## NA Digest Sunday, July 20, 2003 Volume 03 : Issue 29

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

### Submissions for NA Digest:

Mail to na.digest@na-net.ornl.gov.

Information via e-mail about NA-NET: Mail to na.help@na-net.ornl.gov.

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

From: Harvey Greenberg <hgreenbe@math.cudenver.edu>
Date: Wed, 16 Jul 2003 08:39:51 -0600 (MDT)
Subject: SVD Update

I have the SVD of matrix M, and I want the SVD of [M v] -- ie,
append a column (v) to M. Can I use the SVD of M for a fast
update?

Thanks,
Harvey Greenberg
Mathematics Dept

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

From: Charles Wampler <charles.w.wampler@gm.com>
Date: Wed, 16 Jul 2003 15:12:02 -0400
Subject: Solution of Singular Eigenvalue Problem

In V.03, # 26, (24 June 2003), I made the following inquiry to NA Digest:

> We have NxN matrices A,B,C,D with known entries. We wish to find the
> eigenvalues x and eigenvectors v that satisfy
> lim_{q->0} [ A + qB + x(C + qD)] v = 0.
> If A and C are general, then this is just a generalized eigenvalue problem
> with q=0. In the case at hand, the eigenvalue problem is singular at q=0,
> because A and C have a common null space. However, for general q, the
> problem is nonsingular, so the limit values must exist.
>
> I would appreciate any ideas on how to solve this problem in a stable and
> efficient manner, by say, converting it to a nonsingular eigenvalue problem.

I received a number of replies, and so I thought it might be of interest to
post the solution. Ming Gu of U.C. Berkeley provided the best hint, which
resulted in the following algorithm.

First, use singular value decomopsition to find the common null space of
A and C. (In Matlab, use [U,S,V]=svd([A;C]);) So V=[M N] is orthogonal,
and A*N=C*N=0. Then, using the change of variable for the eigenvector
to v=[M N]w = M*w1 + N*w2, we have the equivalent nonsingular eigenvector
problem:
( [A*M B*N] + x*[C*M D*N] ) [w1; q*w2] = 0.

Thanks to all those who sent suggestions. Any improvements or alternatives
to this approach would still be welcome.

Charles Wampler
General Motors R&D Center

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

From: Trevor Misfeldt <misfeldt@centerspace.net>
Date: Mon, 14 Jul 2003 16:50:24 -0700
Subject: New Version of NMath Core

CenterSpace Software Launches NMath Core Version 2.0
Corvallis, OR, July 14, 2003 CenterSpace Software, a leading provider of
enterprise class numerical component libraries for the .NET platform, today
announced the release of NMath Core 2.0.

NMath Core is the foundational library in the NMathTM product suite from
CenterSpace Software. NMath Core provides basic building blocks for
numerical applications on the .NET platform, such as vector classes, matrix
classes, complex number classes, random number generators, and other
high-performance functions for object-oriented numerics. Fully compliant
with the Microsoft Common Language Specification, all NMath Core routines
are callable from any .NET language, including C# and Visual Basic.NET.

"In response to customer demand, version 2.0 of NMath Core adds support for
numerical integration and differentiation," stated Steve Sneller, Chief
Scientist. "We provide two of the most widely used, general purpose
families of quadrature methods: Romberg integration, and Gauss-Kronrod
integration. Numerical differentiation employs Ridders' method of
polynomial extrapolation."

In addition to support for numerical integration and differentiation, NMath
Core 2.0 offers classes for encapsulating and manipulating functions,
including function evaluation and composition, and algebraic manipulation
of functions. A specialized Polynomial class supports polynomial
interpolation, and exact integration and differentiation of polynomials.

NMath Core 2.0 is available immediately from CenterSpace Software. For
customers with current support contracts, NMath Core 2.0 is available as a
free upgrade. A free 14-day evaluation version is also available for
<http://www.centerspace.net>http://www.centerspace.net, along with complete
user documentation, performance benchmarks, a whitepaper, and code examples.

CenterSpace Software is a leading provider of enterprise class numerical
component libraries for the .NET platform. Developers worldwide use
CenterSpace products to develop .NET mathematical, financial, engineering,
and scientific applications. CenterSpace Software has offices in Corvallis,
OR, and can be found on the Internet at
<http://www.centerspace.net>http://www.centerspace.net.

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

From: Daniel Stewart <daniel.stewart@oup.com>
Date: Fri, 18 Jul 2003 13:49:05 +0100
Subject: New Book on Compressible Flow

Mathematical and Computational Methods for Compressible Flow

Miloslav Feistauer, Faculty of Mathematics and Physics, Charles University,
Prague, Czech Republic, Jiri Felcman, Faculty of Mathematics and Physics,
Charles University, Prague, Czech Republic, and Ivan Straskraba,
Mathematical Institute, Academy of Sciences of Czech Republic, Prague, Czech
Republic.

This book is concerned with mathematical and numerical methods for
compressible flow. It aims to provide the reader with a sufficiently
detailed and extensive, mathematically precise, but comprehensible guide,
through a wide spectrum of mathematical and computational methods used in
Computational Fluid Dynamics (CFD) for the numerical simulation of
compressible flow.

Up-to-date techniques applied in the numerical solution of inviscid as well
as viscous compressible flow on unstructured meshes are explained, thus
allowing the simulation of complex three-dimensional technically relevant
problems. Among some of the methods addressed are finite volume methods
using approximate Riemann solvers, finite element techniques, such as the
streamline diffusion and the discontinuous Galerkin methods, and combined
finite volume - finite element schemes. The book gives a complex insight
into the numerics of compressible flow, covering the development of
numerical schemes and their theoretical mathematical analysis, their
verification on test problems and use in solving practical engineering
problems.

The book will be helpful to specialists coming into contact with CFD - pure
and applied mathematicians, aerodynamists, engineers, physicists and natural
and postgraduate students of mathematics and technical sciences.

* Useful as a textbook for students in pure and applied mathematics and
technical sciences
* Excellent handbook for specialists
* Contains recent developments in numerical treatment of compressible fluid flow
* Good reference guide for solving applied problems
* Informs a wide audience

Contents: Fundamental concepts and equations; Some mathematical concepts and
notation; Governing equations and relations of gas dynamics; Some advanced
mathematical concepts and results; Survey of concepts and results from
functional analysis; Basic facts from the theory of the Euler and
Navier-Stokes equations; Hyperbolic systems and the Euler equations;
Existence of smooth solutions; Weak solutions; Nonstationary Navier-Stokes
equations of compressible flow; Existence results for stationary
compressible Navier-Stokes equations; Finite difference and finite volume
methods for non-linear hyperbolic systems and the Euler equations; Further
properties of the Euler equations; Numerical methods for hyperbolic systems
with one space variable; The finite volume method for the multidimensional
Euler equations; Osher-Solomon scheme; Higher order finite volume schemes;
Adaptive methods; Examples of finite volume simulations; Finite element
solution of compressible flow; Finite element method - elementary treatment;
Finite element solution of viscous barotropic flow; Finite element solution
of a heat conductive gas flow; Combined finite volume - finite element
method for viscous compressible flow; Theory of the combined FV-FE method;
Discontinuous Galerkin finite element method.

0-19-850588-4 | 550 pages, numerous figures and halftones
August 2003 | Hardback =A359.95

Numerical Mathematics and Scientific Computation
Series Editors G. H. Golub, Ch. Schwab, W. A. Light, E. S=FCli

<http://www.oup.co.uk/isbn/0-19-850588-4> 0588-4

Telephone orders:
UK & Europe: +44 1536 741519
USA: +1-800-445-9714

Email orders:
UK & Europe: <mailto:book.orders@oup.co.uk> book.orders@oup.co.uk
USA: <mailto:customers@oup-usa.org> customers@oup-usa.org

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

From: Larry Schumaker <s@mars.cas.vanderbilt.edu>
Date: Mon, 14 Jul 2003 12:34:28 -0500 (CDT)
Subject: Proceedings of Conference on Curves and Surfaces

The proceedings of the "Fifth International Conference on Curves
and Surfaces" held June 27 -- July 3, 2002 have just been
proceedings consists of two volumes:

1) Curve and Surface Design: Saint-Malo 2002
Tom Lyche, Marie-Laurence Mazure, and Larry L. Schumaker (eds.)
ISBN 0-9728482-0-7

2) Curve and Surface Fitting: Saint-Malo 2002
Albert Cohen, Jean-Louis Merrien, and Larry L. Schumaker (eds.)
ISBN 0-9728482-1-5

The books can be ordered from the publisher's web site at
www.nashboro.com.

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

From: Shaun Forth <S.A.Forth@rmcs.cranfield.ac.uk>
Date: Tue, 15 Jul 2003 11:15:20 +0100
Subject: Slides for Workshop at Cranfield University

Cranfield University (Shrivenham Campus)

PDF files of all slides from the above EPSRC sponsored meeting may be
found at

http://www-svr3.dmz.rmcs.cranfield.ac.uk/amor/workshop/jun03/

The meeting was the most successful to date with over 30 attendees from
the UK, Europe, USA and Japan. On behalf of the chair, Prof. Bruce
Christianson (Univ. of Hertfordshire) and myself can I thank all
speakers and attendees for their valued contributions to this event.
The next meeting will be held at the University of Hertfordshire in
November 2003 (date to be finalised).

Dr Shaun Forth
Applied Mathematics & Operational Research
Engineering Systems Department
Cranfield University, Shrivenham Campus
Swindon SN6 8LA, England
tel: +44 (0)1793 785311
fax: +44 (0)1793 784196
email: S.A.Forth@rmcs.cranfield.ac.uk

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

From: Erricos Kontoghiorghes <erricos.kontoghiorghes@unine.ch>
Date: Mon, 14 Jul 2003 20:04:19 +0200
Subject: Special Issue on Statistical Signal Extraction and Filtering

Computational Statistics and Data Analysis, Special Issue on
STATISTICAL SIGNAL EXTRACTION AND FILTERING
http://www.elsevier.com/locate/csda

The need to extract signals and other components from time series is a
requirement in many empirical sciences, including Medicine,
Engineering, Economics and Climatology, to name but a few. Nowadays, a
wide variety of methods are available, including Wiener--Kolmogorov
Filtering, Kalman Filtering, Principal Components Analysis, and
Wavelet Analysis. Some of the methods have been conceived in the time
domain and others have originated in the frequency domain. A few of
the methods may be interpreted equally in both domains. The majority
demand skilful use of the computer for their successful
implementation.

Give the variety of the available methods of Statistical Signal
Extraction and Filtering, and given the diversity of the subject areas
in which they are applied, there are plentiful opportunities for cross
fertilisation and technology transfer. We therefore invite submissions
for a special issue of Computational Statistics & Data Analysis
devoted this topic. We will consider papers addressing the use of
computational and numerical methods for solving theoretical and
practical issues associated with filtering and signal extraction
algorithms, the impact of the techniques on the relevant subject
areas, and specific applications involving computing and data
analysis.

The papers submitted to the special issue should contain both
computational and substantive (i.e. subject area) components. Authors
who are uncertain of the suitability of their papers for the special
issue should contact the special issue editors. All papers submitted
must contain original unpublished work that is not being submitted for
publication elsewhere. Manuscripts submitted to this special issue
will be refereed according to standard procedures for Computational
Statistics and Data Analysis. The journal is also interested in
receiving submissions in the broader areas of time-series analysis,
which might be considered for inclusion in the special issue or in
regular issues. Information about the journal can be found at
http://www.elsevier.com/locate/csda

The DEADLINE for submissions is January 31, 2004.

The editorial process is expected to proceed rapidly thereafter
Submission electronically is encouraged. Please e-mail a postscript
or PDF file of your manuscript to one of the special issue editors:

Stephen Pollock
Department of Economics
Queen Mary College
University of London
London E1 4NS
U.K.
Email: stephen_pollock@sigmapi.u-net.com

Peter C. Young,
Environmental Science
Lancaster University
Lancaster LA1 4YF
U.K.
Email P.Young@lancaster.ac.uk

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

From: Christophe Jermann <Christophe.Jermann@epfl.ch>
Date: Mon, 14 Jul 2003 18:16:20 +0200
Subject: Workshop in Lausanne on Global Constrained Optimization

3rd Call for Papers
and
1st Call for Participation

COCOS 2003
Second International Workshop on
Global Constrained Optimization and Constraint Satisfaction

Olympic Museum
Lausanne, Switzerland
November 18th-21st, 2003

http://liawww.epfl.ch/cocos03

* 31st Aug 2003 - Submission deadline
* 20th Sep 2003 - Notification of acceptance
* 20th Oct 2003 - Final camera-ready copies
* 18-21 Nov 2003 - Workshop

OBJECTIVES

Continuous constraints are a natural way to represent
many practical problems and the knowledge they involve.
Such constraints may be simple or complex, linear or
non-linear and may, or may not, involve transcendental
functions. They are widely used to express, for example,
chemical or mechanical models, process descriptions,
building codes or cost restrictions. Many industrial
problems involving continuous constraints can be modeled
as continuous constraint satisfaction and optimization
problems (CSOPs). In practice, such models are often large
in size and non-linear.

As the preceding workshop, this workshop focuses on
complete solving techniques for continuous CSOPs that
provide all solutions with full rigor. Less rigorous solution
techniques are not excluded, since they may be part of
complete relevant techniques. Complete solution techniques
guarantee that all the constraints - e.g. security or
tolerance criteria - are satisfied and the global optima
identified. Completeness would thus benefit directly the
quality and reliability of decisions or analyses based on
the provided solutions. This has obvious implications in
many industrial and economic areas.

None of the existing approaches for solving non-linear
CSOPs is fully satisfactory in practice. Non-linear
programming techniques are routinely used and can solve
large-scale non-linear problems. However, they are
complete only in the convex case and if round off errors
are controlled. In contrast, constraint programming solvers
preserve completeness, but suffer from poor scalability.

The respective strengths of mathematical and constraint
programming appear however to be highly complementary and a
number of recent developments showed that there is a lot to
be gained by merging the different inference techniques they
provide and by combining their specific advantages.

The goal of this workshop is to bring together communities
from global optimization, mathematical programming and
constraint programming, giving the opportunity to promote
presentation and discussion of ongoing work on solving
techniques for continuous CSOPs. The workshop aims at
encouraging cross-fertilization between the various
approaches, including the study of adapted cooperation
strategies between mathematical and constraint programming,
and of new representations and abstractions for which they
can efficiently interact.

TOPICS
------
Relevant topics include, but are by no means restricted
to the following:

* Solution techniques for global optimization problems
* Integration of constraint programming with non-linear
programming techniques
* Linear and nonlinear convex enclosures of nonlinear programs
* Semidefinite programming techniques for global optimization
* Improved consistency techniques for continuous constraints
* Combination of symbolic methods with mathematical and
constraint programming techniques
* Solution techniques for under-constrained systems
* Adaptation of sparse matrix techniques to the non-linear case
* Representation and exploitation of monotonicity and
convexity properties
* Abstractions based on convex decomposition
* Partial boundary representation based on critical points
and topological abstractions

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

From: Roderick Melnik <rmelnik@mci.sdu.dk>
Date: Mon, 14 Jul 2003 19:56:47 +0200
Subject: Workshop in Denmark on Mathematics for Industry

The 47th European Study Group with Industry and
The Mathematics for Industry Workshop,
Denmark, August 24--29, 2003

The 47th ESGI and its embedded Mathematics for Industry Workshop will
take place in Denmark and will be hosted by the University of Southern
Denmark in the picturesque Soenderborg/Graasten area. Five projects will
be presented by some of the leading industrial companies and the event
will feature the Mathematics for Industry workshop with lectures given by
Professor H. Thomas Banks (North Carolina State University),
Professor Martin Brokate (Technical University of Munich),
Professor Mark Cross (University of Greenwich).

If you are a mathematician, an engineer, an industrialist, a research
scientist, or a research student, we invite you to challenge your mind
with real-world problems presented by leading industrial companies at
this one of the premier European industrial and engineering mathematics
problem-solving conferences.

As described at the event web site (http://www.esgi47.sdu.dk), financial
assistance may still be available to some of the potential participants.

(esgi47@mci.sdu.dk), or Professor Roderick Melnik (rmelnik@mci.sdu.dk),
or visit http://www.esgi47.sdu.dk

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

From: Gerd Kunert <gkunert@mathematik.tu-chemnitz.de>
Date: Wed, 16 Jul 2003 12:50:28 +0200
Subject: Chemnitz FEM Symposium

Dear colleagues,
We would like to invite you and your colleagues to the
Chemnitz FEM Symposium 2003
September 22 - 24, 2003.
The conference venue in Ehrenfriedersdorf (near Chemnitz, Germany)
is situated in the beautiful Erzgebirge mountains and provides a
stimulating and cosy atmosphere.

The symposium is organized by the DFG-Sonderforschungsbereich 393
"Numerische Simulation auf massiv parallelen Rechnern"
and the Faculty of Mathematics, TU Chemnitz.

Scientific Topics: Finite Elements, including (but not limited to)
- error estimators,
- high order methods,
- parallel implementations.

This year special emphasis is on
- fast solvers, e.g.
- multi-level methods,
- domain decomposition methods,
- for hp-methods,
- using H-matrices,
- simulation of materials with nonlinear properties,
- deformation,
- damage,
- crack propagation,
- mixed formulations,
- problems with anisotropic solution.

Invited Speakers: M. Dobrowolski (Wuerzburg)
R. Duran (Buenos Aires)
U. Langer (Linz)
M. Melenk (Leipzig)

Special issue: Selected papers will be reviewed and published in an
IMACS journal (APNUM or MATCOM).

Deadlines: August 8, 2003: Submission of abstracts
August 22, 2003: Book accommodation

Registration: via WWW
Information: http://www.tu-chemnitz.de/sfb393/fem-symposium/

Contact: fem03@mathematik.tu-chemnitz.de

The symposium is supported by the Deutsche Forschungsgemeinschaft.

With best regards

Th. Apel, A. Meyer, G. Kunert

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

From: Michael Heroux <maherou@sandia.gov>
Date: Fri, 18 Jul 2003 16:34:08 -0500
Subject: SIAM Parallel Processing Minisymposium

Minisymposia proposals for the SIAM Parallel Processing Conference for
Scientific Computing 2004 are due July 31, 2003. Abstracts for
minisymposium talks, contributed talks and poster sessions are due on August
28th.

Minisymposium Details:

A minisymposium consists of four 25-minute presentations, with an additional
five minutes for discussion after each presentation. Prospective
minisymposium organizers are asked to submit a proposal consisting of a
title, a description (not to exceed 100 words), and a list of speakers and
titles of their presentations.

Conference Details:

The Eleventh SIAM Conference on Parallel Processing for Scientific Computing

Dates: February 25-27, 2004
Location: Hyatt at Fisherman's Wharf, San Francisco, CA

Conference website: http://www.siam.org/meetings/pp04/index.htm

Best regards,

Mike Heroux
Horst Simon

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

From: Daniel Szyld <szyld@euclid.math.temple.edu>
Date: Sat, 19 Jul 2003 08:28:33 -0400
Subject: Faculty Position at Temple University

The Department of Mathematics, in the College of Science and
Technology at Temple University, invites applications for faculty
positions at the level of Full, Associate, or Assistant Professor.

We are seeking mathematicians who will play a prominent role in our
department's research mission and who are committed to excellence in
teaching. Successful candidates will be expected to supervise
Salaries and startup packages for new faculty are highly competitive.

Senior applicants should have a substantial research record; proven
ability to attract significant external funding is expected. More
junior applicants should have a strong, independent research program
and have already demonstrated evidence of outstanding potential.

To apply, send a CV, bibliography, brief statement of research
achievements and research plans, and half-page description of teaching
experience and philosophy to:

Edward S. Letzter
Search Committee Chair
Department of Mathematics
Wachman Hall 038-16
Temple University

Also arrange to have at least three letters of reference sent
specialization and the corresponding AMS subject classification

Alternatively, we welcome electronic applications at
http://www.mathjobs.org.

consideration. Applications received after this date will be
considered if positions are still open.

Temple University is an Equal Opportunity/Affirmative Action
employer. Applications are strongly encouraged from individuals in
groups under-represented in the mathematical sciences.

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

From: Robert Schaback <schaback@math.uni-goettingen.de>
Date: Mon, 14 Jul 2003 15:00:31 +0200
Subject: Faculty Position in Gottingen

The Institute for Numerical and Applied Mathematics
(http://www.num.math.uni-goettingen.de) of Georg-August-Universit=E4t
G=F6ttingen (http://www.uni-math.gwdg.de) is seeking applicants for the
position of a tenured

PROFESSORSHIP IN OPTIMIZATION TECHNIQUES WITHIN SCIENTIFIC COMPUTING
(W2/C3)

starting Oct. 1st, 2003. Applicants are expected to have a specific
expertise in one of the current application areas, e.g. within optimal
process control or discrete optimization. In addition, the applicant
should share the standard teaching and

Cooperation with industry is encouraged.

The University of G=F6ttingen is aiming to increase the share of female
faculty members. Thus qualified women are especially encouraged to
apply. Disabled candidates will be given preference in the case of equal
qualifications.

Applications with CV, list of publications and teaching- and research
resume should be sent by September 15, 2003 to

Dekanin der Mathematischen Fakult=E4t
Bunsenstr. 3-5
D-37073 G=F6ttingen
Germany

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

From: D. D. Lewis <ddlewis4@worldnet.att.net>
Date: Sun, 13 Jul 2003 16:44:25 -0500
Subject: Research Position at Ornarose, Inc.

Company: Ornarose Inc.

Location: Northern New Jersey or Chicago, IL

Title: Research Software Developer - Data
Mining/Statistics/Text Classification

Requirements:

B.S., M.S., or Ph.D. in computer science, statistics,
applied mathematics, or related field.

5+ years professional software development experience.

2+ years experience in professional environment with
one or more of the following: machine learning, data mining,
statistics, pattern recognition, numerical optimization,
numerical analysis.

Experience with designing and running computational
experiments in computer science or statistics highly
desirable. Also desirable is experience in information
retrieval, text categorization, natural language processing,
computational linguistics, or text mining.

C and Perl proficiency required. C++ proficiency is
desirable.

Unix/Linux experience required. Windows experience
desirable.

Excellent verbal and written communication skills in
English.

Demonstrated ability to meet deadlines and communicate
effectively when working from home.

Responsibilities:

This is a short-term (5 to 6 month) position for an
SBIR-supported startup company. Developer will be
responsible for design, implementation, and testing of
advanced algorithms for supervised and unsupervised
learning, prediction, classification, etc. Work also
includes preparation and cleaning of large text and non-text
data sets, experimentation with new algorithms and modeling
techniques, and measuring the effectiveness of these
techniques and their demands for computing resources.

Interested parties should send a resume (leads also
welcome) in ASCII or PDF to job2003a@ornarose.com.

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

Date: Tue, 15 Jul 2003 10:50:04 +0200
Subject: Contents, CALCOLO

CALCOLO Volume 40 Issue 2
or

Daniele Bertaccini, Michael K. Ng:
Block {<omega>}-circulant preconditioners for the systems of differential
equations
CALCOLO 40 (2003) 2, 71-90;

Istvan Farago, Mihaly Kovacs:
On maximum norm contractivity of second order damped single step methods
CALCOLO 40 (2003) 2, 91-108;

M. Frontini:
Hermite interpolation and a new iterative method
for the computation of the roots of non-linear equations
CALCOLO 40 (2003) 2, 109-119;

V. Havu:
An analysis of asymptotic consistency error in a parameter dependent model
problem
CALCOLO 40 (2003) 2, 121-130;

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

From: Science Direct <sciencedirect@prod.lexis-nexis.com>
Date: Sat, 19 Jul 2003 06:24:16 -0400 (EDT)
Subject: Contents, Nonlinear Analysis

Nonlinear Analysis Volume 54, Issue 7, Pages 1205-1353 (September 2003)

Mountain pass solutions to equations of p-Laplacian type, Pages 1205-1219
Pablo De Napoli and Maria Cristina Mariani

On minimization problems which approximate Hardy Lp inequality,
Pages 1221-1240

Aspects of the behaviour of solutions of nonlinear Abel equations,
Pages 1241-1249
M. R. Arias and R. Benitez

Integrability of subdifferentials of certain bivariate functions,
Pages 1251-1269

A pointwise oscillation property of semilinear wave equations with
time-dependent coefficients, Pages 1271-1283
Hiroshi Uesaka

On the existence of periodic solutions for neutral functional differential
equation, Pages 1285-1306
Shiping Lu and Weigao Ge

Spike solutions for a class of singularly perturbed quasilinear elliptic
equations, Pages 1307-1336
Marco Squassina

Regularity properties of constrained set-valued mappings, Pages 1337-1353
Marco Papi and Simone Sbaraglia

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

End of NA Digest

**************************
-------