NA Digest Sunday, September 20, 1998 Volume 98 : Issue 35

Today's Editor:
Cleve Moler
The MathWorks, Inc.
moler@mathworks.com

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: Michael Hanke <hanke@nada.kth.se>
Date: Thu, 17 Sep 1998 16:35:50 +0200 (MET DST)
Subject: History of Krylov-type Methods

While preparing the lecture notes for a course about iterative
methods I met the following problem: While Krylov-type methods are in
use for almost 50 years now, the notion "Krylov subspace" appears to
be introduced a lot later. So my first question: Who coined this
notion and where? I found a hint on a paper (A.N. Krylov, Bull. Acad.
des Sc. de l'URSS, 1931). But this paper does not contain these
spaces. Moreover, there is a method cited (Leverrier, Ann. Obs.
Imperial de Paris, 1859) which reminds a little bit on the spaces in
question. Therefore the second question: Who introduced these spaces
first?

Any hints are welcome.
Thank you.

Regards,
Michael Hanke

Royal Institute of Technology
NADA
S-10044 Stockholm
Sweden


------------------------------

From: Ron Boisvert <boisvert@cam.nist.gov>
Date: Thu, 17 Sep 1998 16:46:58 -0400
Subject: Announcing a Computing Research Repository

Researchers regularly make their papers available by putting them on
personal web pages, departmental pages, and on various ad hoc sites
known only to cognoscenti. Until now, there has not been a single
repository to which researchers from the whole field of computing can
submit reports.

This is about to change. Through a partnership of ACM, the Los
Alamos e-Print archive, and NCSTRL (Networked Computer Science
Technical Reference Library), an online Computing Research Repository
(CoRR) is being established. The Repository has been integrated into
the collection of over 20,000 computer science research reports and
other material available through NCSTRL (http://www.ncstrl.org) and
will be linked with the ACM Digital Library. Most importantly, the
Repository will be available to all members of the community at no
charge. Among the subject classes identified for the repository are

Computational Engineering, Finance and Science
Numerical Analysis
Mathematical Software
Symbolic Computation

We encourage you to start using the Repository right away. For more
details see http://www.acm.org/repository. Please spread the word
among your colleagues and students. CoRR will only gain in value as
more researchers use it.


------------------------------

From: Gregory Kozlovsky <kly@olsen.ch>
Date: Mon, 14 Sep 1998 11:40:09 +0200
Subject: Change of Address for Gregory Kozlovsky

Here is my new address.

Gregory Kozlovsky Olsen & Associates AG
E-mail: kly@olsen.ch Research Institute for Applied Economics
Phone: +41.1.386.48.58 Seefeldstrasse 233
Fax: +41.1.422.22.82 CH-8008 Zurich - Switzerland.
URL: http://www.olsen.ch/people/kly/


------------------------------

From: Ashok Srinivasan <ashok@math.iitb.ernet.in>
Date: Tue, 15 Sep 1998 07:04:02 GMT
Subject: Change of Address for Ashok Srinivasan

Hi Everyone,

I have moved from NCSA, University of Illinois at Urbana-Champaign,
and have taken up a faculty position at the Indian Institute of
Technology, Bombay, India.

- Ashok Srinivasan
New email: ashok@math.iitb.ernet.in


------------------------------

From: Heinz Engl <engl@indmath.uni-linz.ac.at>
Date: Tue, 15 Sep 1998 10:16:10 +0200
Subject: New Edition of Book on Regularization of Inverse Problems

A new edition (essentially unchanged, some typos corrected) of the book

H.W.Engl, M.Hanke, A.Neubauer
Regularization of Inverse Problems
Kluwer, Dordrecht 1996,

which had been sold out, has appeared, so that the book is now
availabe again.

Heinz Engl, Linz, Austria


------------------------------

From: George Karypis <karypis@s1.arc.umn.edu>
Date: Sun, 20 Sep 1998 15:21:51 -0500 (CDT)
Subject: Software for Graphs, Meshes and Sparse Matrices

METIS
A Software Package for Partitioning Unstructured Graphs, Partitioning
Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices

http://www.cs.umn.edu/~metis
http://www.cs.umn.edu/~karypis/metis

Version 4.0

We would like to announce the release of version 4.0 of the METIS package
for partitioning unstructured graphs, partitioning finite element meshes,
and for computing fill-reducing orderings of sparse matrices.
METIS 4.0 contains a number of changes over METIS 3.0. The major changes
are the following:

* METIS now includes partitioning routines that can be used to partition
a graph in the presence of multiple balancing constraints.

* METIS now includes partitioning routines that can be used to directly
minimize the overall communication volume resulted by the partitioning.

* METIS's k-way partitioning routines can now directly minimize the
maximum as well as the total number of adjacent subdomains.

* METIS's k-way partitioning routines can now reduce the number of
non-contiguous subdomains.

Overview of METIS

METIS is a set of programs that implement various graph partitioning algorithms
that are based on the multilevel paradigm. The advantages of METIS compared to
other similar packages are the following:

- Provides high quality partitions!
- It is extremely fast!
- Provides low fill orderings!

Obtaining METIS

METIS is freely distributed. You can download METIS's source code from
the WEB at:
URL: http://www.cs.umn.edu/~metis
or
URL: http://www.cs.umn.edu/~karypis/metis


Contact Information

METIS has been written by George Karypis at the Computer Science Department
of the University of Minnesota. If you have any questions or problems
obtaining METIS, send email to metis@cs.umn.edu.

METIS is Copyrighted by the Regents of the University of Minnesota


------------------------------

From: Heinz Engl <engl@indmath.uni-linz.ac.at>
Date: Mon, 14 Sep 1998 16:03:56 +0200
Subject: Computational Mathematics Driven by Industrial Applications

Preliminary Announcement of a CIME Session
"Computational Mathematics Driven by Industrial Applications"

Scientific Directors:

V.Capasso, Milano
H.W.Engl, Linz
J.Periaux, Paris

Location: Martina Franca, Apulia, Italy
Dates: June 21-27, 1999

There will be 5-hour lectures by the following eminent speakers:

R.Burkard, Graz: Path, trees and flows: graph optimization problems
with industrial applications

P.Deuflhard, Berlin: New computational concepts, adaptive differential
equation solvers, and virtual labs

J.L.Lions, Paris: Mathematical problems in industry

G.Strang, MIT: Wavelet transforms and cosine transforms in signal and
image processing

There will probably be one more 5-hour-speaker still to be confirmed.

In addition, there will be 2-hour lectures by the scientific directors
and by

R.Mattheij, Eindhoven: Mathematics of glass.

The abstracts should soon be available on the CIME web page

http://www.math.unifi.it/CIME/

where also an e-mail address for enquiries about conditions of
attendance can be found.

Heinz W.Engl,
Linz,Austria


------------------------------

From: Lori Freitag <freitag@mcs.anl.gov>
Date: Tue, 15 Sep 1998 11:49:26 -0500
Subject: International Meshing Roundtable

7th INTERNATIONAL MESHING ROUNDTABLE
October 26-28, 1998
Dearborn, Michigan
Sponsored by Sandia National Laboratory
Hosted by Ford Motor Company

We invite you to attend the 7th International Meshing Roundtable to
be held October 26-28, 1998 in Dearborn, Michigan. The goal of this
conference is to bring together researchers and developers from industry,
academia, and government labs in a stimulating, open environment for the
exchange of technical information related to the meshing process.

This year's Roundtable consists of an excellent technical program comprised
of contributed papers, a keynote speaker, four solicited mini-tutorials
on topics related to the mesh generation process, and an invited panel
of experts discussing the development and use of automatic mesh generation
tools. In addition, we will also feature a "Meshing Maestro" competition
and poster session, a Birds-of-a-Feather session, and an open problems
forum, all designed to encourage discussion and participation from a
wide variety of mesh generation tool developers and users.

More information regarding the conference agenda, location, registration
procedures, and special events can be found at the web site
http://www.mcs.anl.gov/~freitag/7IMR.

We hope to see you there!
The 7th International Meshing Roundtable Steering Committee


------------------------------

From: Trini Flores <flores@siam.org>
Date: Thu, 17 Sep 98 08:26:51 -0500
Subject: Two SIAM Meetings, Geosciences and Optimization

1999 SIAM Conference on Mathematical and Computational Issues in the Geosciences
March 24-27, 1999
San Antonio, Texas

DEADLINE FOR SUBMISSION OF CONTRIBUTED ABSTRACTS: OCTOBER 1, 1998.
For more information, visit: www.siam.org/meetings/gs99/.

*********

1999 SIAM Conference on Optimization
May 10-12, 1999
Atlanta, Georgia

DEADLINE FOR SUBMISSION OF MINISYMPOSIUM PROPOSALS: OCTOBER 1, 1998.
DEADLINE FOR SUBMISSION OF CONTRIBUTED ABSTRACTS: OCTOBER 30, 1998.

For more information, visit: www.siam.org/meetings/op99/.


------------------------------

From: Daniel Andresen <dan@cis.ksu.edu>
Date: Thu, 17 Sep 1998 12:43:21 -0500
Subject: Workshop on Irreguarly Sturctured Problems

IRREGULAR'99 (Call for Papers)
April 16, 1999
Caribe Hilton, San Juan, Puerto Rico
In conjunction with IEEE IPPS/SPDP'99 (13th International Parallel
Processing Symposium)

SIXTH INTERNATIONAL WORKSHOP ON
SOLVING IRREGULARLY STRUCTURED PROBLEMS IN PARALLEL

Scope: The workshop on solving irregularly structured problems in parallel
(Irregular'99) - is the sixth in the series, after Geneva, Lyon, Santa
Barbara, Paderborn, and Berkeley. This workshop is intended to be a forum
for bringing together algorithm and system researchers in solving irregular
problems. Papers are solicited in all research areas related to parallelism
of irregular applications, including but not limited to: data structures and
graph algorithms, numerical algorithms, mesh and sparse matrix computations,
approximation and combinatorial optimization, parallel languages and models,
compiler optimization and runtime systems, caching, load balancing and
scheduling, resource management (I/O, memory, and CPU), performance
prediction and simulation, Internet computing and data-intensive
applications.

Publication: Workshop papers will be published by Springer Verlag as part of
their Lecture Notes in the Computer Science Series, and they will also
appear in the CD-ROM version of the IPPS Proceedings. For more information
on IPPS/SPDP'99, check www.ippsxx.org. Extended versions of selected papers
will be solicited for a journal edition. Previous proceedings of Irregular
series appeared as LNCS 980, 1117, 1253 and 1457.

Submission guidelines: Contributions must be submitted electronically to
irregular99@cs.ucsb.edu. The submission should include an extended abstract
using the postscript format in no more than 5 pages, and a cover page with
the ASCII format. The cover page should contain the paper title, authors'
full names, address and fax number, and key terms. Work-in-progress papers
on hot topics are encouraged to submit. It is expected that accepted papers
will be presented at the workshop.

Important Dates

* Submission: October 31, 1998
* Notification: December 7, 1998
* Camera Ready: January 7, 1999

Program Committee: T. Yang (Chair, UCSB), D. Andresen (Kansas State), S.
Baden (UCSD), S. Chakrabarti (IBM Almaden), S. Chatterjee (North Carolina),
R. Correa (DC/UFC, Brazil), M. Cosnard (LORIA, France), G. Fox (Syracuse), A.
Gerasoulis (Rutgers), H. Ho (IBM Almaden), O. Ibarra (UCSB), V. Kumar
(Minnesota), E. Ng (ORNL), K. Pingali (Cornell), S. Ranka (Florida), J.
Saltz (Maryland), H. Simon (NERSC), S. Teng (UIUC), D. Trystram (IMAG,
France), H. Wijshoff (Leiden, Netherlands).

Steering Committee: A. Ferreira (INRIA Sophia-Antipolis), J. Rolim (U. of
Geneva).

Further Information: http://www.cs.ucsb.edu/Conferences/Irregular99


------------------------------

From: Hermann Brunner <brunner@math.ethz.ch>
Date: Thu, 17 Sep 1998 10:23:15 +0200
Subject: Report on the ANODE Meeting in New Zealand

ANODE 98: Auckland, New Zealand / June 29 - July 10, 1998

ANODE 98 -- Auckland Numerical Ordinary Differential Equations
(organized by John Butcher, Robert Chan, Nicolette Goodwin,
Bev Grove and Allison Heard of the Department of Mathematics,
the University of Auckland, New Zealand) was held from June 29
to July 10, 1998, at the pleasant setting of Old Government House
on the city campus of the university. The format chosen by the
organizers (four principal lecture series, a number of minisymposia,
contributed talks -- including talks by many graduate students --
and above all, no parallel sessions) was the ideal basis for
a conducive and inspiring meeting and may well serve as a model
for other conferences with a distinct focus.

Each of the four principal lecturers presented six one-hour
lectures. Marc Spijker (Rijksuniversiteit Leiden, The
Netherlands) spoke on "Error growth analysis for discretizations
of initial value problems" (focusing on stability estimates and
various versions of the Kreiss resolvent condition). The lectures of
Chus Sanz-Serna (University of Valladolid, Spain) dealt with
"Order conditions for Runge-Kutta methods" (giving a new approach
and emphasizing their use in composition methods). Adrian Hill
(University of Bath, England) talked on "Nonlinear stability
theory" (extensive review of classical nonlinear stability for
ODEs and PDEs, followed by recent work on dissipativity and
dynamical systems).
The lectures on "Geometric integration of ODEs" (dealing with
symplectic integration, preservation of symmetry and volume, and
integral preservation and Lyapunov integrators), were given
by Robert McLachlan (Massey University, New Zealand) and
Reinout Quispel (Latrobe University, Australia).

The three minisymposia (organized respectively by Philippe Chartier
(IRISA, Rennes, France), Hermann Brunner (Memorial University of
Newfoundland, Canada), and Ray Zahar (Universite de Montreal,
Canada) had as their topics "Pseudo-spectral methods", "Numerical
delay differential equations" and "Taylor series methods".
Some 16 contributed talks (about half of these given by
graduate students from the Department of Mathematics at
Auckland) complemented the 12 contributions to the minisymposia.

The afternoon of the last day of ANODE 98 was given to a discussion
of open problems. Among the topics covered were questions on
variable stepsize versus stability, and error estimation in
Taylor methods (Robert McLachlan); the notion and use of the
condition number for an initial-value problem (Robert Corless,
University of Western Ontario, Canada); unexplored areas in
geometric integration, e.g. nonautonomous ODEs, variable
time steps, and DAEs, DDEs, integral equations and PDEs
(Reinout Quispel); and observations on the visualization
of flows in ODEs (Chris Blackbourn, University of Auckland).

A number of well-organized social events complemented the
mathematical activities. They included a welcome function
on June 28 at O'Rorke Hall (a university residence where
many of the participants stayed); an excursion on the
afternoon and evening of July 1 to Devonport on the
North Shore, around the city, to the top of Mt Eden,
and finally to Old Government House for a performance by
the Te Ao Hurihanga Cultural Group and a traditional New
Zealand Fish 'n' Chips meal; and on the following day,
the conference dinner at a restaurant in Skytower, Auckland's
new landmark.

The conference was opened by Professor Ian Buckle,
Deputy Vice-Chancellor (Research), University of
Auckland, and it was attended by about 50 participants from
Austria, Australia, Belgium, Canada, France, Japan, The Netherlands,
New Zealand, Spain, the UK, and the USA. The obvious success
of ANODE 98 should be a strong incentive for many numerical
analysts to attend ANODE 99 which will be held from 16 to
20 August 1999, following SciCADE 99 in Australia.


Hermann Brunner
Memorial University of Newfoundland
St. John's, NF, Canada


------------------------------

From: Andy Philpott <a.philpott@auckland.ac.nz>
Date: Fri, 10 Jul 1998 22:53:29 +1200
Subject: Postdoctoral Position at University of Auckland

POSTDOCTORAL RESEARCH FELLOWSHIP AT THE UNIVERSITY OF AUCKLAND

Operations Research Group
University of Auckland
Auckland, New Zealand


The Operations Research Group at the University of Auckland invites
applications for a two year Postdoctoral Research Fellowship in
Mathematical Programming. The position is funded by a Research Grant
from the New Zealand Foundation of Research, Science and Technology.

The purpose of this position is to develop large-scale mathematical
programming techniques with a view to their implementation in industrial
applications. The research is specifically aimed at the large-scale
mathematical programming problems arising in scheduling and planning
under uncertainty. Developing techniques to model and solve integer
stochastic programming problems is one goal of the research.

Applicants should have a doctorate in Mathematical Programming,
Operations Research or a related discipline where Mathematical
Optimization is an essential part of the candidate's background. In
addition candidate should have experience in the implementation of
mathematical programming codes in Fortran or C.

The stipend is (NZ)$45,250 per annum ((NZ)$1.00 = (US)$0.50), with an
allowance for relocation costs where appropriate. Funds are also
available for the fellow to attend at least one international conference
in each year of the fellowship.

Further information is available from

Professor David M Ryan, Telephone 64-9-373 7599 (Ext 8398)
email: d.ryan@auckland.ac.nz

or

Associate Professor Andrew B Philpott, (Ext 8394)
email: a.philpott@auckland.ac.nz


Applications in the form of a detailed curriculum vitae, including the
contact details for two or more referees and their fax numbers, must
reach the Academic Appointments Section, The University of Auckland,
Private Bag 92019, Auckland, New Zealand, by 20 October, 1998.

Please quote Vacancy Number 1019 in all correspondence.


------------------------------

From: Bruce Suter <suterb@rl.af.mil>
Date: Mon, 14 Sep 1998 12:58:59 -0400
Subject: Postdoctoral Positions at Air Force Research Laboratory

Postdoctoral Fellowships Available in Multirate and Wavelet Signal Processing

Recent PhD graduates are invited to apply for a postdoctoral fellowship at
the Air Force Research Laboratory to work on topics in "multirate and
wavelet signal processing", including applications to both compression and
communications. All applicants must be either US citizens or green card
holders. For more information, please contact Dr. Bruce Suter
(suterb@rl.af.mil).


------------------------------

From: Steven Pruess <spruess@Mines.EDU>
Date: Mon, 14 Sep 1998 11:11:42 -0600
Subject: Faculty Position at Colorado School of Mines

COLORADO SCHOOL OF MINES
DIVISION OF ENGINEERING

Applications are invited for a tenure-track position at the Assistant
Professor level, although the possibility exists for placement of highly
qualified advanced candidates. Applicants must have a Ph.D. in mechanical
or chemical engineering or a closely related field with a specialization
in computational fluid dynamics. Applicants must demonstrate depth in:
computational mathematics and development of numerical methods, an ability
to write software, ability to create models from underlying physical and
chemical principles, ability to then create a full simulation of chemically
reacting flowfields, and an ability to use the simulation for design,
optimization, and process control. Preference will be given to applicants
with demonstrated experience in combustion and/or materials processing.
There are excellent opportunities to collaborate with experimental programs
in the same areas at CSM. The successful candidate will be expected to
contribute to collaborative research within the Division, as well as with
the campus-wide interdisciplinary research centers. The successful
candidate must also be capable of building externally funded research
programs.

The Division of Engineering offers an ABET-accredited nontraditional
undergraduate interdisciplinary degree program and interdisciplinary
M.S. and Ph.D. programs in Engineering Systems. The successful candidate
must have a strong interest in teaching at the graduate and undergraduate
level and will be expected to teach courses across the entire thermal
sciences curriculum.

Applicants are required to submit a curriculum vitae and a letter of
application which must include a narrative describing the applicant


------------------------------

From: Alistair Watson <gawatson@mcs.dundee.ac.uk>
Date: Wed, 16 Sep 1998 12:13:53 +0100 (BST)
Subject: Research Position at University of Dundee

University of Dundee
Department of Mathematics

The Department wishes to appoint to a Research Lectureship
a person with interests in Acoustics and Electromagnetic Theory,
Applied Analysis, Mathematical Biology or Numerical Analysis.
This position is intended for an outstanding
young scientist seeking a research-led academic career,
and will provide an opportunity to work
in one of these areas of strength within the Department.
The appointment will be for 5 years with consideration for a
permanent post towards the end of that period, and will carry
limited teaching responsibility.

Further information can be obtained form
Professor Alistair Watson (gawatson@mcs.dundee.ac.uk).
Applications by CV and covering letter (3 copies of each),
with names and addresses of 3 referees, should be sent to
Personnel Services, University of Dundee, Dundee DD1 4HN, Scotland.
The closing date is 9 October, 1998.


------------------------------

From: Manil Suri <suri@math.umbc.edu>
Date: Thu, 17 Sep 1998 12:38:48 -0400 (EDT)
Subject: Faculty Position at University of Maryland Baltimore County

Faculty Position Available at UMBC

The Department of Mathematics and Statistics at the University of
Maryland Baltimore County (UMBC) has a faculty position
in applied mathematics beginning Fall 1999. The position is anticipated
to be at the tenure-track assistant professor level.
The candidate should have an earned doctorate in mathematics
or a related field and be able to interact with one or more of the
department's existing groups in optimization, numerical analysis, PDEs
and systems theory. The applicant should have an active, independent
research program and strong potential for obtaining external funding.

The department offers BS, MS and PhD degrees in applied mathematics and
statistics. Please refer to the web page http://www.math.umbc.edu for
more information. A vita, three letters of reference and a summary of the
candidate's current research program should be sent to: Applied Mathematics
Recruiting Committee, Department of Mathematics and Statistics,
University of Maryland Baltimore County, Baltimore, MD 21250. Screening
of applications will commence December 15, 1998 and will continue until
the position is filled. UMBC is an Affirmative Action/Equal Opportunity
Employer.


------------------------------

From: Chunguang Sun <csun@mcs.drexel.edu>
Date: Thu, 17 Sep 1998 12:50:25 -0400
Subject: Faculty Positions at Drexel University

Tenure-track positions in computer science at Drexel University:

The Department of Mathematics and Computer Science invites applications
for anticipated tenure-track positions beginning Fall 1999, salary and
rank commensurate with qualifications. Ph.D. in computer science or
equivalent and demonstrated excellence in teaching and research required.
Department has undergraduate and graduate programs in mathematics and
computer science. Areas of particular interest: software engineering,
operating systems, distributed systems and networking, databases,
scientific computation and problem solving environments.

Send letter, curriculum vita,and 4 letters of reference to: CS Search
Committee, Department of Mathematics and Computer Science, Drexel University,
Philadelphia, PA 19104

(e-mail: cs_search@mcs.drexel.edu WWW: http://www.mcs.drexel.edu/cs_pos/ ).

Applicant review begins December 15, 1998 and continues until position filled.
Drexel University is an Affirmative Action/Equal Opportunity Employer.


Tenure-track positions in statistics/applied mathematics at Drexel University:

The Department of Mathematics and Computer Science invites applications
for anticipated tenure-track positions beginning Fall 1999, salary and
rank commensurate with qualifications. Ph.D. in statistics, applied
mathematics or equivalent; demonstrated excellence in teaching and research
required. Department has undergraduate and graduate programs in mathematics
and computer science. Areas of particular interest: wavelets, numerical
analysis, computational statistics, and experience with diverse applications
of statistics and mathematical modeling.

Send letter, curriculum vita,and 4 letters of reference to: Math Search
Committee Chair, Department of Mathematics and Computer Science, Drexel
University, Philadelphia, PA 19104

(e-mail: math_search@mcs.drexel.edu; Web: http://www.mcs.drexel.edu/math_pos/).

Applicant review begins December 15, 1998 and continues until position filled.
Drexel University is an Affirmative Action/Equal Opportunity Employer.


------------------------------

From: Thomas Hogan <hogan@math.ohio-state.edu>
Date: Tue, 15 Sep 1998 14:50:53 -0400 (EDT)
Subject: Contents, Journal of Approximation Theory

Table of Contents: J. Approx. Theory, Volume 94, Number 3, September 1998

In memoriam: Oved Shisha (1932--1998)
331

S. B. Damelin and D. S. Lubinsky
Jackson theorems for Erd\H{o}s weights in $L_p(0<p\le\infty)$
333--382

Ant\'onio M. Caetano
About approximation numbers in function spaces
383--395

Michael Felten
Local and global approximation theorems for positive linear operators
396--419

Bengt-Olov Eriksson
Some best constants in the Landau inequality on a finite interval
420--454

Philippe Guillaume
Convergence of the nested multivariate Pad\'e approximants
455--466

Wolfgang Gehlen
On the distribution of alternation points in uniform polynomial
approximation of entire functions
467--480

Kirill A. Kopotun
Approximation of $k$-monotone functions
481--493

Book reviews
494--508

Author index for Volume 94
509


------------------------------

End of NA Digest

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