LEA
44A Sinopis Street
Ampelokipi
Athens 115 27, Hellas
Hellenic European Research on
Mathematics and Informatics Science
(H E R M I S - μ π)
HERMIS: The International Journal of
Computer Mathematics and its Applications
Elias A. Lipitakis, Editor-in-Chief.
ISBN: 1108- 7609
Copyright © 2006, LEA. All rights reserved.
No part of this publication may be reproduced, stored in information retrieval system
or transmitted in any form or by any means, electronic, recording or otherwise,
without the prior written permission of the Publisher, LEA, 44A Sinopis Street,
Ampelokipi, Athens 115 27, Hellas.
No responsibility is assumed by the Publisher for any injury and /or damage of any
kind to persons or property as a matter of products liability, negligence or otherwise,
or from any use or operation of any methods, products, instructions or ideas contained
in the material herein. The text has been reproduced from camera-ready copies
supplied by the Authors.
Printed in Hellas
Cover Designer: Hector Haralambous
Production Supervisor: Aris Symeon
Editorial Technical Assistant: Alexandra Lipitakis
I
EDITORIAL
The main purpose of the Hellenic European Research on Mathematics and
Informatics Science (HERMIS-μπ) Journal is to present original research work of the
highest quality and characteristic representative samples of the current trends in
various directions of research being done in the areas of Computer Mathematics and
its Applications. The topics covered in this issue encompass different aspects of such
subjects.
This special issue of the HERMIS contains two interesting themes of
Computer Mathematics and its Applications, namely (i) Differential and Integral
Equations in Epidemiology, Medicine and Physics: Applications and Numerics (Guest
Editors: Prof. Yang Kuang, Dr. Athena Makroglou and Dr. Anne Skeldon) and (ii)
Actuarial Risk Models:Theory and Computations (Guest Editors: Prof. Claudia
Kluppelberg and Dr. Athena Makroglou). Each theme category contains selected
articles presented in the seventh Hellenic European Research on Computer
Mathematics and its Applications (HERCMA 2005) Conference, which took place on
September 2005 in Athens, Hellas.
The main objective of the biennial HERCMA (Hellenic European Research on
Computer Mathematics & its Applications) Conference series is to create a common
international scientific forum for presentation and discussion of current research
topics of Computer Mathematics, Scientific Computing and Informatics. The
HERCMA Conference series and the HERMIS-μπ Journal are organized and operated
under the auspices of the Advanced Computational Mathematics and Parallel
Processing Research Group of the Athens University of Economics and Business
(AUEB-RG-ACMPP).
The HERMIS-μπ international journal will continue to monitor and report on
current significant research activities in Computer Mathematics and its Applications.
Elias A. Lipitakis
Athens, Hellas
May, 2006
Front Cover: The Greek letters μ and π in the name of the HERMIS- μπ Journal denote
the initials of the Hellenic words "μαθηματικά πληροφορικήs", which correspond to the
term "info-mathematics".
The head of Hermes, ancient Greek God of Commerce, is the emblem of the AUEB since
1920, while 'πυμπε' is the acronym of the Hellenic words 'προηγμένα υπολογιστικά
μαθηματικά και παράλληλη επεξεργασία' [Advanced Computational Mathematics and
Parallel Processing (ACMPP)].
II
AIMS AND SCOPE
The HERMIS-μπ international journal contains original research work of the highest
quality concerning Computer Mathematics and its Applications. The term is usually
referred, in the general sense, to the mathematical and scientific computations,
algorithmic methods and techniques that are used in contemporary computer and
information systems.
Computer Mathematics and its Applications (Μαθηματικά Πληροφορικής) include the
following general categories (main subjects of Informatics): Theory of Computing,
Mathematics of Computing and Methodologies of Computing, as well as their several
hybrid combinations and applications.
The sections of HERMIS journal contain mathematical and computational work that
are of interest to computer users and researchers in the fields of numerical analysis,
discrete mathematics, mathematical software, sparse matrix technology, analysis of
algorithms and complexity, mathematical logic and formal languages, theory and
applications of programming languages, parallel computation and parallel processing,
computational geometry and graphics, image processing and pattern recognition,
simulation and modeling, operational research and statistics, mathematics of
economics and, in general, applied mathematics.
The HERMIS-μπ journal is directed at scientists and researchers in Computer
Mathematics, Scientific Computing, Computer Sciences and Natural Sciences,
engineers and economists who either take part in the development of methods in
Computer Mathematics and Informatics or use such methods in their own research.
CALL FOR PAPERS
Contributions are welcome from all areas of Computer Mathematics and Scientific
Computing, especially topics mentioned explicitly in the above aims and scope. Apart
of original results from the theory and applications of algorithms the HERMIS journal
emphasizes the publication of new Computer Mathematics methods and innovative
software techniques that overcome performance barriers and enhance user
friendliness.
Papers should be submitted to the Editor-in-Chief or the regional Editors, who will
review the papers in close liaison with the members of the editorial board.
SUBMITTED PAPERS
The HERMIS Secretariat is happy to receive articles on floppy disk media or in
electronic form, formatted in TEX. Additionally, hard copy versions must be
submitted in triplicate for refereeing as usual, and must be clear on the submission
letter the form in which the TEX source code is available. Additional details can be
provided on request by writing to the Secretary at the following address:
HERMIS Secretariat
Department of Informatics
Athens University of Economics and Business
76 Patision Street
Athens 104 34, Greece
Phone-Fax: +3-210- 8203 187
III
HERMIS-μπ
Hellenic European Research on Mathematics and Informatics
Science
An International Journal of
Computer Mathematics and its Applications
Editor-in-Chief
Elias A. Lipitakis
Department of Informatics
Athens University of Economics
76 Patision Street
Athens 10434, Greece
Advisory Editorial Board
C.T.H. Baker, Manchester, UK
N. Bakhvalov, Moscow, Russia
R. Beauwens, Brussels, Belgium
V. Capasso, Milan, Italy
P. Deuflhard, Berlin, Germany
D. Dobkin, Princeton, USA
J. Dongarra, Tennessee, USA
H. Engl, Linz, Austria
W. Enright, Toronto, Canada
D. Evans, Nottingham, UK
R. Glowinski, Houston, USA
B. Guo, Shanghai, China
A. Iserles, Cambridge, UK
C. Papadimitriou, Berkeley, USA
R. Piessens, Leuven, Belgium
O. Pironneau, Paris, France
P. Plemmons, Wake-Forest, USA
C. Polychronopoulos, Illinois, USA
A. Sameh, Purdue, USA
V. Thomee, Chalmers, Sweden
H. Van der Vorst, Utrecht, Holland
B. Wegner, Berlin, Germany
L. Xanthis, London, England
M. Yamamoto, Tokyo, Japan
IV
AUEB-RG-ACMPP
The HERMIS-μπ Journal
Instructions to the Authors
The HERMIS-μπ Journal publishes original research papers and short
communications from all the fields of Computer Mathematics and Scientific
Computing in English language. Expository or survey articles may be published in
special cases. Please read and follow the instructions carefully. By doing so you will
ensure that the review and publication of your article will be as rapid and efficient as
possible. The Editors reserve the right to return manuscripts that are not prepared in
accordance with these instructions.
Submission of Manuscripts
Manuscripts should be submitted directly to the Editor or to any of the
regional/ Associate Editors. The Editors will acknowledge receipt of the submitted
paper. Hard copies of the manuscript, conforming with the instruction to the Authors,
as well as figures and tables are requested for formal submission.
Work submitted for publication must be previously unpublished, not under
consideration elsewhere and, id accepted, it should not then submitted for publication
elsewhere in the same form. If previously published figures, tables or parts of text are
to be included, the copyright holders permission must have been obtained prior to the
submission. Submission of a manuscript implies that its publication has been
approved by all co-authors, if any, as well as by the responsible authorities at the
institution where the work has been carried out; that, if and when the manuscript is
accepted for publication the authors agree to automatic transfer of the copyright to the
publishers and that the manuscript will not be published elsewhere in any language
without the written consent of the copyright holders.
All articles published in this Journal are protected by copyright, which covers the
exclusive rights to reproduce and distribute the article, as well as all the translation
rights. No material published in this Journal may be reproduced photographically or
stored on microfilms, in electronic data bases, video disks, or any form of electronic
media etc., without first obtaining written permission from the Publishers.
Preparation of the Manuscripts
Papers must be clearly written in English. An original plus two copies of the
manuscript with accompanying figures and tables should be submitted. The text
should be presented on A4 or equivalent size paper. In general, a contribution should
not exceed 20 pages. An AMS subject classification and suitable keywords and
phrases should be given on the title page. The manuscripts should be preferably
prepared with a text editing system, e.g. LaTex, or with a suitable word processing
system. If typewritten, then must be double spaced on the one side of the paper.
V
Margins of at least 25 mm should be left around all sides of the text. Each page should
be numbered and a short running title on the title page should be provided.
The content of each page should be limited within the following page margin
dimensions: 14cm x 20cm, i.e. page: max height -- 20cm, line: max width-- 14cm.
References and bibliography
The accuracy of the references and bibliography is the author’s responsibility.
Only published articles in the general literature should be cited. The reference list
should appear in alphabetical order. Within the text, references should be cited by
giving the corresponding number in square brackets. References and bibliography
should be arranged in the following form:
(a) Books: name of the author(s), title of book, volume and edition, publishers, place
of publication, year of publication.
(b) Journals: name of the author(s), year (in parentheses), title of the article,
abbreviated title of the journal, volume, pages.
Submission of Tex-based manuscripts
Authors wishing to submit Tex-based manuscripts are encouraged to do so.
Manuscripts should be produced using the LaTex articles style format. The final
version should be supplied on disk containing both .tex and .dvi files. Hard copies of
both the text and any figures should be supplied separately as for conventional
submissions. Authors will receive proofs in the normal way.
Proofs and Reprints
One round of page proofs will be sent to the corresponding author for
checking. To avoid delays in publication, proofs should be checked and returned
immediately be express post or Fax, to the production Editor (HERMIS Secretariat),
Department of Informatics, Athens University of Economics & Business, 76 Patision
Street, Athens 10434, Greece. Fax: +3-210-8203 187. Extensive changes to the text of
the paper may be charged to the author. A free copy of the HERMIS volume will be
sent to the corresponding author following publication of his paper. Extra offprints or
single issues of the Journal may be ordered when the corrected proofs are returned
using the form provided or communicating directly with the HERMIS secretariat.
Subscription Information
Annual subscription rate: EURO 30.00, including carriage charges.
Subscriptions are entered with pre-payment only. This price will cover both the
printed and the electronic versions of the Journal. Orders should be addressed to:
HERMIS Secretariat
Department of Informatics
Athens University of Economics & Business
76 Patision Street
Athens 10434, Greece
Tel./ Fax: +3-210-8203 187
Changes of Address
Allow six weeks for all changes to become effective. All communications
should be include both old and new addresses (with full postal codes) and should be
accompanied by a mailing label from a recent issue.
VI
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GREAT THINKERS, PIONEERS AND RESEARCHERS IN
MATHEMATICS AND COMPUTING SCIENCE
610 B.C. - 100 B.C.
ΘΑΛΗΣ (610), ΠΥΘΑΓΟΡΑΣ (560-480),
ΠΛΑΤΩΝ (472-348)
ΔΗΜΟΚΡΙΤΟΣ (460-370), ΑΡΙΣΤΟΤΕΛΗΣ (384-322),
ΕΥΚΛΕΙΔΗΣ (330-275),
ΑΡΧΙΜΗΔΗΣ (287-212)
100 A.D. - 1600 A.D.
ΗΡΩΝ (100),
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ΕΡΑΤΟΣΘΕΝΗΣ (220),
ΔΙΟΦΑΝΤΟΣ (250), ΠΑΠΠΟΣ (300)
AL KHWARIZMI (800-850), FIBONACCI (1170-1250),
DA VINCI (1452-1519),
TARTAGLIA (1500-1557)
1600 - 1900 A.D.
NAPIER (1550-1617),
KEPLER (1571-1630),
DESCARTES (1596-1650), PASCAL (1623-1662),
FERMAT (1601-1665),
GREGORY (1638-1675),
BERNOULLI (1654-1705), LEIBNIZ (1646-1716),
NEWTON (1642-1727),
TAYLOR (1685-1731),
EULER (1707-1783),
LAGRANGE (1736-1813),
LAPLACE (1749-1822),
CARNOT (1753-1823),
ABEL (1802-1829),
FOURIER (1768-1830),
GALOIS (1811-1832),
LEGENDRE (1752-1833),
POISSON (1781-1840),
BOLZANO (1781-1848),
JACOBI (1804-1851),
BYRON-ADA (1815-1852),
GAUSS (1777-1855),
LOBACHEVSKY(1792-1856),
CAUCHY (1789-1857),
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HAMILTON (1805-1865),
RIEMANN (1826-1866),
BABBAGE (1792-1871),
CHEBYSHEV (1821-1894),
WEIERSTRASS (1815-1897),
1900 - 1950 A.D.
HERMITE (1822-1901),
POINCARE (1854-1912),
CANTOR (1845-1918),
HOLLERITH (1860-1929),
HILBERT (1862-1943),
CARATHEODORI (1873-1950),
TURING (1912-1954),
EINSTEIN (1879-1955),
VON NEUMANN (1903-1957) WIENER (1894-1964),
VII
RUSSEL (1872-1970),
GODEL (1906-1978),
VIII