Volume 5, Number 6
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- November 15, 1998 -
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- O P - S F N E T Volume 5, Number 6 -
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- Editors: -
- Tom H. Koornwinder thk@wins.uva.nl -
- Martin Muldoon muldoon@yorku.ca -
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- The Electronic News Net of the SIAM Activity Group -
- on Orthogonal Polynomials and Special Functions -
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- Please send contributions to: poly@siam.org -
- Subscribe by mailing to: poly-request@siam.org -
- or to: majordomo@wins.uva.nl -
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Today's Topics
1. Retiring as OP-SF NET co-editor (Tom Koornwinder)
2. Election results awaited
3. SIAM 1999 Annual Meeting
4. Minisymposium: Orthogonal polynomials; Theory and Applications
5. Mini-symposium on asymptotics
6. Conference on Analytic Methods of Analysis and Differential
Equations
7. Question about Elliot's formula
8. Article on Weierstrass by U. Skornik
9. Student Travel Awards for 1999
10. Dahlquist Prize
11. OP-SF preprints in xxx archive
12. OPSF ftp site (Hans Haubold)
13. Changes of Address, WWW Pages, etc.
14. Subscribing to OP-SF NET
15. Obtaining back issues of OP-SF NET and submitting contributions
to OP-SF NET and Newsletter
Calendar of Events:
1999
March 29 - April 2: Fifth International Conference on Approximation
and Optimization in the Caribbean, Guadeloupe 5.4 #4
May 12-15: SIAM Annual Meeting in Atlanta 5.6 #3
(Minisymposium: Orthogonal Polynomials; Theory and Practice 5.6 #4)
June 6-11: International Conference on Rational Approximation,
Antwerp, Belgium 5.5 #3
June 21-25: Conference on Special Functions, Hong Kong 5.2 #7, 5.4 #5
July 5-9: ICIAM '99, Edinburgh 5.5 #4
(Minisymposium on asymptotics 5.6 #5)
September 14-18: International Conference on Analytic Methods of Analysis
and Differential Equations, Minsk, Belarus 5.6 #6
September 20-24: International Symposium on Orthogonal Polynomials,
Special Functions and Their Applications, Patras, Greece 5.4 #3
2000
July 10-14: SIAM Annual Meeting in Puerto Rico
Topic #1 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: Tom Koornwinder <thk@wins.uva.nl>
Subject: Retiring as OP-SF NET co-editor
It is about 5 years ago that the first issue of OP-SF NET came out. The
first volume (December 1993 - December 1994) had nine issues, the next
four volumes had six issues in a year. The first two volumes I have edited
alone. Since 1996 I have been co-editing OP-SF NET together with Martin
Muldoon. Now I feel the time has come for me to stop this editorial
activity. First of all because my present administrative duties do not
leave me enough time for this, but also because after five years new ideas
by a new co-editor will be welcome.
It was very interesting for me during these five years to observe and
document, via OP-SF NET, developments in the field of OP & SF, but also in
many other fields of mathematics and other sciences with which OP & SF
interacts. Furthermore, the social context and the technical possibilities
for OP & SF have changed and developed. Most noteworthy are developments
in computer hardware and software. For instance, the World Wide Web was
still unknown in 1993 (except maybe to a very small group). Now it is a
daily tool for most of us.
The field of OP & SF has great promises for the future, provided it is
not defined in the narrow sense. I have high expectations about the new
team of officers we have elected this fall, and I hope to remain a member
of this Activity Group for many years in order to see how they will
continue and expand our mission.
Tom Koornwinder
Topic #2 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: OP-SF NET Editor <muldoon@yorku.ca>
Subject: Election results awaited
I expect to hear the results of the elections of officers for our Activity
Group soon, but have not heard them at the time of going to "press".
Members will recall that one position for January 1999 - December 2001
have been filled by acclamation:
Chair: Daniel W. Lozier
and that there are two candidates for each of the other three positions:
Vice-Chair:
1. Walter Van Assche
2. Rupert Lasser
Secretary:
1. Charles F. Dunkl
2. M. Lawrence Glasser
Program Director:
1. Francisco Marcellan
2. Peter A. McCoy
The results of the elections will be published in the group's website once
they are released. See:
http://www.math.yorku.ca/siamopsf/
Topic #3 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: SIAM
Subject: 1999 Annual Meeting
Dear Colleagues:
A friendly reminder...
The deadline for submission of minisymposium proposals and contributed
abstracts for the 1999 SIAM Annual Meeting is NOVEMBER 16, 1998. The
meeting will be held May 12-15, 1999 at the Sheraton Spirit of Atlanta
Hotel, Atlanta, Georgia. For more information on how to submit your
papers, visit the Web site: www.siam.org/meetings/an99/ or e-mail
the SIAM Conference Department at: meetings@siam.org.
Thank you and we look forward to your participation.
The Organizing Committee
1999 SIAM Annual Meeting
Topic #4 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: Jeff Geronimo <geronimo@math.gatech.edu>
Subject: Minisymposium; Orthogonal polynomials; Theory and Applications
A Minisymposium "Orthogonal polynomials; Theory and Applications"
will be held during the SIAM Annual Meeting in Atlanta, May 12-15,
1999. The invited speakers are:
Percy Deift (New York)
Charles Dunkl (Charlottesville, Virginia)
Jeff Geronimo (Atlanta)
Leonid Golinski (Columbus, Ohio)
Sergei Suslov (Tempe, Arizona)
Walter Van Assche (Leuven)
Gerald Teschl (Vienna)
Hugo Woerdeman (Williamsburg, Virginia)
Further information will appear in a later issue of OP-SF NET.
Topic #5 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: Nico Temme <nicot@cwi.nl>
Subject: Mini-symposium on asymptotics
Adri Olde Daalhuis (Edinburgh) and Nico Temme (Amsterdam) are organizing a
mini-symposium on asymptotics during ICIAM 99 in Edinburgh, 5-9 July 1999.
We have five speakers for a first session. If more people are interested
in participating, we can try to submit a second session. Please respond
soon, and send us your title, abstract, and affiliation.
Title of mini-symposium:
Methods and applications of asymptotic analysis
Asymptotic analysis is an important tool in many branches of mathematics,
physics and other application areas. When solving problems described in
terms of differential equations or integrals, it is often required to
obtain qualitative information on the solution of the problem. Another
area of interest is the study of the behaviour of certain special
functions for large values of one or several (complex) parameters and the
application of uniform asymptotic expansions in computing special
functions for a large domain of the parameters. This mini-symposium
presents several actual problems in which asymptotics plays an important
role.
Speakers:
Roger J. Hosking, James Cook University, Australia.
Title: Asymptotic evaluation of Fourier integral solutions for
the response of a flexible plate to a moving load
David Kaminski, University of Lethbridge, Canada
Title: Hills and valleys at infinity for the steepest descent method
Jose L. Lopez, Universidad de Zaragoza, Spain
Title: Uniform asymptotic expansions of Bernoulli and
Euler polynomials.
Richard B Paris, University of Abertay, Dundee, Scotland
Title: The asymptotic expansion of Gordeyev's integral
Alastair Wood, Dublin City University, Ireland
Title: Asymptotically assisted numerics in MHD stability problems
The ICIAM 99 web site at
http://www.ma.hw.ac.uk/iciam99
contains up-to-date information about the Congress.
(See also OP-SF NET 5.5, Topic #4)
Topic #6 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: OP-SF NET Editors
Subject: Conference on Analytic Methods of Analysis and Differential
Equations
First Announcement
The Institute of Mathematics of the Belarusian National Academy of
Sciences and the Belarusian State University (BSU) together with Moscow
State University and the Computer Center of the Russian Academy of
Sciences will organize the International Conference "Analytic Methods of
Analysis and Differential Equations" (AMADE) on September 14-18, 1999, in
Minsk, Belarus. The arrival and departure days are September 13 and 19.
Section Titles:
1. Integral Transforms and Special Functions.
2. Differential Equations and Applications.
3. Integral, Difference, Functional Equations and Fractional Calculus.
The length of plenary invited lectures is 45 min, reports - 20 min, and
short communications - 10 min. The publication of the abstracts is
planned. The Proceedings of Conference are supposed to be published in
the Journal "Integral Transforms and Special Functions".
Organizing Committee
Chairmen: Academician I.V.Gaishun (Belarus), Academician V.A.Il'in
(Russia) and Rector of BSU A.V.Kozulin. Vice-Chairmen: V.V.Gorokhovik
(Belarus), A.A.Kilbas (Belarus), V.I.Korzyuk (Belarus) and A.P.Prudnikov
(Russia).
Secretaries: M.V.Dubatovskaya (Belarus), S.V.Rogosin (Belarus).
Members: P.Antosik (Poland), C.Brezinski (France), L.Debnath (USA),
I.H.Dimovski (Bulgaria), L.Gatteschi (Italy), J.Gilewicz (France),
H.-J.Glaeske (Germany), R.Gorenflo (Germany), V.I.Gromak (Belarus),
N.A.Izobov (Belarus), N.K.Karapetyants (Russia), V.S.Kiryakova (Bulgaria),
O.I.Marichev (USA), E.I.Moiseev (Russia), A.F.Nikiforov (Russia),
O.A.Oleinik (Russia), O.A.Repin (Russia), V.N.Rusak (Belarus), M.Saigo
(Japan), S.G.Samko (Portugal), A.A.Sen'ko (Belarus), H.M.Srivastava
(Canada), B.Stankovic (Yugoslavia), P.K.Suetin (Russia), N.A.Virchenko
(Ukraine), P.P.Zabreiko (Belarus), A.H.Zemanian (USA), E.I.Zverovich
(Belarus), L.A.Yanovich (Belarus), N.I.Yurchuk (Belarus).
Our address:
Belarus, 220050 Minsk 50, Fr. Skaryny Avenue 4, Belarusian State
University, Department of Math & Mech, AMADE;
e-mail: amade99@im.bas-net.by and amade99@mmf.bsu.unibel.by
Let us know by the end of December 1998, about your intention to
participate in the Conference. Please send the following information:
1. Name, Surname
2. Affiliation and Position
3. Mailing Address and Telephone (FAX)
4. e-mail
5. Section Title
6. Title of Report
The second announcement with preliminary list of participants,
registration fee, travelling information, accommodation, etc will be sent
in March 1999.
Topic #7 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: Matti Vuorinen <vuorinen@csc.fi>
Subject: Question about Elliot's formula
Generalization of Legendre's identity for complete elliptic integrals
Let E, K be the complete elliptic integrals. Then
K'E +KE'-KK' = pi/2 (*)
This is the special case p=r=-a+ 1/2, q=c+a- 3/2 in Elliott's identity
(see Erdelyi e.a., Higher Transcendental Functions, Vol. 1, p. 85):
F(p+ 1/2, -r- 1/2, 1+p+q; z) F(-p+ 1/2, r+ 1/2; 1+q+r; 1-z)
+ F(p+ 1/2, -r+ 1/2, 1+p+q; z) F(-p- 1/2, r+ 1/2; 1+q+r; 1-z)
- F(p+ 1/2, -r+ 1/2, 1+p+q; z) F(-p+ 1/2, r+ 1/2; 1+q+r; 1-z)
= Gamma(p+q+1) Gamma(q+r+1) / Gamma(p+q+r+ 3/2) / Gamma(q+ 1/2) (**)
Question 1. Is there a counterpart of Legendre's identity (*) for
incomplete elliptic integrals?
Question 2. The Elliott identity (**) provides a generalization of
the identity (*) to hypergeometric functions. The only handbook where
I have seen this identity is Bateman vol. I. Has Elliott's identity
been used or mentioned elsewhere in papers/books?
Question 3. Are there generalizations of the Elliott identity (**) to the
pFq case or to other generalizations of hypergeometric functions?
Matti Vuorinen
Topic #8 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: OP-SF NET Editors
Subject: Article on Weierstrass by U. Skornik
[The following item appeared in our Activity Group's Newsletter,
October 1998; it was reprinted, with permission, from the
Russian Newsletter "Integral Transforms and Special Functions" ]
Karl Theodor W. Weierstrass - Life and Work
On the 100th anniversary of his death
by U. Skornik
Institute of Mathematics,
Polish Academy of Sciences,
Staromiejska 8/6, 40-013
Katowice, Poland
E-mail: skornik@impan.gov.pl
19 February 1997 marked the hundredth anniversary of the death of the
great German mathematician, the father of classical mathematical analysis
and theory of Abelian and special functions, Karl Theodor Wilhelm
Weierstrass. He was born on 31 October 1815, the first child of Wilhelm
Weierstrass, secretary of the mayor of Ostenfelde and Theodora
Vonderforst.
Nothing in his early life indicated that he would become a famous
mathematician. Karl attended the Catholic Gymnasium in Paderborn from 1829
to 1834 when he entered the University of Bonn in order to follow a course
in public finance, economics and administration. This choice, far from his
own interests, was dictated by his father with the result that, after four
years spent on fencing, drinking and mathematics, Karl returned home
without having taken any examinations. The years in Bonn, however, were
not entirely wasted. It was during the stay there that Weierstrass
attended lectures of the famous geometer Plucker, studied "Mecanique
Celeste" by Laplace, "Fundamenta nova" by Jacobi and extended his
knowledge by an accidentally found transcript of lectures on elliptic
functions by Gudermann. As a last resort Karl was sent in 1839 to the
Theological and Philosophical Academy at Munster where he was to prepare
for a career as a secondary school teacher. He attended lectures on
elliptic functions given by Cristof Gudermann. The theory of these
functions was initiated by Gauss and developed by Abel and Jacobi. In the
early XIXth century Abel considered the elliptic integral of the form
\alpha = int(0 to x) {dx}\over \sqrt{(1-c^2x^2)(1+e^2x^2)}
and the function x=\varphi(\alpha), inverse to the integral. The function
\varphi(\alpha) is called an elliptic function and, when extended to the
whole complex plane, gives a doubly periodic function. Jacobi based his
theory on the integral
u =int( 0 to \varphi {d\varphi}\over \sqrt{1-k^2\sin^2\varphi}},
with a parameter k, 0<k<1, called the modulus of the elliptic integral.
The elliptic functions obtained from that integral were called modular
functions by Gudermann. It was a new theory and Gudermann was the first
after Jacobi to give lectures on the subject.
On 2 May 1840 Weierstrass was given problems for his final examinations;
one of them was posed by Gudermann in response to a special wish of his
student and concerned elliptic functions. In autumn 1840 Weierstrass
presented the results of his research on the decomposition of modular
functions. He expressed Jacobi modular functions as ratios of entire
functions whose power series coefficients are polynomials in k^2. In
memory of Abel, he called them Al functions. Next, Weierstrass introduced
his famous \sigma-functions, which differ from Al functions by a
multiplier.
His dissertation contained significant new material and could ensure an
academic position for him in Germany or elsewhere. It is not known why
this work, highly prized by Gudermann, was not published until 54 years
later in the first volume of Weierstrass's Collected Papers. Instead of
gaining mathematical fame, Weierstrass, after passing the second oral part
of his examinations in spring 1841, worked for 14 years as a secondary
school teacher.
After a probationary year in Munster, Weierstrass worked at the Catholic
gymnasium (a high level high school) in Deutsch-Krone (West Prussia) from
1842 to 1848 and then in a similar school in Braunsberg (East Prussia)
from 1848 to 1855. He taught not only mathematics and physics but also
German, botany, geography, history, gymnastics and calligraphy. In 1844
Weierstrass took part in a course for gymnastics teachers in Berlin.
During this time he visited the famous geometer Steiner. This, however,
did not change his situation. In Deutsch-Krone Weierstrass had neither
access to the mathematical literature, nor the possibility of exchanging
ideas with any other mathematician. He felt isolated and filled his life
with work. During those years he developed the theory of Abelian functions
which form a larger class than the elliptic functions. Abelian integrals
are defined like elliptic integrals by
u = \int(0 to v) R(t,\sqrt{f(t)})dt = I(v)
where R(x,y) is a rational function of x and y, except that the function f
is of a very general type which includes all polynomials. Inversion then
yields Abelian functions, just as elliptic functions arise from the
inversion of elliptic integrals, i.e. the integrals where f(t) is a
polynomial.
During Weierstrass' probationary year at the gymnasium in Munster he
worked on three papers. The first "Darstellung einer analytischen
Funktion, deren absoluter Betrag zwischen zwei gegebenen Grenzen liegt"
contained a proof of Cauchy's integral theorem without the use of double
or surface integrals. He also introduced Laurent series and arrived at
the Laurent theorem two years before it was officially published in
Comptes Rendus by Cauchy. In that work Weierstrass expressed complex
numbers in the form
r{1+\lambda i}\over {1-\lambda i},
where r is the absolute value and \lambda is a real number given by
\lambda = \tan(\theta/2), where \thet is an amplitude of the complex
number. The paper "Zur Theorie der Potenzreihen" dates from autumn 1841.
In that work Weierstrass introduced the notion of uniform convergence and
examined series in several variables. In the next paper "Definition
analytischer Funktionen einer Veranderlichen vermittelst algebraischer
Differentialgleichungen", dating from 1842, he proved the theorem of
Cauchy concerning the solution of systems of differential equations
dx/dt = G_i(x_1,...,x_n)
with the initial conditions x_i(0) =a_i, where the G_i are polynomials. In
that paper Weierstrass described the process of analytic continuation of
power series. Those papers were published only in the first volume of his
Collected Papers in 1894 but they make it clear that, already in 1842, he
was in full possession of all the methods and ideas which allowed him to
construct his theory of functions. Unfortunately, his first published
paper "Bemerkung uber die analytischen Fakultaten" appeared in a
supplement to the school report of the year 1842 in Deutsch-Krone and
received little attention. The same happened to another paper on Abelian
functions which was published in 1848 in the Braunsberg school prospectus.
Weierstrass would have remained unnoticed but for the fact that in summer
1853 during his stay in Munster he read Gudermann's opinion of his
dissertation for the first time. Already in 1840 Cristof Gudermann not
only recognised Karl's rare talent but also placed him among famous
discoverers and suggested that his student should work at a university
rather than as a secondary school teacher. This note encouraged
Weierstrass to publish his paper ``Zur Theorie der Abelschen Funktionen".
Its appearance in 1854 in Crelle's Journal caused a sensation in the
mathematical world. The consequences were amazing. The first recognition
was the award of an honorary doctorate by the University of Konigsberg.
Then the Prussian ministry of education gave him a year's paid leave from
the Braunsberg gymnasium to enable him to concentrate on his research.
Weierstrass gained enough confidence to apply for the post at the
University in Breslau which was vacated by Kummer's appointment as
professor in Berlin. It may sound strange that Weierstrass's application
was rejected because of Kummer. The reason was that Kummer, who spent 13
years teaching in Breslau, intended to take Weierstrass to Berlin. He
applied on 12 June 1856 to the university in Berlin with a request for a
post for Weierstrass. He was not successful on that occasion but his
eventual success gave to mathematics in Berlin three great names:
Weierstrass, Kummer and Kronecker.
Weierstrass's "Theorie der Abelschen Funktionen" published in Crelle's
Journal in 1856 contained results of his dissertation. D. Hilbert
considered these results concerning the solution of the Jacobi inversion
problem for the hyperelliptic integral the greatest achievement of
analysis. This publication was a turning point in the life of Karl
Weierstrass. He became famous abroad and the Austrian government made
inquiries about him through Alexander von Humboldt. This pushed von
Humboldt to action and on 1 July 1856 Weierstrass was appointed professor
at the Industry Institute in Berlin.
In September 1856 Weierstrass and Kummer went to Vienna. There, Graf Thun
offered Weierstrass 2000 Gulden and a professorship at an Austrian
university of his choice. Weierstrass declined that offer but it became
clear to Kummer that if they wanted to keep the great mathematician in
Germany he had to take action again.
Shortly afterwards as a result of Kummer's efforts, Weierstrass was
appointed Associate Professor at the University in Berlin. In November
1856 he became a member of the Berlin Academy. From then until 1890 he
lectured on a great variety of topics, including periodic lectures on
elliptic functions, lectures on geometry, and on mechanics. The famous
mathematical seminar which he initiated together with Kummer in 1861
attracted international interest. From 1862 it was customary to make
awards to the best participants. It is worth mentioning that the first
mathematical-physical seminar was founded in Konigsberg in 1834 by
Jacobi, Neumann and Sohnke, the second in Halle in 1838 and the third in
Gottingen in 1850.
Weierstrass' heavy work load resulted in a breakdown in his health in
December 1861. He returned to teaching after a year but he lectured from a
sitting position with a student writing the necessary text on the
blackboard. For the rest of his life he suffered recurring bouts of
bronchitis and phlebitis, but his determination kept him teaching and
pursuing his research. In his lectures Weierstrass initiated the logical
and rigorous development of analysis starting with his own construction of
the real number system. He established the epsilon-delta notions in the
concept of continuity and convergence, uniform convergence, absolute
value, neighbourhood (a-\delta, a+\delta) of a point $a$, and many others.
He rejected intuitive arguments which were still prevalent among many
contemporary mathematicians. It was Weierstrass who in his lectures of
1862 gave the famous example of a continuous nowhere differentiable
function. In that year he first developed in his lectures the theory of
the \gamma(u) and \sigma(u) functions. His famous approximation theorem
appeared in connection with the heat equation and was published in July
1885 in the Proceedings of the Meetings of the Berlin Academy of Sciences.
He also contributed to the development of the Calculus of Variations on
which he lectured in 1879. His main lectures however concentrated on
Abelian functions. His periodically presented lectures included
"Introduction to the Theory of Analytic Functions", "The Theory of
Elliptic Functions", once approached from the point of view of
differential equations, another time from the point of view of the theory
of functions, "Application of Elliptic Functions to Geometry and
Mechanics", "Application of Abelian Functions to Geometric Problems and
the Calculus of Variations". His lectures drew audience of up to 250,
among them over 100 future professors, including S. Kovalevsky, Schwarz,
Fuchs, G. Mittag-Leffler, L. Koenigsberger, H. Minkowski, and Cantor.
Weierstrass became the leading influence on the mathematical world. He
obtained high recognition throughout Europe. The Swedish mathematician
Mittag-Leffler mentions a nice anecdote. When he got a scholarship to
study abroad in 1873 he went to Paris where Hermite greeted him with the
words "Vous avez fait erreur, Monsieur, vous auriez du suivre les cours
de Weierstrass a Berlin". And of course Mittag-Leffler followed Hermite's
advice and went to Berlin.
The most remarkable among Weierstrass's students was Sonia Kovalevsky, the
daughter of a Russian artillery general. Women were not allowed to study
in Russia so in 1868 she contracted a marriage of convenience to a young
paleontologist, Vladimir Kovalevsky, and the couple went to study abroad.
They first enrolled at the University of Heidelberg but after two years
they separated. Vladimir went to Jena and Sonia travelled to Berlin hoping
to attend Weierstrass's lectures. Unfortunately, there was a ban on women
students at the University in Berlin and her application was rejected. So
she went straight to Weierstrass with her Heidelberg references. He gave
her some problems to solve and her solutions and enthusiasm impressed him
so he decided to teach her privately. During the four years that she spent
in Berlin, she became his close friend and an irreplaceable partner for
scientific discussions. We do not know much about Weierstrass' private
life. Sonia, however, the second woman (after Maria Sklodowska Curie) to
hold a university post, a novelist and a revolutionary, became a wonderful
topic for many biographies and novels. Weierstrass regarded her as his
most talented student. In fact during her stay in Berlin she produced
three outstanding papers; on differential equations, on Abelian integrals
and on Saturn's rings, and managed to obtain a doctorate from the
University of Gottingen. However, Weierstrass, much to his regret, could
not secure a job for her in Germany and she had to return to Russia.
Their friendship, although based on purely scientific interaction, became
the subject of rumour. Weierstrass felt deeply hurt by persistent
insinuations surrounding his student and her mathematical achievements. On
return to Russia her interest in mathematics ceased. She couldn't work at
the University in Petersburg because her qualifications were not
recognised. She returned to family life, gave birth to a daughter in 1878
and together with her husband, Vladimir, tried to make money as an estate
entrepreneur, but this venture ended in bankruptcy.
Weierstrass and Sonia Kovalevsky corresponded fairly regularly from the
time they met till her death in 1891. His letters and encouragement to
take up mathematics again inspired her and helped her through financial
difficulties and her husband's suicide in 1883. In 1884 Mittag-Leffler
succeeded in getting her a post as lecturer at the University in
Stockholm. In 1888 she achieved great success, when her famous paper {\it
"On the rotation of a solid body about a fixed point"} won the French
Academy's Bordin prize.
Sadly, Weierstrass burned all Sonia's letters after her early death. His
letters, however, survived and are preserved at the Mittag-Leffler
Institute in Djursholm, Sweden. The vast correspondence to Mittag-Leffler,
H. Schwarz, Paul du Bois-Reymond, L. Koenigsberger, Riemann, L. Fuchs and
Sonia, which contains mostly mathematical problems, also illuminates
Weierstrass's life. He was considered successful but, in fact, his life
was full of sufferings and personal problems. He did not marry after an
engagement in Deutsch-Krone was broken due to the unfaithfulness of the
fiancee, according to his brother, Peter. His career in Berlin had hardly
started when his health collapsed. Moreover, towards the end of his life,
rather than enjoying fame and appreciation, he felt isolated. This was
because of a conflict with the mathematician and philosopher Leopold
Kronecker.
Weierstrass and Kronecker were friends for more than twenty years, sharing
many fruitful mathematical discussions and ideas. Unfortunately, at the
end of 1870's their views on mathematics, especially the foundations of
mathematics, diverged gradually. Weierstrass's work on limits and
convergence led him to develop a theory of irrational numbers based on
convergent sequences of rationals which he called ``aggregates". His
student, Georg Cantor, founded the theory of transfinite numbers which
caused a revolution in mathematical thought. Before Cantor, mathematicians
had accepted the notion of the infinite in the situation of a sequence
"tending to infinity", but were not prepared to accept an actual infinity
per se. Cantor's great achievement was to introduce this precise concept,
in fact a whole class of different infinities -- that corresponding to the
countable sets such as the natural numbers, that of the continuum of real
numbers, and so on. For Kronecker, the type of non-constructive reasoning
used by Weierstrass and Cantor was deeply suspect. His famous dictum, "God
made the integers, all the rest is the work of man", pronounced at the
Berlin Congress in 1886, encapsulated his philosophy, and he envisaged the
inclusion of essentially the whole of mathematics within the terms of
arithmetic.
Kronecker did not hide his objections to the work of Weierstrass and
Cantor and criticized them openly in front of students. No wonder that
this mathematical conflict turned into personal quarrels. Towards the end
of the 1880's Weierstrass evidently admitted that his long friendship with
Kronecker was over though Kronecker himself seemed unaware of it.
Weierstrass even considered the possibility of leaving Berlin for
Switzerland to avoid the continuing conflict; but, since he did not wish
his successor at the university to be chosen by Kronecker, he decided to
stay. It became clear to him, however, that if he did not publish his
lectures and works his achievements might fall into oblivion.
His worry was probably exaggerated because his students were spread all
over Europe and continued his research. His greatest successor was H.
Poincare in Paris. Nevertheless the situation in Berlin was tense. In
1885 a special commission responsible for editing his works was set up.
Weierstrass himself was no longer able to supervise the whole process so
his students undertook the task of gathering and polishing up his lectures
based on their own notes or transcripts. Weierstrass intended to give to
mathematics an extensive treatment of analysis, clear and complete. So
Knoblauch and Hettner were to prepare the theory of Abelian functions, his
greatest aim in life. His dream was not fulfilled, however, and the draft
was highly unsatisfying in his opinion and not up to the standard he
expected. The lack of precision and printing errors worried him too. The
first volume appeared in 1894 and contained his collected papers. The
second was printed in 1895 but the next five volumes were published
between 1902 and 1927, after his death. It is worth mentioning that it is
to Weierstrass that we owe the publication of the collected papers of
Jacobi, Dirichlet, Steiner and the letters of Gauss. In his old age he
worked as an editor to supplement his salary which was not sufficient to
maintain his family. He lived in Berlin with his sisters Elise and Klara
who kept house, his father who died in 1869 and his uncle's grandson whom
he took custody of as a two-year-old in 1884. He also took care of
Borchardt's six children after his closest friend's death in 1880.
In 1892 Weierstrass received the Helmholtz medal and in 1895 he was
awarded the Copley Medal, the highest honour of the Royal Society of
London. In the same year he celebrated his 80th birthday among his
students. He spent his last three years in a wheelchair and died on 19
February 1897, after an inflammation of the lungs.
References
1. Ahrens, W.: Skizzen aus dem Leben Weierstrass'. Math.-naturwiss.
Blatter 4 (1907), 41-47.
2. ---: Gudermanns Urteil uber die Staatsexamensarbeit von Weierstrass.
Math.-naturwiss Blatter 13 (1916), 44-46.
3. Baker, A. C.: Karl Theodor Wilhelm Weierstrass, the father of modern
analysis. Math. Spectrum 1996/7, vol.29, No.2, 25-29.
4. Biermann, K. R.: Karl Weierstrass, Ausgewahlte Aspekte seiner
Biographie. Journal fur die reine und angewandte Mathematik, 223 (1966),
191-220.
5. Bolling, R.: Karl Weierstrass - Stationen eines Lebens. Jahresber.
Dt. Math.-Vereinigung, 96 (1994), 56-75.
6. Dorofeeva, A. & Chernova, M.: Karl Weierstrass. Mathematics and
Cybernetics 7 (1985), Moscow (in Russian).
7. Flaskamp, F.: Herkunft und Lebensweg des Mathematikers Karl
Weierstrass. Forsch. u. Fortschr. 35 (1961), 236-239.
8. Hensel, K.: Gedachtnisrede auf Ernst Eduard Kummer. Festschr. zur
Feier des 100. Geburststages Eduard Kummers. Leipzig und Berlin 1910,
1-37.
9. Hilbert, D.: Zum Gedachtnis an Karl Weierstrass. Nachrichten v. d.
Kgl. Ges. d. Wissensch. zu Gottingen 1897, 60-69.
10. ---: Uber das Unendliche. Mathematische Annalen 95 (1926), 161-185.
11. Kiepert, L.: Personliche Erinnerungen an Karl Weierstrass.
Jahresber. d. Dt. Math.-Vereinigung 35 (1926), 56-65.
12. Kochina, P.: Karl Weierstrass. Moscow "Nauka" 1985 (in Russian).
13. Lampe, E.: Karl Weierstrass. Jahresber. d. Dt. Math.-Vereinigung 6
(1899), 27-44.
14. ---: Zur hundertsten Wiederkehr des Geburtstages von Karl
Weierstrass. Jahresber. d. Dt. Math.-Vereinigung 34 (1915), 416-438.
15. von Lilienthal, R.: Karl Weierstrass. Westfalische Lebensbilder 2
(1931), 164-179.
16. Lorey, W.: Die padagogischen Ansichten des Mathematikers Karl
Weierstrass. Blatter fur hoheres Schulwesen 32 (1915), 626-629.
17. ---: Karl Weierstrass zum Gedachtnis. Zeitschr. f. math. u.
naturwiss. Unterricht 46 (1915), 597-607.
18. ---: Das Studium der Mathematik an den deutschen Universitaten seit
Anfang des 19. Jahrhunderts. IMUK-Abhandlungen, Bd. 3, H. 9. Leipzig und
Berlin 1916.
19. Mittag-Leffler, G.L: Une page de la vie de Weierstrass. Compte Rendu
du deuxieme international des mathematiciens. Paris, 1902, 131-153.
20. ---: Zur Biographie von Weierstrass. Acta Mathematica 35 (1912),
29-65.
21. ---: Die ersten 40 Jahre des Lebens von Weierstrass. Acta
Mathematica 39 (1923), 1-57.
22. ---: Sophie Kovalevsky: Notice biographique. Acta Mathematica 16
(1892/93), 385-395.
23. ---: Weierstrass et Sonja Kovalevsky. Acta Mathematica 39 (1923),
133-198.
24. Rachmanowa, A.: Sonja Kovalevski. Zurich 1953.
25. Rothe, R.: Bericht uber den gegenwartigen Stand der Herausgabe der
Mathematischen Werke von Karl Weierstrass. Jahresber. d. Dt.
Math.-Vereinigung 15 (1916), 59-62.
26. ---: Bericht uber die Herausgabe des 7. Bands der Mathematischen
Werke von Karl Weierstrass. Jahresber. d. Dt. Math.-Vereinigung 37 (1928),
198-208.
27. Runge, C.: Personliche Erinnerungen an Karl Weierstrass. Jahresber.
d. Dt. Math.-Vereiningung 35 (1926), 175-179.
28. Schubert, H.: Zum Andenken an Karl Weierstrass. Zeitschr. f. math.
u. naturwiss. Unterricht 28 (1897), 228-231.
29. Siegmund-Schultze, R.: Der Beweis des Weierstrassschen
Approximationssatzes 1885 vor dem Hintergrund der Entwicklung der
Fourieranalysis. Historia Mathematica 15 (1988).
30. Voit, K. & Lindemann, F.: Karl Theodor Wilhelm Weierstrass.
Sitzungsberichte d. math.-physikal. Klasse der k. b. Akademie der
Wissenschaften zu Munchen 27, 1897 (1898), 402-409.
Topic #9 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: Allison Bogardo <bogardo@siam.org>
Subject: Student Travel Awards for 1999
SIAM Student Travel Awards
for 1999 Conferences
During 1999, SIAM will make a number of awards for $300 to support
student travel to each of the following SIAM conferences:
Tenth Annual ACM-SIAM Symposium on Discrete Algorithms, January
17-19, Baltimore, MD
Ninth SIAM Conference on Parallel Processing for Scientific
Computing, March 22-24, San Antonio, TX
Fifth SIAM Conference on Mathematical and Computational Issues in
the Geosciences, March 24-27, San Antonio, TX
Sixth SIAM Conference on Optimization, May 10-12, Atlanta, GA
SIAM Annual Meeting, May 12-15, Atlanta, GA
Fifth SIAM Conference on Applications of Dynamical Systems,
May 23-27, Snowbird, UT
Sixth SIAM Conference on Geometric Design, November 2-5,
Albuquerque, NM
The awards are to be made from the SIAM Student Travel Fund, created
in 1991 and maintained through book royalties donated by generous
SIAM authors.
Any full-time student in good standing is eligible to receive an
award plus gratis meeting registration. Top priority will be given to
students presenting papers at the meeting, with second priority to
students who are co-authors of papers to be presented at the
meetings. Only students traveling more than 100 miles to the
meetings are eligible for the awards.
An application for a travel award must include:
(1) A letter from the student describing his/her academic standing
and interests, his/her expected graduation date and degree, advisor's
name, and, if available, a URL for a working Web page.
(2) A one-page vita that includes the student's research interests,
projects, and papers published.
(3) A detailed letter from the student's faculty advisor indicating
why the student is deserving of receiving a travel award and any
special circumstances.
(4) If applicable, the title(s) of the paper(s) to be presented
(co-authored) by the student at the meeting.
Applications should be sent to the SIAM office (Attention: SIAM
Student Travel Awards), 3600 University City Science Center,
Philadelphia, PA 19104-2688. Students also may apply by e-mail to
bogardo@siam.org or by fax to 215-386-7999.
Complete applications must be received at the SIAM office no later
than TWO MONTHS before the first day of the meeting for which support
is requested.
Winners will be notified FIVE WEEKS before the first day of the
meeting. Checks for the awards will be given to the student awardees
when they arrive at the given meeting and pick up their registration
packet at the SIAM Registration Desk.
Topic #10 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: Allison Bogardo <bogardo@siam.org>
Subject: Dahlquist Prize
The Dahlquist Prize
-------------------
SIAM will present the Dahlquist Prize at the Fourth International
Congress on Industrial and Applied Mathematics (ICIAM 99) in
Edinburgh, Scotland, July 5-9, 1999. The award honors the
contributions of Germund Dahlquist to numerical analysis and
scientific computing.
Eligibility
-----------
The prize, established in 1995, is awarded to a young scientist
(normally less than 45) for original contributions to fields
associated with Germund Dahlquist, especially the numerical solution
of differential equations and numerical methods for scientific
computing.
Description of the Award
------------------------
The award is to include a certificate containing the citation and a
cash prize of $1,000 plus reasonable travel costs to ICIAM 99. The
recipient is expected to present a talk at the conference and
encouraged to submit a paper to an appropriate SIAM publication.
Nominations
-----------
A letter of nomination, including a description of the achievements,
should be sent by January 15, 1999, to:
Dahlquist Prize Selection Committee
c/o Allison Bogardo
SIAM
3600 University City Science Center
Philadelphia, PA 19104-2688
Supporting letters, or names of knowledgeable persons from whom such
letters might be solicited, are also welcome.
Topic #11 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: OP-SF NET editors <thk@wins.uva.nl> <muldoon@yorku.ca>
Subject: OP-SF preprints in xxx archive
The following preprints related to the field of orthogonal polynomials and
special functions were recently posted or cross-listed to one of the
subcategories of the xxx archives. See:
http://front.math.ucdavis.edu/math.CA
http://front.math.ucdavis.edu/math.CO
http://front.math.ucdavis.edu/math.QA
http://xxx.lanl.gov/archive/solv-int
math.CA/9810149. Y. Gaspar. A new integral solution of the hypergeometric
equation. 15 pages. CA.
math.NT/9811068. Alain Connes. Trace formula in noncommutative geometry
and the zeros of the Riemann zeta function. 88 pages. NT (CA).
math-ph/9811001. A. Voros (CEA/Saclay, SPhT, France). Airy function (exact
WKB results for potentials of odd degree). SPhT-T98/101. MP (CA).
math.CO/9811041. R. Milson. Composition sums related to the hypergeometric
function. 5 pages. CO
math.CA/9809125. Wolfram Koepf. Software for the Algorithmic Work with
Orthogonal Polynomials and Special Functions. 31 pages. CA.
math.QA/9811050. Vitaly Tarasov. Combinatorial Identities Related to
Representations of $U_q(\tilde{gl_2})$. 8 pages. MPI 98-119. QA (CO).
math.QA/9810018. S. Ole Warnaar. $q$-Trinomial identities. 21 pages. ITF
98-23. QA (CO).
math.CO/9809128. F. Bergeron, G. Garsia. Science Fiction and Macdonald's
Polynomials. 47 pages. CO (QA).
math-ph/9810012. S. Chatyrvedi, V. Gupta. Identities involving elementary
symmetric functions. 7 pages. MP.
math-ph/9810007. A. V. Kitaev, D. A. Korotkin. On solutions of the
Schlesinger Equations in Terms of $\Theta$-Functions. International
Mathematics Research Notices No.17 (1998) 877-905. MP.
hep-ph/9809213. Luis G. Cabral-Rosetti, Miguel A. Sanchis-Lozano.
Generalized Hypergeometric Functions and the Evaluation of Scalar One-loop
Integrals in Feynman Diagrams. 9 pages. FTUV/98-67, IFIC/98-68. (MP).
math.NT/9809090. N. V. Kuznetsov. The true order of the riemann
zeta--function. 89 pages. NT (CA MP).
Topic #12 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: Hans Haubold <haubold@kph.tuwien.ac.at>
Subject: OPSF ftp site
[Note from Editors: The migration of Hans Haubold's ftp site to the xxx
site has been discussed in recent issues, most recently in OP-SF NET 5.5,
Topic #16.]
Electronic publishing is making fast progress and gets gradually
better organized.
Further to discussions in the OPSF Newsletter and the OP-SF NET, the
OPSF-FTPSITE will be "frozen" effectively immediately. No new submissions
should be made to the OPSF-FTPSITE. In January 1999, the OPSF-FTPSITE will
be disconnected entirely from the WWW.
All papers at the OPSF-FTPSITE had been archived as submitted. You can
find these papers by visiting the URL
http://front.math.ucdavis.edu
and then typing in the search window the author's name followed by a space
and the (unquoted) string "op-sf". You are kindly invited to inspect your
paper(s) at the LANL Mathematics E-print Archive. If you discover any
problem in the postscript format of your paper(s), you may wish to send me
by e-mail a detailed description of the problem. I will compile a list of
such problems to be forwarded to the staff of the LANL Mathematics E-print
Archive who have kindly agreed to take care of them. Authors may also
send email messages about problems directly to www-admin@xxx.lanl.gov (as
mentioned on URL http://front.math.ucdavis.edu/people.html )
I look forward reading your papers at the LANL Mathematics E-print
Archive.
Thank you for your patience and cooperation.
Best wishes,
Hans J. Haubold
haubold@kph.tuwien.ac.at
Topic #13 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: OP-SF NET Editors
Subject: Changes of Address, WWW Pages, etc.
Erik Koelink informs us that his new home page is at:
http://aw.twi.tudelft.nl/~koelink/
Akalu Tefera has a home page at
http://www.math.temple.edu/~akalu/
Eugene Tomer informs us that his new e-mail address is:
wi6x@ix.netcom.com
Topic #14 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: OP-SF NET Editors <thk@wins.uva.nl>, <muldoon@yorku.ca>
Subject: Subscribing to OP-SF NET
There are two ways to subscribe to OP-SF NET:
1. Send a message to
poly-request@siam.org
with your name and email address in the body of the message. If
everything works well, you will be put on the mailing list of
OP-SF NET which is maintained by SIAM.
2. Send a message to
majordomo@wins.uva.nl
and put in the body of the message only the words:
subscribe opsfnet
This is handled by an automatic list server. You will receive a
confirmation, with a list of further commands. You will be put on the
opsfnet mailing list of this list server. A new issue of OP-SF NET will be
mailed to people on this list immediately after the mailing by SIAM to the
people on the list maintained by SIAM.
Topic #15 ------------ OP-SF NET 5.6 ----------- November 15, 1998
From: OP-SF NET Editors <thk@wins.uva.nl>, <muldoon@yorku.ca>
Subject: Obtaining back issues of OP-SF NET and submitting contributions
to OP-SF NET and Newsletter
Back issues of OP-SF NET can be obtained from
ftp: ftp.wins.uva.nl, in directory
pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir
or WWW: http://turing.wins.uva.nl/~thk/opsfnet/
or WWW: http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html
Contributions to the OP-SF NET 6.1 should reach the email address
poly@siam.org before January 1, 1999.
The Activity Group also sponsors a (printed) Newsletter edited by Renato
Alvarez-Nodarse and Rafael Yanez. The deadline for submissions to be
included in the February 1999 issue is January 15, 1999 and for the June
1999 issue it is May 15, 1999.
Please send your Newsletter contributions directly to the Editors:
Renato Alvarez-Nodarse
Departamento de Analisis Matematico
Universidad de Sevilla
Apdo. Postal 1160,
Sevilla E-41080 Spain
fax: +34-95-455-7972
e-mail: renato@gandalf.ugr.es
ran@cica.es
Rafael J. Yanez
Departamento de Matematica Aplicada
Universidad de Granada
E-18071 Granada, Spain
phone: +34-58-242941
fax: +34-58-242862
e-mail: ryanez@ugr.es
preferably by email, and in latex format. Other formats are also
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Please note that submissions to the Newsletter (if not containing
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Previous issues of the Newsletter, but not the most recent one, can
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or by anonymous ftp at
ftp.zib.de in directory pub/UserHome/Koepf/SIAM
In order to join the SIAM Activity Group on Orthogonal Polynomials and
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