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 C3C_3, and related problems

For a binary quadratic form $Q$, we consider the action of $\mathrm{SO}_Q$ 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 $D$, the shape is equidistributed in the class group $\mathrm{Cl}_D$ of binary quadratic forms of discriminant $D$. 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

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 $q$--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.