IPNet Digest Volume 8, Number 03 May 7, 2001 Today's Editor: Patricia K. Lamm Michigan State University Today's Topics: IPNet Back Online Symposium: Inverse Problems in Engineering Workshop: Inverse Problems in Applications Workshop: Inverse Problems and Imaging Conference: Inverse Problems in Hong Kong Workshop: Scientific Computing, including Image Processing New Books on Optimization, Nonconvex Systems Free Access to Inverse Problems Journal Table of Contents: Inverse Problems Table of Contents: Inverse Problems in Engineering Table of Contents: Mathematics of Control, Signals, and Systems Table of Contents: Electronic Transactions on Numerical Analysis Table of Contents: Linear Algebra and Its Applications Submissions for IPNet Digest: Mail to ipnet-digest@math.msu.edu Information about IPNet: http://www.mth.msu.edu/ipnet Mail to ipnet-request@math.msu.edu ----------------------------- From: ipnet-digest@math.msu.edu Subject: IPNet Back Online Date: Mon, 07 May 2001 The IPNet host server was hacked last month, and reinstallation of software caused the IPNet to be down for several weeks. This meant that new subscribers could not join and that mailing of the IPNet Digest was greatly delayed. Although the IPNet is back online and appears to be fully functional, our sincere apologies go to those contributors with news items that may now be out-of-date (these items have been edited below where necessary) and to all IPNet subscribers. -Ed. ----------------------------- From: Chemical Engineering - TAMU Subject: Inverse Problems in Engineering Symposium Date: Thu, 08 Mar 2001 Reminder: 2001 Inverse Problems in Engineering Symposium at Texas A&M University June 14-16, 2001. Please see the Symposium web page http://inverse2001.tamu.edu for information. I do hope you will participate in our symposium! Best regards, Ted Watson Professor A. Ted Watson Department of Chemical Engineering Texas A&M University College Station, TX 77843-3122 Office: (979) 845-3484 Fax: (979) 845-6446 e-mail: atw@tamu.edu http://www-chen.tamu.edu/EIL/ http://www-chen.tamu.edu/chen/faculty/watson/ ----------------------------- From: Volker Schulz To: ipnet-digest@math.msu.edu Date: Fri, 16 Mar 2001 First Announcement Workshop on "INVERSE PROBLEMS IN APPLICATIONS" Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany September, 10 - 12, 2001 Organizers Heinz Engl (University of Linz, Austria) Peter Maass (University of Bremen, Germany) Volker Schulz (WIAS Berlin, Germany) Scope: Inverse problems play a major role in all aspects of mathematical modeling and optimization of physical, technical and biological systems. Although rather elegant theory is involved in the analysis of inverse problem, there are also many interesting problems in real world applications. This workshop is particularly devoted to specific challenges that practical applications pose to the inverse modeler and to numerical solution approaches which make it possible to deal with these challenges. The following speakers will present invited lectures: A.F. Grunbaum (Lawrence Berkeley, USA) O. Scherzer (Univ. Bayreuth, Germany) V. Dicken (Univ. Bremen, Germany) B. Kaltenbacher (Univ. Linz, Austria) J. Schloeder (IWR Heidelberg, Germany) It is intentionally planned as a satellite conference to the first SIAM-EMS conference in Berlin (http://www.zib.de/amcw01/). In order to alleviate the organizational effort we encourage people intending to participate and to present a contributed talk to fill in the registration form at http://www.wias-berlin.de/ws-inv as soon as possible. The final registration deadline is June 30, 2001. The registration fee is DM 70 and is to be payed on-site. For further questions contact Anke Giese (giese@wias-berlin.de). ----------------------------- From: Gunther Uhlmann Subject: Workshop on Inverse Problems and Imaging Date: Mon, 2 Apr 2001 The PIMS-MITACS Workshop on "Inverse Problems and Imaging" will be held June 9-10, 2001 at the Pacific Institute of Mathematical Sciences (PIMS) site at the University of British Columbia, Vancouver, Canada. This is also the Third Inverse Problems Seminar of the Pacific Northwest. The meeting is supported by MITACS, NSF and PIMS. The URL for the workshop is: http://www.pims.math.ca/industrial/2001/ipi/ Please contact Michael Lamoureux (mikel@math.ucalgary.edu) or Gunther Uhlmann (gunther@math.washington.edu) for any additional information. ----------------------------- From: Jane Hui Subject: Conference on Inverse Problems in Hong Kong Date: Wed, 02 May 2001 First Announcement and Call for Papers International Conference on Inverse Problems - Recent Development in Theories and Numerics (Inverse2002) City University of Hong Kong, Hong Kong January 9-12, 2002 ANNOUNCEMENT: On behalf of the Organizing Committee, I would like to invite you to attend the above conference Inverse2002 to be held at the City University of Hong Kong during January 9-12, 2002. Up-to-date information on the Inverse2002 can be found from the webpage: http://personal.cityu.edu.hk/~maychon/conference/inverse2002/inverse2002.htm The purpose of this conference is to establish a first and strong collaboration link among the universities of Asia-Pacific and worldwide leading researchers in inverse problems. The conference will address both theoretical (mathematics), applied (engineering) and development aspects on inverse problems. Your participation at the conference will be much appreciated. You may pre-register and submit an abstract in your field of expertise through the above webpage. Papers accepted for presentation at the Conference will be published in special issues of international journals after normal refereed processes. I am also enclosing a list of conference sessions, invited speakers and members of committees for your reference. [Please see the above webpage for members of committees. -Ed ] Looking forwards to meeting you in Hong Kong. Yours sincerely, Benny HON, Y.C. Co-Chair for the Inverse Conference 2002 Department of Mathematics City University of Hong Kong email: Benny.Hon@cityu.edu.hk http://www.cityu.edu.hk/ma/staff/ychon.html (Office) 852 - 2788 8675 (Fax) 852 - 2788 8561 List of Sessions: Main Scopes/Applicable Disciplines Financial Problems Image Processing Problems Inverse Problems Related to the Industries Medical Problems Nodal Problems Optimization Problems Parameter Identification and Control Sampling Problems Spectral Problems The following recent theoretical developments and numerical approaches in related to the above scopes are emphasized: Theoretical Development and Numerical Approaches Well-Posedness Uniqueness Stability Reconstruction Scheme Numerical Methods Plenary Speakers/Invited Speakers: Invited Plenary Speakers on keynote talks: G. Bao ( Michigan University, USA ) J. Cheng ( Fudan University, China ) V. Isakov ( Wichita State University, KS, USA ) P. C. Sabatier ( Univ. des Sciences et Tech. du Languedoc, France ) Invited Speakers on introductory talks: D. Anikonov ( Institute of Applied Mathematics, Vladivostok ) H. Engl ( Johannes Kepler Universitat Linz, Austria ) J. Frankel ( Tennessee University, USA ) D. Fujiwara ( Kyoto University, Japan ) A. Kirsch ( Fridericiana Karlsruhe University, Germany ) J. S. Pang ( The Johns Hopkins University, USA ) J. K. Seo ( Yonsei University, Korea ) K. Tanuma ( Osaka Kyoiku University, Japan ) D. D. Trong ( HoChiMing City University, Vietnam ) J. Z. Zhang ( City University of Hong Kong, HKSAR ) Call for Papers: Titles and abstracts of contribution papers must be received by 31 August 2001. The abstracts should be typed in LaTeX, not to exceed one A4 page, and sent to the Secretary (see address below) by e-mail. Address: Ms Jane Hui Secretary Department of Mathematics City University of Hong Kong 83 Tat Chee Avenue Kowloon Tong Hong Kong Tel: (852) 2788 7140 Fax: (852) 2788 8561 E-mail: maip@cityu.edu.hk ----------------------------- From: "Laurence T. Yang" Subject: Workshop on Scientific Computing, including Image Processing Date: Thu, 01 Mar 2001 CALL FOR PAPERS The 3rd Workshop on High Performance Scientific and Engineering Computing with Applications (HPSECA-01) Valencia, Spain, September 03-07, 2001 in conjunction with 2001 INTERNATIONAL CONFERENCE ON PARALLEL PROCESSING (ICPP-2001) Scope and Interests: Parallel and distributed scientific and engineering computing has become a key technology which will play an important part in determining, or at least shaping, future research and development activities in many academic and industrial branches. This special workshop is to bring together computer scientists, applied mathematicians and researchers to present, discuss and exchange idea, results, work in progress and experience of research in the area of parallel and distributed computing for problems in science and engineering applications. Among the main topics (but not limited to) are: * development of advanced parallel and distributed methods, * parallel and distributed computing techniques and codes, * practical experiences using various supercomputers with software such as MPI, PVM, and High Performance Fortran, OpenMP, etc. * applications to numerical fluid mechanics and material sciences, * applications to signal and image processing, dynamic systems, semiconductor technology, and electronic circuits and system design etc. Submission Information: Authors should send one copy of paper in either PS or PDF format at most 15 pages to the workshop organizers (lyang@stfx.ca or pan@cs.gsu.edu) via electronic mail or three copies via postal mail. Contributions will be reviewed by at least three reviewers from both Program Committee and external reviewers for relevance and technical contents on basis of papers. Accepted papers with at most 8 pages will be published by IEEE Computer Society Press as proceedings of the ICPP 2001 workshops. A special issue of International Journal of Supercomputer Applications and High Performance Computing is scheduled. Further information about the conference proceedings and registration fee can be found by web sites: http://www.stfx.ca/people/lyang/activities/icpp01-hpseca.html http://www.cis.ohio-state.edu/~panda/icpp01/workshops.html Important Deadlines: Paper submission Due (April 1, 2001) Notification of Acceptance (May 1, 2001) Final camera-ready paper June 1, 2001 Workshop Organizers: Prof. Laurence T. Yang (chair) Department of Computer Science PO Box 5000, St. Francis Xavier University Antigonish, B2G 2W5, Nova Scotia, Canada lyang@stfx.ca Prof. Yi Pan (Co-Chair) Department of Computer Science, Georgia State University, Atlanta, GA 30303, USA Email: pan@cs.gsu.edu Technical Committee: (see conference page) ----------------------------- From: David Gao Subject: New Books on Optimization, Nonconvex Systems Date: Mon, 05 Mar 2001 New books on optimization, nonconvex systems: 1. Duality Principles in Nonconvex Systems: Theory, Methods and Applications by David Yang Gao Dept. of Mathematics Virginia Polytechnic and State University Blacksburg, USA NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 39 Short description: Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed. For more details and for table of contents see: http://www.wkap.nl/book.htm/0-7923-6145-8 http://www.math.vt.edu/people/gao/books.html 2. Nonsmooth/Nonconvex Mechanics: Modeling, Analysis and Numerical Methods. A Volume dedicated to the memory of Professor P.D. Panagiotopoulos Edited by: D.Y. Gao, R.W. Ogden, and G.E. Stavroulakis Kluwer Academic Publishers, Nonconvex Optimization and Its Applications Vol. 50 Hardbound, ISBN 0-7923-6786-3, February 2001, 516 pp. Short description: Nonsmooth and nonconvex models arise in several important applications of mechanics and engineering. The interest in this field is growing from both mathematicians and engineers. The study of numerous industrial applications, including contact phenomena in statics and dynamics or delamination effects in composites, require the consideration of nonsmoothness and nonconvexity. The mathematical topics discussed in this book include variational and hemivariational inequalities, duality, complementarity, variational principles, sensitivity analysis, eigenvalue and resonance problems, and minimax problems. Applications are considered in the following areas among others: nonsmooth statics and dynamics, stability of quasi- static evolution processes, friction problems, adhesive contact and debonding, inverse problems, pseudoelastic modeling of phase transitions, chaotic behavior in nonlinear beams, and nonholonomic mechanical systems. This volume contains 22 chapters written by various leading researchers and presents a cohesive and authoritative overview of recent results and applications in the area of nonsmooth and nonconvex mechanics. For more details and for table of contents see: http://www.wkap.nl/book.htm/0-7923-6786-3 http://www.math.vt.edu/people/gao/books.html ----------------------------- From: "Elaine Longden-Chapman" Subject: Free Access to Inverse Problems Journal Date: Wed, 14 Mar 2001 Free access to the latest issue of Inverse Problems for non-subscribers If you haven't already taken this opportunity since it was announced in January, visit the Journal Web site at www.iop.org/Journals/ip or www.iop.org/free2001/ to find out more and to register for free access to the latest issue of Inverse Problems as well as to the latest issue of another 28 of IOPP's journals. Following an incredible response to our recent Free Access promotion, Institute of Physics Publishing is pleased to announce another new initiative -- designed to benefit the international scientific community further still. From today until further notice, non-subscribers can enjoy free electronic access to the latest issues of 29 of our journals. As a learned society not-for-profit publisher, Institute of Physics Publishing is committed to promoting physics and to serving physicists world-wide. This latest initiative supports our prime objective and Royal Charter to disseminate information in this field. We are keen to raise the visibility of our authors' work through the programme and we are confident that it will be positively received by all involved in physics. The Free Current Issues can be accessed via the Welcome page of our Electronic Journals service. Please note that a username and password are required to gain access. Readers that do not already have a username and password for our Electronic Journals service can create them, (go to http://www.iop.org/EJ/S/2/IOPP/passwd). Lost Password Assistance is also available for those that have registered their details in the past but have now forgotten their passwords. The free issues in question (`Latest Complete Issue') are easily identifiable -- they are marked as `Free'. Issues are only available to non-subscribers once they are complete. Accelerated Publication remains a benefit exclusive to subscribers. Only they are able to access `accelerated articles', i.e. those that appear online as soon as they are accepted and ready for publication (`Next Issue (partial)'). Our subscribers continue to enjoy other important benefits of course. They receive the printed copies of our journals as well as full access to our Electronic Journals service, including an extensive online archive of back issues plus full reference linking functionality. [ For more journal information, including details on pricing and how to order, see the IOP website. -Ed. ] ----------------------------- From: "Janet Thomas" Subject: Contents list for Inverse Problems vol 17, issue 2 Date: Wed, 21 Mar 2001 Inverse Problems 2001 Volume 17 Issue 2 Table of Contents PAPERS Integrable perturbations of the harmonic oscillator and Poisson pencils K Marciniak and S Rauch-Wojciechowski $m$-functions and inverse generalized eigenvalue problem K Ghanbari Analysis of the scattering map of a linearized inverse medium problem for electromagnetic waves H Ammari and G Bao Synthesis of limited-bandwidth minimum-phase filters J Skaar Inverse matrix evaluation for linear systems M Tadi and Wei Cai Backus--Gilbert algorithm for the Cauchy problem of the Laplace equation Y C Hon and T Wei Stability for the inverse potential problem by finite measurements on the boundary J Cheng and G Nakamura Fast realization algorithms for determining regularization parameters in linear inverse problems Y Wang and T Xiao A new SPECT reconstruction algorithm based on the Novikov explicit inversion formula L A Kunyansky Modified $(n-1,1)$th Gelfand--Dickey hierarchies and Toda-type systems A K Svinin New integrable differential-difference systems: Lax pairs, bilinear forms and soliton solutions X-B Hu and H-W Tam A nonlinear multigrid for imaging electrical conductivity and permittivity at low frequency L Borcea ERRATA The inverse nodal problem on the smoothness of the potential function C K Law, C-L Shen and C-F Yang Phase recovery with nondecaying potentials T Aktosun and P E Sacks Submitted by: Janet Thomas, Senior Production Editor Institute of Physics Publishing Dirac House, Temple Back, Bristol BS1 6BE, UK Tel: +44 (0)117 930 1081 Fax: +44 (0)117 929 4318 E-mail: janet.thomas@ioppublishing.co.uk=20 WWW: http://www.iop.org=20 ----------------------------- From: james beck Subject: Contents, Inverse Problems in Engineering Date: Sun, 29 Apr 2001 Inverse Problems in Engineering 2001 Vol. 9, No. l Table of Contents A Numerical Investigation of the Inverse Potential Conductivity Problem in a Circular Inclusion D. Lesnic On the Identification of Elastoviscoplastic Constitutive Laws from Indentation Tests A. Constantinescu and N. Tardieu A Source-detector Methodology for the Construction and Solution of the One-dimensional Inverse Transport Equation A. T. Kauati. A. J. S. Neto and N. C. Roberty Statistical Inversion of Aerosol Size Measurement Data A. Voutilainen, V. Kolehmainen and J. P. Kaipto ----------------------------- From: Secretary Support - Magrijn Subject: Contents, Mathematics of Control, Signals, and Systems Date: Fri, 27 Apr 2001 Mathematics of Control, Signals, and Systems 2001 Vol. 14, No. 1 Table of Contents Small parameter limit for ergodic, discrete-time, partially observed, risk-sensitive control problems F. Albertini, P. Dai Pra and C. Prior Analyses and numerical solution of control problems in descriptor form P. Kunkel, V. Mehrmann and W. Rath Risk-sensitive and robust escape control for degenerate processes M. Boue and P. Dupuis Spectral analysis of stochastically sampled dynamic systems. R. Banning and W.L. de Koning INFORMATION Information on MCSS including tables of contents is available at its home pages: www.cwi.nl/~schuppen/mcss/mcss.html www.math.rutgers.edu/~sontag/mcss.html Address for submissions: J.H. van Schuppen (Co-Editor MCSS) CWI P.O.Box 94079 1090 GB Amsterdam The Netherlands Bradley Dickinson, Eduardo Sontag, Jan van Schuppen (Editors) Contributed by Jan H. van Schuppen (J.H.van.Schuppen@cwi.nl) ----------------------------- From: Lothar Reichel Subject: Contents, Electronic Transactions on Numerical Analysis (ETNA) Date: Sun, 29 Apr 2001 Electronic Transactions on Numerical Analysis 2000 Vol. 11 Table of Contents Neumann-Neumann methods for vector field problems A. Toselli Perturbation analysis for eigenstructure assignment of linear multi-input systems M. A. Cawood and C. L. Cox A multigrid method for saddle point problems arising from mortar finite element discretizations B. I. Wohlmuth High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems S. Serra Capizzano and C. Tablino Possio Cholesky-like factorizations of skew-symmetric matrices P. Benner, R. Byers, H. Fassbender, V. Mehrmann, and D. Watkins Numerical analysis of the radiosity equation using the collocation method K. Atkinson, D. D.-K. Chien and J. Seol Approximation of hypergeometric functions with matricial argument through their development in series of zonal polynomials R. Gutie'rrez J. Rodriguez, and A. J. Sa'ez Continuous Theta-methods for the stochastic pantograph equation `C. T. H. Baker and E. Buckwar ETNA is available at http://etna.mcs.kent.edu and several mirror sites as well as on CDROM. Publication of volume 12 of ETNA is in progress. Presently the following papers are available: Numerical experiments with algebraic multilevel preconditioners G. Meurant Numerical condition of polynomials in different forms H. Zhang On parallel two-stage methods for Hermitian positive definite matrices with applications to preconditioning M. J. Castel, V. Migallo'n, and J. Penade's ----------------------------- From: Hans Schneider Subject: Contents, Linear Algebra and Its Applications Date: Mon, 19 Mar 2001 Linear Algebra and its Applications April 15, 2001 Vol. 327, Issue 1-3 Table of Contents Analysis on eigenvalues for preconditioning cubic spline collocation method of elliptic equations S. Dong Kim, Y. HunLee A variant of the Hausdorff theorem for multi-index matrices II S. Keska Matrix groups with independent spectra G. Cigler Square nearly nonpositive sign pattern matrices Y. Hou, J. Li Possible line sums for a qualitative matrix C.R. Johnson, S.A. Lewis, D.Y. Yau On the potential stability of star sign pattern matrices Y. Gao, J. Li Corrigendum/addendum to: Sets of matrices all infinite products of which converge I. Daubechies, J.C. Lagarias On Perron complements of totally nonnegative matrices S.M. Fallat, M. Neumann On invertibility and positive invertibility of matrices M.I. Gil' Pattern correlation matrices and their properties A. Rukhin A generalization of Saad's theorem on Rayleigh-Ritz approximations G.W. Stewart Complete positivity of matrices of special form J. Drew, C. Johnson, F. Lam Approximating commuting operators J. Holbrook, M. Omladic Products of transvections in one conjugacy class of the symplectic group over the p-adic numbers E.W. Ellers, H. Lausch Chebyshev-Hankel matrices and the splitting approach for centrosymmetric Toeplitz-plus-Hankel matrices G. Heinig Additive mappings on operator algebras preserving absolute values M. Radjabalipour, K. Seddighi, Y. Taghavi Generalized controlled and conditioned invariances for linear @w-periodic discrete-time systems N. Otsuka Linear Algebra and its Applications May 1, 2001 Vol. 328, Issue 1-3 Table of Contents Condensed forms of linear control system under output feedback J. Stefanovski Perron-Frobenius theorem for matrices with some negative entries P. Tarazaga, M. Raydan, A. Hurman On positivity of analytic matrix functions in polydisks V. Bolotnikov, L. Rodman The four-block Adamjan-Arov-Krein problem for discrete-time systems V. Ionescu, C. Oara Distribution results on the algebra generated by Toeplitz sequences: a finite-dimensional approach S.S. Capizzano Monotone matrix functions of two variables M. Singh, H.L. Vasudeva de Caen's inequality and bounds on the largest Laplacian eigenvalue of a graph J.-S. Li, Y.-L. Pan Graph theoretic methods for matrix completion problems L. Hogben The Hadamard core of the totally nonnegative matrices A.S. Crans, S.M. Fallat, C.R. Johnson Linear Algebra and its Applications May 15, 2001 Vol. 329, Issue 1-3 Table of Contents On the spectral radius of trees G.J. Ming, T.S. Wang On Stein's equation, Vandermonde matrices and Fisher's information matrix of time series processes. Part I: The autoregressive moving average process A. Klein, P. Spreij Stirling matrix via Pascal matrix G.-S. Cheon, J.-S. Kim Numerical ranges, Poncelet curves, invariant measures B. Mirman, V. Borovikov, L. Ladyzhensky, R. Vinograd Bounds for determinants of meet matrices associated with incidence functions I. Korkee, P. Haukkanen On upper bound for the quantum entropy W. Hebisch, R. Olkiewicz, B. Zegarlinski The linearization of boundary eigenvalue problems and reproducing kernel Hilbert spaces B. Curgus, A. Dijksma, T. Read Asymmetric algebraic Riccati equation: Ahomeomorphic parametrization of the set of solutions A. Ferrante, M. Pavon, S. Pinzoni n-Transitivity and the complementation property L. Livshits, G. MacDonald On the orbit of invariant subspaces of linear operators in finite-dimensional spaces (new proof of a Halmos's result) A. Faouzi Automorphisms of the Lie algebra of strictly upper triangular matrices over certain commutative rings Y. Cao NOTES: ContentsDirect, which is automatically generated, lists the first author of each paper and the corresponding author (if different). Visit the journal at http://www.elsevier.nl/locate/jnlnr/07738 Submitted by: Hans Schneider hans@math.wisc.edu. Department of Mathematics 608-262-1402 (Work) Van Vleck Hall 608-271-7252 (Home) 480 Lincoln Drive 608-263-8891 (Work FAX) University of Wisconsin-Madison 608-271-8477 (Home FAX) Madison WI 53706 USA http://www.math.wisc.edu/~hans (URL) ------- end -------