Newsgroups: ut.na Path: utzoo!utgpu!jarvis.csri.toronto.edu!neat.ai.toronto.edu!krj From: krj@na.toronto.edu (Ken Jackson) Subject: NA Digest Volume 89 : Issue 22 Message-ID: <89Jun11.105710edt.11708@neat.ai.toronto.edu> Organization: Department of Computer Science, University of Toronto Date: Sun, 11 Jun 89 10:57:00 EDT NA Digest Sunday, June 4, 1989 Volume 89 : Issue 22 Today's Editor: Cleve Moler Today's Topics: Code for Graph Algorithms Sought Vienna Conference New Reports from Stanford New Journal on Applicable Algebra Dundee Conference Program ------------------------------------------------------- From: Rodrigo Fontecilla Date: Tue, 30 May 89 16:12:19 EDT Subject: Code for Graph Algorithms Sought I am looking for a robust source code for finding the shortest path in a network. Also I need a Branch and Bound algorithm. Either Fortran or C will be ok. Any information related to these topics will be appreciated. My e-mail address; rod@brillig.umd.edu Rodrigo Fontecilla ------------------------------ From: E115N06%AWITUW01.BITNET@Forsythe.Stanford.EDU Date: 01 JUN 89 16:33:38 Subject: Vienna Conference Conference on Scientific Computation Vienna, Austria, 14 - 16 June, 1990 On the occasion of the 60th birthday of Professor Hans J. Stetter, a Conference on Scientific Computation will be held in the spring of 1990 at the Technical University of Vienna. The following three areas will be emphasized: numerical methods for differential equations (ODEs and PDEs), numerical software and validated computation; contributions from other areas of scientific computation are also welcome. The scientific program will consist of contributed talks only (approximate length: 25 minutes). The social program will include a conference dinner and a half day excursion. The conference fee will cover the participation in the social events. There will be no proceedings of the conference but a special issue of the journal 'Computing' will be published on the occasion of Professor Stetter's 60th birthday. Those who wish to dedicate a paper to Professor Stetter and have it included in this issue should send the manuscript (conforming with the usual requirements of 'Computing') either to Professor Rudolf Albrecht Institut fuer Informatik, Universitaet Innsbruck Innrain 52 A-6020 Innsbruck AUSTRIA or to Professor Hansjoerg Wacker Institut fuer Mathematik, Universitaet Linz A-4045 Linz AUSTRIA before October 1st, 1989. The papers will be refereed. They need not be connected with a contribution at the conference. If you consider to participate in this conference you should complete the slip below and mail it to na.stetter@na-net.stanford.edu You will then receive more detailed information on the conference very early in 1990. We are looking forward to have you in Vienna for an interesting conference and a cheerful celebration of Professor Stetter's birthday. Sincerely yours Christoph W. Ueberhuber, Richard Weiss Institut fuer Angewandte und Numerische Mathematik Technische Universitaet Wien Wiedner Hauptstrasse 8-10/115 A-1040 Wien AUSTRIA Conference on Scientific Computation Vienna, Austria 14-16 June, 1990 I will / may / will not participate. I will / may / will not give a talk. Topic: ODEs / PDEs / num.software / validated coputation / other ------------------------------ From: Gene Golub Date: Thu, 1 Jun 1989 18:26:43 PDT Subject: New Reports from Stanford Here is a list of new reports from Stanford. We will be pleased to send them as long as copies are available. Be sure to send me your postal mail address. --Gene Report: NA-89-03 The Restricted Singular Value Decomposition: Properties and Applications Bart L.R. De Moor and Gene H. Golub The restricted singular value decomposition (RSVD) is the factorization of a given matrix, relative to two other given matrices. It can be interpreted as the ordinary singular value decomposition with different inner products in row and column spaces. Its properties and structure are investigated in detail as well as its connection to generalized eigenvalue problems, canonical correlation analysis and other generalizations of the singular value decomposition. Applications that are discussed include the analysis of the extended shorted operator, unitarily invariant norm minimization with rank constraints, rank minimization in matrix balls, the analysis and solution of linear matrix equations, rank minimization of a partitioned matrix and the connection with generalized Schur complements, constrained linear and total linear least squares problems, with mixed exact and noisy data, including a generalized Gauss-Markov estimation scheme. Two constructive proofs of the RSVD in terms of other generalizations of the ordinary singular value decomposition are provided as well. Report: NA-89-04 UPDATING AND DOWNDATING OF ORTHOGONAL POLYNOMIALS WITH DATA FITTING APPLICATIONS Sylvan Elhay, Gene Golub, Jerry Kautsky We derive and assess new methods for updating and downdating least squares polynomial fits to discrete data using polynomials orthogonal on all the data points being used. Rather than fixing on one basis throughout, the methods adaptively update and downdate both the least squares fit and the polynomial basis. This is achieved by performing similarity transformations on the tridiagonal Jacobi matrices representing the basis. Although downdating is potentially unstable, experimental results show that the methods give satisfactory results for low degree fits. We give details of new algorithms implementing the methods, the most economical of which needs 14n + O(1) flops and 2n square roots to update a fit of order n. Report: NA-89-05 Generalized Singular Value Decompositions: A proposal for a standardized nomenclature. Bart L.R. De Moor and Gene H. Golub A mnemonic system of names for several matrix decompositions related to the singular value decomposition is proposed: the O SVD: Ordinary Singular Value Decomposition P SVD: Product Singular Value Decomposition Q SVD: Quotient Singular Value Decomposition R SVD: Restricted Singular Value Decomposition S SV: Structured Singular Value T SVD: Takagi Singular Value Decomposition The main purpose of this article is to propose a standardization of the nomenclature and the structure of these matrix decompositions. Report: NA-89-06 On the structure and geometry of the product singular value decomposition Bart De Moor The product singular value decomposition is a factorization of two matrices, which can be considered as a generalization of the ordinary singular value decomposition, at the same level of generality as the quotient (generalized) singular value decomposition. A constructive proof of the product singular value decomposition is provided, which exploits the close relation with a symmetric eigenvalue problem. Several interesting properties are established. The structure and the non-uniqueness properties of the so called contragredient transformation, which appears as one of the factors in the product singular value decomposition, are investigated in detail. Finally, a geometrical interpretation of the structure is provided in terms of principal angles between subspaces. Report: NA-89-07 Iterative Methods for Cyclically Reduced Non-Self-Adjoint Linear Systems II Howard Elman and Gene Golub We perform an analytic and experimental study of line iterative methods for solving linear systems arising from finite difference discretizations of non-self-adjoint elliptic partial differential equations on two-dimensional domains. The methods consist of performing one step of cyclic reduction, followed by solution of the resulting reduced system by line relaxation. We augment previous analyses of one-line methods, and we derive a new convergence analysis for two-line methods, showing that both classes of methods are highly effective for solving the convection-diffusion equation. In addition, we compare the experimental performance of several variants of these methods, and we show that the methods can be implemented efficiently on parallel architectures. ------------------------------ From: Jacques Calmet Date: 1 Jun 89 07:56:15 GMT Subject: New Journal on Applicable Algebra Journal Announcement Applicable Algebra in Engineering, Communication and Computer Science Arrangements have been finalized with Springer-Verlag to publish a new journal entitled "Applicable Algebra in Engineering, Communication and Computer Science" The first issue of this quarterly journal will appear in the beginning of 1990. Authors are encouraged to submit papers. This is a good opportunity for good papers to be quickly published! This journal aims to cover all aspects of applicable algebra in the fields of Communication, Engineering, Artificial Intelligence and Computer Science. This includes, but is not limited to, domains such as: (i) Engineering: Vision, robotics, system design, VLSI, signal processing, fault tolerance and dependability of systems .... (ii) Communication: Signal theory, coding, error control techniques, cryptography, protocol specification .... (iii) Computer science and Artificial intelligence: arithmetics, algorithm engineering, complexity, algebraic algorithms, computer algebra, logic and functional programming, programming languages, term rewriting systems algebraic specification, theorem proving, graphics, modeling, knowledge engineering, expert systems, artificial intelligence methodology .... The scope of the journal is best illustrated by the two key-words in its title: "Applicable Algebra". This implies that it does not cover domains which are not linked to algebra such as applicable analysis or analytical methods to mention two obvious ones. Purely theoretical papers will not primarily be sought for even when they belong to "algebraic" domains such as combinatorics, finite geometry, computer algebra or cryptography for instance. But, papers dealing with problems in domains such as commutative or non-commutative algebra, group theory, field theory, real or algebraic geometry for instance, which are of interest for applications in the previously mentioned fields are relevant for this journal. On the opposite, technology and know-how transfer papers from engineering which either stimulate or illustrate research in Applicable Algebra do fit the scope of this journal. The editorial board consists of: Th. Beth(Univ. of Karlsruhe), W. Buettner (Siemens, Munich), J. Calmet (Univ. of Karlsruhe - Managing Editor), P. Camion (INRIA, Paris), J. Cannon (Univ. of Sydney), J. Heintz (Inst. of Math., Buenos Aires), C.M. Hoffmann (Purdue Univ.), H. Imai( Yokohama National Univ.), D. Jungnickel (Justus-Liebig Univ. Giessen), E. Kaltofen (Rensselaer Poly- technic Inst., Troy), D. Kapur (SUNY at Albany), P. Lescanne (CRIN, Nancy), H. Lueneburg (Univ. of Kaiserslautern), H.F. Mattson (Syracuse Univ.), T. Mora (Univ. of Genoa), J. Mundy ( GE Co., Schenectady), H. Niederreiter (Austrian Academy of Sciences, Vienna), A. Poli (Univ. Sabatier, Toulouse), S.A. Vanstone ( Univ. of Waterloo). Submissions are to be sent to: Calmet Jacques e-mail : calmet@ira.uka.de (csnet) calmet@DKAUNI0I.BITNET (bitnet) Universitaet Karslruhe - Institut fuer Algorithmen und Kognitive Systeme Postfach 6980 - D-7500 Karlsruhe 1 - BRD - tel.: (49) 721 6084043 ------------------------------ From: MA37%primea.dundee.ac.uk@nsfnet-relay.ac.uk Date: Sun, 04 Jun 89 15:10:10 GMT Subject: Dundee Conference Program DUNDEE BIENNIAL CONFERENCE ON NUMERICAL ANALYSIS Program starts: 9.15am, Tuesday 27 June ends: 5.50pm, Friday 30 June We shall continue to accept registrations up to the time of the conference. Enquiries to na.griffiths Registration will take place in West Park Hall on Monday afternoon/evening and in the University Tower Building thereafter. There will be 16 invited talks. There will be 96 submitted talks. These have been allotted 20 minutes and will be presented in three parallel sessions each morning and four parallel sessions during the afternoons. TUESDAY am Invited Talks: ============= Title to be announced. T. Coleman, Cornell University, USA. The hunting of the SNARK, or Why the trapezoidal rule is algebraically stable K. Burrage, University of Aukland, New Zealand. Parallel multilevel preconditioners. J. Bramble, J. Pasciak and J. Xu, Cornell University, USA. Submitted Talks: =============== Discretisation and Asymptotic Behaviour of Dissipative Dynamical Systems. C. M. Elliott, University of Sussex, U.K. An Interval Step Control for Continuation Methods. R. B. Kearfott, University of Southwestern Louisiana, U.S.A. Polynomial higher order predictors in numerical path following schemes. K. Ulrich, University of Hannover. TUESDAY pm Invited Talks: ============= Moving Finite Elements. M. J. Baines, University of Reading, U.K. Rapid Generation of Weights in Finite Difference Formulas. B. Fornberg, Exxon Research and Engineering Co., USA. Submitted Talks: =============== Constrained Moving Finite Elements Using Piecewise Cubics In 2-d. P. Jimack, University of Bristol. A Moving-Grid Interface for Systems of One-Dimensional Time-Dependent Partial Differential Equations. P. A. Zegeling, and J. G. Blom, CWI, The Netherlands. Accurate Fourier pseudospectral solution of the RLW equation D. M. Sloan, University of Strathclyde, UK. On Optimally High Order in Time Approximations for the Korteweg - de Vries Equation. O. Karakashian, and W. McKinney, University of Tennessee, U.S.A. Finite Element Approximation of a Free Boundary Problem Arising in the Theory of Liquid Drops and Plasma Physics. J. W. Barrett, and C. M. Elliott, Imperial College and University of Sussex. The Numerical Solution of Parabolic Free Boundary Problems Arising >From Thin Film Flows. R. Hunt, University of Strathclyde, U.K. Using Divergent Iterations in High Speed, High Accuracy Computations. P. Pedersen, Technical University of Denmark. Parallel Evaluation of Some Recurrence Relations by Recursive Doubling A. Kiper and D. J. Evans. Middle East Technical University, Turkey and Loughborough University. Estimation of convergence orders in repeated Richardson extrapolation. E. Christiansen, Odense University, Denmark. Some Preconditioners for Multi-Vector Processing of Nonsymmetric Systems. S. Doi, INRIA, France. Solution of Elliptic Systems of P.D.E.'s by Cell Discretization. J. Greenstadt, University of Cambridge, U.K. New families of convergence acceleration methods: The P-algorithms. K. J. Overholt, University of Bergen, Norway. Fast, Reliable Numerical Algorithms for Sturm-Liouville Computations. M. Marletta, and J. D. Pryce, RMCS Shrivenham, U.K. Reliable Computation of Weyl's $m( lambda )$ Function. J. D. Pryce, M. Brown and V. Kirby, RMCS and U.C. Cardiff. Solving Large ODE Problems Using the Iterative Matrix Solver WATSIT W. L. Seward, University of Waterloo, Canada. The Numerical Solution of Large Scale Systems of Differential Equations G. D. Byrne, Exxon Research and Engineering Company, USA. WEDNESDAY am Invited Talks: ============= The Updating of Matrices of Conjugate Directions in Optimisation Algorithms. M. J. D. Powell, University of Cambridge, U.K. Towards Reliable Linear Programming. R. Fletcher and J. A. J. Hall, University of Dundee. Submitted Talks: =============== Conjugate Basis Matrices and Local Convergence for the Algorithm REQP for Constrained Minimisation. M. C. Bartholomew-Biggs, and T. T. Nguyen, Hatfield Polytechnic, U.K. Preconditioned Conjugate Gradient Methods for Equality Constrained Least Squares Problems. N. K. Nichols, University of Reading, U.K. The relationship between theorems of the alternative, least square problems, and steepest descent directions. A. Dax, Hydrological Service, Israel. Parallel Hopscotch Solutions of the Ginzberg-Landau Equation. D.B. Duncan, Heriot-Watt University, Edinburgh. Hopscotch for Parabolic PDEs. A. S. Wood, University of Bradford, U.K. Unconditional Convergence of some Crank-Nicholson LOD Schemes. W. Hundsdorfer, Centre for Mathematics and Computer Science, The Netherlands. Error Estimation in Automatic Quadrature Routines. J. Berntsen, and T. O. Espelid, University of Bergen, Norway. Software for Adaptive Multidimensional Integration. T. O. Espelid, University of Bergen, Norway. Validated Anti-Derivatives. G. F. Corliss, Marquette University, USA. WEDNESDAY pm Invited Talks: ============= Finite Element Methods for Compressible Flow. C. Johnson, Chalmers University of Technology, Sweden. Title to be announced A. Spence, University of Bath, U.K. Submitted Talks: =============== Optimal Grids and Solutions for Compressible Flows in Nozzles. J. Wixcey, University of Reading, U.K. Stability of wide-angle absorbing boundary conditions for the wave equation. R. A. Renaut, Arizona State University, USA. Existence and Linear Stability of Period 2 Solutions of Discrete Reaction-Diffusion Models with Various Types of Nonlinear Diffusion. S. W. Schoombie, University of the Orange Free State, South Africa. Spurious Dynamics in Numerical Simulations of Differential Equations. A. Stuart, University of Bath, U.K. Embedded Runge-Kutta Methods on Parallel Computers. P. J. van der Houwen, CWI, Amsterdam. Block Runge-Kutta Methods on Parallel Computers. B. P. Sommeijer, CWI, Amsterdam. Towards a Parallel, Commercial Oil Reservoir Simulator. C. A. Addison, University of Liverpool, U.K. Optimisation of Heavy Oil Recovery. R. L. Brown, University of Reading, U.K. Equilibria of Runge-Kutta Methods. A. Iserles, and J. M. Sanz-Serna, University of Cambridge and University of Valladolid, Spain. Highly Continuous Runge-Kutta Interpolants. D. J. Higham, University of Toronto, Canada. Stability of Approximations from Radial Basis Function Spaces. M. D. Buhmann and M. J. D. Powell, University of Cambridge, U.K. Faber polynomials on circular sectors. G. Opfer, University of Hamburg, F. R. Germany. Galerkin and Petrov-Galerkin Methods for the Semiconductor Problems. T. Murdoch, University of Oxford, U.K. Finite Element Approximation of a Model Reaction - Diffusion Problem with a Non - Lipschitz Nonlinearity. R. M. Shanahan, and J. W. Barrett, Imperial College, London. The Global Error Estimate of Exponential Splitting. Q. Sheng, University of Cambridge, U.K. L inf Errors in Finite Volume Approximations. R. Jones, University of Oxford, U.K. THURSDAY am Invited Talks: ============= Uniqueness Theorems for Stiff ODE Initial Value Problems. P. Deuflhard, Konrad-Zuse-Zentrum fur Informationstechnik, Berlin, F.R. Germany. Eulerian-Lagrangian Localized Adjoint Methods for Advection-Dominated Problems. T. F. Russell, University of Colorado at Denver, USA. Submitted Talks: =============== An option for implicit Runge-Kutta methods. J. C. Butcher, University of Auckland, New Zealand. Starting Methods for the Iteration of IRK's. J. Sand, University of Copenhagen, Denmark. The Finite-element Method with Nodes Moving along the Characteristics for Convection-Diffusion Equations. Y. Tourigny, and E. Suli, University of Oxford, U.K. Multi-Grid Techniques with Non-Standard Coarsening and Group Relaxation Methods. A. Danaee, International Centre for Theoretical Physics, Trieste, Italy. FFT solution of the Robbins problem W. M. Pickering and P. J. Harley, University of Sheffield. A Quadratically Convergent Parallel Jacobi-like Eigenvalue Algorithm. M. H. C. Paardekooper, Tilburg University, The Netherlands. A Parallel Algorithm for Banded Linear Systems. S. J. Wright, Argonne National Laboratory, U.S.A. High order explicit Runge-Kutta pairs. P. W. Sharp, and E. Smart, University of Toronto, Canada. Trajectory Optimisation Applications using the Program STOMP for Generating Cost Function and Gradient Evaluations. K. Horn, Messerschmitt-Boelkow-Blohm, Germany. THURSDAY pm Invited Talks: ============= Knot Removal and Condition Numbers for B-Splines. T. Lyche, University of Oslo, Norway. Computing the structured singular value, and some related problems G. A. Watson, University of Dundee, Scotland. Submitted Talks: =============== Optimal Distribution of Knots in Tensor-Product Splines Approximation. N. Dyn and I. Yad-Shalom, Tel-Aviv University, Israel. The Difference Interpolation Method for Splines. W. Volk, Berlin, F.R. Germany. On a Certain Approximation problem for Matrices. W. Light, University of Lancaster, U.K. The Solution of Semi-infinite Programming Problems by Discretization Methods. R. Reemtsen, Technical University of Berlin, F.R. Germany. Some Observations on the Streamline Upwind Petrov Galerkin Method for Convection-Diffusion Problems. S. Sigurdsson, University of Iceland. Spectral Transport-diffusion Algorithm for Convection-diffusion Problems. E. Suli and A. Ware, University of Oxford, U.K. On Positive Shock Capturing Schemes. B. Einfeldt, Cranfield Institute of Technology, U.K. Comparison of Roe's Scheme and a Directional Difference Scheme for Gas Network Flows. S. Emmerson, University of Reading, U.K. Optimal Lattice rules in Dimension 2 and 3. T. Sorevik and J. N. Lyness, University of Bergen and Argonne National Laboratory. Sub-lattices of Integration Lattices. P Keast, J. N. Lyness and T. Sorevik, Dalhousie University, Argonne National Laboratory and University of Bergen. Multistep Methods for Ordinary Differential Equations based on Algebraic and First Order Trigonometric Polynomials. G. Vanden Berghe, Rijksuniversiteit Gent, Belgium. Multistep Methods based on Continued Fractions for solving Initial Value Problems. D. Eyre, and S. Abelman, Potchefstroom University and University of the Order results for R-K methods applied to Differential Algebraic Equations. M. Roche, Universite de Geneve, Switzerland. A Regularization-Technique for the Numerical Solution of Index-2 - Differential - Algebraic Equations M. Knorrenschild, Lawrence Livermore National Laboratory, USA. A note on the construction of continuous quadric patches. M. L. Baart, Potchefstroom University, South Africa. A shape preserving curve interpolation scheme using parametric rational cubic splines. K. Unsworth, and T.N.T. Goodman FRIDAY am Invited Talks: ============= How Accurate is Gaussian Elimination? N. J. Higham, Cornell University and University of Manchester. Some numerical aspects of Divide and Conquer Methods for Eigenvalue Problems. D.C. Sorensen, Argonne National Laboratory, USA. Submitted Talks: =============== Stable solvers for singular linear systems and application to block linear systems. W. Govaerts, University of Gent, Belgium. The Use of the Basic Linear Algebra Subprograms (BLAS) in improving supercomputer speeds. Jerzy Wasniewski, The Danish Computer Centre for Research and Education. Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices. J. Barlow and J. Demmel, Pennsylvania State University and Courant Institute. Conjugate Gradient Algorithms for Stabilised Mixed Finite Element Methods. D. J. Silvester and N. Kechkar, UMIST, U.K. Finite Element Computation on Multiprocessor computer R. Wait and C. J. Willis, University of Liverpool, U.K. Galerkin Methods for Nonlinear Elliptic PDES. C. Budd, and T. Murdoch, Oxford University Computing Laboratory, U.K. Generalised Pade approximations to the exponential function. F. H. Chipman and J. C. Butcher, Acadia University, Canada and University of Auckland, New Zealand. Numerical solution of retarded ode-systems. P. G. Thomsen, Technical University of Denmark. The Construction of Cubature Formulae using Software from Bifurcation Theory. R. Cools, Catholic University, Belgium. FRIDAY pm Invited Talks: ============= Boundary Integral Methods for Laplace's Equation. I. Graham, University of Bath, U.K. Submitted Talks: =============== Ill - posedness and singular integrals in the boundary integral method. J. Steinberg, Technion - Israel Institute of Technology. Solution of exterior Helmholtz problems by improved boundary element methods. S. M. Kirkup, Brighton Polytechnic, U.K. Chebyshev Polynomial Solutions of First Kind Integral Equations for Numerical Conformal Mapping. J. Levesley, D. M. Hough and S. N. Chandler-Wilde, Coventry Polytechnic, U.K. A Cahn-Hilliard Type Model for Phase Separation. J. F. Blowey, University of Sussex, U.K. Numerical Simulation of the Cahn-Hilliard Equation. M. I. M. Copetti, and C. M. Elliott. University of Sussex, U.K. The Effect of Filtering on the Pseudospectral Solution of Evolutionary Partial Differential Equations. L. S. Mulholland, University of Strathclyde, U.K. A Tool for Analysing Ill-conditioned Equations. W. M. Connolley, and J. S. Rollett, Oxford University Computing Laboratory, U.K. Thin Plate Spline Approximants, P. Gonzalez-Casanova, University of Oxford, U.K. Some New Ideas on Conjugate Gradient Methods. Y. F. Hu and C. Storey, Loughborough University of Technology, U.K. Least Squares Data Smoothing by Non-Negative Second Divided Differences. I. C. Demetriou, Greece. A deficient spline function approximation to third order O.D.E. T. Fawzy, Suez-Canal University, Egypt. On Approximate Solutions of Integral Equations of the Mixed Type Lechoslaw Hacia, Poznan University, Poland. Differential and integro-differential equations as population growth models with applications in Agriculture. A. Makroglou, Agricultural University of Athens, Greece. New Stopping Criterions for Some Iterative Methods for a Class of Unsymmetric Linear Systems. C. Li and D. J. Evans, Loughborough University of Technology, U.K. The Whittaker-Henderson graduation method A. J. Macleod, Paisley College, Glasgow. A Criterion Test for Self-scaling Variable Metric Algorithms. M. Al-Baali, University of Damascus, Syria. Implementation of a Multigrid Method on a Transputer Network. G. J. Shaw and A. Stewart, University of Oxford and Queen's University, Belfast. Title to be announced. K. Zietak, Poland. ------------------------------ End of NA Digest ************************** ------- Reposted by -- Kenneth R. Jackson, krj@na.toronto.edu (on Internet, CSNet, Computer Science Dept., ARPAnet, BITNET) University of Toronto, krj@na.utoronto.ca (CDNnet and other Toronto, Canada M5S 1A4 X.400 nets (Europe)) (Phone: 416-978-7075) ...!{uunet,pyramid,watmath,ubc-cs}!utai!krj