Subject: NA Digest, V. 94, # 52 NA Digest Monday, December 26, 1994 Volume 94 : Issue 52 Today's Editor: Cleve Moler The MathWorks, Inc. moler@mathworks.com Today's Topics: Birthday Puzzle Charta of Free Electronic Access to Publications Pentium Hypertext and the Sofware Taxi Prelude to Pentium LIPSOL Beta-2 Release New Mail Address for Los Alamos PPNS Group New Book, Practical Bifurcation and Stability Analysis New Book, Stochastic Programming South African N.A. Symposium Conference on Parallel Algorithms Position at University of the Federal Armed Forces, Munich Position at Illinois Institute of Technology Contents, SIAM Applied Mathematics Contents, SIAM Optimization Contents, Journal of Approximation Theory 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: Gene Golub Date: Mon, 19 Dec 94 8:35:20 PST Subject: Birthday Puzzle What TWO famous numerical analysts will be celebrating their 60th birthday on Dec 26, 1994? Hint: Their birthplaces are antipodes. I'm sure they'll be happy to hear from you. Gene ------------------------------ From: R. Jeltsch Date: Mon, 19 Dec 94 15:32:35 +0100 Subject: Charta of Free Electronic Access to Publications Charta of free electronic access to publications: The EMS (European Mathematical Society) has set up a committee to draft a Charta of free electronic access to publications. I am on this committee and would like to get some input from the NA-NET community. Please respond either to me or to the electronic internet address ems-e-jour-committee@esi.ac.at distributes every message it receives to all members of this committee, which consists now of bayer@grenet.fr (Eva Bayer) brunovsk@dcs.fmph.uniba.sk (Pavol Brunovski) chlebik@dcs.fmph.uniba.sk (Miro Chlebik) cea@unice.fr (Jean Cea) groetschel@ZIB-berlin.de (Groetschel) guil@fourier.grenet.fr (Laurent Guillope) jeltsch@sam.math.ethz.ch (R. Jeltsch) amo@research.att.com (Odlyzko) uimrozek@plkrcy11.bitnet (Marian Mrozek) michor@esi.ac.at (Peter Michor, chair) The first draft of such a charta has been proposed Peter Michor and he has presented it at the Conference on the Future of Mathematical Communications electronic publishing MSRI, Berkeley, Nov. 30 -- Dec. 3. First draft (shortened for Na-net) The role of a printed copy of a journal nowadays is sitting in a library waiting for an article out of it to be photocopied. A conservative estimate is that on the average an article is photocopied 50 times, all over the world, and read 25 times. To typeset, print, and distribute it is a waste of human and natural resources, the same service could be done via computer quicker and more widespread. There is an oncoming revolution on the use of electronic media for scientific publication. New electronic journals appear, they are FREELY accessible up to now, some existing journals open their files for FREE electronic access, and some only to subscribers. There is the possibility to lower drastically the overall cost of mathematical publications, and the danger that we will have all the traditional journals, new electronic ones, and that after some time the electronic journals also start to charge for their access. If there is no easy access to the mathematical literature, a lot of work will be duplicated in the future. The European Mathematical Society feels responsible for the health and accessibility of the mathematical literature. The rationale behind this charta is the following. We should distinguish carefully between the final electronic version of a paper into which besides the work of writing and refereeing only marginal costs have been invested, and the printed and distributed version, which makes use of a somewhat industrial process. The costs of the former, since they are small, should be carried locally, by academic institutions or libraries. Important libraries could adopt existing journals and take over their costs up to the electronic product. Free personal access to the electronic product should be ensured. The costs of the latter industrial process should be borne by the consumer (library) who prefers to have at hand a nicely printed version. There will be not so few of them, perhaps. CHARTA OF FREE ELECTRONIC ACCESS TO PUBLICATIONS: 1. The right of access to the electronic file of a paper which was prepared in that way by the author or his institution lies with the author(s). 2. If the author submits this paper to a preprint server or a refereeing process he automatically acknowledges the right of free electronic access to this paper to the (mathematical) public. 3. If a journal prints a refereed article the right to distribute and sell this paper lies completely with the publisher of the journal. This is called the RIGHT TO DISTRIBUTE. But the right of free electronic access to the paper remains at the public. 4. Everybody who uses the right of electronic access to a paper is entitled to print freely one copy of this for personal or restricted use. He is not entitled to sell copies of this paper at profit. This is called PERSONAL USE. 5. Libraries are entitled and asked to keep permanently accessible files of electronically accessible journals, in order to ensure their perpetuity, besides or without printed copies. We ask authors, readers, institutions and libraries, profit and non-profit oriented publishers to adopt the rules of this charta, for the benefit of the science of Mathematics, and thus also for the benefit of those commercial organizations serving it. ------------------------------ From: John C. Nash Date: Mon, 19 Dec 1994 11:51:58 -0500 (EST) Subject: Pentium Hypertext and the Sofware Taxi Mainly for the benefit of non-NA colleagues and for some local computer store operators, I edited and collected commentary and test codes for the Pentium FDIV bug. These have been built into a hypertext form so the comments can be viewed easily and a 1-key command will execute Mathisen's test. The hypertext viewer is my own Software Taxi which NA Digest readers may also find interesting as a way to present "live" demonstrations of software along with commentary. Simple text files are used for the hypertexts and control files. Freeware. The Pentium hypertext and the Software Taxi are available by anonymous FTP from either MacNash.admin.uottawa.ca (look in the "binaries" subdirectory) or ftp.synapse.net in the info/nashinfo/ subdirectory. The files in the LHA archive PENTIUM0.LZH contain information, comments and test programs about the Intel Pentium FDIV bug. They are designed to be used in conjunction with the Software Taxi hypertext viewer in SWTAXI0.LZH. You should unpack the files from both archives into the same directory (or diskette -- 1.2 MB or 1.4MB format). To view/run the files, type ST0 PENTIUM0 [Enter] To run the Software Taxi general introduction, simply type ST0 [Enter] and accept defaults. The Software Taxi is only 23K and designed for student use on low-power PCs; it is fast enough to run from a diskette. John C. Nash, Professor of Management, Faculty of Administration 136 Jean-Jacques Lussier Private, University of Ottawa, Ottawa Ontario, K1N 6N5 Canada jcnash@aix1.uottawa.ca fax 613 564 6518 ------------------------------ From: Garry Tee Date: Thu, 22 Dec 1994 17:23:12 +1200 Subject: Prelude to Pentium In 1960, when Leslie Fox was Director of Oxford University Computing Laboratory, a Sirius computer (of the 2nd generation) was installed there. Fox had gained his computing experience on Turing's Pilot ACE (built in 1950 by J. H. Wilkinson) and on its commercial version DEUCE; and hence he was accustomed to programming in which every bit was correct, including fixed-point arithmetic in which round-off was in the range -1/2 to +1/2 bit in the least significant place. His testing of Sirius had revealed persistent errors in the arithmetic performed; and eventually he was horrified to discover that the arithmetic hardware performed fixed-point division with roundoff between +1 and +2 bits! Leslie Fox erupted with scandalized outrage at that inexcusable blunder by the manufacturers of Sirius! Garry J. Tee, University of Auckland. ------------------------------ From: Yin Zhang Date: Wed, 21 Dec 1994 13:54:26 -0400 Subject: LIPSOL Beta-2 Release LIPSOL Beta-2 Release Announcement I am pleased to announce the Beta-2 release of LIPSOL -- Linear programming Interior-Point SOLvers. LIPSOL is a package that uses Matlab's sparse-matrix data structure and MEX utilities to achieve both programming simplicity and computational efficiency. --- What's New? --- Release Beta-2 is a major step-up from the first Beta release (now called Beta-1) with important enhancements and bug-fixings. The highlights are: 1. Beta-2 now solves 94 Netlib LP problems out of 95 (fit2p, still untested, is too costly without a dense-column handling strategy); while Beta-1 could only solve 80 problems. A single set of default parameter values is used to solve 93 problems (except for dfl001). 2. Beta-2 is much faster than Beta-1 for large problems. Here are some statistics on an SGI machine (R4400/150Mhz processor) for 3 of the largest problems: CPU-seconds Name rows cols iter Beta-2 Beta-1 ---------------------------------------------------- pilot87 2031 4883 40 569 2315 maros-r7 3137 9408 14 508 untested stocfor3 16676 15695 38 206 untested ---------------------------------------------------- LIPSOL is still under active development. Further improvements and speedups are expected. --- What platforms are supported? --- The Beta versions contain binary files and is machine-dependent. LIPSOL Beta-2 includes distributions for DEC (Ultrix 4.x), SGI (IRIX 5.2) and Sun Sparcs (SunOS 4.1.3) UNIX workstations. -- Where to get LIPSOL? -- LIPSOL Beta-2 is free and may be down-loaded through anonymous FTP from the internet site: ftp.math.umbc.edu in the directory: pub/zhang/lipsol/beta-2 (also available from the WWW URL: http://math.umbc.edu/~yzhang). The installation and use of LIPSOL are simple. See the README files for information. (Sorry, a new user's guide is not available yet.) Acknowledgment LIPSOL Beta-2 includes mex-files constructed from a sparse Cholesky Fortran package developed by Esmond Ng and Barry Peyton at ORNL, which is in part responsible for the significant speed-up on large problems. During the development of LIPSOL Beta-2, I received programming assistance from Detong Zhang at UMBC and valuable feedbacks from Steve Wright at ANL. Thank you all, folks. Yin Zhang http://math.umbc.edu/~yzhang/ Dept. of Mathematics and Statistics Email: yzhang@math.umbc.edu Univ. of Maryland Baltimore County Phone: (410) 455--3298 Baltimore, Maryland 21228-5398, USA Fax : (410) 455--1066 ------------------------------ From: David Brown Date: Mon, 19 Dec 1994 11:52:59 -0700 Subject: New Mail Address for Los Alamos PPNS Group The Los Alamos National Laboratory Parallel Processing and Numerical Analysis Research Cell now has a new (US postal) mail address: Mail Stop B256 Los Alamos National Laboratory Los Alamos, NM 87545 USA Members of this research group who can be reached at this new address are: Kristi Brislawn kdb@lanl.gov David L. Brown dlb@lanl.gov Geoffrey Chesshire geoff@lanl.gov William Henshaw henshaw@lanl.gov Charlotta Olsson lotta@c3.lanl.gov Karen Pao kip@lanl.gov Daniel Quinlan dquinlan@lanl.gov Ellen Randall randall@c3.lanl.gov William Rider wjr@lanl.gov Jeffrey S. Saltzman jss@lanl.gov The PPNS research group is funded to develop algorithms and software for adaptive overlapping grid methods for computational fluid dynamics and combustion. ------------------------------ From: Ruediger Seydel Date: Wed, 21 Dec 94 11:59:24 +0100 Subject: New Book, Practical Bifurcation and Stability Analysis Title: Practical Bifurcation and Stability Analysis. From Equilibrium to Chaos. Second Edition. Series Name: Interdisciplinary Applied Mathematics, Vol. 5 Published by: Springer, New York, 1994 ISBN: 0-387-94316-1 This textbook gives an introduction to nonlinear phenomena on a practical level, and an account of computational methods. It covers the central role that bifurcations play, and explains mechanisms of how stability is gained or lost. Emphasis is on basic strategies for numerical methods. The book is illustrated by many examples from science and engineering. 414 pp. 186 figs. 547 references. This is a new version of the book "From Equilibrium to Chaos," which was published by Elsevier 1988 (Math.Reviews 89e:58084, Zentralblatt fuer Math. Vol.652 #34059). The book has been updated, revised, and significantly enlarged. ------------------------------ From: Stein W. Wallace Date: Thu, 22 Dec 94 13:56:57 +0100 Subject: New Book, Stochastic Programming There is a new book: Title: "STOCHASTIC PROGRAMMING" ISBN 0 471 95108 0; 0 471 95158 7 (pbk) Authors: Peter Kall (University of Zurich) kall@ior.unizh.ch Stein W. Wallace (University of Trondheim) sww@iok.unit.no Series: Wiley - Interscience Series in Systems and Optimization 1991 MATHEMATICS SUBJECT CLASSIFICATION: Primary: 90-01; Secondary: 90C15 Published by: John Wiley & Sons Ltd. Baffins Lane, Chichester West Sussex, PO19 1UD, England Telephone: + 44 243 779777 'Stochastic Programming' is the first textbook to provide a thorough and self-contained introduction to the subject. Carefully written to cover all necessary background material from both linear and non-linear programming, as well as probability theory, the book draws together the methods and techniques previously described in disparate sources. After introducing the terms and modelling issues when randomness is introduced in a deterministic mathematical programming model, the authors cover decision trees and dynamic programming, recourse problems, probabilistic constraints, preprocessing and network problems. Exercises are provided at the end of each chapter. Throughout, the emphasis is on the appropriate use of the techniques, rather than on the underlying mathematical proofs and theories, making the book ideal for researchers and students in mathematical programming and operations research who wish to develop their skills in stochastic programming. The book has 6 chapters Ch1: Basic concepts Ch2: Dynamic Systems Ch3: Recourse problems Ch4: Probabilistic constraints Ch5: Preprocessing Ch6: Network problems Stein W. Wallace - sww@iok.unit.no Phone: + 47 73 593609 Fax: + 47 73 593603 ------------------------------ From: Dirk Laurie Date: Wed, 14 Dec 94 14:42 Subject: South African N.A. Symposium Call for Papers South African Symposium on Numerical Mathematics (SANUM '95) July 10-12, 1995 Cutty Sark Hotel, Scottburgh (near Durban) SANUM '95 is jointly organized by the South African Society for Numerical Mathematics and the Department of Computer Science of the University of Natal, Durban. Research papers on any aspect of numerical analysis or computational mathematics are welcomed. This Symposium, now into its 21st year, traditionally also accommodates talks on applications of mathematics. Organizing Committee Dirk Laurie (wskdpl@puknet.puk.ac.za) Japie Spoelstra (wskjs@puknet.puk.ac.za) Lucas Venter (wsklmv@puknet.puk.ac.za) Andre Weideman (weideman@math.orst.edu) Colin Wright (wright@gauss.cam.wits.ac.za) Venue The Cutty Sark is a moderately priced seafront hotel about 30km south of Durban. The month of July is a very pleasant one in this subtropical region, with the daytime temperature around 20 degrees Centigrade. Further information You will be put on the mailing list if you send your address to: Dr. Lucas Venter Department of Mathematics Potchefstroom University for Christian Higher Education 2520 Potchefstroom South Africa Or you may send e-mail to Lucas or any other member of the organizing committee. Answers to frequently asked questions on the conference programme, hotel bookings, travel arrangements etc. may be obtained by fingering sanum@calvyn.puk.ac.za ------------------------------ From: Chuanxia Rao Date: Sat, 24 Dec 94 14:11:47 PST Subject: Conference on Parallel Algorithms CALL FOR PAPERS ICPA'95 International Conference on Parallel Algorithms Wuhan University, Wuhan, China October 15 -19, 1995 Organized by Wuhan University, Wuhan, China and Changsha College of Technology, Changsha, China Sponsored by Natural Science Foundation of China, National Defence Research Council of Science and Technology of China, and State Education Committee of China Topics include, but are not limited to, the following: . High performance parallel computer systems and their performance evaluation . Theory and implementation of parallel and distributed computing . Parallel algorithms based on domain decomposition methods and multigrid methods . Design and analysis of numerical and non-numerrical parallel algorithms . Theory of cellular automaton models and their applications . Lattice gas and lattice Boltzmann . Evolutionary algorithms and parallel problem solvers from nature . Software tools and environments for parallel computers . Systolic algorithms and parallel implementation . Software engineering aspects relating to parallel computing . Industrial, scientific and commercial applications for pipelined, vector, array, parallel and distributed computers . Other aspects and applications relating to massively parallel computations Prospective authors are invited to submit 4 hard copies of the full paper with no more than 25 11pt single-spaced, single-column pages. All submitted manuscripts are strongly encouraged to be prepared in LaTeX. Important Dates: March 31, 1995: Submission of full papers May 31, 1995: Notification of acceptance/rejection to authors July 31, 1995: Submission of revisedd final camera-ready papers To receive further information send your name and address to Conference Coordinator Professor Lishan Kang, ICPA'95, Institute of Software Engineering Wuhan University, Wuhan 430072, P.R. China Tel: +86-27-7822712 ext 2438 Fax: +86-27-7812661 ------------------------------ From: Ulrich Hornung Date: Wed, 21 Dec 1994 17:59:56 --100 Subject: Position at University of the Federal Armed Forces, Munich Research position in numerical modeling of multiphase flow At the Institute of Mathematics in the University of the Federal Armed Forces Munich, a two-year research scientist position is open to be filled as soon as possible. The position is connected with a research project in applied mathematics on "Optimization of venting techniques for remediation of NAPL contaminated soils (Soil Venting)". The project funded by the German Federal Department for Research and Technology started in 1994 and is supposed to end by April 1997. The goal is to find applicable solutions for practical problems in cooperation with a German company. Further details may be found on the special page in the World Wide Web: http://www.informatik.unibw-muenchen.de/informatik/institute/inst1/lhkw.html The candidate is expected to simulate three-dimensional (3-D) gas flow in soils of different industrial sites, to model 3-D contaminant transport of NAPL's, and eventually, to determine optimal strategies for the remediation process. The numerical methods to be used are mixed finite elements combined with domain decomposition. The code to be written will be based on the C++ - package GOOFE developed at the Technical University Munich in the research group of Ronald Hoppe. The ideal candidate has a degree (preferably Ph.D.) in mathematics or physics; he should be familiar with scientific computing, in particular with partial differential equations and their numerical solution by finite element methods. Experience with the programming language C is required, and basic knowledge in thermodynamics and/or physical chemistry would be helpful. Salary is according to the German BAT IIa tariff. Salary includes payments for social security, health care, and benefits and depends on age and family status, e.g., a 27 year old unmarried person receives in 1994 DM 65,832 (appr. $44,000) gross payment per annum. Knowledge of the German language is not expected, and only necessary as far as everyday life is concerned. Candidates should contact me as soon as possible, and provide their CV, a list of publications, and a description of their scientific background and interests. Prof. Ulrich Hornung Department of Computer Science University of the Federal Armed Forces Munich D-85577 Neubiberg Phone: +49-89-6004-3386 (-2030) Fax: +49-89-6004-3560 e-mail: ulrich@informatik.unibw-muenchen.de ------------------------------ From: George Byrne Date: Fri, 23 Dec 1994 15:14:45 -0500 (CDT) Subject: Position at Illinois Institute of Technology Illinois Institute of Technology The Department of Mathematics at Illinois Institute of Technology is seeking at least one tenure-track faculty member to assume duties in September 1994. A successful candidate must be demonstrably good in the classroom and will also be expected to carry out a successful research program. The successful candidate will be interested in collaboration with colleagues in science and engineering and will be expected to acquire external funding. Candidates at the Assistant Professor level and at the Associate Professor level are being sought. For the Associate Professor level, a track record of funded research will also be necessary. The fields of interest lie in computational and applied mathematics. The Department of Mathematics is situated in the Armour College of Science and Engineering and strong interdisciplinary links are a long-standing tradition at IIT. The main IIT campus is itself an architectural landmark in Chicago. IIT has about 5000 students and is well-established as a small, urban, private, technical university with both graduate and undergraduate programs. The Department of Mathematics is strengthening its activities in computational and applied mathematics. Applicants should send a curriculum vitae (with publications list, history of external funding, and supporting documentation of teaching skills) to and arrange for three letters of reference to be sent to: Dr. George D. Byrne Professor and Chairman Department of Mathematics Illinois Institute of Technology 10 West 32nd Street Chicago, IL 6061603793 Telephone: 312/567-3164 FAX: 312/567-3135 E-mail: mathbyrne@minna.acc.iit.edu ------------------------------ From: SIAM Date: Mon, 19 Dec 94 15:08:36 EST Subject: Contents, SIAM Applied Mathematics CONTENTS SIAM Journal on Applied Mathematics APRIL 1994 Volume 55, Number 2 Preface Biography of Joseph B. Keller Exact Nonreflecting Boundary Conditions for the Time Dependent Wave Equation Marcus J. Grote and Joseph B. Keller Instability of Rapidly Rotating Polytropes N. J. Balmforth, L. N. Howard, and E. A. Spiegel Shock Layer Movement for Burgers' Equation Jacques G. L. Laforgue and Robert E. O'Malley, Jr. Shock Formation in a Multidimensional Viscoelastic Diffusive System Donald S. Cohen, Andrew B. White, Jr., and Thomas P. Witelski On-Surface Conditions for Structural Acoustic Interactions in Moving Media Lu Ting Asymptotic Evaluation of Integrals Related to Time-Dependent Fields Near Caustics Robert Burridge Limit Process Expansions and Homogenization Julian D. Cole Internal Layers, Small Eigenvalues, and the Sensitivity of Metastable Motion Michael J. Ward and Luis G. Reyna Weakly Nonlinear Waves for a Class of Linearly Unstable Hyperbolic Conservation Laws with Source Terms J. Kevorkian, J. Yu, and L. Wang Mean Field Effects for Counterpropagating Traveling Wave Solutions of Reaction- Diffusion Systems A. J. Bernoff, R. Kuske, B. J. Matkowsky, and V. Volpert High-Order Finite Element Methods for Singularly Perturbed Elliptic and Parabolic Problems Slimane Adjerid, Mohammed Aiffa, and Joseph E. Flaherty Singular Perturbation Solutions of Noisy Systems Frank C. Hoppensteadt Turbulent Baker's Maps Stephen Childress A Theory of Sustainable Harvesting Donald Ludwig ------------------------------ From: SIAM Date: Tue, 20 Dec 94 09:24:28 EST Subject: Contents, SIAM Optimization TABLE OF CONTENTS SIAM J. OF OPTIMIZATION, NO. 5, VOL. 1 FEBRUARY 1995 1 Why a Pure Primal Newton Barrier Step may be Infeasible Margaret H. Wright 13 Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization Farid Alizadeh 52 Infeasible-Interior-Point Primal-Dual Potential-Reduction Algorithms for Linear Programming Shinji Mizuno, Masakazu Kojima, and Michael J. Todd 68 A Fast Heuristic Method for Polynomial Moment Problems with Boltzmann-Shannon Entrophy J. M. Borwein and W. Z. Huang 100 Symmetric Quasidefinite Matrices Robert J. Vanderbei 114 On the Primal-Dual Steepest Descent Algorithm for Extended Linear-Quadratic Programming Ciyou Zhu 129 A Positive Algorithm for the Nonlinear Complementarity Problem Renato D. C. Monteiro, Jong-Shi Pang, and Tao Wang 149 Practical Interior-Point Method for Convex Programming Florian Jarre and Michael A. Saunders 172 An All-Inclusive Efficient Region of Updates for Least Change Secant Methods Henry Wolkowicz and Qing Zhao 192 An Optimal Positive Definite Update for Sparse Hessian Matrices R. Fletcher 218 Trust Region Algorithms for Solving Nonsmooth Equations Liqun Qi ------------------------------ From: Marilyn Radcliff Date: Thu, 22 Dec 1994 12:44:28 -0500 (EST) Subject: Contents, Journal of Approximation Theory Table of Contents Journal of Approximation Theory, Volume 80, Number 1, January 1995 Jos\'e L. Fern\'andez Mu\~niz. Qualitative Korovkin Type Theorems for $R_F$-Convergence, 1-9. Mario Milman. On Extrapolation Spaces and a.e. Convergence of Fourier series, 10-24. Aleksei Shadrin. Error Bounds for Lagrange Interpolation, 25-49. H. A. Hakopian and A. A. Sahakian. Multivariate Polynomial Interpolation to Traces on Manifolds, 50-75. Kirill A. Kopotun. Uniform Estimates of Monotone and Convex Approximation of Smooth Functions, 76-107. Gilbert G. Walter. Pointwise Convergence of Wavelet Expansions, 108-118. Leonardo Colzani and Marco Vignati. The Gibbs Phenomenon for Multiple Fourier Integrals, 119-131. Notes Jos\'e A. Adell, Jes\'us de la Cal, and Miguel San Miguel. On the Property of Monotonic Convergence for Multivariate Bernstein--type Operators, 132-137. Valeri Kaliaguine. A Note on Asymptotics of Orthogonal Polynomials on a Complex Arc: The case of Measure with Discrete Part, 138-145. S. P. Zhou. An Inequality for Derivatives of Polynomials with Positive Coefficients, 146-149. Addendum Volume 75, Number 3 (1993): Gundorph K. Kristiansen, "On the Existence of Real Entire Functions with a Prescribed Ordered Set of Stationary Values," pp.266-294, 150. ------------------------------ End of NA Digest ************************** -------