affordable housing and good schools, as well as easy access to the cultural attractions of the city. Applicants must have received their Ph.D. not more than three years prior to the beginning of the appointment. Applications should be addressed to Walter McFall, Box mcs-postdoc5, Employment and Placement, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, and must include a resum e and the names and addresses of three references. For further information, contact M. K. Kwong or P. T. Peter Tang (open positions@mcs.anl.gov). Argonne is an affirmative action/equal opportunity employer. ------------------------------ From: Ian Sloan Date: Fri, 7 Jan 94 16:18:44 +1100 Subject: Position at University of New South Wales POSITIONS IN SUNNY SYDNEY If you think you might fit into the broad range of research positions advertised below, I look forward to hearing from you, or to receiving an application. If you want to contact me in the near future, e-mail will be best, as I shall be in Europe, but in intermittent e-mail contact, until the end of January. (Non-Australian residents are probably not eligible for appointment at the Research Assistant level.) Ian Sloan I.Sloan@unsw.edu.au THE UNIVERSITY OF NEW SOUTH WALES School of Mathematics Research Associate/Research Fellow (Ref. 022xx) Research Assistant (Ref. 023xx) (2 positions, full-time or fractional) Applications are invited for two research positions on an Australian Research Council funded project, "Numerical analysis of continuous phenomena", held by Professor I.H. Sloan and Dr. W. McLean. One part of the project is concerned with new methods for boundary integral equations, including the development of software to implement novel methods for 3D problems. Another part of the project is concerned with the analysis, design and implementation of novel numerical methods for high dimensional numerical integration. Applicants for the Research Assistant position should have an Honours degree in some area of the mathematical sciences, have credentials and a strong interest in scientific computation, and be capable of working without close supervision. Applicants for the Research Associate position should have a PhD degree in Mathematics, or equivalent qualifications. Applicants for the Research Fellow position should have a strong record of independent post-doctoral research and proven analytical strengths, and be capable of initiating research in a relevant area. For any of the positions a knowledge of the following areas would be an advantage: partial differential equations, numerical analysis, applied functional analysis, number theory, algebra, mathematical physics, finite elements, vector and parallel computing, UNIX, structured programming, object-oriented programming. Persons appointed will have access to and training opportunities on a wide u range of modern computing equipment, including the Thinking Machines 32-processor CM5 of the Sydney Regional Centre for Parallel Computing, located at the University of New South Wales, the 2 processor Cray EL of the UNSW Centre for Advanced Numerical Computation in Engineering and Science, and UNIX work stations within the School of Mathematics. Appointment on either a full-time or fractional basis will be countenanced. Appointment as Research Associate or Research Assistant will be initially for 1 year, with a possibility of renewal for up to two further years. Appointment as Research Fellow will be initially for up to 2 years, with a possibility of renewal for a further year. Applications close February 25, 1995. Further information from Professor I.H. Sloan, by telephone 61-2-697-3357 after January 31, or (and preferably) by e-mail, I.Sloan@unsw.edu.au Salary: Research Assistant $A27,358 - $A33,868 per annum Research Associate $A36,285 - $A38,950 per annum Research Fellow $A41,000 - $A42,538 per annum Level of appointment and commencement salary are dependent upon qualifications and experience. Applicants should submit a written application QUOTING REFERENCE NUMBER. Include business and private telephone numbers; whether interested in a full-time or fractional position (or both), a complete vita (with copies of academic transcript and qualifications where appropriate); and the names, addresses, and preferably fax numbers of at least two referees to: The Recruitment Officer, Human Resources, University of New South Wales, Kensington NSW 2033, Australia, by the closing date. ------------------------------ From: Lothar Reichel Date: Fri, 7 Jan 1994 19:59:24 -0500 (EST) Subject: Electronic Transactions on Numerical Analysis Contents Electronic Transactions on Numerical Analysis, Volume 1, 1993 1. C. Schneider, Analysis of the linearly implicit mid-point rule for differential-algebraic equations. File: vol.1.1993/pp1-10.ps 2. G.L.G. Sleijpen and D.R. Fokkema, BiCGstab(l) for linear equations involving unsymmetric matrices with complex spectrum. File: vol.1.1993/pp11-32.ps 3. G.S. Ammar, P. Benner and V. Mehrmann, A multishift algorithm for the numerical solution of algebraic Riccati equations. File: vol.1.1993/pp33-48.ps 4. M. Eiermann and R.S. Varga, Zeros and local extreme points of Faber polynomials associated with hypocycloidal domains. File: vol.1.1993/pp49-71.ps 5. V. Mehrmann and W. Rath, Numerical methods for the computation of analytic singular value decompositions. File: vol.1.1993/pp72-88.ps 6. M. Hanke and M. Hochbruck, A Chebyshev-like semiiteration for inconsistent linear systems. File: vol.1.1993/pp89-103.ps 7. G. Csordas, A.M. Odlyzko, W. Smith and R. S. Varga, A new Lehmer pair of zeros and a new lower bound for the de Bruijn-Newman constant. File: vol.1.1993/pp104-111.ps ACCESSING ETNA BECOMING A SUBSCRIBER TO ETNA. To be included in ETNA's quarterly mailing list of the titles and abstracts of papers published in ETNA, send an e-mail message to etna@mcs.kent.edu with the subject ``ETNA Registration''. ACCESSING ETNA USING GOPHER. ETNA is running a gopher server. Its hostname is: etna.mcs.kent.edu. If you are running gopher on your system the command gopher etna.mcs.kent.edu will connect you directly to ETNA. Provided your system is suitably configured, keyword searches and the on-line-graphical display of papers will then be available. The ETNA directory, ``viewers'', contains the source files for programs that will provide most UNIX workstations with direct-display and keyword-search capabilities. Contact your system administrator about installing these programs. OBTAINING AN ETNA PAPER WITH FTP. Papers can be obtained at any time from ETNA via anonymous ftp from etna.mcs.kent.edu. A paper's location will always correspond to its reference. For instance, a paper which is referenced as ``...,Elec. Trans. Numer. Anal., Vol 1, 1993, pp. 11-32'', will be stored in the directory ``vol.1.1993'', and its file name will be ``pp11-32.ps''. To obtain that paper using ftp: a) ftp etna.mcs.kent.edu b) login as anonymous c) enter your e-mail address as your password d) cd to vol.1.1993 e) get pp11-32.ps To obtain only the list of titles and abstracts for the papers published is volume 1 of ETNA, repeat a)-d) above but change e) to e) get index OBTAINING AN ETNA PAPER VIA E-MAIL. ETNA is using a mailer program which will scan incoming e-mail messages for requests and then e-mail the requested file to the sender. The program was written by Eric Grosse for netlib and modified slightly by Arden Ruttan for ETNA. A PostScript file of any paper published in ETNA may be obtained by sending an e-mail message to ``mailer@etna.mcs.kent.edu'' containing a phrase of the form ``send pagenumber.ps from vol.number.year''. For instance, to use ETNA's mailer to obtain a paper which is referenced as ``...,Elec. Trans. Numer. Anal., Vol 1, 1993, pp. 11-32'', send e-mail to ``mailer@etna.mcs.kent.edu'' containing the phrase ``send pp11-32.ps from vol.1.1993''. To obtain only the list of titles and abstract for the papers published in volume 1 of ETNA, send an e-mail message to ``mailer@etna.mcs.kent.edu'' containing the phrase ``send index from vol.1.1993''. The requested paper will be e-mailed to you in several pieces. The subject of each piece of e-mail indicates the number of that piece. To reconstruct the original file, a) Edit each piece deleting all lines that are not strictly between the two occurrence of the phrase ``CUT HERE............'' including the lines containing those phrases. b) Using the file containing piece 1, successively append the remaining pieces in order to the END of the that file. Unix users can also re-assemble the paper by removing the mail headers. The resulting files are ``sh'' scripts which can reassembled by issuing the commands (here we are assuming that the various parts of the papers are stored in ``file1'', ``file2'',...,``filen''). sh file1 sh file2 . . . sh filen Unix users may also use the following script which will automatically reconstruct the original PostScript file. #!/bin/sh # This is a shell script which will re-assemble the PostScript file # mailed to you by ETNA's mailer program. To use this script # 1) Copy this script to a file in an empty directory and name it reassm. # 2) Save each mail message from ETNA with a unique name in the # directory which contains this file. # 3) Change to that directory and execute the command # sh reassm # or alternately you can # 1) Change to a directory containing this a script in a file. # 2) Save each mail message from ETNA with a unique name but with a common # prefix shared by only the ETNA files. For example, you could save the # respective ETNA files in ff1, ff2, ... # 3) Assuming the name of this file is reassm, execute the command # sh reassm ff ls $1* | grep -v $0 > .f$$ for file in `cat .f$$` do echo $file awk 'BEGIN{i=0};$1=="#!/bin/sh" {i=1};{if (i>0) print $0}' $file > .awk$$ /bin/sh .awk$$ done rm .f$$ rm .awk$$ SUBMITTING A PAPER TO ETNA. To obtain information as to how to submit a paper to ETNA, ftp the file ``info-for-authors'' which is located in the directory ``etna-info''. Alternately you may send an e-mail message to ``mailer@etna.mcs.kent.edu'' containing the phrase ``send info-for-authors from etna-info''. ------------------------------ From: SIAM Date: Mon, 03 Jan 94 13:00:10 EST Subject: Contents, SIAM Math Analysis TABLE OF CONTENTS SIAM Math Anal. March 1994 A Hypergeometric Analysis of the Genus Series for a Class of 2-Cell Embeddings in Orientable Surfaces G. E. Andrews, D. M. Jackson, and T. I. Visentin On Connection Coefficients for Q-Difference Systems of A-Type Jackson Integrals Kazuhiko Aomoto Group Theoretical Interpretations of Special Function Identities: Two Examples L. C. Biedenharn and K. Ciftci Asymptotic Approximations for Symmetric Elliptic Integrals B. C. Carlson and J. L. Gustafson Uniform Airy-Type Expansions of Integrals A. B. Olde Daalhuis and N. M. Temme Uniform Asymptotic Solutions of Second-Order Linear Differential Equations Havin g a Simple Pole and a Coalescing Turning Point in the Complex Plane T. M. Dunster On the Derivative with Respect to a Parameter of a Zero of a Sturm-Liouville Function Arpad Elbert and Martin E. Muldoon Remez- and Nikolskii-Type Inequalities for Logarithmic Potentials Tamas Erdelyi, Xin Li, and E. B. Saff On Necessary Multiplier Conditions for Laguerre Expansions II George Gasper and Walter Trebels Scattering Theory, Orthogonal Polynomials, and q-Series Jeffrey S. Geronimo On the Asymptotics of the Tricomi-Carlitz Polynomials and Their Zero Distributio n (I) William M. Y. Goh and Jet Wimp Watson's Basic Analogue of Ramanujan's Entry 40 and Its Generalization Dharma P. Gupta and David R. Masson Some q-Beta Integrals on SU(n) and Sp(n) That Generalize the Askey-Wilson and Nasrallah-Rahman Integrals Robert A. Gustafson On the Struve Transformation P. Heywood and P. G. Rooney Asymptotics of Pollaczek Polynomials and Their Zeros Mourad E. H. Ismail Asymptotic Remainders D. S. Jones Application of Szego Polynomials to Frequency Analysis William B. Jones, Olav Njastad, and Haakon Waadeland Models of Q-Algebra Representations: The Group of Plane Motions E. G. Kalnins, W. Miller, Jr., and S. Mukherjee Some Results on Co-Recursive Associated Laguerre and Jacobi Polynomials Jean Letessier Bounds and Monotonicities for the Zeros of Derivatives of Ultraspherical Bessel Functions Lee Lorch and Peter Szego Best Weighted Polynomial Approximation Via Jacobi Expansions Doron S. Lubinsky and Vilmos Totik The Cl Rogers-Selberg Identity Stephen C. Milne Positivity of Integrals of Bessel Functions Jolanta K. Misiewicz and Donald St. P. Richards Generalized Jacobi Weights, Christoffel Functions, and Jacobi Polynomials Thomas Erdelyi, Alphonse P. Magnus, and Paul Nevai Regularization of Nonlinear Differential-Algebraic Equations Leonid V. Kalachev and Robert E. O'Malley, Jr. A Generalization of Pearcey's Integral R. B. Paris The Pearson Equation and the Beta Integrals Mizan Rahman and Sergei K. Suslov The Classical Umbral Calculus G.-C. Rota and B. D. Taylor Specializations of Generalized Laguerre Polynomials R. Simion and D. Stanton Discrete and Continuous Liouville-Green-Olver Approximations: A Unified Treatmen t Via Volterra-Stieltjes Integral Equations Renato Spigler and Marco Vianello Truncation Error for Limit Periodic Schur Algorithms W. J. Thron Asymptotic Analysis of Some Associated Orthogonal Polynomials Connected with Elliptic Functions Galliano Valent On the Relative Extrema of the Jacobi Polynomials Pn(0,-1)(x) R. Wong and J.-M. Zhang Towards a WZ Evolution of the Mehta Integral Doron Zeilberger ------------------------------ End of NA Digest ************************** -------