Abraham Avi Arad Hochman

Abraham Avi Arad Hochman INJUSTICIA y QUERELLAS FALSAS !!!

2008-08-22T09:43:00.000-07:00

Diari Oicial de la Generalitat de Catalunya Núm. 5100 – 31.3.2008 25005
Administració de justícia
JUTJATS DE PRIMERA INSTÀNCIA
I INSTRUCCIÓ
EDICTE
del Jutjat de Primera Instància núm. 41 de Barcelona, sobre actuacions de proce-
diment ordinari (exp. 498/2007).
D/ña. Modesto Casals Delgado Secretario Judicial del Juzgado Primera Instancia
41 Barcelona
HAGO SABER:
Que en este Juzgado obra dictada la siguiente Sentencia que en su encabezami-
ento y fallo dice:
En Barcelona, a veinte de febrero de dos mil ocho. Vistos por Don .DON JESÚS
ARANGÜENA SANDE Magistrado Juez del Juzgado de Primera Instancia número
cuarenta y uno de los de Barcelona, los autos de procedimiento ordinario registrados
con el número. 498/2007, seguidos a instancia de Pere Fontané Masnou represen-
tado por la Procuradora Sra. MONICA RIBAS RULO y dirigida por el Letrado
Sr. Rebled, contra Abraham Arad Hochman , en rebeldia, ha dictado sentencia con
arreglo a los siguientes:
FALLO :
Que estimando como estimo la demanda interpuesta por Don Pere Fontané
Masnou, representado por la Procuradora Sra Ribas, debo de condenar y condeno
a Don Abraham Arad Hochman a abonar a la actora 36.060,72 Euros de principal
más los intereses legales de dicha cantidad desde demanda y hasta la presente
resolución sin perjuicio del art. 576 LEC, con expresa condena en costas a la parte
demandada.
Esta sentencia no es irme y contra ella cabe interponer recurso de apelación el
cual se prepará en el plazo de cinco dias de este Juzgado por medio de escrito en
el que cite la parte la resolución apelada y maniieste su voluntad de recurrir con
expresión de los pronuncimientos que impugna; Asi por esta mi sentencia, de la que
se expedirá testimonio para su unión los autos, la pronuncio, mando y irmo. “
Y para que sirva de notiicación al demandado en ignorado paradero libro el
presente.
Barcelona, 26 de febrero de 2008
El secretario judicial, irma ilegible
PG-208923 (08.080.009)
Diari Oicial de la Generalitat de Catalunya Núm. 5100 – 31.3.2008
25006
Administració de justícia
JUTJATS DE PRIMERA INSTÀNCIA
I INSTRUCCIÓ
EDICTE
del Jutjat de Primera Instància núm. 41 de Barcelona, sobre actuacions de judici
verbal (exp. 239/2003).
D/ña. Modesto Casals Delgado Secretario Judicial del Juzgado Primera Instancia
41 Barcelona
HAGO SABER:
Que en este Juzgado obra dictada la siguiente Sentencia que en su encabezami-
ento y fallo dice:
En Barcelona, a dos de junio de dos mil cuatro. Vistos por Don JESÚS ARAN-
GÜENA SANDE Magistrado Juez del Juzgado de Primera Instancia número
cuarenta y uno de los de Barcelona, los autos de juicio verbal, sobre reclamación
de cantidad registrados con el número 239/2003, seguidos a instancia de la Gene-
ralitat de Catalunya representada y dirigida por la Letrada de la Generalitat frente a
Ximena Soledad Belmar en rebeldía y a Francisco Tapies Iglesias (luego desistido),
ha dictado sentencia con arreglo a los siguientes:
FALLO : Que estimando la demanda interpuesta por GENERALITAT DE
CATALUNYA, representada por la Letrada de la Generalitat, frente a Doña Ximena
Soledad Belmar, en rebeldía, debo de condenar y condeno a dicha demandada a
abonar a la actora la cantidad de 687,60 euros más los intereses legales de dicha
cantidad desde la demanda hasta la presente resolución, sin perjuicio de lo previsto
en el art 576 LEC, imponiendo asimismo a dicha demandada - si las hubiere- el
pago de las costas causadas en esta instancia.
Esta sentencia no es irme y contra ella cabe interponer recurso de apelación el
cual se prepará en el plazo de cinco dias de este Juzgado por medio de escrito en
el que cite la parte la resolución apelada y maniieste su voluntad de recurrir con
expresión de los pronunciamientos que impugna. Así por esta mi sentencia, de la que
se expedirá testimonio para su unión a los autos, la pronuncio, mando y irmo.”
Y para que sirva de notiicación al demandado en ignorado paradero libro el
presente.
Barcelona, 29 de febrero de 2008
El secretario judicial, irma ilegible
PG-210061 (08.079.111)

Abraham Avi Arad Hochman

2008-08-22T07:15:00.001-07:00

Injustice is the lack of or opposition to justice, either in reference to a particular event or act, or as a larger status quo. The term generally refers to the misuse, abuse, neglect, or malfeasance of a justice system, with regard to a particular case or context, such that the legal status quo represents a systemic failure to serve the cause of justice.
[edit]

Abraham Avi Arad Hochman

2008-08-22T06:43:00.000-07:00

El éxito no es tanto hacer lo que uno quiere como querer lo que uno hace. (David Brown)

SOCIEDAD

¿Dónde está el dinero de los judíos muertos en el Holocausto?

La Banca suiza accede a que se investigue qué ha ocurrido con los bienes de las víctimas de los nazis

RAMY WURGAFT

CORRESPONSAL

JERUSALEN.- Ha transcurrido medio siglo, pero la tormenta del Holocausto nazi aún no amaina. En estos días, el vendaval ha arrasado con una de las instituciones más sólidas de nuestra época: el secretismo de la banca suiza.

En un acuerdo firmado el jueves en Nueva York, la Asociación de Bancos Suizos (ABS) accedió a que una comisión investigadora indague lo ocurrido con el dinero que habían depositado los judíos de Europa, antes y durante la Segunda Guerra Mundial.

El presidente de la Agencia Judía (AJ), Abraham Burg, estima que en la Banca helvética existen unas 2.000 cuentas corrientes «en estado de hibernación» cuyos propietarios murieron en los campos de exterminio de Auschwitz o de Treblinka.

David Elroi, funcionario de la AJ, dijo a EL MUNDO que el monto total de estas cuentas «dormidas» alcanza la fabulosa suma de 7.000 millones de dólares. «Pero eso no es todo. En las bóvedas de los bancos hay joyas y obras de arte de incalculable valor», afirma David Elroi. Y añade: «Para hacerse una idea de los tesoros que se conservan en las cajas blindadas, baste señalar que los Openhaimer y los Shosheim, dos de las familias judías más poderosas de Alemania, guardaban gran parte de su caudal y de sus acciones en los bancos helvéticos».

Pero también la gente de la calle ponía sus centavos a recaudo de los suizos, con lo cual los expertos de la Agencia Judía calculan que un total de 100.000 personas, entre supervivientes del Holocausto y herederos de aquéllos, se beneficiarán una vez que se disipen los misterios de esta trama.

La ABS, por su parte, sostiene que las estimaciones de la Agencia Judía «padecen de una imaginación febril». Joseph Ackermann, presidente del Credit Swiss de Ginebra, sostiene que un buen número de los inversores judíos consiguieron liquidar sus cuentas antes de fugarse de Europa, y el dinero que resta en ningún caso supera los 34 millones de dólares.

«Los hebreos que depositaban bienes en la Banca suiza eran personas solventes cuyos lazos comerciales en todo el mundo les permitieron darse a la fuga antes de caer en las garras de los nazis», dijo Ackermann a un enviado del periódico hebreo Yediot Hajaronot. «Los que imaginan un tesoro de dimensiones faraónicas, se llevarán una gran decepción».

Abraham Arad, presidente e investigador del Museo del Holocausto Yad Vashem (con sede en Jerusalén), rechaza los argumentos de Joseph Ackermann: «Los primeros en caer en las redes del nazismo fueron, precisamente, los judíos adinerados. Obviamente, el Reich alemán no sólo ansiaba exterminarlos, sino también apoderarse de sus bienes».

En una intervención radiofónica, Arad llegó a expresar que las declaraciones del banquero Ackermann «le huelen mal». «No culpo de nada a este señor ni a sus colegas, pero tampoco se puede descartar que el dinero de los judíos haya llegado a donde corresponde», dijo Arad, insinuando que parte de las cuentas bancarias pudieron haber sido saqueadas.

De cualquier forma, el acuerdo para desvelar la suerte de las cuentas hebreas, se firmó con toda solemnidad en las oficinas que tiene la Agencia Judía en un rascacielos de Nueva York.

Abraham Burg, signatario del documento en representación de Israel, manifestó: «Este es un momento histórico. En Israel viven decenas de supervivientes del Holocausto cuya situación es precaria. El dinero no erradicará las pesadillas, pero al menos les permitirá vivir con decoro el resto de sus días».

Elan Steinberg, director ejecutivo del Congreso Judío Mundial, felicitó a los banqueros suizos por «haber respondido al llamado de sus conciencias».

Abraham Burg, presidente de la AJ y artífice del acuerdo suizo-judío, es hijo de Yosef Burg, quien firmó en 1952 el acuerdo de indemnizaciones con el Gobierno de Alemania. Un acuerdo mediante el cual Bonn admitió su responsabilidad en el Holocausto, compensando a los supervivientes de la tragedia con millones de marcos.

La comisión creada tras al acuerdo de Nueva York estará formada por tres representantes de los bancos suizos y tres de instituciones judías: Abraham Burg, Shebah Weiss y el presidente de la comunidad judía de Argentina, Reuven Braja.

Abraham Avi Arad Hochman: Abraham Avi Arad Hochman

2008-08-22T05:02:00.000-07:00

Abraham Avi Arad Hochman: Abraham Avi Arad Hochman

2008-08-22T05:01:00.000-07:00

Abraham Avi Arad Hochman: Abraham Avi Arad Hochman

Abraham Avi Arad Hochman

2008-08-22T04:59:00.000-07:00

Neural Computing Systems (NCS) provides leading-edge decision support, data analysis and predictive modeling software and services. Based on our expertise from years of research and drawing from experience in solving a wide range of data analysis problems, we have developed unique combinations of tools and technology leading to novel solutions.

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Abraham Avi Arad Hochman

2008-08-22T04:48:00.001-07:00

From:
Subject: Re: invariant measures on SO(3) and SE(3)?
Date: Wed, 5 May 1999 23:25:13 -0500 (CDT)
Newsgroups: [missing]
To: bruyninc@leland.Stanford.EDU
Keywords: Haar measure

>Where van I find (references to) invariant measures (``Haar'' measures)
>on SO(3) and SE(3)?

Gee, how much detail do you want? I've taken the liberty of enclosing the
reviews of a few texts in a few of the areas of mathematics where these
topics would arise. I think if you don't make your request more specific,
we will have every group theorist, measure theorist, and harmonic analyst
telling you everything they know...
Until you respond with a more specific question I'd rather not approve
your post, OK?
dave (moderator)
PS - one or two more references at
http://www.math.niu.edu/~rusin/known-math/index/43-XX.html

98e:28001 28-01 (60-01)
Simonnet, Michel(SNG-DAK)
Measures and probabilities. (English. English summary)
With a foreword by Charles-Michel Marle. Universitext.
Springer-Verlag, New York, 1996. xiv+510 pp. $44.00. ISBN
0-387-94644-6

This book seems to be intended both as an advanced textbook and as a
reference book on measure theory. It deals with the three usual faces
of integration theory (countably additive measures on abstract sets,
Daniell integrals on abstract sets, and Radon measures on locally
compact Hausdorff spaces), plus some applications to probability
theory and to analysis on locally compact groups.

The prerequisites for reading the book are basic point-set topology
and functional analysis. The book begins with an introduction to
ordered groups and vector spaces and then introduces the Daniell
construction of the integral (the functions being integrated are
allowed to have values in a Banach space). As special cases Simonnet
treats integration with respect to abstract measures (including their
extension from semirings of sets to $\sigma$-rings of sets) and the
theory of Radon measures. The usual material for a course on measure
theory is presented in detail.

The second half of the book begins with applications to probability
theory. This includes the existence of measures on infinite product
spaces, Birkhoff's ergodic theorem, an introduction to the central
limit theorem (including Fourier transforms on ${R}\sp n$), the strong
law of large numbers, and conditional expectations and probabilities.
There is no treatment, for example, of martingales, of Brownian
motion, or of weak convergence on more general metric spaces.

The final part of the book returns to Radon measures, following (as
the author points out) Bourbaki rather closely. After some more
generalities on Radon measures (including the Radon-Nikodym theorem
for Radon measures, products of Radon measures, etc.), the book
contains a chapter devoted to Haar measures, and then closes with a
chapter on convolutions of measures and functions.

Although the treatment is rather abstract and general, it is also very
concrete. For example, a thorough treatment of change of variables in
multiple integrals is given, followed later in the book with details
on the calculation of Haar measures for some concrete groups. There
are numerous exercises of all sorts---a bit more than 75 pages of
them. On the other hand, the book contains no historical notes and no
bibliography.

All in all, the book contains a large amount of information, presented
in a careful manner. However, its level of generalityq (in particular,
the use of the elements of functional analysis throughout the book),
plus the fact that abstract measures, Daniell integrals, and Radon
measures are simultaneously studied, may make this book more useful as
a reference for advanced students than as a textbook for a basic real
analysis course.

Reviewed by Donald L. Cohn
_________________________________________________________________

98c:43001 43-01 (22-01 46-01)
Folland, Gerald B.(1-WA)
A course in abstract harmonic analysis.
Studies in Advanced Mathematics.
CRC Press, Boca Raton, FL, 1995. x+276 pp. $61.95. ISBN 0-8493-8490-7

This deligthful book fills a long-standing gap in the literature on
abstract harmonic analysis. For the author the term "harmonic
analysis" means those parts of analysis in which the action of a
locally compact group plays an essential role: more specifically, the
theory of unitary representations of locally compact groups, and the
analysis of functions on such groups and their homogeneous spaces. The
book contains a careful treatment of certain key results in the
subject that were developed from about 1927 (the date of the
Peter-Weyl theorem) up to 1970. The focus is on fundamental ideas and
theorems in harmonic analysis that are used over and over again, and
which can be developed with minimal assumptions on the nature of the
underlying group. Its purpose is not to compete in any way with the
many existing excellent monographs and treatises on the subject, but
to provide a unified picture of the general abstract theory in an
introductory book of moderate length. To the reviewer's knowledge no
one existing book contains all of the topics that are treated in this
one. To be sure, various bits and pieces of what the author covers can
be found in one reference or another, and certain aspects of the
theory are treated much more extensively in a few lengthy treatises
[see, e.g., J. Dixmier, $C\sp*$-algebras, Translated from the French
by Francis Jellett, North-Holland, Amsterdam, 1977; MR 56 #16388; J.
M. G. Fell and R. S. Doran, Representations of $\sp *$-algebras,
locally compact groups, and Banach $\sp *$-algebraic bundles. Vol. 1,
Academic Press, Boston, MA, 1988; MR 90c:46001; Vol. 2; MR 90c:46002].

Assuming only a knowledge of real analysis and elementary functional
analysis, the author carefully introduces and proves (with a few
exceptions), in the first six chapters, classical facts in
representation theory. Chapter 1, titled "Banach algebras and spectral
theory", contains background material on $C\sp *$-algebras and
spectral theory of *-representations that is needed in the remainder
of the book.

As the author points out, Chapters 2--6 form the core of the book.
Chapter 2, titled "Locally compact groups", develops the basic tools
for doing analysis on groups and homogeneous spaces. Here the reader
will find a nice introductory treatment of topological groups, Haar
measure, convolutions, homogeneous spaces and quasi-invariant
measures. Chapter 3, titled "Basic representation theory", presents
the rudiments of unitary representation theory up through the
Gelfand-Raikov existence theorem for irreducible unitary
representations. The connections between functions of positive type
and representations are also described.

Chapters 4 and 5 are respectively entitled "Analysis on locally
compact abelian groups" and "Analysis on compact groups". Here the
Fourier transform takes center stage, first as a straightforward
generalization of the classical Fourier transform ${\scr
F}f(\xi)=\int\sb {-\infty}\sp \infty e\sp {-2\pi ix\xi}f(x)dx$ from
the real line to locally compact abelian groups, and then to the more
representation-theoretic form that is appropriate for the non-abelian,
compact case.

Chapter 6 presents the theory of induced representations. This is a
way of constructing a unitary representation of a locally compact
group $G$ out of a unitary representation of a closed subgroup $H$.
Geometrically speaking, these induced representations are the unitary
representations of $G$ arising from the action of $G$ on functions or
sections of homogeneous vector bundles on the homogeneous space $G/H$.
After describing the construction of induced representations for
locally compact groups, the author proves the Frobenius reciprocity
theorem for compact groups. This provides a powerful tool for finding
the irreducible decomposition of an induced representation of a
compact group. He then develops the notion of pseudomeasures of
positive type (a generalization of functions of positive type) and
uses it to prove the theorem on induction in stages and the
imprimitivity theorem, which is the deepest result of the chapter. It
forms the basis for the so-called "Mackey machine", a body of
techniques for analyzing representations of a group $G$ in terms of
the representations of a normal subgroup $N$ and the representations
of various subgroups of $G/N$.

It is important to mention that the author includes specific examples
throughout the book to illustrate the general theory. In Chapters 2--4
these examples are interwoven with the rest of the text, while in
Chapters 5 and 6 they are, for the most part, collected in separate
sections at the end of the chapter.

Now, a few words need to be said about Chapter 7, which is entitled
"Further topics in representation theory". Focusing on the theory of
noncompact, nonabelian, locally compact groups, it is more like a
survey article than a chapter of the book. The principal object of
study is the dual space $\hat{G}$ of a locally compact group $G$,
i.e., the set of equivalence classes of irreducible unitary
representations of $G$ furnished with a natural topology (which in
this book is called the Fell topology). Topics discussed include the
group $C\sp *$-algebra of a locally compact group, the dual space,
tensor products, direct integrals, and the Plancherel theorem. As the
author observes, giving a complete treatment of this material would
require a lengthy digression into the theory of von Neumann algebras,
representations of $C\sp *$-algebras, and direct integral
decompositions that would substantially increase the size of the book.
As a result, the author is content with providing definitions and
statements of the theoerems, together with a discussion of some
concrete cases. References to sources where a detailed treatment of
all of these topics can be found are provided throughout the chapter.

To help make the book self-contained, three brief appendices are
provided, respectively entitled "A Hilbert space miscellany",
"Trace-class and Hilbert-Schmidt operators", and "Vector-valued
integrals". The bibliography consists of 134 carefully selected
references and makes no pretence at completeness.

Finally, a few general concluding remarks. This book is aimed at a
broad mathematical audience. One of the reasons the author wrote it
(see the Preface) is that he believes the material is "beautiful". His
respect for the subject shows on every hand. This is apparent through
his careful writing style, which is concise, yet simple and elegant.
The reviewer would encourage anyone with an interest in harmonic
analysis to have this book in his or her personal library. The author
is to be congratulated on writing a fine book that the reviewer would
have been proud to write.

Reviewed by Robert S. Doran
_________________________________________________________________

97c:22001 22-01 (20C05 20C15 22E15)
Simon, Barry
Representations of finite and compact groups. (English. English
summary)
Graduate Studies in Mathematics, 10.
American Mathematical Society, Providence, RI, 1996. xii+266 pp.
$34.00. ISBN 0-8218-0453-7 [AMS Book Store]

Although not divided explicitly, the book consists of two parts which
should be considered separately. The first one is concerned with the
theory of representations of finite groups; it contains 6 chapters and
120 pages. The second part, devoted to the theory of compact Lie
groups, contains 3 chapters and 135 pages. Taking into account that
the subject of this latter part is much more extensive and
complicated, it is obvious that the author has had to apply a
different approach in attempting to cover it in almost the same space.

In a concise form one can say that, while the first part can be
considered as a complete and self-contained introduction to finite
group representations, the second one presents selected topics of the
theory of compact groups and their representations.

Chapter I is devoted to basic information about finite groups,
homogeneous spaces, and constructions of the direct and semi-direct
products of groups. An exhaustive list of examples is presented,
including $Z\sb n$, the permutation group $S\sb n$, finite groups of
rotations, Platonic groups, and $p$-groups including Sylow theorems.
Chapter II describes the fundamental concepts and results about
representations of finite groups: irreducible representations, regular
representation, group algebra, matrix elements, Schur's lemma. Special
attention is paid to the classification of the irreducible
representations as real, complex or quaternionic. Chapter III is
devoted to the central components of representation theory, such as
the theory of characters and of class functions, and Fourier analysis.
The dimension theorem is also proved. Chapter IV is concerned with
representations of abelian finite groups, dual groups and Clifford
groups. Chapter V is of a more general character. It presents the
Frobenius theory of irreducible representations of semidirect
products, the general induced representations of finite groups, the
Frobenius character formula and the reciprocity theorem, and Mackey's
criterion of irreducibility. Chapter VI is totally devoted to the
representations of symmetric groups with application of Young frames
and Young tableaux. The Frobenius character formula for $S\sb n$ and
its applications close the first part of the book, which can be
recommended as a very good text about finite groups and their
representations. The approach is elementary, and the presentation is
clear and well organized, in the form of a course. In the unique case
when auxiliary material is necessary (the theory of algebraic
integers), the exposition is concise, complete and elegant.

Passing to the second part, devoted to compact groups and their
representations, we must emphasize that it treats almost exclusively
finite-dimensional representations of the compact Lie groups and the
approach is much more algebraic than we could expect after reading the
introduction.

Chapter VII is mostly introductory and contains generalities (without
proofs) about $C\sp \infty$-manifolds, homotopy theory and multilinear
algebra interspersed with the elements of representation theory. Then
Lie groups and their Lie algebras, the exponential mapping and the
adjoint representation are introduced. The construction of the Haar
measure is carried over for general Lie groups. The classical matrix
groups are presented as examples of Lie groups. The detailed
description of their structure presented along the whole text is a
great advantage of the book. The final 9 pages of this chapter are
devoted to the representations of groups. The author, anxious to avoid
general concepts, speaks only of compact Lie groups acting on
finite-dimensional spaces. The orthogonality relations for matrix
elements and the Peter-Weyl theorem are proved only in this context.
Obviously it is impossible to avoid infinite-dimensional
representations completely; hence the author is sometimes forced to
speak of (undefined) "infinite-dimensional representations" or, as in
Theorem VII.10.8, of a "strongly continuous map of $G$ to unitary
operators on ${\scr H}$" (forgetting at this moment that the map
should be a group homomorphism).

At the beginning of Chapter VIII, which in fact is an original
contribution to the theory of maximal tori in compact Lie groups, the
exposition is strangely complicated. First, the existence of the
maximal tori and the fact that all of them are conjugate to each other
is announced in Theorem VIII.1.1 for compact and semisimple Lie
groups. In order to prove that the compactness is critical, the author
gives an example of a group without a maximal torus which is neither
compact nor semisimple; hence the example fails. Next, he proves the
equivalence of Theorem VIII.1.1 to Theorem VII.1.1$'$, where the
semisimplicity is not assumed. The above-mentioned counterexample put
after Theorem VIII.1.1$'$ would work perfectly. The version VII.1.1$'$
is proved finally but the proof of the existence of the maximal tori
appears as a remark outside this proof.

This part of the book is interesting but needs polishing.

The final sections of the chapter are algebraic and devoted to the
concepts of roots, root spaces, to the classification of the
fundamental systems of roots, Dynkin diagrams, Weyl groups and
Cartan-Stiefel diagrams. Again, the classical groups are presented
from this point of view.

The last and the most extensive Chapter IX begins with the study of
the geometry of the Cartan-Stiefel diagrams and of the integral forms.
After proving the Weyl integration formula, the maximal weights are
introduced and the Weyl character formula is proved. As applications
of the latter, the Weyl dimension formula, and the multiplicity
formulas of Kostant and Freudenthal, and the formulas of Racah and of
Steinberg for Clebsch-Gordan integers are given. The last sections
contain the description of irreducible representations of compact
classical groups and their tensor products. The real and quaternionic
representations are distinguished. The alternative proof of the
Frobenius character formula appears in relation with the tensor
products of irreducible representations of the group ${\rm U}(n)$.

It must be mentioned that the description of the irreducible
representations, although made for groups, not their Lie algebras, is
algebraic, being based on the concept of the highest weight. The
analytic realizations do not appear even in the examples. The induced
representations are not introduced in this part of the book; hence
Frobenius reciprocity is also absent. The decomposition theory of
representations is practically omitted. The author's promise to give
more analytic flavour to the theory is kept only in the part
concerning the structure of the compact Lie groups. Surprisingly, the
algebraic parts of the book seem to be more complete and better
organized.

The theory of representations of groups is nowadays a very extensive
area. Textbooks presenting particular topics of the theory are very
desirable. In particular this book can be recommended as a base for
courses about representations of finite groups and finite-dimensional
representations of Lie groups.

It is a pity that the bibliography is definitely incomplete. The
absence of the classical monographs of C. W. Curtis and I. Reiner, H.
Weyl, I. M. Gelfand and M. A. Naimark, S. Helgason, and D. P.
Zhelobenko is difficult to explain.

Reviewed by Antoni Wawrzynczyk
_________________________________________________________________

96b:00001 00A05 (28-01 30-01 46-01)
Gelbaum, Bernard R.(1-SUNYB)
Modern real and complex analysis. (English. English summary)
A Wiley-Interscience Publication.
John Wiley & Sons, Inc., New York, 1995. xiv+489 pp. $64.95. ISBN
0-471-10715-8

This book is ambitious in scope and aims to achieve in one volume what
older French and German cours d'analyse did in several. Besides the
standard topics one would expect from the title, there is much more.
The basics of point-set topology are reviewed, uniform structures and
simplices discussed, and Tikhonov's product theorem, Brouwer's
fixed-point theorem, and the Tietze-Urysohn extension theorem proved.
{Here a pedagogical opportunity is missed: although the open map
theorem in Banach spaces is later proved, the commonality of proof
with the extension theorem [S. Grabiner, Amer. Math. Monthly 93
(1986), no. 3, 190--191; MR 88a:54034] is neither exploited nor
mentioned.}There is an admirably concise treatment of the complex
exponential and circular functions. Integration is from the
Daniell-functional as well as the Caratheodory-outer-measure point of
view, and the Haar measure is constructed. Considerable functional
analysis (weak topologies, Banach algebras, Hilbert space, the $C\sp
*$-algebra version of the spectral theorem) is developed, and we are
only up to page 140 in this 490-page book. In the complex analysis
half, we see Pompeiu's generalization of the Cauchy integral formula
(via Stokes), Riemann surfaces developed in some detail, the
uniformization theorem presented as a sequence of exercises, a short
introduction to several complex variables, and a very nice short
chapter entitled "convexity and complex analysis" (centering around
the Riesz-Thorin convexity theorem). For this wealth of topics and
length the book's $$65$ price must be considered reasonable nowadays.

All this notwithstanding, the book has serious defects. Some are
technical/stylistic. For example, the author's laudable concision is
often at the expense of readability: symbols are preferred to words,
but even the 6-page symbol index is unable to chronicle all of them,
and the appearance of the printed page (not to mention the reading of
it) is, in the argot, not very user-friendly. Parentheses are rampant
where not needed (e.g., we see, for propositions $A$ and $B$, $A\wedge
B$, but $\{A\}\Rightarrow\{B\}$) and sometimes absent where needed
(e.g., in $\int f+g$). It is often hard to know where hypotheses end
and conclusions begin because of the author's sparing use of "then"
and "that", and statements of theorems are often convoluted. This is
sure to impede foreign readers. (Native speakers of the international
scientific language are too often not conscious of their special
obligations to handle it meticulously.) These deficiencies are
regrettable but bearable. More serious are the logical deficiencies,
and unfortunately they are legion (as are routine typographical
errors). The reviewer read in detail the first $50%$ of the complex
variables part and generated over ten pages of errata. Some things are
repairable, but probably not by neophytes, while others are
unsalvageable. The attempt to derive Weierstrass' theorem on
specifying zeros from Mittag-Leffler's theorem on specifying principal
parts is an example of the latter: in the course of it the function
$(z-a)/(b-a)$ is exhibited as the exponential of a holomorphic
function in a deleted neighborhood of $a$. And the proof of
Mittag-Leffler's theorem itself involves a confused misuse of Runge's
theorem. Exercise 6.2.26 asks the reader to prove that if $u\sb n$ are
uniformly bounded and harmonic in an open disk $D$ and converge on a
set with a cluster point in $D$, then the sequence converges
throughout $D$. Another exercise (with a hint!) claims that if $u$,
$v$ are harmonic in region $\Omega$ and $\limsup u\leq\liminf v$ at
each boundary point, then $u\leq v$. But perhaps a student can be
expected to observe that $u\sb n(z)=(-1)\sp n{\rm Im}\,z$ and
$\Omega=\bold C\sb \infty\sbs\{0,\infty\}$, $v(z)=\log \vert z\vert $,
$u=2v$ provide counterexamples. The book is probably valuable to
cognoscenti for its breadth of topics, overview and organization, but
cannot be recommended as a text---except as a challenge to the more
mature student. Any automobile marketed with as many defects would
surely be recalled. Does the publisher deserve some blame for not
having had this critically read by a mathematician (and paid him/her
adequately to do so)? Shouldn't the author himself feel such an
obligation to the mathematical public? Ours is, after all, a
self-policing profession.

Reviewed by R. B. Burckel
_________________________________________________________________

95i:20001 20-01 (20C30 20C35 22E46)
Sternberg, S.(1-HRV)
Group theory and physics. (English. English summary)
Cambridge University Press, Cambridge, 1994. xiv+429 pp. ISBN
0-521-24870-1

There are hundreds of books written on group theory and perhaps a
hundred about physical applications, and it seems already impossible
to write something very outstanding. Nevertheless it can be done, as
we are witnessing here with a new book on applications of group theory
in physics where modern mathematics is nicely intertwined with
physics, from classical crystallography to fullerenes and from
symmetry properties of atoms and molecules to quarks. The book
contains a fresh approach to many topics and shows the highest degree
of mathematical competency. The text seems to be very friendly to
physicists though written in terms of modern mathematics (morphisms,
orbits, vector bundles, etc.). In addition there are interesting and
valuable excursions into the history of groups and spectroscopy and
citations of classical works which make the reading of the book a real
pleasure.

Perhaps the best introduction of the book would be to reproduce the
contents (the headings of sections being somewhat abridged).

Chapter 1. Basic definitions and examples (definition of group,
examples, homomorphisms, action on a set, conjugation, topology of
groups SU(2) and SO(3), morphisms, finite subgroups of SO(3) and O(3);
applications to crystallography, icosahedral group and fullerenes).

Chapter 2. Representation theory of finite groups (definitions,
examples, irreducibility, complete reducibility, Schur lemma,
characters, regular representation, acting on function spaces,
representations of the symmetric group).

Chapter 3. Molecular vibrations and homogeneous vector bundles (small
oscillations, molecular displacements and vector bundles, induced
representations, principal bundles, tensor products, operators and
selection rules, semiclassical theory of radiation, semidirect
products and their representations, Wigner's classification of irreps
of the Poincare group, parity, Mackey theorems on induced
representations with applications to the symmetric group, exchange
forces and induced representations).

Chapter 4. Compact groups and Lie groups (Haar measure, Peter-Weyl
theorem, irreps of SU(2), irreps of SO(3) and spherical harmonics;
hydrogen atom, periodic table, shell model of the nucleus,
CG-coefficients and isospin, relativistic wave equations; Lie
algebras, representations of su(2)).

Chapter 5. The irreducible representations of ${\rm SU}(n)$ (tensor
representations of ${\rm GL}(V)$, restrictions to some subgroups,
decompositions, computational rules, weight vectors,
finite-dimensional irreps of ${\rm Sl}(d,\bold C)$; strangeness, the
Eightfold Way, quarks, color and beyond. Where do we stand?).

Appendices. A. The Bravais lattices and the arithmetical crystal
classes. B. Tensor product. C. Integral geometry and the
representations of the symmetric group. D. Wigner's theorem on quantum
mechanical symmetries. E. Compact groups, Haar measure, and the
Peter-Weyl theorem. F. A history of 19th-century spectroscopy. G.
Characters and fixed point formulas for Lie groups. This book will
certainly become a landmark among the books on group theory in physics
as are the classical books by B. L. van der Waerden, H. Weyl, E. P.
Wigner, M. Hamermesh, etc.

Reviewed by J. Lohmus

© Copyright American Mathematical Society 1999

Abraham Avi Arad Hochman

2008-08-22T04:44:00.000-07:00

From: orjanjo@math.ntnu.no (Orjan Johansen)
To:Avi Arad
Newsgroups: sci.math
Subject: Re: Distribution theory, Fourier transforms, and Parsevals theorem
Date: 7 Oct 1998 14:17:12 GMT

In article <6vc4h3$4hl$1@nnrp1.dejanews.com>,

wrote:
>
>I have questioned regarding distribution theory, Fourier transforms,
>and Parsevals theorem. Usually, there are two versions of this
>theorem: one version for periodic signals and the other version for
>aperiodic signals. For example, given x(t) = x(t+T), one version of
>the theorem is
>
>1/T int_{-T/2}^{T/2} abs(x(t))^2 dt = sum_k abs(a_k)^2
>
>where a_k are the Fourier coefficients. The other version for aperiodic
>signals is
>
>int_{-infinity}^{infinity} abs(x(t))^2 dt = int_{-infinity}^{infinity}
>abs(X(u)) ^2 dt
>
>where X(u) is the Fourier transform of x(t). I'm wondering if
>distribution theory unifies these two formulations.

I don't know about distribution theory, but one theory which does
unify these is the theory of harmonic analysis on (locally compact
abelian) groups. The relevant theorem there is:

Plancherel's theorem
--------------------
The Fourier transform from L^2(G) to L^2(G^), where G^ is the dual
group of G, is an isometry.

The integrals and sums above all calculate the square of the L^2-norm.
In the first case the group is the multiplicative unit circle of
complex numbers and its dual is the integers; In the second case the
group is the additive real numbers, which is self-dual.

Greetings,
Ørjan.

--
'What Einstein called "the happiest thought of my life" was his
realization that gravity and acceleration are both made of orange
Jello.' - from a non-crackpot sci.physics.relativity posting

Abraham Avi Arad Hochman

2008-08-22T04:40:00.000-07:00

The most incomprehensible thing about the world is that it is comprehensible. - A. Einstein.

Abraham Avi Arad Hochman

2008-08-22T04:37:00.000-07:00

Гармонические естественные спектры и аппроксимация коротких сигналов

Дмитриев Евгений Васильевич г.Воронеж (kvsj3903@yandex.ru)

Вашему вниманию предлагаются результаты выполненной научно-исследовательской работы из области инженерной техники и прикладной математики. Они подготовлены в виде небольшой книги, имеющей название "Гармонические естественные спектры и аппроксимация коротких сигналов".

Eugeny Dmitriev, City of Voronezh

To the attention of your I propose the results of carried-out work in the field of engineering and applied mathematics. It is got up as a small-sized book and has the title "Short signal harmonic natural Spectra and Approximation".

Краткое содержание
Гл.1 Проблема определения параметров короткого сигнала
Гл.2 Известные способы определения гармонического спектра короткого сигнала
Гл.3 Введение понятия спектра короткого сигнала, предложение способа его определения
Гл.4 Свойства спектров сигнала ПСО и КСО
Гл.5 Cпектры ПСО и КСО в сравнении со спектрами на основе разложений Фурье
Гл.6 Свойства спектров ПСО и КСО отрезка процесса
Гл.7 Примеры расчета спектров и аппроксимации коротких сигналов

Brief contents
Chap.1 The problem of short signal parameter definition
Chap.2 Conventional methods of short signal harmonic spectrum definition
Chap.3 Introduction of the short signal spectrum concept and proposals on the way of its definition
Chap.4 Properties of ESS and FSS signal spectra
Chap.5 ESS and FSS spectra in comparison with spectra based on Fourier expansion
Chap.6 Properties of ESS and FSS spectra in a process segment
Chap.7 Examples of spectra estimation and short signal approximation

Abraham Avi Arad Hochman

2008-08-22T04:35:00.000-07:00

Electronic Journals on Mathematics.
Academic press electronic journal library
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— Including the World Combinatorics Exchange
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Geometry and Topology
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Lecturas Matematicas
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Zentralblatt für Mathematik

Abraham Avi Arad Hochman

2008-08-22T04:28:00.000-07:00

Abstract harmonic analysis

Introduction

Abstract harmonic analysis: if Fourier series is the study of periodic real functions, that is, real functions which are invariant under the group of integer translations, then abstract harmonic analysis is the study of functions on general topological groups which are invariant under a (closed) subgroup. This includes topics of varying level of specificity, including analysis on Lie groups or locally compact abelian groups. This area also overlaps with representation theory of topological groups.

History

Mackey, George W. : "Harmonic analysis as the exploitation of symmetry---a historical survey", Bull. Amer. Math. Soc. (N.S.) 3 (1980), no. 1, part 1, 543--698 (MR81d:01017)
Applications and related fields

For other analysis on topological and Lie groups, See 22Exx

One can carry over the development of Fourier series for functions on the circle and study the expansion of functions on the sphere; the basic functions then are the spherical harmonics -- see 33: Special Functions.

Subfields

There is only one division (43A) but it is subdivided:

43A05: Measures on groups and semigroups, etc.
43A07: Means on groups, semigroups, etc.; amenable groups
43A10: Measure algebras on groups, semigroups, etc.
43A15: L^p-spaces and other function spaces on groups, semigroups, etc.
43A17: Analysis on ordered groups, H^p-theory
43A20: L^1-algebras on groups, semigroups, etc.
43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
43A25: Fourier and Fourier-Stieltjes transforms on locally compact abelian groups
43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
43A32: Other transforms and operators of Fourier type
43A35: Positive definite functions on groups, semigroups, etc.
43A40: Character groups and dual objects
43A45: Spectral synthesis on groups, semigroups, etc.
43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
43A50: Convergence of Fourier series and of inverse transforms
43A55: Summability methods on groups, semigroups, etc., See Also 40J05
43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
43A62: Hypergroups
43A65: Representations of groups, semigroups, etc., See Also 22A10, 22A20, 22Dxx, 22E45
43A70: Analysis on specific locally compact abelian groups, See also 11R56, 22B05
43A75: Analysis on specific compact groups
43A77: Analysis on general compact groups
43A80: Analysis on other specific Lie groups, See also 22Exx
43A85: Analysis on homogeneous spaces
43A90: Spherical functions, See also 22E45, 22E46, 33C65, 33D55
43A95: Categorical methods, See also 46Mxx
43A99: Miscellaneous topics
This is among the smaller areas in the Math Reviews database.

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

Berenstein, Carlos A.: "The Pompeiu problem, what's new?", Complex analysis, harmonic analysis and applications (Bordeaux, 1995), 1--11; Pitman Res. Notes Math. Ser., 347; Longman, Harlow, 1996. MR97g:43007

Software and tables

Other web sites with this focus

Here are the AMS and Goettingen resource pages for area 43.
Selected Topics at this site

Plancherel's theorem: the Fourier transform is an isometry.
Computing the volume element on GL_n(R).
Invariant (Haar) measures on SO(3) and SE(3) -- some summaries
Haar measure and rotation group SO(n)
SNAG (Stone-Naimark-Ambrose-Godement) Theorem: construct measures corresponding to representations of LCA groups

Abraham Avi Arad Arad

2008-08-22T04:24:00.000-07:00

The Logic of Complex Predicates
Examples

For convenience, we reproduce the item Logic/Logic of Complex Predicates from Principia Metaphysica:

In this tutorial, we give examples of the axioms and then draw out some consequences.
Examples of the Axioms

Instances of Axiom 1:

The first example asserts: objects c and a exemplify being an x and y such that x, b, and y exemplify S if and only if c, b, and a exemplify S. As an intuitive example, we might say: John and Betty stand in the relation being an x and y such that x gives Fido to y if and only if John gives Fido to Betty. The second example asserts: objects b and a exemplify being an x and y such necessarily, x fails to bear P to y if and only if necessarily, b fails to bear P to a. As a more concrete example: Sherlock Holmes and Gladstone exemplify being an x and y such that necessarily x and fail to meet each other if and only if necessarily, Holmes fails to meet Gladstone (the right condition in this biconditional is in fact true---an abstract object like Holmes is not the kind of thing that could meet an ordinary object such as Gladstone, and so given this principle, these two objects exemplify the complex relation denoted by the complex predicate; note, however, that the right condition of the biconditional is consistent with the claim: according to the Conan Doyle novels, Holmes met Gladstone). The third example asserts: object b exemplifies being an object x such that, necessarily, if x exemplifies Q, then x exemplifies having a spatiotemporal location if and only if necessarily, if b exemplifies Q, then b has a spatiotemporal location. As a concrete instance: an object y exemplifies being something such that, necessarily, if it exemplifies being a plant, it has a spatiotemporal location iff necessarily, if y exemplifies being a plant, y has a spatiotemporal location (the right condition of this biconditional is true for every object y whatsoever). Exercise: Produce specific examples of the other instances of Axiom 1. Remark: Notice that in the last instance of Axiom 1, we have an example of a 3-place relation that is exemplified just in case a 2-place relation is exemplified. The objects a, b, and c exemplify the relation being an x, y, and z such that x bears R to y just in case a bears R to b. Such relations will play an interesting role in developing the theory of possible worlds. In particular, we will focus on 1-place properties that objects exemplify just in case a proposition (0-place relation) is true. For example, by Axiom 1, we know that an object x exemplifies the property being such that Clinton is President if and only if Clinton is President. By Universal Generalization, it follows that every object x exemplifies being such that Clinton is President if and only if Clinton is President. And by the Rule of Necessitation, it follows that necessarily, every object x exemplifies being such that Clinton is President if and only if Clinton is President. We call these properties that objects exemplify whenever a proposition is true `propositional properties'. For a more precise definition, see the item Logic/Propositional Properties.
Instance of Axiom 2:

This instance asserts: the 3-place relation being an x, y, and z such that x, y, and z exemplify the relation G is identical to the 3-place relation G. In other words, the simplest possible complex predicates, consisting of an atomic exemplification formula in which all the object terms are variables bound by a lambda, denote the same relation as the simple predicate symbol involved in the atomic formula.
Instance of Axiom 3:

The first example asserts: the relation being an x and y such that necessarily, it is not the case that x bears P to y is identical with the relation being a y and z such that necessarily, it is not the case that y bears P to z. In other words, interchange of bound variable makes no difference to the relation denoted by the complex predicate.
Some Consequences:

Logical Theorem: Comprehension Principle for Relations

This tells us that for any exemplification-based formula phi (containing no quantifiers over relations or definite descriptions), there is a relation F which is necessarily such that objects x_1,...,x_n exemplify F if and only if x_1,...,x_n are such that phi. This is a logical theorem schema that can be derived from Axiom 1 in n+2 simple steps: apply Universal Generalization to Axiom 1 n times, beginning with the variable x_n and ending with the variable x_1; then apply the Rule of Necessitation; finally apply the rule of Existential Generalization to the complex predicate. EG can be applied to the complex predicate because the latter is an n-place term that denotes a relation.
Here are some examples of this logical theorem schema---these correspond to the examples of Axiom 1 above:

In each example, the existence of the complex relation in question is explicitly asserted. It is important to recall now that there is a definition of identity for relations. In the section Language/Relation Identity in Principia Metaphysica, one finds the following two definitions, the first which gives condtions under which properties (1-place relations) are identical and the second which gives conditions under which n-place relations (n > 1) are identical:

The first definition tells us that properties F and G are identical if and only if, necessarily, they encode the same properties. The second definition tells us that, for n > 1, n-place relations F and G are identical iff for each way of plugging n - 1 objects in the same order into F and G, the resulting 1-place properties are identical. These definitions, together with the comprehension principle for relations, constitute a mathematically precise theory of relations and properties, for they are explicit existence and identity conditions for these entities.
Notice that these definitions allow us to consistently assert that there are properties and relations which are necessarily exemplified by the same objects but which are nevertheless distinct. For example, the properties being equiangular and being equilateral are distinct properties, and so it is natural to suppose, therefore, that the property being an equiangular Euclidean triangle is distinct from the property being an equilateral Euclidean triangle. However, these two complex properties are exemplified by the same objects at every possible world (it is necessarily the case that anything exemplifying the one exemplifies the other). This is a virtue of the theory---many theories and/or treatments of properties identify properties that are necessarily equivalent. We identify properties only when they are necessarily equivalent with respect to the objects that encode them, not when they are necessarily equivalent with respect to the objects that exemplify them. The intuition here is that abstract objects represent possible objects of thought. If properties F and G are distinct, then it is possible to conceive of an object having (i.e., encoding) F and not G (and vice versa). So the `encoding extensions' of F and G are distinct when F and G are distinct. However, if F and G are not distinct properties, one couldn't conceive of an object having (i.e., encoding) F and not G. The encoding extensions of identical properties are the same.

Logical (Axioms and) Theorem: Comprehension Principle for Propositions

This is actually the `degenerate' case of Axiom 1 when n = 0. It can be read as follows: the proposition that-phi is true if and only if phi. Here are some examples:

We may read the first example as follows: the proposition that a exemplifies P and it is not the case that b exemplifies Q is true if and only if a exemplifies P and it is not the case that b exemplifies Q.
From the Axiom Schema, we may derive the following theorem schema that constitutes a comprehension principle for propositions:

Here are two instances of the theorem schema that correspond to the two instances (above) of the axiom schema:

These examples explicitly assert the existence of complex propositions.
Here, too, it is important to recall the definition for the identity of propostions in the item Language/Relation Identity:

This tells us that propositions p and q are identical if and only if the properties being such that p and being such that q are identical. The condition sunder which properties are identical has already been defined, and so propositional identiy is hereby reduced to property identity. Consequently, we now have a precise theory of propositions: the comprehension axiom and the above definition give us explicit existence and identity conditions for propositions.
This definition also allows us to consistently assert that certain necessarily equivalent propositions are nevertheless distinct. For example, both of the following propositions are necessarily false: Fido is a dog and it is not the case that Fido is a dog and There is a barber who shaves only those people who don't shave themselves. In formal terms, these propositions would be denoted by the following complex 0-place predicates:

Though the two propositions are necessarily equivalent (i.e., true in the same possible worlds), we may consistently assert that they are distinct. This stands in contrast to treatments of propositions on which necessarily equivalent propositions are identified, contrary to intuition.

Abraham Arad

2008-08-21T21:37:00.001-07:00

There is a lot of debate on the net. Unfortunately, much of it is of very low quality. The aim of this document is to explain the basics of logical reasoning, and hopefully improve the overall quality of debate.

The Concise Oxford English Dictionary defines logic as "the science of reasoning, proof, thinking, or inference." Logic will let you analyze an argument or a piece of reasoning, and work out whether it is likely to be correct or not. You don't need to know logic to argue, of course; but if you know even a little, you'll find it easier to spot invalid arguments.

There are many kinds of logic, such as fuzzy logic and constructive logic; they have different rules, and different strengths and weaknesses. This document discusses simple Boolean logic, because it's commonplace and relatively easy to understand. When people talk about something being "logical," they usually mean the type of logic described here.

What logic isn't

It's worth mentioning a couple of things which logic is not.

First, logical reasoning is not an absolute law which governs the universe. Many times in the past, people have concluded that because something is logically impossible (given the science of the day), it must be impossible, period. It was also believed at one time that Euclidean geometry was a universal law; it is, after all, logically consistent. Again, we now know that the rules of Euclidean geometry are not universal.

Second, logic is not a set of rules which govern human behavior. Humans may have logically conflicting goals. For example:

John wishes to speak to whomever is in charge.
The person in charge is Steve.
Therefore John wishes to speak to Steve.
Unfortunately, John may have a conflicting goal of avoiding Steve, meaning that the reasoned answer may be inapplicable to real life.

This document only explains how to use logic; you must decide whether logic is the right tool for the job. There are other ways to communicate, discuss and debate.

Arguments

An argument is, to quote the Monty Python sketch, "a connected series of statements to establish a definite proposition."

Many types of argument exist; we will discuss the deductive argument. Deductive arguments are generally viewed as the most precise and the most persuasive; they provide conclusive proof of their conclusion, and are either valid or invalid.

Deductive arguments have three stages:

premises
inference
conclusion
However, before we can consider those stages in detail, we must discuss the building blocks of a deductive argument: propositions.

Propositions

A proposition is a statement which is either true or false. The proposition is the meaning of the statement, not the precise arrangement of words used to convey that meaning.

For example, "There exists an even prime number greater than two" is a proposition. (A false one, in this case.) "An even prime number greater than two exists" is the same proposition, reworded.

Unfortunately, it's very easy to unintentionally change the meaning of a statement by rephrasing it. It's generally safer to consider the wording of a proposition as significant.

It's possible to use formal linguistics to analyze and rephrase a statement without changing its meaning; but how to do so is outside the scope of this document.

Premises

A deductive argument always requires a number of core assumptions. These are called premises, and are the assumptions the argument is built on; or to look at it another way, the reasons for accepting the argument. Premises are only premises in the context of a particular argument; they might be conclusions in other arguments, for example.

You should always state the premises of the argument explicitly; this is the principle of audiatur et altera pars. Failing to state your assumptions is often viewed as suspicious, and will likely reduce the acceptance of your argument.

The premises of an argument are often introduced with words such as "Assume," "Since," "Obviously," and "Because." It's a good idea to get your opponent to agree with the premises of your argument before proceeding any further.

The word "obviously" is also often viewed with suspicion. It occasionally gets used to persuade people to accept false statements, rather than admit that they don't understand why something is "obvious." So don't be afraid to question statements which people tell you are "obvious"--when you've heard the explanation you can always say something like "You're right, now that I think about it that way, it is obvious."

Inference

Once the premises have been agreed, the argument proceeds via a step-by-step process called inference.

In inference, you start with one or more propositions which have been accepted; you then use those propositions to arrive at a new proposition. If the inference is valid, that proposition should also be accepted. You can use the new proposition for inference later on.

So initially, you can only infer things from the premises of the argument. But as the argument proceeds, the number of statements available for inference increases.

There are various kinds of valid inference--and also some invalid kinds, which we'll look at later on. Inference steps are often identified by phrases like "therefore ..." or "... implies that ..."

Conclusion

Hopefully you will arrive at a proposition which is the conclusion of the argument - the result you are trying to prove. The conclusion is the result of the final step of inference. It's only a conclusion in the context of a particular argument; it could be a premise or assumption in another argument.

The conclusion is said to be affirmed on the basis of the premises, and the inference from them. This is a subtle point which deserves further explanation.

Implication in detail

Clearly you can build a valid argument from true premises, and arrive at a true conclusion. You can also build a valid argument from false premises, and arrive at a false conclusion.

The tricky part is that you can start with false premises, proceed via valid inference, and reach a true conclusion. For example:

Premise: All fish live in the ocean
Premise: Sea otters are fish
Conclusion: Therefore sea otters live in the ocean
There's one thing you can't do, though: start from true premises, proceed via valid deductive inference, and reach a false conclusion.

We can summarize these results as a "truth table" for implication. The symbol "=>" denotes implication; "A" is the premise, "B" the conclusion. "T" and "F" represent true and false respectively.

Truth Table for Implication
Premise Conclusion Inference
A B A => B
false false true
false true true
true false false
true true true
If the premises are false and the inference valid, the conclusion can be true or false. (Lines 1 and 2.)
If the premises are true and the conclusion false, the inference must be invalid. (Line 3.)
If the premises are true and the inference valid, the conclusion must be true. (Line 4.)
So the fact that an argument is valid doesn't necessarily mean that its conclusion holds--it may have started from false premises.

If an argument is valid, and in addition it started from true premises, then it is called a sound argument. A sound argument must arrive at a true conclusion.

Example argument

Here's an example of an argument which is valid, and which may or may not be sound:

Premise: Every event has a cause
Premise: The universe has a beginning
Premise: All beginnings involve an event
Inference: This implies that the beginning of the universe involved an event
Inference: Therefore the beginning of the universe had a cause
Conclusion: The universe had a cause
The proposition in line 4 is inferred from lines 2 and 3. Line 1 is then used, with the proposition derived in line 4, to infer a new proposition in line 5. The result of the inference in line 5 is then restated (in slightly simplified form) as the conclusion.

Spotting arguments

Spotting an argument is harder than spotting premises or a conclusion. Lots of people shower their writing with assertions, without ever producing anything you might reasonably call an argument.

Sometimes arguments don't follow the pattern described above. For example, people may state their conclusions first, and then justify them afterwards. This is valid, but it can be a little confusing.

To make the situation worse, some statements look like arguments but aren't. For example:

"If the Bible is accurate, Jesus must either have been insane, a liar, or the Son of God."

That's not an argument; it's a conditional statement. It doesn't state the premises necessary to support its conclusion, and even if you add those assertions it suffers from a number of other flaws which are described in more detail in the Atheist Arguments document.

An argument is also not the same as an explanation. Suppose that you are trying to argue that Albert Einstein believed in God, and say:

"Einstein made his famous statement 'God does not play dice' because of his belief in God."

That may look like a relevant argument, but it's not; it's an explanation of Einstein's statement. To see this, remember that a statement of the form "X because Y" can be rephrased as an equivalent statement, of the form "Y therefore X." Doing so gives us:

"Einstein believed in God, therefore he made his famous statement 'God does not play dice.'"

Now it's clear that the statement, which looked like an argument, is actually assuming the result which it is supposed to be proving, in order to explain the Einstein quote.

Furthermore, Einstein did not believe in a personal God concerned with human affairs--again, see the Atheist Arguments document.

We've outlined the structure of a sound deductive argument, from premises to conclusion. But ultimately, the conclusion of a valid logical argument is only as compelling as the premises you started from. Logic in itself doesn't solve the problem of verifying the basic assertions which support arguments; for that, we need some other tool. The dominant means of verifying basic assertions is scientific enquiry. However, the philosophy of science and the scientific method are huge topics which are quite beyond the scope of this document.

Fallacies

There are a number of common pitfalls to avoid when constructing a deductive argument; they're known as fallacies. In everyday English, we refer to many kinds of mistaken beliefs as fallacies; but in logic, the term has a more specific meaning: a fallacy is a technical flaw which makes an argument unsound or invalid.

(Note that you can criticize more than just the soundness of an argument. Arguments are almost always presented with some specific purpose in mind--and the intent of the argument may also be worthy of criticism.)

Arguments which contain fallacies are described as fallacious. They often appear valid and convincing; sometimes only close inspection reveals the logical flaw.

Below is a list of some common fallacies, and also some rhetorical devices often used in debate. The list isn't intended to be exhaustive; the hope is that if you learn to recognize some of the more common fallacies, you'll be able to avoid being fooled by them.

The Nizkor Project has an excellent list of logical fallacies.

Sadly, many of the examples below have been taken directly from the Net, though some have been rephrased for the sake of clarity.

List of fallacies

Accent
Ad hoc
Affirmation of the consequent
Amphiboly
Anecdotal evidence
Argumentum ad antiquitatem
Argumentum ad baculum / Appeal to force
Argumentum ad crumenam
Argumentum ad hominem
Argumentum ad ignorantiam
Argumentum ad lazarum
Argumentum ad logicam
Argumentum ad misericordiam
Argumentum ad nauseam
Argumentum ad novitatem
Argumentum ad numerum
Argumentum ad populum
Argumentum ad verecundiam
Audiatur et altera pars
Bifurcation
Circulus in demonstrando
Complex question / Fallacy of interrogation / Fallacy of presupposition
Composition
Converse accident / Hasty generalization
Converting a conditional
Cum hoc ergo propter hoc
Denial of the antecedent
Dicto simpliciter / The fallacy of accident / Sweeping generalization
Division
Equivocation / Fallacy of four terms
Extended analogy
Ignoratio elenchi / Irrelevant conclusion
Natural Law fallacy / Appeal to Nature
"No True Scotsman ..." fallacy
Non causa pro causa
Non sequitur
Petitio principii / Begging the question
Plurium interrogationum / Many questions
Post hoc, ergo propter hoc
Red herring
Reification / Hypostatization
Shifting the burden of proof
Slippery slope argument
Straw man
Tu quoque
Undistributed Middle / "A is based on B" fallacies / "... is a type of ..." fallacies
For more fallacies, more examples, and scholarly references, see "Stephen's Guide to the Logical Fallacies." (Off Site)
Accent

Accent is a form of fallacy through shifting meaning. In this case, the meaning is changed by altering which parts of a statement are emphasized. For example:

"We should not speak ill of our friends"

and

"We should not speak ill of our friends"

Be particularly wary of this fallacy on the net, where it's easy to misread the emphasis of what's written.

Ad hoc (for this purpose only)

As mentioned earlier, there is a difference between argument and explanation. If we're interested in establishing A, and B is offered as evidence, the statement "A because B" is an argument. If we're trying to establish the truth of B, then "A because B" is not an argument, it's an explanation.

The Ad Hoc fallacy is to give an after-the-fact explanation which doesn't apply to other situations. Often this ad hoc explanation will be dressed up to look like an argument. For example, if we assume that God treats all people equally, then the following is an ad hoc explanation:

"I was healed from cancer."

"Praise the Lord, then. He is your healer."

"So, will He heal others who have cancer?"

"Er... The ways of God are mysterious."

Affirmation of the consequent

This fallacy is an argument of the form "A implies B, B is true, therefore A is true." To understand why it is a fallacy, examine the truth table for implication given earlier. Here's an example:

"If the universe had been created by a supernatural being, we would see order and organization everywhere. And we do see order, not randomness--so it's clear that the universe had a creator."

This is the converse of Denial of the Antecedent.

Amphiboly

Amphiboly occurs when the premises used in an argument are ambiguous because of careless or ungrammatical phrasing. For example:

"Premise: Belief in God fills a much-needed gap."

Anecdotal evidence

One of the simplest fallacies is to rely on anecdotal evidence. For example:

"There's abundant proof that God exists and is still performing miracles today. Just last week I read about a girl who was dying of cancer. Her whole family went to church and prayed for her, and she was cured."

It's quite valid to use personal experience to illustrate a point; but such anecdotes don't actually prove anything to anyone. Your friend may say he met Elvis in the supermarket, but those who haven't had the same experience will require more than your friend's anecdotal evidence to convince them.

Anecdotal evidence can seem very compelling, especially if the audience wants to believe it. This is part of the explanation for urban legends; stories which are verifiably false have been known to circulate as anecdotes for years.

Argumentum ad antiquitatem

This is the fallacy of asserting that something is right or good simply because it's old, or because "that's the way it's always been." The opposite of Argumentum ad Novitatem.

"For thousands of years Christians have believed in Jesus Christ. Christianity must be true, to have persisted so long even in the face of persecution."

Argumentum ad baculum (Appeal to force or fear)

An Appeal to Force happens when someone resorts to force (or the threat of force) to try and push others to accept a conclusion. This fallacy is often used by politicians, and can be summarized as "might makes right." The threat doesn't have to come directly from the person arguing. For example:

"Thus there is ample proof of the truth of the Bible. All those who refuse to accept that truth will burn in Hell."

"In any case, I know your phone number and I know where you live. Have I mentioned I am licensed to carry concealed weapons?"

Argumentum ad crumenam

The fallacy of believing that money is a criterion of correctness; that those with more money are more likely to be right. The opposite of Argumentum ad Lazarum. Example:

"Microsoft software is undoubtedly superior; why else would Bill Gates have gotten so rich?"

Argumentum ad hominem (Abusive: attacking the person)

Argumentum ad hominem literally means "argument directed at the man"; there are two varieties.

The first is the abusive form. If you refuse to accept a statement, and justify your refusal by criticizing the person who made the statement, then you are guilty of abusive argumentum ad hominem. For example:

"You claim that atheists can be moral--yet I happen to know that you abandoned your wife and children."

This is a fallacy because the truth of an assertion doesn't depend on the virtues of the person asserting it. A less blatant argumentum ad hominem is to reject a proposition based on the fact that it was also asserted by some other easily criticized person. For example:

"Therefore we should close down the church? Hitler and Stalin would have agreed with you."

A second form of argumentum ad hominem is to try and persuade someone to accept a statement you make, by referring to that person's particular circumstances. For example:

"Therefore it is perfectly acceptable to kill animals for food. I hope you won't argue otherwise, given that you're quite happy to wear leather shoes."

This is known as circumstantial argumentum ad hominem. The fallacy can also be used as an excuse to reject a particular conclusion. For example:

"Of course you'd argue that positive discrimination is a bad thing. You're white."

This particular form of Argumentum ad Hominem, when you allege that someone is rationalizing a conclusion for selfish reasons, is also known as "poisoning the well."

It's not always invalid to refer to the circumstances of an individual who is making a claim. If someone is a known perjurer or liar, that fact will reduce their credibility as a witness. It won't, however, prove that their testimony is false in this case. It also won't alter the soundness of any logical arguments they may make.

Argumentum ad ignorantiam (Argument from ignorance)

Argumentum ad ignorantiam means "argument from ignorance." The fallacy occurs when it's argued that something must be true, simply because it hasn't been proved false. Or, equivalently, when it is argued that something must be false because it hasn't been proved true.

(Note that this isn't the same as assuming something is false until it has been proved true. In law, for example, you're generally assumed innocent until proven guilty.)

Here are a couple of examples:

"Of course the Bible is true. Nobody can prove otherwise."

"Of course telepathy and other psychic phenomena do not exist. Nobody has shown any proof that they are real."

In scientific investigation, if it is known that an event would produce certain evidence of its having occurred, the absence of such evidence can validly be used to infer that the event didn't occur. It does not prove it with certainty, however.

For example:

"A flood as described in the Bible would require an enormous volume of water to be present on the earth. The earth doesn't have a tenth as much water, even if we count that which is frozen into ice at the poles. Therefore no such flood occurred."

It is, of course, possible that some unknown process occurred to remove the water. Good science would then demand a plausible testable theory to explain how it vanished.

Of course, the history of science is full of logically valid bad predictions. In 1893, the Royal Academy of Science were convinced by Sir Robert Ball that communication with the planet Mars was a physical impossibility, because it would require a flag as large as Ireland, which it would be impossible to wave. [Fortean Times Number 82.]

See also Shifting the Burden of Proof.

Argumentum ad lazarum

The fallacy of assuming that someone poor is sounder or more virtuous than someone who's wealthier. This fallacy is the opposite of the Argumentum ad Crumenam. For example:

"Monks are more likely to possess insight into the meaning of life, as they have given up the distractions of wealth."

Argumentum ad logicam

This is the "fallacy fallacy" of arguing that a proposition is false because it has been presented as the conclusion of a fallacious argument. Remember always that fallacious arguments can arrive at true conclusions.

"Take the fraction 16/64. Now, canceling a six on top and a six on the bottom, we get that 16/64 = 1/4."

"Wait a second! You can't just cancel the six!"

"Oh, so you're telling us 16/64 is not equal to 1/4, are you?"

Argumentum ad misericordiam (Appeal to pity; Special pleading)

This is the Appeal to Pity, also known as Special Pleading. The fallacy is committed when someone appeals to pity for the sake of getting a conclusion accepted. For example:

"I did not murder my mother and father with an axe! Please don't find me guilty; I'm suffering enough through being an orphan."

Argumentum ad nauseam

This is the incorrect belief that an assertion is more likely to be true, or is more likely to be accepted as true, the more often it is heard. So an Argumentum ad Nauseam is one that employs constant repetition in asserting something; saying the same thing over and over again until you're sick of hearing it.

On the Net, your argument is often less likely to be heard if you repeat it over and over again, as people will tend to put you in their kill files.

Argumentum ad novitatem

This is the opposite of the Argumentum ad Antiquitatem; it's the fallacy of asserting that something is better or more correct simply because it is new, or newer than something else.

"BeOS is a far better choice of operating system than OpenStep, as it has a much newer design."

Argumentum ad numerum

This fallacy is closely related to the argumentum ad populum. It consists of asserting that the more people who support or believe a proposition, the more likely it is that that proposition is correct. For example:

"The vast majority of people in this country believe that capital punishment has a noticeable deterrent effect. To suggest that it doesn't in the face of so much evidence is ridiculous."

"All I'm saying is that thousands of people believe in pyramid power, so there must be something to it."

Argumentum ad populum (Appeal to the people or gallery)

This is known as Appealing to the Gallery, or Appealing to the People. You commit this fallacy if you attempt to win acceptance of an assertion by appealing to a large group of people. This form of fallacy is often characterized by emotive language. For example:

"Pornography must be banned. It is violence against women."

"For thousands of years people have believed in Jesus and the Bible. This belief has had a great impact on their lives. What more evidence do you need that Jesus was the Son of God? Are you trying to tell those people that they are all mistaken fools?"

Argumentum ad verecundiam (Appeal to authority)

The Appeal to Authority uses admiration of a famous person to try and win support for an assertion. For example:

"Isaac Newton was a genius and he believed in God."

This line of argument isn't always completely bogus when used in an inductive argument; for example, it may be relevant to refer to a widely-regarded authority in a particular field, if you're discussing that subject. For example, we can distinguish quite clearly between:

"Hawking has concluded that black holes give off radiation"

and

"Penrose has concluded that it is impossible to build an intelligent computer"

Hawking is a physicist, and so we can reasonably expect his opinions on black hole radiation to be informed. Penrose is a mathematician, so it is questionable whether he is well-qualified to speak on the subject of machine intelligence.

Audiatur et altera pars

Often, people will argue from assumptions which they don't bother to state. The principle of Audiatur et Altera Pars is that all of the premises of an argument should be stated explicitly. It's not strictly a fallacy to fail to state all of your assumptions; however, it's often viewed with suspicion.

Bifurcation

Also referred to as the "black and white" fallacy and "false dichotomy," bifurcation occurs if someone presents a situation as having only two alternatives, where in fact other alternatives exist or can exist. For example:

"Either man was created, as the Bible tells us, or he evolved from inanimate chemicals by pure random chance, as scientists tell us. The latter is incredibly unlikely, so ..."

Circulus in demonstrando

This fallacy occurs if you assume as a premise the conclusion which you wish to reach. Often, the proposition is rephrased so that the fallacy appears to be a valid argument. For example:

"Homosexuals must not be allowed to hold government office. Hence any government official who is revealed to be a homosexual will lose his job. Therefore homosexuals will do anything to hide their secret, and will be open to blackmail. Therefore homosexuals cannot be allowed to hold government office."

Note that the argument is entirely circular; the premise is the same as the conclusion. An argument like the above has actually been cited as the reason for the British Secret Services' official ban on homosexual employees.

Circular arguments are surprisingly common, unfortunately. If you've already reached a particular conclusion once, it's easy to accidentally make it an assertion when explaining your reasoning to someone else.

Complex question / Fallacy of interrogation / Fallacy of presupposition

This is the interrogative form of Begging the Question. One example is the classic loaded question:

"Have you stopped beating your wife?"

The question presupposes a definite answer to another question which has not even been asked. This trick is often used by lawyers in cross-examination, when they ask questions like:

"Where did you hide the money you stole?"

Similarly, politicians often ask loaded questions such as:

"How long will this EU interference in our affairs be allowed to continue?"

or

"Does the Chancellor plan two more years of ruinous privatization?"

Another form of this fallacy is to ask for an explanation of something which is untrue or not yet established.

Composition

The Fallacy of Composition is to conclude that a property shared by a number of individual items, is also shared by a collection of those items; or that a property of the parts of an object, must also be a property of the whole thing. Examples:

"The bicycle is made entirely of low mass components, and is therefore very lightweight."

"A car uses less petrochemicals and causes less pollution than a bus. Therefore cars are less environmentally damaging than buses."

A related form of fallacy of composition is the "just" fallacy, or fallacy of mediocrity. This is the fallacy that assumes that any given member of a set must be limited to the attributes that are held in common with all the other members of the set. Example:

"Humans are just animals, so we should not concern ourselves with justice; we should just obey the law of the jungle."

Here the fallacy is to reason that because we are animals, we can have only properties which animals have; that nothing can distinguish us as a special case.

Converse accident / Hasty generalization

This fallacy is the reverse of the Fallacy of Accident. It occurs when you form a general rule by examining only a few specific cases which aren't representative of all possible cases. For example:

"Jim Bakker was an insincere Christian. Therefore all Christians are insincere."

Converting a conditional

This fallacy is an argument of the form "If A then B, therefore if B then A."

"If educational standards are lowered, the quality of argument seen on the Net worsens. So if we see the level of debate on the net get worse over the next few years, we'll know that our educational standards are still falling."

This fallacy is similar to the Affirmation of the Consequent, but phrased as a conditional statement.

Cum hoc ergo propter hoc

This fallacy is similar to post hoc ergo propter hoc. The fallacy is to assert that because two events occur together, they must be causally related. It's a fallacy because it ignores other factors that may be the cause(s) of the events.

"Literacy rates have steadily declined since the advent of television. Clearly television viewing impedes learning."

This fallacy is a special case of the more general non causa pro causa.

Denial of the antecedent

This fallacy is an argument of the form "A implies B, A is false, therefore B is false." The truth table for implication makes it clear why this is a fallacy.

Note that this fallacy is different from Non Causa Pro Causa. That has the form "A implies B, A is false, therefore B is false," where A does not in fact imply B at all. Here, the problem isn't that the implication is invalid; rather it's that the falseness of A doesn't allow us to deduce anything about B.

"If the God of the Bible appeared to me, personally, that would certainly prove that Christianity was true. But God has never appeared to me, so the Bible must be a work of fiction."

This is the converse of the fallacy of Affirmation of the Consequent.

Dicto simpliciter / Fallacy of accident / Sweeping generalization

A sweeping generalization occurs when a general rule is applied to a particular situation, but the features of that particular situation mean the rule is inapplicable. It's the error made when you go from the general to the specific. For example:

"Christians generally dislike atheists. You are a Christian, so you must dislike atheists."

This fallacy is often committed by people who try to decide moral and legal questions by mechanically applying general rules.

Division

The fallacy of division is the opposite of the Fallacy of Composition. It consists of assuming that a property of some thing must apply to its parts; or that a property of a collection of items is shared by each item.

"You are studying at a rich college. Therefore you must be rich."

"Ants can destroy a tree. Therefore this ant can destroy a tree."

Equivocation / Fallacy of four terms

Equivocation occurs when a key word is used with two or more different meanings in the same argument. For example:

"What could be more affordable than free software? But to make sure that it remains free, that users can do what they like with it, we must place a license on it to make sure that will always be freely redistributable."

One way to avoid this fallacy is to choose your terminology carefully before beginning the argument, and avoid words like "free" which have many meanings.

Extended analogy

The fallacy of the Extended Analogy often occurs when some suggested general rule is being argued over. The fallacy is to assume that mentioning two different situations, in an argument about a general rule, constitutes a claim that those situations are analogous to each other.

Here's real example from an online debate about anti-cryptography legislation:

"I believe it is always wrong to oppose the law by breaking it."

"Such a position is odious: it implies that you would not have supported Martin Luther King."

"Are you saying that cryptography legislation is as important as the struggle for Black liberation? How dare you!"

Ignoratio elenchi / Irrelevant conclusion

The fallacy of Irrelevant Conclusion consists of claiming that an argument supports a particular conclusion when it is actually logically nothing to do with that conclusion.

For example, a Christian may begin by saying that he will argue that the teachings of Christianity are undoubtedly true. If he then argues at length that Christianity is of great help to many people, no matter how well he argues he will not have shown that Christian teachings are true.

Sadly, these kinds of irrelevant arguments are often successful, because they make people to view the supposed conclusion in a more favorable light.

Natural Law fallacy / Appeal to Nature

The Appeal to Nature is a common fallacy in political arguments. One version consists of drawing an analogy between a particular conclusion, and some aspect of the natural world--and then stating that the conclusion is inevitable, because the natural world is similar:

"The natural world is characterized by competition; animals struggle against each other for ownership of limited natural resources. Capitalism, the competitive struggle for ownership of capital, is simply an inevitable part of human nature. It's how the natural world works."

Another form of appeal to nature is to argue that because human beings are products of the natural world, we must mimic behavior seen in the natural world, and that to do otherwise is "unnatural":

"Of course homosexuality is unnatural. When's the last time you saw two animals of the same sex mating?"

An example of "Appeal to Nature" taken to extremes is The Unabomber Manifesto.

"No True Scotsman ..." fallacy

Suppose I assert that no Scotsman puts sugar on his porridge. You counter this by pointing out that your friend Angus likes sugar with his porridge. I then say "Ah, yes, but no true Scotsman puts sugar on his porridge.

This is an example of an ad hoc change being used to shore up an assertion, combined with an attempt to shift the meaning of the words used original assertion; you might call it a combination of fallacies.

Non causa pro causa

The fallacy of Non Causa Pro Causa occurs when something is identified as the cause of an event, but it has not actually been shown to be the cause. For example:

"I took an aspirin and prayed to God, and my headache disappeared. So God cured me of the headache."

This is known as a false cause fallacy. Two specific forms of non causa pro causa fallacy are the cum hoc ergo propter hoc and post hoc ergo propter hoc fallacies.

Non sequitur

A non sequitur is an argument where the conclusion is drawn from premises which aren't logically connected with it. For example:

"Since Egyptians did so much excavation to construct the pyramids, they were well versed in paleontology."

(Non sequiturs are an important ingredient in a lot of humor. They're still fallacies, though.)

Petitio principii (Begging the question)

This fallacy occurs when the premises are at least as questionable as the conclusion reached. Typically the premises of the argument implicitly assume the result which the argument purports to prove, in a disguised form. For example:

"The Bible is the word of God. The word of God cannot be doubted, and the Bible states that the Bible is true. Therefore the Bible must be true.

Begging the question is similar to circulus in demonstrando, where the conclusion is exactly the same as the premise.

Plurium interrogationum / Many questions

This fallacy occurs when someone demands a simple (or simplistic) answer to a complex question.

"Are higher taxes an impediment to business or not? Yes or no?"

Post hoc ergo propter hoc

The fallacy of Post Hoc Ergo Propter Hoc occurs when something is assumed to be the cause of an event merely because it happened before that event. For example:

"The Soviet Union collapsed after instituting state atheism. Therefore we must avoid atheism for the same reasons."

This is another type of false cause fallacy.

Red herring

This fallacy is committed when someone introduces irrelevant material to the issue being discussed, so that everyone's attention is diverted away from the points made, towards a different conclusion.

"You may claim that the death penalty is an ineffective deterrent against crime--but what about the victims of crime? How do you think surviving family members feel when they see the man who murdered their son kept in prison at their expense? Is it right that they should pay for their son's murderer to be fed and housed?"

Reification / Hypostatization

Reification occurs when an abstract concept is treated as a concrete thing.

"I noticed you described him as 'evil.' Where does this 'evil' exist within the brain? You can't show it to me, so I claim it doesn't exist, and no man is 'evil.'"

Shifting the burden of proof

The burden of proof is always on the person asserting something. Shifting the burden of proof, a special case of Argumentum ad Ignorantiam, is the fallacy of putting the burden of proof on the person who denies or questions the assertion. The source of the fallacy is the assumption that something is true unless proven otherwise.

For further discussion of this idea, see the "Introduction to Atheism" document.

"OK, so if you don't think the grey aliens have gained control of the US government, can you prove it?"

Slippery slope argument

This argument states that should one event occur, so will other harmful events. There is no proof made that the harmful events are caused by the first event. For example:

"If we legalize marijuana, then more people would start to take crack and heroin, and we'd have to legalize those too. Before long we'd have a nation full of drug-addicts on welfare. Therefore we cannot legalize marijuana."

Straw man

The straw man fallacy is when you misrepresent someone else's position so that it can be attacked more easily, knock down that misrepresented position, then conclude that the original position has been demolished. It's a fallacy because it fails to deal with the actual arguments that have been made.

"To be an atheist, you have to believe with absolute certainty that there is no God. In order to convince yourself with absolute certainty, you must examine all the Universe and all the places where God could possibly be. Since you obviously haven't, your position is indefensible."

The above straw man argument appears at about once a week on the net. If you can't see what's wrong with it, read the "Introduction to Atheism" document.

Tu quoque

This is the famous "you too" fallacy. It occurs if you argue that an action is acceptable because your opponent has performed it. For instance:

"You're just being randomly abusive."

"So? You've been abusive too."

This is a personal attack, and is therefore a special case of Argumentum ad Hominem.

Undistributed Middle / "A is based on B" fallacies / "... is a type of ..." fallacies

These fallacies occur if you attempt to argue that things are in some way similar, but you don't actually specify in what way they are similar. Examples:

"Isn't history based upon faith? If so, then isn't the Bible also a form of history?"

"Islam is based on faith, Christianity is based on faith, so isn't Islam a form of Christianity?"

"Cats are a form of animal based on carbon chemistry, dogs are a form of animal based on carbon chemistry, so aren't dogs a form of cat?"

Extinction Time of Some Stochastic Differential Equations

2008-08-21T20:49:00.000-07:00

Author(s):

Diabate Nabongo

Universite d'Abobo-Adjame, UFR-SFA,
Departement de Mathщmatiques et Informatiques,
16 BP 372 Abidjan 16, (Cote d'Ivoire)

nabongo_diabate@yahoo.fr

Theodore K. Boni

Institut National Polytechnique
Houphouet-Boigny de Yamoussoukro,
BP1093 Yamoussoukro, (Cote d'Ivoire)

theokboni@yahoo.fr

Abstract:

In this paper, we consider a stochastic differential equation. Under some conditions, we show that any solution of the above problem extincts in a finite time and its extinction time goes to that of the solution of certain differential equation when the parameter of the diffusion tends to zero. We also extend the above result to other classes of extinction problems.
AMS subject classifications(2000): 60H10, 60G17, 34F05
Key-words: Stochastic differential equations, extinction, extinction time.

Full text (pdf)

Phase Flows of One Family of Cubic Systems in a Poincare Circle. II.

2008-08-21T20:47:00.000-07:00

Author(s):

A. F. Andreev

Russia, 198504, Petergof, Universitetski pr.28
S.Peterburg State University
Faculty of Mathematics and Mechanics

irandr@inbox.ru

I. A. Andreeva

Russia, 195251, Saint-Petersburg, Politekhnicheskaya str., 29,
Saint-Petersburg state technic university,
dept. of Higher mathematics

irandr@inbox.ru

Abstract:

On a real (x,y)-plane a normal system of ordinary differential equations is considered, being the right parts are respectively quadratic and cubic forms of x and y with arbitrary constant coefficients. The task is to investigate the behavior of its trajectories on an extended (x,y)- plane or, in equivalent terms, in a Poincare circle. In Part I of this investigation all possible for this system topological types of a singular point O(0,0) are revealed, and criteria of their realization are formulated. Topological types of the point O are given:

in terms of bundles of O-semiorbits of the system of N (node) and S (saddle) types, and
in terms of O-sectors of Bendixon of E (elliptic), H (hyperbolic) and P (parabolic) types.
Full text (pdf)

Arad Hochman

2008-08-21T20:45:00.000-07:00

"Even if you're not a genius, you can use the same strategies as Aristotle and Einstein to harness the power of your creative mind and better manage your future."

The following eight strategies encourage you to think productively,
rather than reproductively, in order to arrive at solutions to problems. "These strategies are common to the thinking styles of creative geniuses in science, art, and industry throughout history."

Flash version (illustrated--new perspective!)

1. Look at problems in many different ways, and find new perspectives that no one else has taken (or no one else has publicized!)

Leonardo da Vinci believed that, to gain knowledge about the form of a problem, you begin by learning how to restructure it in many different ways. He felt that the first way he looked at a problem was too biased. Often, the problem itself is reconstructed and becomes a new one.

2. Visualize!

When Einstein thought through a problem, he always found it necessary to formulate his subject in as many different ways as possible, including using diagrams. He visualized solutions, and believed that words and numbers as such did not play a significant role in his thinking process.

3. Produce! A distinguishing characteristic of genius is productivity.

Thomas Edison held 1,093 patents. He guaranteed productivity by giving himself and his assistants idea quotas. In a study of 2,036 scientists throughout history, Dean Keith Simonton of the University of California at Davis found that the most respected scientists produced not only great works, but also many "bad" ones. They weren't afraid to fail, or to produce mediocre in order to arrive at excellence.

4. Make novel combinations. Combine, and recombine, ideas, images, and thoughts into different combinations no matter how incongruent or unusual.

The laws of heredity on which the modern science of genetics is based came from the Austrian monk Grego Mendel, who combined mathematics and biology to create a new science.

5. Form relationships; make connections between dissimilar subjects.

Da Vinci forced a relationship between the sound of a bell and a stone hitting water. This enabled him to make the connection that sound travels in waves. Samuel Morse invented relay stations for telegraphic signals when observing relay stations for horses.

6. Think in opposites.

Physicist Niels Bohr believed, that if you held opposites together, then you suspend your thought, and your mind moves to a new level. His ability to imagine light as both a particle and a wave led to his conception of the principle of complementarity. Suspending thought (logic) may allow your mind to create a new form.

7. Think metaphorically.

Aristotle considered metaphor a sign of genius, and believed that the individual who had the capacity to perceive resemblances between two separate areas of existence and link them together was a person of special gifts.

8. Prepare yourself for chance.

Whenever we attempt to do something and fail, we end up doing something else. That is the first principle of creative accident. Failure can be productive only if we do not focus on it as an unproductive result. Instead: analyze the process, its components, and how you can change them, to arrive at other results. Do not ask the question "Why have I failed?", but rather "What have I done?"

But How Do I Do Mathematical Research?”

2008-08-21T20:32:00.000-07:00

But How Do I Do Mathematical Research?”

By Jeff Suzuki

Many schools include a research project as part of the graduation requirements for their mathematics majors. But most students are at a loss to create their own research questions, leaving this task to their advisors. It would be better if the student came up with their own research question that involved significant mathematical investigation and the creation of original mathematics. This is a daunting task: most graduate students are unable to do this, and rely on their advisors to frame a suitable area for investigation. The task is further complicated by the fact that many questions relating to undergraduate mathematics have “already been solved,” while many of the unsolved questions require so much specialized background to understand or so much existing research to review that the preparation needed to tackle the problem is itself a major project.

So how can students be guided to create a question that is non-trivial but amenable to investigation? One guide to the process of creating a question is to look at what mathematical research is. The vast majority of mathematical research falls into one of five (non-exclusive) categories which, after some thought, fit nicely into the acronym PEACE: Proof, Extension, Application, Characterization, and Existence.

Proof: Of course, every mathematical research project involves proof; in this context, proof is the focus of the project. For example, “Prove Fermat’s Last Theorem.” More generally, though, we note that reproof is also a valid line of mathematical research: Gauss, for example, earned his doctoral dissertation by providing a new proof of the Fundamental Theorem of Algebra. It might be argued that no rigorous proof existed before Gauss, but clearly Gauss felt that proving a theorem once was insufficient: he eventually gave four proofs of the Fundamental Theorem of Algebra and six proofs of the Law of Quadratic Reciprocity.

Extension: This takes some existing concept and extends it. For example, Newton took the expansion of (a + b)n, where n is a whole number, and extended it to the expansion of (a + b)n where n was a positive or negative rational number. The Lebesgue integral is another example of an extension.

Application: We may take an existing idea and apply it to a new area. This is frequently the focus of projects in applied mathematics, but it also can be used to originate new areas of pure mathematics: the application of algebra to problems in geometry led to Descartes’s creation of analytic geometry, while the application of power series techniques to problems in number theory led to Euler’s creation of analytic number theory.

Characterization: We can try to characterize or classify a mathematical object or concept. For example, Cauchy’s great contribution was to characterize what was really meant by continuity, differentiability, and integrability, while Cantor characterized the naive notions of “infinity,” and the Enormous Theorem is a classification of finite simple groups.

Existence: Strictly speaking, this is part of “characterization,” since one quality of an object is whether or not it exists. However, existence (or non-existence) theorems tend to be treated separately: this is reasonable, since unless the object exists, there is no point investigating its mathematics! Examples of existence results are Euclid’s proof of the existence of an infinite number of primes or Gödel’s incompleteness theorem (a non-existence proof).

With these five lines of research as a guide, students at both graduate and undergraduate levels may find it easier to generate their own research questions.

Jeff Suzuki is Visiting Assistant Professor of Mathematics and Director of Quantitative Support at Bard College.

Textbooks in Mathematics

2008-08-21T20:28:00.000-07:00

Secure Heterogeneous Information Presentation
– SHIP –
(heterogeneous contents on heterogeneous platforms)
The Programming Technology Group (PTG)
Department of Computer Science, University of Bergen
April 26, 2006
1 Context and relevance
The networked society is entirely dependent on the access to and use of information.
A typical problem for a user is that the information he is seeking is available but not
organised in the way matching his actual needs. E.g., it is in a diﬀerent format which does
not conform to the user’s interface, it has a diﬀerent logical structure which is not handled
properly by the user’s software, the user is not authorised to access it, typically, for some
security reasons. By the word “presentation” in the title we mean the general process
of information disclosure, exchange and use. It poses problems to the user like those just
mentioned, and puts serious demands on the service providers in order to circumvent them.
One can distinguish two complementary aspects of this general situation:
(i). On one hand, the user wants easily accessible information structured for his purposes
and tailored for presentation in the format available to him – this is the presentation
aspect.
(ii). On the other hand, the information provider must not just ensure the widest possible
availability of the stored data, but also their consistency accross diﬀerent presentation
forms (the information content should be the same no matter on what platform or in
what form it is presented) and their security (preventing unauthorised access, etc.)
– this is the security aspect.
Problems related to both these aspects can be, most generally, viewed as originating from
heterogeneity: of formats and platforms, of demands and expectations, of user types and
information content, of communication channels and security ob jectives. This pro ject
addresses the problem of tailoring content (text, sound, images or video) to the possibili-
ties/limitations of various platforms (terminals, PDA, mobile telephone, laptop computer,
home video installation) and the preferences of the user (mute, large font or even braille,
black-and-white, only the headlines, etc.).
1
2 Pro ject description
2.1 Background and state-of-the-art
The problem identiﬁed in the previous paragraph has been attacked by several R&D groups,
both in academia and in industry. This has resulted in a number of practical, but ad hoc
proposals or attempts to solve it. For example, LSDI (Large Scale Distributed Information
Systems) laboratory has specialized in the emerging area of the Semantic Web, [1]. W3C
has adopted SMIL which is an XML application that enables simple authoring of interactive
audiovisual presentations, [4]. Vizrt’s graphics solutions are tailored for the broadcasting
industry (http://www.vizrt.no/).
Although these are cutting-edge solutions, they are too speciﬁc, and generally fall short
with respect to solving the general problem in a satisfying way. A deeper analysis of this
failure reveals that while the enormous heterogeneity is a fact of network-life, the existing
proposals tend toward suggesting possible standards rather than approaching systemati-
cally their shortcomings.
Certainly, establishing common standards is a desirable process and result but, in the
meantime, one has to address heterogeneous agents acting in heterogeneous environments.
(There is little to indicate that the situation will change dramatically even if some more
standards will be established.) Multiplicity of solutions is understandable, and probably
even desirable, when one considers the great variety of speciﬁc problems which must be
addressed – expecting one uniﬁed approach does not seem realistic. However, one would
expect that some common issues, appearing in many diﬀerent situations, can be identiﬁed
and organised for the beneﬁt of the future users.
This pro ject takes up the challenge of addressing in a systematic way this very prob-
lem. It does not aim at designing the uniﬁed methodology addressing all possible ways
of disseminating information. But it does aim at providing a general framework of wide
applicability for disseminating heterogeneous contents on heterogeneous platforms in a way
which ensures consistency of various presentations, is adaptable to the needs of the par-
ticular user and does not compromise the security issues. (One can propose the following
analogy: problems with organising large amounts of data resulted, in the early days of
databases, in a wide variety of methods and particular solutions; the emergence of the re-
lational model neither suppressed all of them, nor precluded further development of models
for speciﬁc applications; it did not even prevent one from developing ill-designed relational
databases; but it identiﬁed a series of key issues to be considered in the design process and
provided a general methodology for handling them.)
We ﬁnish this section with the observation that Information Network Management has
become strongly multidisciplinary in recent years, with important inﬂuences from Software
Engineering, Formal Methods and Artiﬁcial Intelligence.
2.2 Goals
The overall goals of the SHIP pro ject are as follows:
2
G1. Advancing the state-of-the-art of network technology
by developing a ﬂexible framework for
• handling data and
• organising software
for heterogeneous content on heterogeneous platforms which provides a solution to
the problem sketched above.
G2. Strengthening the national competence base around these issues
• Increasing the knowledge base of the researchers involved in the pro jet
• Educating new experts (M.Sc. and Ph.D.) in the ﬁeld
G3. Transfer of the existing and acquired knowledge to industry
• Close cooperation with industrial partners
• Development of prototype solutions based on the acquired insights
G4. Disseminating and exchganing the emerging knowledge
• Publications in both (inter)national conferences and journals
• Continuing and strengthening the existing cooperation with the researchers
abroad
2.3 Results
The following results are planned:
R1. qualiﬁed competence in the form of Ph.D. and M.Sc. degrees in connection with the
pro ject (goal G2)
R2. a framework for handling data and organizing software for secure information pre-
sentation (goal G1, G2)
R3. a prototype in the ﬁeld of distance learning (goal G3, G2, G1)
R4. workshops with industrial partners included (goal G3)
R5. publications on the framework and on the new theoretical insights (goal G4)
3
2.4 Challenges and how to approach the problem
The ma jor challenge is to combine the two inter-dependent aspects suggested in Section 1:
(i) the presentation aspect: the desired ﬂexibility to adapt to diﬀerent preferences/technical
possibilities of diﬀerent user/platform combinations, and even to the possibly chang-
ing preferences of one user, and
(ii) the security aspect: the concern for the adequacy, consistency and security of the
presented information and oﬀered services.
These two aspects will be addressed under four main headlines.
2.4.1 Design and formalisation of presentation patterns
The ﬁrst necessary step is the development of a language for specifying presentation pat-
terns and modalities. It should allow one to correlate the (logical and physical) format
of the stored data with the intended (logical and physical) presentation medium. For the
eﬀective deployment of formal methodology, this should be a declarative language with
a sound operational semantics. A plausible way to proceed seems to be enriching XML
style sheets with suitable presentation primitives. One of the beneﬁts of this choice is easy
syntax and parsing.
The challenge here is to ensure a reasonable genericity of the solutions which can be
reused in diﬀerent contexts [9]. The language should also provide a modular structure
allowing for reuse of larger components and not only of the low level partial solutions.
Here we will build on earlier experiences and develop further the technology of presentation
patterns with which we have been working over last years.
Aiming at reusability and genericity of the results, we will generalise the speciﬁc solu-
tions capturing them in a rigorous, yet user friendly, diagrammatic speciﬁcation formalism
based on generalized sketches (The existing results and earlier experiences show that they
can be used for a variety of purposes like modelling of data, processes and metadata, gener-
alizing a series of diagrammatic techniques used in software engineering like FDM-schemas,
ER- and UML-diagrams, interaction diagrams, schema grids, [7, 8].)
2.4.2 Typing discipline as a basic security mechanism
Generalized sketches provide, along with the diagrammatic description formalism, a rigor-
ous semantic model which will be developed along the way. However, this model provides
only the basic semantics at the most general level and should be augmented with a more re-
ﬁned semantics addressing resource-sensitive and operational aspects. This problem will be
approached by introducing adequate typing system allowing one to statically type presen-
tation speciﬁcations and conclude that if they are well-typed, they can be safely executed
under the operational semantics. Type-checking provides thus the ﬁrst and general secu-
rity mechanism, which can be designed and used in all situations without addressing the
application speciﬁc issues, [10].
4
Note that “software security” does not mean here the classical issues of the program
correctness, loop or deadlock detection, let alone any speciﬁc encryption mechanisms. We
mean this in the general sense of preventing unauthorized changing, destroying or leak-
ing data from the client and server devices. Strict typing can contribute signiﬁcantly to
preventing such security failures analogous to the way in which typing in programming
languages increases reliability of software. The inspiration comes from Java, where the
sandbox principle has been applied to similar purposes in the context of a general purpose
programming language. As far as we know this principle has not been applied in a plat-
form independent environment. This is on one hand much more diﬃcult, but keep in mind
that the context of presenting content is limited and therefore easier than that of general
purpose programming language like Java.
Here we propose to elaborate the type systems such as developed, albeit for diﬀerent
purposes, in the earlier pro ject MoSIS (see 2.7 and [12]).
2.4.3 Application/context dependent security analysis
Static typing, as described above, can preclude only, and only to some degree, the most
general kinds of failures (e.g., format-not-supported, resource-not-available). The impor-
tant task of their identiﬁcation and handling should be, as far as possible, delegated to
the automatic type-checking mechanism. However, types do not address many more spe-
ciﬁc security issues which are dependent on the actual problem domain and which must
be handled explicitly by the system designer. A further challenge is therefore to design
a ”security language”. On one hand, it should allow one to state precisely a variety of
possible security ob jectives. On the other hand, it should provide appropriate abstraction
mechanisms for describing the security aspects of the actual programs. Finally, it should
facilate validation of programs with respect to the stated security ob jectives. [5, 6].
Here we will continue earlier work started in the MoSIS pro ject which, so far, has
resulted in a kernel language. Due to its modular structure, it can be combined with a
variety of speciﬁc languages and thus adapted to speciﬁc system descriptions.
2.4.4 Testing and validation of the methodology
The pragmatics will be explored in a number of small to medium size examples. One will
also develop a large prototype for actual use in practical situations. Given the earlier ex-
perience in the ﬁeld, the prototype will most probably be designed for a distance learning,
which provides an excellent example of all the issues raised above: the adequacy of presen-
tation form, its accessibility on diﬀerent platforms, access restrictions (e.g., solutions can
be accessed by the teacher, but cannot be compromised by being accessed/intercepted by
the students before the exam).
Here, cooperation with the industrial partners will contribute to the speciﬁcation of the
requirements, as well as to the technical solutions and eventual utility of the product.
5
2.5 Pro ject plan
2.5.1 Work packages
W1. Pro ject management
(T1) Task: Pro ject coordination
Deliverables: Internal reports, work notes, drafts of reports and articles, pre-
sentations
(T2) Task: Pro ject reporting
Deliverables: Annual reports to NFR, status reports, web-updates, ﬁnal re-
port
W2. Supervision package (result R1)
(T1) Task: Ph.D. 1
(T2) Task: Ph.D. 2
(T3) Task: M.Sc. students
Deliverables: Graduate candidates in the ﬁeld
The supervision of M.Sc. students will be according to the university procedures on
this point. Ph.D. students will join the PhD Research School in Information and
Communication Technology at the Department of Informatics, University of Bergen.
For every Ph.D. student there will be one senior staﬀ member involved in the pro ject
made responsible for the supervision, and each candidate will spend between a half
and a whole year in an associate institution abroad (see 2.7.3). The supervision will
be reviewed in the pro ject meetings, if necessary.
The doctoral candidates will be assigned tasks under work package W3-W5 depend-
ing on their speciﬁc bacground.
W3. Presentation patterns – syntax and semantics (results R2, R3)
(T1) Task: Design of a (diagrammatic) language for describing presentation patterns
Research challenges: 2.4.1, 2.4.2
(T2) Task: Sketch-based semantics for the language
Research challenges: 2.4.1
(T3) Task: Exploring expressivity of the language by embedding into it some existing
(diagrammatic) formalisms
Research challenges: 2.4.1
Deliverables: language deﬁnition and documentation, publications
W4. Security speciﬁcation and analysis (results R2, R3)
6
(T1) Task: Division of security issues between the generic (type system) and appli-
cation dependent
Research challenges: 2.4.1, 2.4.2, 2.4.3
(T2) Task: Typing system and type-checking mechanism
Research challenges: 2.4.2
(T3) Task: Language and semantics for describing application dependent security
aspects
Research challenges: 2.4.3
(T4) Task: Implementation of type-checker (T2) and veriﬁcation system (T3)
Research challenges: 2.4.1, 2.4.3
Deliverables: type system, type checking algorithm, language for security speciﬁca-
tion with documentation, algorithms and support system for veriﬁcation, publications
W5. Prototype development (result R3)
(T1) Task: Requirement analysis and functional speciﬁcation (with the industrial
partners)
(T2) Task: Coordination of and selection from the theoretical knowledge
(T3) Task: Operational semantics of the language from W3
(T4) Task: Programming the prototype
All subtasks respond jointly to the challenge 2.4.4.
Deliverables: documented requirement analysis, working prototype with docu-
mented code, test results, user manual
W6. Dissemination and collaboration package (result R3, R4, R5)
(T1) Task: Evalution of the prototype by the industrial partners
Deliverables: evaluation report
(T2) Task: Workshops with the industrial partners
Deliverables: workshop materials and proceedings
(T3) Task: Publications and conference participation
Deliverables: publications in journals and conference proceedings, presenta-
tions at conferences
7
2.5.2 Time schedule: see the e-application
2.6 Budget: see the e-application
2.7 Leadership and organisation
The pro ject will be carried out by the Programming Technology Group (PTG) at the
Department of Informatics, University of Bergen, in cooperation with national and inter-
national partners (see 2.7.2, 2.7.3).
Professor Marc Bezem (CV enclosed) will function as the Principal Investigator
(PI). He is internationally recognized, both as (co-)author of over 50 refereed scientiﬁc
publications (
≥ 400 citations in ResearchIndex) and as (co-)editor (≥ 500 citations in
ResearchIndex). He has been involved in a series of international and national pro jects,
both as participant and as principal investigator. The 6 PhD students he has supervised
all graduated successfully. (The ﬁrst MoSIS PhD graduates 15 May [12].)
2.7.1 Background competency
PTG has well-documented skills in software development methodology, the ability to take
theory into practice, as well as an excellent record on education. The group was qualiﬁed as
‘very good’ by an international panel of research experts, [11]. It has produced several PhD
degrees in recent years and is currently supervising seven doctoral students, in addition to a
considerable number of master students. It has industrial contacts with several companies,
among others, Intelinet, CellVision, Nera and Rogaland Research.
The research activities of the group are at a high international level and range from
foundational work on logical and algebraic foundations of programming, to program trans-
formation techniques and web technologies with focus on the component technologies in
software engineering. Its members have long experience and high expertise in the ﬁelds of
type theory, algebraic structuring mechanisms, logic and speciﬁcation, secure network sys-
tems, diagrammatic methods, component software design, handling of bounded resources,
which all contribute to the ob jectives of the proposed pro ject.
The group has the following members (main research interests given in parentheses):
• Prof. Marc Bezem (type theory, declarative programming languages, component soft-
ware)
• Prof. Magne Haveraaen (algebraic software methodologies and frameworks, modular
software, program transformation)
• Assoc. Prof. Khalid A. Mughal (ob ject orientation, Java, web-based systems, distance-
learning)
• Assoc. Prof. Micha􏰀l Walicki (algebraic and logical methods for abstraction and mod-
ularization, modular reasoning, multiagent systems)
8
• Assoc. Prof. Uwe Wolter (algebraic speciﬁcations, diagrammatic formalisms, cate-
gorical semantics, heterogeneous abstract model theory)
The group has in the years 2002-2006 worked under the NFR founded pro ject MoSIS (NFR
146967/431). It addressed the issues of modularity and interacting components, which is
of particular relevance for the proposed pro ject.
To a large extent, the proposed pro ject will beneﬁt from the successful contributions
made in the MoSIS pro ject: modularity of the design and veriﬁcation addressed in MoSIS
will contribute to addressing the challenges 2.4.1 and 2.4.2, while description and validation
of interacting components from MoSIS will provide the starting point for 2.4.3.
2.7.2 National partners
• Intelinet AS (www.intelinet.no) This company will be an active partner in the
pro ject. The (enclosed) letter conﬁrming the cooperation gives additional information
on Intelinet. They will play a key role in Workpackage W5, the prototype. Part of
the budget for the Research Associate will be reserved for this.
• CellVision AS (www.cellvision.no) Norwegian company which develops commu-
nication products for mobile operators. CellVision’s products are founded on the op-
erators’ demand for solutions that convert complex network data and processes into
useful and simple applications. CellVision has developed cutting-edge technology in
so-called scalable graphics (grid- and vector-based), which is of obvious relevance to
SHIP.
• Høgskolen i Bergen: (Bergen University College) At present, PTG collaborates
with HiB (Assoc. Prof. Yngve Lamo) in a pro ject on Diagrammatic Software Speciﬁ-
cations based on Sketches. The goal of the pro ject is to develope a software engineer-
ing tool for diagrammatic software development. The cooperation will be strength-
ened within the proposed pro ject and its results will be further developed towards
the current goals.
2.7.3 International cooperation
• DFKI-Lab Bremen The recently founded Bremen Laboratory for Safe and Se-
cure Cognitive Systems (SCCS) of the German Research Center for Artiﬁcial In-
telligence www.dfki.de/web/research/sks.en.html is headed by Prof. Dr. Bernd
Krieg-Br¨
uckner and is an active partner, see the enclosed letter conﬁrming the co-
operation. SCCS is willing to host one or two SHIP PhDs for their stay abroad.
There are close connections between SHIP and the MMISS pro ject (MultiMedia In-
struction in Safe Systems, www.informatik.uni-bremen.de/mmiss/), also headed
by Prof. Krieg-Br¨
uckner.
• Leicester University The University of Leicester has a strong and visible group in
Software Science and Engineering, headed by Prof. Jos´e Luis Fiadeiro. PTG has a
9
standing collaboration with this group (visits, CALCO, WADT). The enclosed letter
conﬁrms their willingness to host our PhD students for their stay abroad.
• Cornell University Mughal will have a sabbatical at Cornell, Department of Com-
puter Science, in the academic year 2007/8 (see the enclosed invitation letter). There
will be active collaboration with the group working on security (www.cs.cornell.
edu/Research/Security). Supervision of SHIP PhDs will be guaranteed by regular
visits of various length.
The group will also continue cooperation with its network of European researchers,
among others, in the EU pro jects:
– Marie Curie RTN proposal Computability in Europe, [2]
– Coordination Action TYPES 510996, [3]
References
[1] http://lsdis.cs.uga.edu/.
[2] http://www.amsta.leeds.ac.uk/cie/.
[3] http://www.cs.chalmers.se/Cs/Research/Logic/Types/.
[4] http://www.w3.org/2005/12/smil-pressrelease.html.en.
[5] Dimacs workshop on computational and formal security analysis of protocols. DI-
MACS, Rutgers University, Piscataway, New Jersey, USA, June 2004, http://
dimacs.rutgers.edu/Workshops/Protocols/sec-any-prot6.pdf.
[6] IFIP WG 1.7. http://www.dsi.unive.it/~focardi/IFIPWG1_7/.
[7] Z. Diskin. Mathematics of UML: Making the odysseys of UML less dramatic. In
H. Kilov and K. Baclawski, editors, Practical Foundations of Business System Speci-
ﬁcations, pages 348–381. Kluwer Academic Publishers, 2003.
[8] Z. Diskin, B. Kadish, F. Piessens, and M. Johnson. Universal arrow foundations for
visual modeling. In M. Anderson, P. Cheng, and V. Haarslev, editors, Theory and
Application of Diagrams, pages 345–360. Springer, LNAI 1889, 2000.
[9] Jos´e Luiz Fiadeiro. Software services: Scientiﬁc challenge or industrial hype? In
Proceedings ICTAC, volume 3407 of Lecture Notes in Computer Science, pages 1–13.
Springer, 2004.
[10] David Naccache, Alexei Tchoulkine, Christophe Tymen, and Elena Trichina. Reducing
the memory complexity of type-inference algorithms. In Proceedings ICICS, volume
2513 of Lecture Notes in Computer Science, pages 109–121. Springer, 2002.
10
[11] The Research Council of Norway. Research in ICT in Norwegian universities and
colleges – a review. 2002.
[12] H.A. Truong. Type Systems for Guaranteeing Resource Bounds of Component Soft-
ware. PhD thesis, Department of Computer Science, University of Bergen, 2006.
11

Textbooks in Mathematics

2008-08-21T20:26:00.000-07:00

Mathematical Analysis I
by Elias Zakon
Description: This text carefully leads the student through the basic topics of real analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material.

For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text.

This text is designed to be used as early as possible in the undergraduate mathematics curriculum; indeed, it was used for many years as the text for a two-semester class for second-year mathematics majors at the University of Windsor. If desired, the material can easily be specialized to n-dimensional (or even two-dimensional) Euclidean space.

Mathematical Analysis II (in preparation) completes this series with material on measure and integration and calculus on normed linear spaces.

Audience: This text is appropriate for any undergraduate mathematics course in real analysis or mathematical analysis, or for a preparatory class for beginning mathematics graduate students who will later advance to courses in measure theory and functional analysis. Knowledge of this material will also be of benefit to graduate students in economics, signal and image processing, fluid and structural mechanics, etc.

This text covers similar material to the books (we give US list prices for current hardcover editions at Amazon on July 10, 2006): Principles of Mathematical Analysis by W. Rudin ($130.00); Introductory Real Analysis by F. D'Angelo and M. Seyfried ($137.56); Introduction to Real Analysis by R. Bartle and D. Sherbert ($125.95); Real Analysis by H. Royden ($124.80); Introduction to Real Analysis by W. Trench ($114.40), etc.

Publishing Information: Mathematical Analysis I, by Elias Zakon, ISBN 1-931705-02-X, published by The Trillia Group, 2004. 355+xii pages, 554 exercises, 26 figures, hypertextual cross-references, hyperlinked index of terms. Download size: 2088 to 2298 KB, depending on format. Currrent version released November 19, 2007.

Textbooks in Mathematics

2008-08-21T20:20:00.000-07:00

Basic Concepts of Mathematics
by Elias Zakon
Description: This book helps the student complete the transition from purely manipulative to rigorous mathematics. The clear exposition covers many topics that are assumed by later courses but are often not covered with any depth or organization: basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers (including consequences of the completeness axiom), fields, and basic properties of n-dimensional Euclidean spaces.

The many exercises and optional topics (isomorphism of complete ordered fields, construction of the real numbers through Dedekind cuts, introduction to normed linear spaces, etc.) allow the instructor to adapt this book to many environments and levels of students. Extensive hypertextual cross-references and hyperlinked indexes of terms and notation add truly interactive elements to the text.

Audience: This book gives students the skills they need to succeed in the first courses in Real Analysis (it is designed specifically to prepare students for the author's Mathematical Analysis I) and Abstract Algebra/Modern Algebra. Students who plan to advance to upper-level classes in computer science (discrete structures, algorithms, computability, automata theory, ...), economics, or electrical and computer engineering (signal and image processing, AI, circuit design, ...) will benefit from mastering the material in this text.

This text is appropriate for courses that might otherwise use the books (we give US list prices for current hardcover editions at Amazon on July 10, 2006): A Transition to Advanced Mathematics by D. Smith, M. Eggen, and R. St. Andre ($117.95); Transition to Higher Mathematics: Structure and Proof by B. Dumas and J. McCarthy ($106.88); An Introduction to Abstract Mathematics by R. Bond and W. Keane ($132.95); Foundations of Higher Mathematics by P. Fletcher and C. W. Patty ($149.95); Mathematical Reasoning: Writing and Proof by T. Sundstrom ($103.00); Foundations of Mathematical Thinking: Problem-Solving and Proofs by J. D'Angelo and D. West ($111.00); etc.

Publishing Information: Basic Concepts of Mathematics, by Elias Zakon, ISBN 1-931705-00-3, published by The Trillia Group, 2001. 198+x pages, 332 exercises, 23 figures, hypertextual cross-references, hyperlinked indexes of notation and terms. Download size: 1378 to 1410 KB, depending on format. Current version released February 12, 2007.

Library Catalogue Information: Librarians at the University of Windsor have prepared a catalogue entry for this book.

Excerpts from the Text: The Terms and Conditions, the Preface, the Table of Contents, and the Index.

Reviews and Recognition: Reviews and recognition for Basic Concepts of Mathematics are noted here. You can review this book at The Assayer.

Terms and Conditions: All uses of this text are subject to the Terms and Conditions contained in this text. As part of these terms, we offer this text free of charge to students using it for self-study, and to lecturers evaluating it as a required or recommended text for a course. All other uses of this text are subject to a charge of $10US for individual use and $300US for use by all individuals at a single site of a college or university. Check our list of site licenses to see whether you are a member of a group that has purchased a site license.