Subject: NA Digest, V. 95, # 37 NA Digest Sunday, September 17, 1995 Volume 95 : Issue 37 Today's Editor: Cleve Moler The MathWorks, Inc. moler@mathworks.com Today's Topics: MATLAB Conference Change of Address for Zhongxiao Jia Quadrature for Optimization and Search N-dimensional Rotation Matrices New Journal, Monte Carlo Methods and Applications Software for Mathews Numerical Methods Book UMFPACK Version 2.0: General Unsymmetric Sparse Matrix Solver Workshop on Numerical Fluid Flow In Spherical Geometry SIAM Conference on Numerical Combustion Parallel Supercomputing Conference in Japan Report on the Second Workshop on Applied Parallel Computing Position at University of Bradford, England Postdoctoral Position at University of Nottingham. Postdoctoral Position at Johannes Kepler University Position at UNICAMP, Brazil Contents, Linear Algebra and its Applications Contents, Computers and Mathematics Submissions for NA Digest: Mail to na.digest@na-net.ornl.gov. Information about NA-NET: Mail to na.help@na-net.ornl.gov. URL for the World Wide Web: http://www.netlib.org/na-net/na_home.html ------------------------------------------------------- From: Cleve Moler Date: Sun, Sept. 17, 1995, 11:51 EST Subject: MATLAB Conference A quick reminder that the 1995 MATLAB will be held October 16-18, at the Hyatt Regency Cambridge, overlooking the Charles River, halfway between Harvard and MIT. We will have invited speakers, expository and tutorial talks by MathWorks developers and Toolbox authors, user contributions, minicourses, the MATLAB Lab, and a party. Further information is available off our home page http://www.mathworks.com Or, if you aren't wired to the Web, send me email and we will send you a conference annoucement. -- Cleve Moler moler@mathworks.com ------------------------------ From: Zhongxiao Jia Date: Mon, 11 Sep 1995 16:55:53 +0200 (MET DST) Subject: Change of Address for Zhongxiao Jia Dear colleagues, I will begin to work at a new institution next month. The following address is valid from now on: Zhongxiao Jia Department of Applied Mathematics Dalian University of Technology Dalian 116023 P.R. China Thanks for your attention! Sincerely yours, Zhongxiao Jia ------------------------------ From: Art Owen Date: Mon, 11 Sep 1995 16:04:29 -0700 Subject: Quadrature for Optimization and Search I would like to get some pointers to the literature on the following problem area: Given the function f(x,t), integrate out x to obtain the function I(t). Suppose interest centers on minimizing I over t, or on finding t to solve I(t) = 0. In the second problem t and I may be vectors of the same dimension. An obvious approach to this is to pick a good quadrature rule in x, and approximate I(t) by \sum w_i f( x_i, t ) and then optimize or solve using the approximation. Another approach is to use points x_i(t) that depend on t. Under the former method, the x_i must be good "uniformly in t". Under the second rule there could be unpleasant numerical artifacts if x_i is not a smooth function of t. Where might I find a good discussion of how to solve these problems, and of the resulting error analysis? [For random x_i and w_i==1, the problem looks like statistical asymptotics. It may be possible to modify statistical analysis, but I'd hate to reinvent a wheel.] -Art Owen, Dept Statistics, Stanford University ------------------------------ From: Robert Nachbar {w1',0,0,0} (R1 is 4*4). then, once I've fixed the first point, then I want to fix the second, say {w2,x2,y2,z2}.R2 -> {w2',x2',0,0} (R2is 4*4). In fact, the second step could be simplified to {x2,y2,z2}.R2' -> {x2',0,0} (R2' is 3*3). Can anyone point me in the right direction for an algorithm or cite a pertainant reference? Thanks in advance, Bob Dr. Robert B. Nachbar Merck Research Laboratories 908/594-7795 nachbar@merck.com RY50S-100 908/594-4224 FAX PO Box 2000 Rahway, NJ 07065 ------------------------------ From: Karl Sabelfeld Date: Sun, 10 Sep 1995 06:20:35 GMT Subject: New Journal, Monte Carlo Methods and Applications This year a new international journal "Monte Carlo Methods and Applications" started. Three first issues are available. The publisher is VSP, Utrecht, The Netherlands. To submit a paper, please send a Latex file to the Editor, Sabelfeld Karl (karl@osmf.comcen-1.nsk.su) or a hard copy to Karl Sabelfeld, 630090, Novosibirsk, Akad. Lavrentieva, 6 Computing Centre. Russia. or to any member of the Editorial Board. All the information about subscription is available via E-mail 100341.2372@compuserve.com Regards, Karl Sabelfeld, The Editor. ------------------------------ From: John Mathews Date: Sun, 10 Sep 1995 08:29:25 -0800 (PST) Subject: Software for Mathews Numerical Methods Book I am glad to announce the availability of: NUMERICAL METHODS: Mathematica Notebooks These files are located at: www.wri.com/MathSource/Publications/BookSupplements/Mathews-1995/0207-874 Also available are: NUMERICAL METHODS: Matlab; C; FORTRAN; Pascal Programs The files are located at: http://www.mathworks.com/pub/books/mathews Best Regards, John Mathews Dept. of Mathematics California State University Fullerton Fullerton, CA 92634 USA E-mail: mathews@fullerton.edu ------------------------------ From: Tim Davis Date: Thu, 14 Sep 1995 12:28:24 -0400 Subject: UMFPACK Version 2.0: General Unsymmetric Sparse Matrix Solver I would like to announce the release of UMFPACK Version 2.0, the unsymmetric- pattern multifrontal package. UMFPACK Version 2.0 is a package for solving systems of sparse linear systems, Ax=b, where A is sparse and can be unsymmetric. It is written in ANSI Fortran 77. There are options for choosing a good pivot order, factorizing a subsequent matrix with the same pivot order and nonzero pattern as a previously factorized matrix, and solving systems of linear equations with the factors (with A, L, or U, or their transposes). Iterative refinement, with sparse backward error estimates, can be performed. Both single and double precision routines are available. UMFPACK Version 2.0 is based on a combined unifrontal/multifrontal algorithm that enables a general fill-in reduction ordering to be applied but avoiding some of the data movement of previous multifrontal approaches. Version 2.0 is up to twice as fast as Version 1.1, and uses at little as half the memory. For some matrices, Version 2.0 has about the same performance as Version 1.1. The improvement obtained depends on the matrix, and how much can be gained from exploiting unifrontal-style data movement. UMFPACK Version 2.0 is available via anonymous ftp to ftp.cis.ufl.edu:pub/umfpack/UMFPACK2.tar.gz, and in NETLIB (http://www.netlib.org/linalg/umfpack2.tar.gz). Some licensing restrictions apply. For related technical reports, see http://www.cis.ufl.edu/~davis (you can also obtain UMFPACK Version 2.0 from my home page). Tim Davis Joint work with Iain Duff, Rutherford Appleton Laboratory. ------------------------------ From: Steve Hammond Date: Mon, 11 Sep 1995 16:56:06 -0600 Subject: Workshop on Numerical Fluid Flow In Spherical Geometry PRELIMINARY ANNOUNCEMENT FIFTH WORKSHOP ON NUMERICAL METHODS FOR COMPUTING FLUID FLOW IN SPHERICAL GEOMETRY (PDEs on the Sphere) June 11-14, 1996 Breckenridge, Colorado BACKGROUND: As part of the DOE CHAMMP program a workshop on 'Numerical solutions of fluid flow in spherical geometry' will be held in Breckenridge, Colorado, June 11-14, 1996. This is the fifth in the series of meetings which have been hosted on a rotating basis by Argonne National Laboratory, the National Center for Atmospheric Research, and Oak Ridge National Laboratory. PROGRAM: The primary emphasis of the workshop is: The development of new methods for and application of new and existing methods for computing fluid flow in spherical geometry; in particular, how new methods eliminate shortcomings of current methods and how they address the problems unique to spherical geometry. Application to the shallow water equations and to complete baroclinic models are of interest as well as pure transport for chemistry models. The workshop will also cover: 1. Topics of interest include monotone advection, geodesic grid systems, TVD methods, flux correction methods, vector and scalar spectral methods, alternative discretizations, and Eulerian and semi-Lagrangian methods. These can be applied to three dimensional baroclinic equations, two dimensional shallow water equations, or pure transport in spherical geometry. 2. The presentation of results from current or new methods is encouraged. The comparison of these methods is facilitated by application to standard test sets. 3. Performance of current methods of choice and new methods on parallel computers, including limitations associated with algorithm and computer design are appropriate. Implementation details for distributed and shared memory architectures as well as discussion of attendant difficulties are of interest. Characteristics of parallel computers that may affect computational algorithms, in particular, future design aspects could be considered as they might affect algorithm implementation. ORGANIZING COMMITTEE: The organizing committee for the workshop consists of: James Hack (jhack@ncar.ucar.edu, (303) 497-1387) Steven Hammond (hammond@ncar.ucar.edu, (303) 497-1811) Paul Swarztrauber (pauls@ncar.ucar.edu, (303) 497-1220) David Williamson (wmson@ncar.ucar.edu, (303) 497-1372) Please contact the organizing committee if you have any questions about the conference program. LOCATION: The workshop will be held at the Beaver Run Resort in the victorian town of Breckenridge, Colorado. Breckenridge is located approximately 2 hours west of Denver International Airport. Hourly shuttle service is available between DIA and Breckenridge. For questions concerning the conference logistics please contact: Karen Friedman Scientific Computing Division NCAR P.O. Box 3000 Boulder, CO 80307 (303) 497-1276 FAX: (303) 497-1804 karen@ncar.ucar.edu ------------------------------ From: Trini Flores Date: Tue, 12 Sep 95 16:23:19 EST Subject: SIAM Conference on Numerical Combustion SIAM Conference on Numerical Combustion March 4-6, 1996 Le Meridien Hotel, New Orleans, Louisiana The Call for Papers is accessible through the World Wide Web. Point your browser to: http://www.siam.org/meetings/co96/cfp/co96home.htm The deadline for submission of an extended abstract is SEPTEMBER 25. Send submissions to: meetings@siam.org The Preliminary Programs, hotel and registration information, for the 1995 SIAM Annual Meeting and the 1995 SIAM Conference on Geometric Design are now available through the World Wide Web. Point your browser to the following URLs, respectively: http://www.siam.org/meetings/an95/an95home.htm http://www.siam.org/meetings/gd95/gd95home.htm The Call for Participation for the following conferences are likewise on the World Wide Web: 1996 SIAM Conference on Optimization http://www.siam.org/op96/op96home.htm 1996 SIAM Workshop on Computational Differentiation http://www.siam.org/ad96/cfp/ad96home.htm 1996 SIAM Conference on Discrete Mathematics http://www.siam.org/dm96/cfp/dm96home.htm ------------------------------ From: Hirofumi Amano Date: Sat, 16 Sep 95 15:08:47 +0900 Subject: Parallel Supercomputing Conference in Japan Dear Colleagues, Though we have very little time left, we are going to have: International Symposium on Parallel and Distributed Supercomputing (PDSC'95) on September 26-28 in Fukuoka, Japan. The WWW page for the symposium is now available at: http://www.nc.kyushu-u.ac.jp/PDSC95.html Some of the highlights of this symposium are: KEYNOTE ADDRESSES Practical Parallel Processing David Kuck (Kuck & Associates) Parallel Computation: Views from End-User Pragmatism Takao Tsuda (Kyoto Univ.) INVITED TALKS The Effect of Optimizing Compilers on Architecture and Programs Michael Wolfe (Oregon Graduate Institute) Application of Program Dependence Analysis in Distributed Software Engineering Jingde Cheng and Kazuo Ushijima (Kyushu Univ.) A Multicomputer HPC Platform: Experiments and Outcomes Bob Gingold (Australian National Univ.) Emerging Supercomputer Applications in Information Infrastructure George Cybenko, Carl Beckmann, Robert Gray, Katsuhiro Moizumi (Dartmouth College) Massively Parallel Processing System Jump-1 Hidehiko Tanaka (Univ. Tokyo) Vienna Fortran and the Path Towards a Standard Parallel Language Barbara Chapman (Univ. Vienna), Piyush Mehrotra (NASA Langley Res. Center), Hans P. Zima (Univ. Vienna) Hirofumi Amano Computer Center Kyushu University Hakozaki, Higashi, Fukuoka 812-81 Japan Phone: (+81)-92-641-1101 Ext. 2510 FAX: (+81)-92-631-3196 E-mail: amano@cc.kyushu-u.ac.jp ------------------------------ From: Jerzy Wasniewski Date: Fri, 15 Sep 1995 16:26:07 +0200 (METDST) Subject: Report on the Second Workshop on Applied Parallel Computing Report on the Second Workshop on Applied Parallel Computing, PARA95 The Second International Workshop on Applied Parallel Computing in Physics, Chemistry and Engineering Science (PARA95), and the Tutorial on ScaLAPACK and Parallel NAG Library on IBM SP2 and SGI Power Challenge were held in Lyngby, Denmark August 21-24, 1995. The Conference was organized and sponsored by the Danish Computing Centre for Research and Education (UNI*C) and the Institute of Mathematical Modelling (IMM) of the Technical University of Denmark (DTU). Support was also received from the Danish Natural Science Research Council through a grant for the EPOS project (Efficient Parallel Algorithms for Optimization and Simulation) and from the IBM and SGI computing organizations. The Workshop was preceded by a one-day Tutorial on ScaLAPACK and the Parallel NAG Library. The ScaLAPACK (Linear Algebra Package for Parallel Distributed Memory Computers) and the Parallel NAG (Numerical Algorithms Group) Library were presented and discussed. During the Tutorial time was allocated for practical exercises on the IBM SP2 and SGI Power Challenge computers. More than 60 people attended the Tutorial. The Workshp attracted more than 90 participants from around the world. Authors from 17 countries submitted 60 papers, of which 12 were invited and 48 were contributed. There were three parallel sessions. The conference was opened by remarks from Professor Kaj Madsen (Technical University of Denmark) and Professor Dorte Olesen (The Danish Computing Centre for Research an Education). Tuesday 22 August, 1995: Paul Woodward (University of Minessota), "Using clusters of shared memory multiprocessors to simulate turbulent fluid flows". Aake Nordlund (Copenhagen University), "Visualizing astrophysical MHD turbulence". Ahmed Sameh (University of Minessota), "Parallel algorithms for block tridiagonal systems". Zahari Zlatev (Danish Environmental Research Institute), "Parallel computations with large atmospheric models" Wednesday 23 August, 1995: Rob Bisseling (University of Utrecht), "Sparse matrix computations on bulk synchronous parallel computers". Peter Lomdahl (Los Alamos National Laboratory), "Multi-million particle molecular dynamics on MPPs". Jerzy Wasniewski (the Danish Computing Centre for Research and Education, UNI*C), "Portable parallel numerical libraries". Jack Dongarra (Tennessee University and Oak Ridge National Laboratory), "Templates and client server computing for linear algebra". Fred Gustavson (IBM Research Centre), "An efficient 3d parallel algorithm for matrix multiplication". Thursday 24 August, 1995 James Glimm (University at Stony Brook), "Front tracking: A parallelized CFD method for internal boundaries and interfaces". Alex Krasnitz (University of Copenhagen), "Lattice field theory in a parallel environment". Antonio Lagana (University of Perugia), "Parallel approaches to the solution of reactive scattering equations". Martyn Guest (CCL, Daresbury Laboratory), "High performance computational chemistry: NWCHEM and fully distributed parallel algorithms". Due to the excellent work of the organizing committee the Workshop went very smoothly. The informality of the meeting gave the participants much time to converse with new and old colleagues. Tuesday afternoon saw the Inauguration of the new supercomputer IBM SP2, followed by the PARA95 reception. IBM contributed 120 bottles of champagne. On Wednesday night conference participants met at the "Peter Liep" restaurant, Dyrehaven, where Professor Knut Conradsen (Technical University of Denmark) gave a very entertaining speech after an excellent dinner. The PARA95 papers, both invited and submitted, will be published by Springer-Verlag in their Lecture Notes in Computer Science series. Jack Dongarra & Jerzy Wasniewski ------------------------------ From: P. R Graves-Morris Date: Wed, 13 Sep 1995 14:40:05 +0100 (BST) Subject: Position at University of Bradford, England CHAIR IN APPLIED MATHEMATICS, UNIVERSITY of BRADFORD, ENGLAND. This new post of professor (or reader) in applied mathematics has been created as part of the university's policy of excellence in research. Aimed at strenghthening and reinforcing the existing wide-ranging research carried out by the department, it should also raise the department's profile in a number of new areas, including the university's science and engineering departments and industry. Appropriately qualified applicants from either an industrial or an engineering background must have an established international reputation in original research, including recent quality publications. Their research interests should ideally complement or reinforce existing strengths in heat/mass transfer, computational PDEs, or solid and fluid mechanics. Further particulars and an application form (quoting ref CRM/NANET) are available from the Personnel Office at Bradford University, Bradford, West Yorkshire BD7 1DP, England, or by phoning the office on 0044-1274-383105, or by FAX on 0044-1274-385009. Closing Date for applications: 6 October 1995. P.R.Graves-Morris. ------------------------------ From: Paul Matthews Date: Wed, 13 Sep 1995 11:57:54 +0100 Subject: Postdoctoral Position at University of Nottingham. Postdoctoral Research Opportunity Applications are invited for a 3-year postdoctoral research assistant in the Department of Theoretical Mechanics at the University of Nottingham. The project title is `The effect of rotation on the formation of buoyant flux tubes in the Sun' and funding is from the Particle Physics and Astronomy Research Council. Applicants should hold, or expect to obtain in the near future, a PhD in an applied mathematical discipline. Some knowledge of numerical methods and fluid mechanics will be required. The project will be based in Nottingham under the joint direction of Dr.P.C.Matthews (University of Nottingham), Prof.D.W.Hughes (University of Leeds) and Dr.M.R.E.Proctor (University of Cambridge). The proposed start date is 1 January 1996. Applications, including a full CV and the names and addresses of two academic referees, should be made in writing to Dr.P.C.Matthews, Department of Theoretical Mechanics, University of Nottingham, Nottingham NG7 2RD, UK. There is no application form. The closing date for applications is 31 October 1995. Informal enquiries may be made to: Dr.P.C.Matthews (Tel: 0115 951 3840, email: paul.matthews@nottingham.ac.uk) ------------------------------ From: Heinz W. Engl Date: Fri, 15 Sep 1995 11:07:37 EDT Subject: Postdoctoral Position at Johannes Kepler University Open Postdoc Positions in Industrial Mathematics At the Chair for Industrial Mathematics at the Johannes Kepler Universitdt in Linz (Austria), a full-time research position is to be filled immediately (now for 18 months, renewable for up to 4 years). The position is financed by industry and involves research in inverse problems, especially in connection with parameter identification and inverse heat conduction problems that arise in steel industry. Good knowledge about the numerical solution of pdes is essential, knowledge about inverse problems is desirable. The gross annual salary will be (depending on prior experience and age) between 360.000 and 420.000 Austrian Schilling. Citizens of E.C. countries and of Switzerland and Norway do not need visa or work permit, others do. In a few months, a second position of the same type will probably be open. Applications should be sent to Prof.Heinz W. Engl, Chair for Industrial Mathematics, Johannes Kepler Universitdt, A-4040 Linz, Austria. E-Mail: engl@indmath.uni-linz.ac.at Information about the Chair for Industrial Mathematics can be obtained in the WWW at http://www.indmath.uni-linz.ac.at/ ------------------------------ From: Francisco de A.M.Gomes Neto Date: Wed, 13 Sep 95 16:30:27 EST Subject: Position at UNICAMP, Brazil OPERATIONS RESEARCH/INDUSTRIAL ENGINEERING FACULTY POSITIONS The Department of Applied Mathematics of the State University of Campinas (UNICAMP) invites applications for faculty positions in the area of operations research/industrial engineering. A Ph.D. or equivalent qualification is required. Appointments are for three years initially with possible extension. Candidates are expected to contribute to research and teaching activities in a system oriented program on production research. Applications to arrive by *October 31, 1995* should consist of a full c. v. including a list of publications, and names and addresses of at least two referees. Applications and requests for information should be addressed to: Prof. Jose Plinio de Oliveira Santos IMECC/UNICAMP Caixa Postal 6065 13083-970 Campinas, SP Brazil Tel.: + 55 192 397900 Fax: + 55 192 395808 ------------------------------ From: Richard Brualdi Date: Mon, 11 Sep 1995 15:45:04 -0500 (CDT) Subject: Contents, Linear Algebra and its Applications LINEAR ALGEBRA AND ITS APPLICATIONS Contents Volume 229, November 1, 1995 Krzysztof C. Kiwiel (Warsaw, Poland) Iterative Schemes for the Least 2-Norm Solution of Piecewise Linear Programs 1 Changqin Xu (Heifei, Anhui, People's Republic of China) Bellman's Inequality 9 Isabel Faria (Lisboa, Portugal) Multiplicity of Integer Roots of Polynomials of Graphs 15 F. A. Arlinghaus (Youngstown, Ohio), L. N. Vaserstein (University Park, Pennsylvania), and Hong You (Changchun, People's Republic of China) Products of Involutory Matrices Over Rings 37 Carmine Di Fiore and Paolo Zellini (Roma, Italy) Matrix Decompositions Using Displacement Rank and Classes of Commutative Matrix Algebras 49 Khalide Jbilou (Villeneuve d'Ascq, France) Projection-Minimization Methods for Nonsymmetric Linear Systems 101 Jin-Hsien Wang (Kaohsiung, Taiwan, Republic of China) Sums and Products of Two Quadratic Matrices 127 John A. Holbrook (Guelph, Ontario, Canada) Interpenetration of Ellipsoids and the Polynomial Bound of a Matrix 151 H. Hu (DeKalb, Illinois) Positive Definite Constrained Least-Squares Estimation of Matrices 167 Yixun Shi (Bloomsburg, Pennsylvania) Solving Linear Systems Involved in Constrained Optimization 175 Author Index 191 ------------------------------ From: George Anastassiou Date: Fri, 15 Sep 1995 12:31:03 CDT Subject: Contents, Computers and Mathematics An International Journal COMPUTERS AND MATHEMATICS with Applications Editor in Chief: Ervin Y. Rodin Special issue on "Concrete Analysis" Guest Editor George A. Anastassiou Publisher Peramon Contents Volume 30, Number 3-6, Sept. 1995 CONCRETE ANALYSIS G. A. Anastassiou XV Preface J. A. Adell and J. de la Cal 1 Bernstein-Durrmey Operators G. A. Anastassiou 15 Comparison Theorems on Moduli of Continuity C. Badea 23 K-Functionals and Moduli of Smoothness of Functions Defined G. Baszenski, F. J. Delvos 33 A United Approach to Accelerating Trigonometric Expansions L. Chong and G. A. Watson 51 Characterization of a Best and Unique Best Approximation from Constrained Rationals H. Esser, St. J. Goebbels, 59 Sharp Error Bounds for the G. Luttgens and R. J. Nessel Crank-Nicolson and Saulyev Difference Scheme in Connections with an Initial Boundary Value Problem for the Inhomogeneous Heat Equation B. Germano, P. Natalini 69 Computing the Moments of the and P. E. Ricci Density of Zeros for Orthogonal Polynomials H. H. Gonska and 83 Local Smoothness of Functions D. X. Zhou and Bernstein-Durrmeyer Operators H. H. Gonska and 103 The Strong Converse Inequality X. I. Zhou for Berstein-Kantorovich Operators C. W. Groetsch 129 Regularized Product Integration for Hadamard Finite Part Integrals Y. K. Hu 137 Positive and Copositive Spline Approximation in Lp {0,1} R. K. Kovacheva 147 A Note on the Limiting Distribution of the Zeros of Pade' Approximants for Some Classes of Functions G. Mastroianni and 155 Interlacing Properties of the D. Occorsio Zeros of the Orthogonal Polynomials and Approximation of the Hilbert Transform J. Prestin and F. Sprengel 169 Multivariate Trigonometric Wavelet Decompositions J. B. Prolla 183 Semilattices and Lattices of Bounded Continous Functions B. Shekhtman 191 Interpolation of Individual Functions J. Shi and R. Huotari 197 Simultaneous Approximation From Convex Sets O. Shisha 207 The Genesis of the Generalized Riemann Integral A. K. Varma and E. Landau 213 New Quadrature Formulas Based on the Zeros of Jacobi Polynomials W. R. Wade 221 A Walsh System for Polar Coordinates M. Weba 229 Cubature of Random Fields by Product-Type Integration Rules R. A. Zalik 235 Some Remarks on Spectral Approximation M. Zhou and G. A. 243 Some Saturation Properties of Anastassiou the Representation Formulate for {C_o} m-Parameter Operator Semigroups M. Bartelt and W. Li 255 Error Estimates and Lipschitz Constants for Best Approximation in Continuous Function Spaces M. Campiti, G. Metafune 269 Uniformly Convergent Lagrange- and D. Pallara Type Approximation B. L. Chalmers and 277 The Geometry of Minimal Shape- M. P. Prophet Preserving Projections Onto II_n Z. Ciesielski 283 Fractal Functions and Schauder Bases S. Dahlke and P. Maass 293 The Affine Uncertainty Principle in One and Two Dimensions M. He 307 The Faber Polynomials for Circular Lunes T. X. He 317 Shape Criteria of Bernstein- Bezier Polynomials Over Simplexes O. Kounchev 335 Optimal Recovery of Linear Functionals of Peano Type through Data on Manifolds E. B. Lin 353 Multi-Dimensional Wavelet Stieltjes Transforms K. Marti 361 Differentiation of Probability Functions: The Transformation Method R. N. Mohapatra, 383 Norm Inequalities which Yield F. Salzmann and D. Ross Inclusion for Euler Sequence Spaces T. Nishishiraho 389 Approximation Processes with Respect to Positive Multiplication Operators P. E. Ricci 409 Improving the Asympototics for the Greatest Zeros of Hermite Polynomials F. Feher and M. J. Strauss 417 Weak-Type Interpolation and Orbits M. Genuit and 433 A Problem of L. Campbell on G. Schottler the Equivalence of the Kramer and Shannon Sampling Theorems ------------------------------ End of NA Digest ************************** -------