662 research outputs found
Bernhard Riemann's Lebenslauf / neu hrsg. von Gabriele Dörflinger, Universitätsbibliothek Heidelberg
Richard Dedekind (1831-1916) schrieb die Biographie des vielseitigen Mathematikers Bernhard Riemann für dessen posthum zusammengestellter Werkausgabe. Riemann gründete u.a. die Funktionentheorie und untersuchte die Eigenschaften gekrümmter Flächen (Riemannsche Geometrie). Die Seitenzählung des Originals ist am Seitenrand angegeben
Violence against women : a prospective study of women presenting to a South African trauma centre
Background - Violence against Women is a major public health issue, and it is universally under reported. Objective - To conduct an injury surveillance of severe or life threatening violent acts against women, to determine the demographics of the injured women and to identify the nature of the perpetrators. Methods - A standardized structured questionnaire administered in an interview conducted on female patients admitted to the Trauma Centre at Groote Schuur Hospital as a result of interpersonal violence. Age, level of education, employment status, housing and substance abuse was recorded
On the number of cubic orders of bounded discriminant having automorphism group , and related problems
For a binary quadratic form , we consider the action of on
a two-dimensional vector space. This representation yields perhaps the simplest
nontrivial example of a prehomogeneous vector space that is not irreducible,
and of a coregular space whose underlying group is not semisimple. We show that
the nondegenerate integer orbits of this representation are in natural
bijection with orders in cubic fields having a fixed "lattice shape". Moreover,
this correspondence is discriminant-preserving: the value of the invariant
polynomial of an element in this representation agrees with the discriminant of
the corresponding cubic order.
We use this interpretation of the integral orbits to solve three
classical-style counting problems related to cubic orders and fields. First, we
give an asymptotic formula for the number of cubic orders having bounded
discriminant and nontrivial automorphism group. More generally, we give an
asymptotic formula for the number of cubic orders that have bounded
discriminant and any given lattice shape (i.e., reduced trace form, up to
scaling). Via a sieve, we also count cubic fields of bounded discriminant whose
rings of integers have a given lattice shape. We find, in particular, that
among cubic orders (resp. fields) having lattice shape of given discriminant
, the shape is equidistributed in the class group of binary
quadratic forms of discriminant . As a by-product, we also obtain an
asymptotic formula for the number of cubic fields of bounded discriminant
having any given quadratic resolvent field.Comment: 33 page
The creative photographic image
ThesisThe author ha.s chosen to explore the po ss ibilit y that the
creative talent exhibited by an artist's perceptive powers can be
equalled
effects.
by the photographer through subtle use of special
To this e nd the author has explo l'ed a pl'obiem encountered
particularly in 1990's photography which has resulted ill a mass
of high quality photographs taken by large numbers of amateurs
world- wide, who are u si ng sophisticated moderrl camet's technology
as a recording tool without achieving that element of creativity
which captul'es DU I' attention and communicates with our inmost
beings.
The authol' ha s used his own photogl'aphic work and t.ha t of
contempor"ary photogr'aphers in his field of s tudy, to su bstantiate
the claim that thl'ough use of subtle special effects in a ,'ariety
of topics, the photograph can be used a s imaginatively and
c reative ly a s an i mage pI'oduced by a competent artist o r' painter.
This observati.on could have important implication s for an
industry which throug}l co mput er' tec}lnology PI'oposes t o go beyond
the technical re strictions o f the painter whil s t main tai ning that
p rofession's cl"eative flexibility. These spec ial effects should, i n the Buttlo r"s opinion be u sed not
as an e nd to th e mselves, bu t as a mea n s o f transfol~ min g the
of ten c linical med ium of pho tography into a creative tool li lni te d
only by th e photographer's imaginative power's
Rapunzel syndrome: A South African variety
Trichobezoars are intraluminal accretions of ingested hair. Rapunzel syndrome is a rare and extreme presentation, with the trichobezoar extending into the small intestine. It is most frequently reported in children and psychiatric patients. We report a South African series of 5 patients who presented with trichobezoars. Each patient was retrospectively reviewed and analysed with regard to background, demographics, clinical presentation, diagnosis, surgical management and complications. Five female patients with a median age of 19 (range 12 - 27) years presented with clinical symptoms, including early satiety, intermittent vomiting with gastric outlet obstruction, abdominal pain and weight loss. The diagnosis was made by endoscopy, abdominal computed tomography (CT) imaging, barium meal examination or plain abdominal radiography. Two patients presented with sealed/contained gastric perforations, and 1 patient with a smallbowel perforation. All 5 bezoars, 2 of which consisted entirely of artificial hair extensions, extended into the jejunum, the longest measuring 1.4 m. All were removed by laparotomy. While trichobezoars are a rare entity, they may present with significant complications, such as obstructions and perforations. In view of the infection risk and considerable size of many of these bezoars, an open removal is probably safer than any minimally invasive attempt.S Afr Med J 2018;108(7):559-562
The Caesar Problem in its Historical Context: Mathematical Background
The issues surrounding the Caesar problem are assumed to be inert as far as ongoing mathematics is concerned. This paper aims to correct this impression by spelling out the ways that, in their historical context, Frege's remarks would have had considerable resonance with work that other mathematicians such as Riemann and Dedekind were doing. The search for presentation-independent characterizations of objects and global definitions was seen as bound up with fundamental methodological questions in complex analysis and number theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72188/1/j.1746-8361.2005.01029.x.pd
Gesammelte mathematische Werke / Richard Dedekind. Hrsg. von Robert Fricke; Emmy Noether; Øystein Ore ; Bd. 1
Modular Solutions to Equations of Generalized Halphen Type
Solutions to a class of differential systems that generalize the Halphen
system are determined in terms of automorphic functions whose groups are
commensurable with the modular group. These functions all uniformize Riemann
surfaces of genus zero and have --series with integral coefficients.
Rational maps relating these functions are derived, implying subgroup relations
between their automorphism groups, as well as symmetrization maps relating the
associated differential systems.Comment: PlainTeX 36gs. (Formula for Hecke operator corrected.
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