NA Digest Monday, October 18, 1999 Volume 99 : Issue 41

Today's Editor:
Cleve Moler
The MathWorks, Inc.

Submissions for NA Digest:

Mail to

Information about NA-NET:

Mail to

URL for the World Wide Web:

From: Douglas Arnold <>
Date: Tue, 12 Oct 1999 10:43:37 -0400
Subject: Re: Query About Rounding Error

I'll take the opportunity of Pete Stewart's query concerning real-life
embarrassments due to rounding error to mention that I have a web page,, on real-life disasters
attributable to bad numerics, It reports on the failure of the Patriot
Missile battery at Dharan, which is directly attributable to
accumulation of round-off errors, and also on the explosion of the
Ariane 5, which was caused by an overflow, and the loss of the Sleipner
offshore platform, which was due to bad finite element technology. In
each case I studied the investigative reports, but just posted a small
summary to whet the appetites of my students.

I would be interesting to hear of other events that fit this
description. I find that these can be great student motivators.

Doug Arnold


From: David Stewart <>
Austin Dubrulle <>
Date: Tue, 12 Oct 1999 08:21:31 -0500
Subject: Re: Difference Between 1x1 Matrices and Scalars

In NA Digest V. 99, # 39, a question of Ilse Ipsen's appeared:

> There can be a difference between 1x1 matrices and scalars.
> Consider the matrix product A*B*C where
> A = [1 1] B = [1] C=[1]
> [1] [2]
> [3]
> The product A*B*C is not defined because B*C is not defined.
> Nevertheless MATLAB 5.3 computes the answer [2]
> [4]
> [6]
> presumably because it associates (A*B)*C. In this case A*B
> happens to be a scalar but should be treated as a 1x1 matrix.
> Is this something to worry about?
> Ilse Ipsen

David Stewart replies:

I don't think it is anything to worry about... in any case
MATLAB can't tell the difference between a scalar and a 1 x 1
matrix because there is no scalar "type" in MATLAB.

The question remains: Is this potentially dangerous?
Should there be a scalar type in MATLAB, and should we be
required to write something like


for the product to work?

Here's why I don't think we need it:

A re-associated product (what we get by re-arranging the
parentheses) will only be defined if the 1 x 1 matrix
and scalar interpretations are both correct.

If we have a product A_1*A_2*...*A_p, if some sub-expression is
a scalar (say A_i*...*A_j), then A_i is 1 x n_i and A_j is m_j x 1.
If we try to re-associate this product from




it will only work if A_{i-1} is m_{i-1} x 1. If s > j then we would
also need A_{j+1} to be 1 x n_{j+1}. Then the 1 x 1 matrix and
scalar interpretations are equivalent. If s = j, then
A_{r+1}*...*A_{i-1}*A_i*...*A_s is an m_{r+1} x 1 matrix.
Then we can only multiply by (A_{s+1}*...) if A_{s+1} = A_{j+1} is
a 1 x n_{j+1} matrix. Thus the 1 x 1 matrix and scalar interpretations
are equivalent in this case as well. If we choose A_i*...*A_j
to be a minimal product where m_i = 1 and n_j = 1, then if s < j,
n_s is not equal to one, and A_{s+1} has m_{s+1} not equal to one
either. Then following through with the matrix rules, we see that
the product that follows A_s up to A_j is associative, and this
reduces the question to the previous case (s = j).

So if MATLAB can do the product, the result is independent of whether
1 x 1 matrices are treated as matrices or scalars.

If you had some software that didn't check the matrix compatibility
condition (n_i = m_{i+1} for all i) then you would have reason
to worry.

David Stewart
Dept. Mathematics
University of Iowa

Austin Dubrulle replies:

1. Ilse's question is pertinent, but there should be "something to worry
about" only when teaching a freshman class in linear algebra with MATLAB
(see item 2 below). For that purpose, MATLAB is no substitute for a brain,
a no. 2 pencil, a writing tablet, and MacLane/Birkhoff or Bourbaki.
Otherwise, for anyone who has background in mathematics and who uses MATLAB
as a programming language, there is little to worry about.

2. The MATLAB guide annonces up front that the only data type for
computational linear algebra is "matrix," i.e., a column vector is an mx1
matrix, a row vector, a 1xn matrix, and a scalar, a 1x1 matrix. This, of
course, defines an algebra that is a bit different from matrix algebra.
Under these conditions, multiplication of a column vector by a MATLAB
scalar should be written as
(1) 'vector*scalar' and not 'scalar*vector.'
The opposite is true for the scalar multiplication of a row vector. The
multiplication of a matrix by a scalar should not exist, only the
multiplication by the proper diagonal matrix. There are more such quirks.
Yet, at the cost of a violation of matrix algebra---the conflation of the
1x1 matrix and the scalar definitions---things become simpler, so that both
expressions (1) are acceptable, and so is the multiplication of a matrix by
a 1x1 matrix. Since the field of 1x1 matrices is isomorphic to the field of
complex numbers, the violation is mild in its practical consequences.
Yet, the 1x1 matrix ends up having two personalities, each of which being
determined by expression context. Perhaps the MATLAB manual should
emphasize this peculiarity instead of bluntly asserting that "a scalar is a
1x1 matrix."

3. Given MATLAB's matrix definition, someone concerned about algebra should
not write
(2) A*B*C
with A=[1 1], B=[1 1]', and C=[1 2 3]', but
(3) C*A*B
which, of course, formally gives the same result, and respects
associativity. In fact, I suspect that most of us mean (3) when writing
(2). It turns out that MATLAB has an order of operation that makes (2)
acceptable. But why not write the expression as (3) in the first place, in
the form C*(A*B) as a concession to efficiency of operation? Or (A*B)*C?

I think that MATLAB should not be considered as the strict embodiment of an
algebra, but as a convenient computational engine that gets useful things
done without too much pain and suffering, and delivers decent performance.
It can do that because of pragmatic design choices, not unlike FORTRAN in
that respect. Other languages that enforce rigid, saintly syntaxes
(algebras) along with attendant limitations---e.g., PASCAL---have not been
too useful outside CS departments.

A. A. Dubrulle


From: Stephen Wright <>
Date: Fri, 15 Oct 1999 18:15:45 -0500
Subject: New Book, Numerical Optimization

We are pleased to announce a new book:


Jorge Nocedal, Stephen J. Wright,
Northwestern University Argonne National Laboratory

Published by Springer, Series in Operations Research, ISBN 0-387-98793-2
Can be ordered now through or

Go to URL for further
information on contents and ordering.

NUMERICAL OPTIMIZATION presents a comprehensive and up-to-date
description of the most effective methods in continuous
optimization. It responds to the growing interest in optimization in
engineering, science, and business by focusing on the methods that are
best suited to practical problems.

Drawing on their experiences in teaching, research, and consulting,
the authors have produced a textbook that will be of interest to
students and practioners alike. Each chapter begins with the basic
concepts and builds up gradually to the best techniques currently

Because of the emphasis on practical methods, as well as the extensive
illustrations and exercises, the book is accessible to a wide
audience. It can be used as a graduate text in engineering, operations
research, mathematics, computer science, and business. It also serves
as a handbook for researchers and practitioners in the area.

Above all, the authors have strived to produce a text that is pleasant
to read, informative, and rigorous---one that reveals both the
beautiful nature of the discipline and its practical side.


From: Will Light <>
Date: Mon, 18 Oct 1999 12:15:44 +0100 (BST)
Subject: New Book, A Course in Approximation Theory

We are pleased to announce our new book:

A Course in Approximation Theory

by EW Cheney and WA Light

ISBN: 0-534-36224-9 Pages: 359 Publisher: Brookes Cole

This book covers many of the modern developments particularly in multivariate
approximation. Each of the 36 short chapters provides a succinct introduction
to a modern topic in Approximation Theory:
Linear Interpolation Operators, Optimization of the Lagrange Operator,
Multivariate Polynomials, Moving the Nodes, Projections, Tensor Product
Interpolation, The Boolean Algebra of Projections, The Newton Paradigm for
Interpolation, The Lagrange Paradigm for Interpolation, Interpolation by
Translates of a Single Function, Positive Definite Functions, Strictly Positive
Definite Functions, Completely Monotone Functions, The Schoenberg Interpolation
Theorem, The Micchelli Interpolation Theorem, Positive Definite Functions on
Spheres, Approximation by Positive Definite Functions, Approximate
Reconstruction of Functions and Tomography, Approximation by Convolution, The
Good Kernels, Ridge Functions, Ridge Function Approximation via Convolutions,
Density of Ridge Functions, Artificial Neural Networks, Chebyshev Centers,
Optimal Reconstruction of Functions, Algorithmic Orthogonal Projections,
Cardinal B-Splines and the Sinc Function, The Golomb-Weinberger Theory, Hilbert
Function Spaces and Reproducing Kernels, Spherical Thin-Plate Splines, Box
Splines, Wavelets, Part I, Wavelets, Part II, Quasi-Interpolation.

Further information can be found on the website:

Will Light


From: Edward Aboufadel <>
Date: Mon, 18 Oct 99 08:43:15 -0500
Subject: New Book, Discovering Wavelets

"Discovering Wavelets" has just been published by Wiley and Sons. The
purpose of this book is to make wavelets accessible to anyone with a
background in basic linear algebra (for example, graduate and
undergraduate students), and to serve as an introduction for the
nonspecialist. The level of the applications and the format of this
book make it an excellent textbook for an introductory course on
wavelets or as a supplement to a first or second course in linear
algebra or numerical analysis.

For more information about the book, including a table of contents:

To order the book online, use the following URL:

The Discovering Wavelets web site is:

Edward Aboufadel & Steven Schlicker
Grand Valley State University


From: Alan Edelman <>
Date: Tue, 12 Oct 1999 09:58:30 -0400 (EDT)
Subject: Meeting Honoring Gil Strang

STRANGFEST at MIT on December 3--4, 1999

Our preliminary schedule and other information
may be found on line. Please mark your calendars
to attend this event at MIT to honor Gil Strang.


From: Uwe Naumann <>
Date: Tue, 12 Oct 1999 08:39:49 +0200
Subject: Conference on Automatic Differentiation

The third international workshop on Automatic Differentiation (AD)
will take place
from June 19th to June 23rd at Nice (Cote d'Azur, France).

AD 2000 will be organized locally by INRIA Sophia-Antipolis under
the direction of an international program commitee. It
represents a follow up on the two previous workshops held in
Breckenridge (USA) in 1991 and in Santa Fe (USA) in 1996. Special
emphasis will be placed on relationships and synergies between
AD techniques and other software tools such as compilers and
parallelizers. Apart from recent advances in research and software
development conference topics include applications of AD to
optimization, ODEs/DAEs, inverse problems, biomedical research,
and mathematics of finance.

Invited presentations have been confirmed by

W. Klein, Siemens, Munich V. Selmin, Alenia, Turin
D. Fylstra, Frontline Syst. Nev N.N CADOE, Lyon

J. More, Argonne, Ill. F. Bodin, IRISA, Rennes
S. Watt, Univ. of Western Ontario S. Hague, NAG, Oxford
D. Keyes, NASA, Langley O. Pironneau, Univ Paris
B. Walster, Sun Micro Systems F-X. LeDimet, Univ. Grenoble

Specifics on the location, prodecures for registration and submission
(abstracts, posters, special interest groups), and the preliminary
program can be found at


From: Eugenio Ferreira <>
Date: Tue, 12 Oct 1999 10:37:49 +0100
Subject: Portuguese Conference on Automatic Control


First Announcement and Call for Papers

4-6 October 2000, GUIMARAES Portugal

Organized by APCA - Portuguese Association of Automatic Control
(IFAC National Member Organization) and supported by Universidade do Minho

The Portuguese Association of Automatic Control (APCA) invites
researchers, professionals, students, industrialists and businessmen
to participate in the CONTROLO'2000: 4th PORTUGUESE CONFERENCE
ON AUTOMATIC CONTROL, which will be held at the Campus of
Azur=E9m of the University of Minho, in the town of Guimar=E3es.
The conference is intended as an international forum where an
effective exchange of knowledge and experience amongst researchers
active in various theoretical and applied areas of systems and control
can take place. This is also an excellent opportunity to promote the
Portuguese control community and stimulate the establishment of
new international links.
The program will include an ample space for promoting the
implementation of new technologies, emphasizing simultaneously the
real-world challenges in their applications.
The program includes a "Student Forum on Automatic Control", a
mean to atract young students to the area of control.

The working language of the conference is English.

February 14, 2000:
Submission of full papers and proposals of special sessions

April 15, 2000:
Notification of acceptance

June 30, 2000:
Final version of the papers accepted and pre-registration

An online pre-registration form is availabe at the internet

C. Couto (Chairman) (Dep. Industrial Electronics)
E. Bicho (Dep. Industrial Electronics)
E. Ferreira (Dep. Biological Eng.)
J. Ferreira da Silva (Dep. Mechanical Eng.)
J. Martins (Dep. Industrial Electronics)
J. Monteiro (Dep. Industrial Electronics)
F. Soares (Dep. Industrial Electronics)
F. Ribeiro (Dep. Industrial Electronics)

CONTROLO'2000 (c/o Filomena Soares)
Departamento de Electr=F3nica Industrial
Universidade do Minho
Campus de Azur=E9m
4800-058 Guimar=E3es PORTUGAL

Phone: 351-253- 510190 Fax: 351-253-510189


From: Stanly Steinberg <>
Date: Tue, 12 Oct 1999 23:00:02 -0600
Subject: Pan-American Workshop in Applied and Computational Mathematics

C. Bailey and I invite you to participate in the III Pan-American Workshop in
Applied and Computational Mathematics to be held December 12-17, 1999 in
Santiago, Chile ( and
particularly in the mini-workshop we are organizing:

Modelling the Response of Materials in Manufacturing Processes
Chris Bailey
Stanly Steinberg

A wide range of industrial processes are governed by complex sets of physics
such as fluid flow, heat transfer with solidification, electromagnetics, solid
deformation, etc. Materials used within the process may also be inhomogeneous.

Predicting such phenomena provides a number of challenges for the modelling
community.This mini-workshop will focus on the modeling techniques used to
simulate manufacturing processes that may involve distinct or interacting
physics. Appropriate discretization methods for such modelling will also be

The organizers will organize a special issue of Journal of Applied
Mathematical Modelling based on the papers presented in this mini-workshop.

for a list of all mini-workshops.

Stan Steinberg


From: Nick Trefethen <>
Date: Sun, 17 Oct 1999 15:35:13 +0100 (BST)
Subject: Faculty Position at Oxford

NA-Net friends,

I would like to draw your attention to a permanent lecturership being
advertised at Oxford University. The successful candidate will join
a leading Numerical Analysis group of about forty academics, post-docs,
D. Phil. students, and support staff. Promotions to Reader or Professor
are possible after appointment. Among our permanent academic staff
are myself, Mike Giles, Endre Suli, and Andy Wathen.

Nick Trefethen


Applications are invited for this post, tenable from 1 October 2000, from
candidates with research interests in any branch of numerical analysis
or scientific computing, including numerical optimization. University
salary according to age on the scale 17,238 to 32,095 per annum. The
successful candidate may be offered an applied mathematics tutorial
fellowship by Pembroke College, in which case the combined university
and college salary would be according to age on a scale up to 38,412 per
annum. Additional college allowances may be available. Further
particulars (containing details of the duties and full range of emoluments
and allowances attaching to both the university and the college posts)
may be obtained from the Director, Oxford University Computing Laboratory,
Wolfson Building, Parks Road, Oxford OX1 3QD, UK (telephone Oxford +44
1865 273840; fax +44 1865 273839; e-mail
The closing date is Friday 10 December 1999.


From: Francois Vanderbeck <>
Date: Mon, 11 Oct 1999 19:03:49 +0200 (MET DST)
Subject: Faculty Position at University of Bordeaux

A post (Maitre de Conference) in Operations Research (OR) is to be
offered at the University of Bordeaux 1, France, sarting September 1,
2000. The successful candidate will be attached to the
Applied Math Laboratory to reinforce the OR team. Indeed, the lab is
willing to expand its competence in OR subjects and their applications.

The ideal candidate should have a solid background in OR and a proved
track record in research in one (or more) of the following topics:
- Probability and stochastic Programming
- Linear and Non-Linear Programming
- Combinatorial Optimisation, Network Flows, and Graph
Theory. The candidate will be expected to promote research in OR in
the department and to join the research group in OR (seminars, etc).

The teaching attached to this post is mainly in the M-Phil
degree in Stochastic Models and Operations Research and in the master
degree in Mathematical Engineering. Moreover, the successful candidate
will be called upon to supervise student placement in industry and
research projects. The candidate is required to be fluent in French.

IMPORTANT: To apply, candidates must be qualified as "Maitre de
Conference" (cfr In order to get this
qualification in due time, candidates must submit their application
NOW (opening date is 12 Oct 1999, closing date is 10 Nov 1999). They
should be consulted to provided further information by 31 Jan 2000. It
is therefore required to have defended their Phd thesis successfully
by 31 Jan 2000.

Interested candidates are invited to contact Paul Morel or
Francois Vanderbeck from whom any complementary information
can be requested:
MAB (Mathematiques Appliquees Bordeaux)
Universite Bordeaux 1
351, Cours de la Liberation
33405 Talence Cedex, FRANCE
Phone: +(33/0) 5 56 84 61 07
Fax: +(33/0) 5 56 84 26 26


From: Kelly Black <>
Date: Mon, 11 Oct 1999 17:38:34 -0400
Subject: Faculty Position at University of New Hampshire

University of New Hampshire
Department of Mathematics
Durham, NH 03824
Tenure-Track Faculty Position

Position Description:

The Department of Mathematics of the University of New Hampshire
invites applications for at least one tenure track position in applied
mathematics with a possibility of a second appointment pending college
approval. Preference will be given to candidates whose interests are
aligned with existing strengths in the applied mathematics program.
The current strengths in the applied mathematics program include but
are not limited to the areas of non-linear dynamics, time-series
analysis, computational fluid dynamics, and numerical analysis.

Candidates are expected to have a Ph.D. in Mathematics by August 2000
and demonstrated research ability. Strong commitment to teaching is
expected. The position will begin in the fall semester of 2000. Review
of applications will begin on January 1, 2000, and there is a strong
internal candidate for one of the positions. All applications will be
considered until the position is filled.

Please submit resume, e-mail address if possible, and three letters of
recommendation to:
Kenneth Appel
Chair, Department of Mathematics
University of New Hampshire
Durham, NH 03824.

UNH is committed to excellence through diversity of its faculty
and strongly encourages women and minorities to apply.


From: Michael Trosset <trosset@MATH.WM.EDU>
Date: Tue, 12 Oct 1999 14:16:11 -0400 (EDT)
Subject: Faculty Positions at William & Mary

Two tenure-track assistant professor positions beginning August 2000.
Demonstrated excellence in scholarship and teaching, and a Ph.D., are
required. We seek strong applicants in all parts of mathematics and for
one of the positions we especially welcome applicants in applied or
computational mathematics, including statistics. Candidates likely to
interact with Departmental colleagues are preferred (
Competitive compensation and start-up packages are designed to attract the
strongest candidates. Visiting positions may also be available.

Submit application letter, AMS Standard Cover Sheet, CV, research
description, and three or more recommendation letters (at least one
concerning teaching) to:

Search Committee
Mathematics Department
P.O. Box 8795
College of William & Mary
Williamsburg, VA 23187-8795

Review begins December 17 and continues until appointments are made.

The College is an EEO/AA employer.


From: Russ Merris <>
Date: Tue, 12 Oct 1999 12:24:29 PSD8PDT
Subject: Faculty Positions at Cal State, Hayward

Department of Mathematics and Computer Science

The Department invites applications for a tenure-track position in
applied mathematics. The appointment, effective Fall 2000, is at the
Assistant Professor rank. The candidate will be expected to teach
undergraduate courses in mathematical modeling leading to projects
suitable for undergraduate modeling competitions. In addition,
responsibilities include teaching a variety of mathematics courses,
ranging from service courses to graduate-level courses, with classes
meeting both day and evening. Beyond a commitment to excellent
teaching, candidates should exhibit the potential for significant
professional activities, including research and publication, and for
leadership in curricular development. For full details of our
programs and of the position offered, see
e-mail inquiries: Send resume and
arrange to have three letters of reference sent to Math Search
Committee, Dept. of Math/CS, Cal State University, Hayward, CA
94542-3092. Refer to position #00-01 MCS-APPLIEDMATH-TT. Review of
applications will begin January 1, 2000. CSUH, situated in the hills
overlooking the San Francisco Bay, is an EOE, committed to its mission
of "Educational excellence for a diverse society".


From: David Keyes <>
Date: Sun, 17 Oct 1999 03:34:58 -0400 (EDT)
Subject: Faculty and Graduate Positions at Old Dominion University

Faculty positions, a post-doctoral research position, and several doctoral
fellowships are available in a growing group of computational scientists
in the Department of Mathematics & Statistics and the Department of
Computer Science at Old Dominion University. The departments have strong
ties to the Institute for Computer Applications in Science and Engineering
(ICASE) at the NASA Langley Research Center and the biostatistics research
group at the Eastern Virginia Medical School, as well as growing ties to
DOE's nearby Thomas Jefferson National Accelerator Facility (TJNAF). The
university hosts a DOE ASCI "Level II" center and a Department of
Education "Graduate Assistantships in Areas of National Need" (GAANN)
program. The university's computing resources include a 32-processor Sun
Starfire cluster, SGI Origin and Onyx machines, and a CAVE. A 64-processor
Beowulf is available at ICASE.

Two of the faculty positions are new assistant professorships in
Mathematics & Statistics, created under a university-wide Computational
Science Initiative, and are available in July 2000, with interviewing to
begin in January. See for details.

The postdoctoral position is in either department, is available
immediately, and renewable for a second year. See for details. Its previous holder, Linda
Stals, recently assumed an assistant professorship on the ODU CS faculty.

The graduate fellowships, with attractive research allowances, are in
Computer Science, and are available January 2000 or August 2000. See for details. Two recent holders have
assumed positions at Lawrence Livermore and Argonne National Labs.

An announcement for an Assistant or Associate Professorship in Computer
Science is pending administrative approval. See unofficial wording at


From: Manuel Salas <>
Date: Fri, 15 Oct 1999 12:36:54 -0400
Subject: Research Position at ICASE

ICASE research position in Applied & Numerical Math

The Institute for Computer Applications in Science
and Engineering (ICASE) is seeking a highly qualified
Ph.D. scientist to conduct scientific research
relating to numerical analysis of nontraditional
(non-PDE based), nondeterministic, stochastic, and/or
meshless algorithms with application to large-scale
compressible flow simulations. A strong background in
at least two of the following areas will be considered
critical to fulfilling job requirements: applied
mathematics, fluid mechanics, computer science. Selected
candidates will be offered appointments as ICASE Staff
Scientists to pursue independent research in
collaboration with scientists at NASA Langley Research
Center, and will have access to NASA computing facilities
and ICASE resources. This solicitation is aimed at all
levels from post-doctoral to senior scientists.
Appointments are expected to be for two years with a
possible third-year extension, exact start dates are
negotiable. Compensation will be commensurate with
experience and qualification. U.S. citizens or permanent
resident aliens are preferred, but foreign nationals are not
excluded. Applications from women and minorities are encouraged.

ICASE is an institute located at NASA Langley Research Center
conducting unclassified basic research in applied and numerical
mathematics, applied computer science and parallel computing,
fluid mechanics, material sciences, structural dynamics, and
multidisciplinary optimization. The Institute serves as Langley's
gateway to a large pool of prominent scientists from major
universities. Additional information about ICASE and its
research programs is available via the World Wide Web at

NASA Langley Research Center has been instrumental in shaping
aerospace history for more than eight decades. Established in
1917 as the first national civil aeronautics laboratory, NASA
Langley has become a world-class center for aeronautics, earth
science, space technology and structures and materials research.

To apply send a current vita and contact information for three
professional references to:

3 West Reid Street
Hampton VA 23681-2199

or by e-mail to:

ICASE is a nonprofit equal opportunity employer.


From: Chris Ding <>
Date: Mon, 11 Oct 1999 16:48:37 -0700 (PDT)
Subject: Postdoctoral Position at NERSC/LBL

Postdoctoral Fellow at NERSC/LBL

Computational Science Postdoctoral Fellow

The National Energy Research Scientific Computing (NERSC) Division
at Lawrence Berkeley National Laboratory
is seeking a Postdoctoral Fellow to develop and implement
climate and earth sciences applications on highly parallel
high performance computers. This is a one-year appointment
with a salary range of $4500-$4920/Month with the possibility of renewal.
NERSC is on the hills of UC Berkeley campus and has a strong
inter-desciplinary computational sciences research program.

The successful candidate should have strong background in
computing or computational science. Applicants with Ph.D.
in atmospheric/earth sciences, physics, mathematics or
related disciplines are preferred.

For more information, see
Send application/inquiry to employment@LBL.GOV.
Refer to Job NE/11088/CJO in the subject of your message.


From: Marcin Paprzycki <>
Date: Thu, 14 Oct 1999 01:45:12 -0500 (CDT)
Subject: Graduate Assistantships at University of Southern Mississippi

Graduate Assistantships Available

Ph.D. Program in Scientific Computing
University of Southern Mississippi

Applications are invited to the Ph.D. Program in Scientific Computing at
the University of Southern Mississippi (Starting date January 10th,
2000). Applicants must have an MS (or equivalent) degree with grades
significantly above average. GRE results (and for international students
TOEFL results) required for admission. Interdisciplinary Ph.D. program is
jointly run by faculty members from Computer science and Statistics,
Mathematics and Physics Departments. Financial support available. At
least one of Graduate Assistantships will be involved in work in the
newly formed Trent Lott Center for Visualization (located at the Stennis
Space Center).

For more info, please immediately contact:

Marcin Paprzycki, Interim Coordinator
Scientific Computing Ph.D. Program


From: George Anastassiou <>
Date: Mon, 11 Oct 1999 16:31:15 -600
Subject: Contents, Journal of Computational Analysis and Applications

Table of Contents Journal of Computational Analysis and Applications

Vol.1,No.4,October 1999

1) Sturm-Liouville Problems with Coupled Boundary Conditions and
Lagrange Interpolation Series 319
W.N.Everitt and G.Nasri-Roudsari

2) Multivariate Geometric Stable Laws 349
T.J.Kozubowski and S.T.Rachev


From: "SibJNM" <>
Date: Thu, 14 Oct 1999 11:56:08 +0600
Subject: Contents, Siberian Journal of Numerical Mathematics

CONTENTS, Siberian Journal of Numerical Mathematics
Volume 2, No. 4 1999

For information to contributors and about subscriptions

Andreev A.B., Todorov T.D.
Lumped mass approximation for an isoparametric finite element
eigenvalue problem
(in English), pp. 295-308

Bagaev B.M., Roos H.-G.
The finite element method on adapted meshes for the two-dimensional
convection diffusion problem
(in Russian), pp. 309-320

Voevodin A.F., Yushkova T.V.
Numerical solution to initial value problems for the Navier--Stokes
equations in closed regions based on splitting method
(in Russian), pp. 321-332

Kel'manov A.V., Khamidullin S.A.
Optimal detection of given number of identcal subsequences in
quasiperiodic sequence
(in Russian), pp. 333-349

Kolobov B.P., Molorodov Yu.I.
{Calculation of the optimal collocation points for solving
parabolic equations using high precision schemes
(in Russian), pp. 351-360

Laevsky Yu.M., Matsokin A.M.
Decomposition methods for the solution to elliptic and parabolic
boundary value problems
(in Russian), pp. 361-372

Paasonen V.I.
The improved boundary conditions at the singular points of coordinate
systems for non-stationary boundary value problems
(in Russian), pp. 373-384

Smelov V.V.
On representation of piecewise-smooth functions by rapidly convergent
trigonometric series
(in Russian), pp. 385-394


End of NA Digest