Cette thèse concerne des propriétés des variétés jacobiennes de courbes de genre 2 qui couvrent des courbes elliptiques. Soit E une courbe plane, donnée par une équation y^2=F(x), où F(x)=x^3+a2x^2+a1x+a0 est un polynôme à coefficients rationnels, qui a trois racines distinctes. Pour des raisons historiques, une telle courbe est appelée courbe elliptique. On sait que toute courbe elliptique E peut être équipée d'une structure de groupe commutatif - on peut additionner et soustraire ses points. Un point O « à l'infini », qui est contenu dans toutes les droites verticales (droites de la forme x=c), est l'élément neutre. Cette structure de groupe est décrite par la condition que trois points P,Q,R sur E satisfont P+Q+R=O si et seulement s'ils sont alignés. Les surfaces avec une structure de groupe commutatif sont appelées abéliennes. Par exemple, un produit de deux courbes elliptiques E1xE2 est une surface abélienne, de façon évidente. Considérons maintenant une courbe plane C donnée par une équation y^2=G(x), où G(x)=x^6+b5x^5+b4x^4+b3x^3+b2x^2+b1x+b0 est un polynôme à coefficients rationnels, qui a six racines distinctes. La courbe C est appelée hyperelliptique et n'a pas de structure de groupe. Par contre, nous pouvons lui associer, d'une façon naturelle, une surface abélienne Jac(C), appelée la jacobienne de C. En plus, nous pouvons plonger C dans Jac(C). Certaines courbes hyperelliptiques sont spéciales car elles couvrent des courbes elliptiques. Par exemple, considérons une courbe C donnée par l'équation y^2=x^6+ax^4+bx^2+c, dans laquelle seulement des puissances paires de x apparaissent. Si (x,y) est un point de cette courbe alors de même (-x,y), et nous pouvons définir une application algébrique f:(x,y)->(x^2,y) de degré 2, c'est-à-dire, de fibre générale à deux points. Alors (X,Y)=(x^2,y) est un point de la courbe elliptique E donnée par Y^2=X^3+aX^2+bX+c et nous disons que C est un revêtement double de E. Si E1 est une courbe elliptique, si C est une courbe hyperelliptique, et si C->E1 est un revêtement de degré n qui n'est pas une composition de revêtements, alors nous pouvons plonger E1 dans la surface Jac(C) comme un sous-groupe. De plus, il existe une autre courbe elliptique E2 et un revêtement C->E2 de degré n, tel que la surface Jac(C) a une propriété spéciale - elle peut être obtenue comme quotient de la surface E1xE2 par un sous-groupe fini. Le chapitre 1 de cette thèse traite les aspects géométriques de cette situation. Nous cherchons à savoir quelles courbes peuvent avoir une telle relation et nous nous concentrons surtout sur les cas n=2 et n=3, qui ont déjà été analysés dans la littérature. Dans le cas général, nous obtenons quelques résultats, mais une description complète s'avère très difficile de manière explicite. Le chapitre 2 traite les aspects arithmétiques de la situation, via la théorie des fonctions hauteurs, qui sont un outil très utile pour répondre à des questions concernant des points rationnels de courbes et surfaces. Pour tout nombre rationnel x=a/b, avec a et b des entiers premiers entre eux, on définit la hauteur h(x) de x, de façon très précise, comme une mesure de sa complexité arithmétique - la hauteur dit approximativement combien de chiffres sont nécessaires pour écrire les entiers a et b. De la même façon, la hauteur d'un point rationnel d'une courbe ou surface nous dit combien de chiffres ont les coordonnées. Par exemple, (3,5) et (1749/1331,-1861/1331) sont deux points rationnels de complexités plutôt différentes de la courbe y^2=x^3-x+1, tandis que (2,√7) n'est pas un point rationnel. Il est possible d'attacher une hauteur aux courbes elliptiques et aux surfaces abéliennes qui mesure leur complexité arithmétique totale. Une relation spécifique entre ces deux notions de hauteur est alors conjecturée et nous étudions cette conjecture dans la situation décrite plus haut. Nous montrons que cette relation est vraie pour E1xE2 si et seulement si elle est vraie pour Jac(C). / This thesis deals with properties of Jacobians of genus two curves that cover elliptic curves. Let E be a curve in the plane, given by an equation y^2=F(x), where F(x)=x^3+a2x^2+a1x+a0 is a polynomial with rational coefficients and with three distinct roots. For historical reasons, such a curve is known as an elliptic curve. It is known that every elliptic curve E can be equipped with a structure of a commutative group - its points can be added and subtracted. A point O "at infinity", which is contained in all vertical lines (lines of form x=c), is the neutral element. This group structure is described by the condition that three points P,Q,R in E satisfy P+Q+R=O if and only if they are collinear. Surfaces with a commutative group structure are called abelian. For example, a product of two elliptic curves E1xE2 is an abelian surface in the obvious way. Next we consider a planar curve C given by an equation y^2=G(x), where G(x)=x^6+b5x^5+b4x^4+b3x^3+b2x^2+b1x+b0 is a polynomial with rational coefficients and six distinct roots. The curve C is called hyperelliptic and it does not have a group structure. However, we can associate to it, in a natural way, an abelian surface Jac(C), called the Jacobian of C. Moreover, we can embed C into it. Some hyperelliptic curves, of the form y^2=G(x) as above, are special because they cover elliptic curves. For example, consider a curve C given by y^2=x^6+ax^4+bx^2+c, so that only even powers of x appear. If (x,y) is a point on this curve then so is (-x,y) and we can define an algebraic map f:(x,y)->(x^2,y), that is of degree 2, i.e. 2-to-1. Now (X,Y)=(x^2,y) is a point on the elliptic curve E given by Y^2=X^3+aX^2+bX+c and we say that C is a double cover of E. If E1 is an elliptic curve, C is a hyperelliptic curve, and C->E1 is an n-to-1 covering that is not a composition of coverings, then we can embed E1 into the surface Jac(C) as a subgroup. Moreover, there exists another elliptic curveE2 and an n-to-1 covering C->E2, such that the surface Jac(C) has a special property - it can be obtained as the quotient of the surface E1xE2 by a finite subgroup. The first chapter of the thesis deals with the geometric aspects of this setup. We investigate which curves can form this special relationship and we focus mostly on the cases n=2 and n=3, which have already been analysed in literature. We also gain some insight into the general case, but a full description proves to be very difficult computationally. The second chapter deals with the arithmetic aspects of the setup, via the theory of height functions, which are a very useful tool in answering questions about rational points on curves and surfaces. For every rational number x=a/b, where a and b are coprime integers, one can define its height h(x), in a very precise way, as a measurement of its arithmetic complexity - the height roughly tells us how many digits are needed to write down the integers a and b. Likewise, the height of a rational point on a curve or surface tells us about the number of digits of the coordinates. For example, (3,5) and (1749/1331,-1861/1331) are two rational points of rather different complexity on the curve y^2=x^3-x+1, while (2,√7) is not a rational point. It is also possible to associate a height to an elliptic curve or an abelian surface and measure its arithmetic complexity as a whole. A specific relation between these two heights is conjectured and we investigate it in the context of the setup above. We show that this relation holds for E1xE2 if and only if it holds for Jac(C).

AFRIKAANS: Die doel van die navorsing was om te bepaal wat die status van die klassieke pianis in die postmoderne wêreld is, en hoe hierdie moontlikhede deur die loopbane van Lang Lang (1982- ) en sy model Vladimir Horowitz (1903-1989) vergestalt word. Die verhandeling begin met ‘n oorsig oor Lang Lang as pianis en mens. Dit dien as vertrekpunt vir die res van die besprekings. Lang Lang se pianistiek as ‘n voortsetting van ‘n reeds bestaande klaviertradisie word ook in oënskou geneem. Daar word spesifiek ondersoek ingestel na Horowitz se invloed op Lang Lang se musikale ontwikkeling. Die beeld van Lang Lang as pianis wat in die voorafgaande besprekings na vore gekom het, word aan die hand van tekste oor die Postmodernisme krities bespreek. In die gevolgtrekking word die postmoderne status van die hedendaagse pianistiek, met Lang Lang as verteenwoordiger daarvan, oorweeg. Aangesien die uitvoerende kuns in die eerste plek op kommunikasie met die luisteraar gemik is, speel die menings van ooggetuies ‘n buitengewoon belangrike rol in die bestudering van die uitvoerende kunstenaar se kuns. Data wat in die studie gebruik is, sluit onder andere resensies, koerantberigte, tydskrifartikels, transkripsies van radio-onderhoude, gepubliseerde onderhoude, gepubliseerde CV’s, biografieë en outobiografieë in. Tydens die studie het dit na vore gekom dat Lang Lang se klavierstyl byna parallel met dié van Horowitz loop. Verder is al die simptome van die Postmodernisme wat in hierdie studie in oënskou geneem is in ‘n meerdere of mindere mate in Lang Lang se pianistiek en bemarkingstrategieë teenwoordig. ‘n Interessante aspek is dat hierdie simptome, en spesifiek Lang Lang se herbenutting (“recycling”) van Horowitz se klavierstyl, as postmodern sowel as Romanties geïnterpreteer kan word. Indien die leser Andreas Huyssen en John Butt se siening huldig dat die Postmodernisme se herbenutting van historiese style as gevolg van die tydsverloop in wese nuut en daarom postmodern sal wees, kan Lang Lang se klavierstyl en die huidige klaviertradisie as postmodern beskou word. As die leser in ooreenstemming met Linda Hutcheon voel dat postmoderne herbenutting noodwendig ironies en daarom polities van aard moet wees, kan Lang Lang se pianistiek sowel as die hedendaagse klaviertradisie as Romanties beskou word. ENGLISH: The aim of this research was to determine the status of the classical pianist in the postmodern world, and how these possibilities are embodied by the careers of Lang Lang (1982-) and his model Vladimir Horowitz (1903-1989). The dissertation commences with a summary of Lang Lang as a pianist and a person. This serves as a point of departure for the remaining discussions. Lang Lang’s pianism as a continuation of an already existing piano tradition is explored and Horowitz’s influence on Lang Lang’s musical development is assessed. Lang Lang’s image as a pianist, determined during the preceding discussions, is examined with reference to texts pertinent to Postmodernism. The postmodern status of contemporary pianism, with Lang Lang as its representative, is expanded upon in the conclusion. As performing art is primarily aimed at communication with the listener, the views of eyewitnesses play an exceptionally important role in the study of the performer. Data used in this study include, amongst others, reviews, newspaper clippings, journal articles, transcriptions of radio interviews, published interviews, printed CVs, biographies and autobiographies. During the study it came to light that Lang Lang’s piano style is similar to that of Horowitz. Furthermore, all the symptoms of Postmodernism investigated in this study are to a greater or lesser extent present in Lang Lang’s pianism and marketing strategies. An interesting aspect is that these symptoms, and specifically that of Lang Lang’s recyling of Horowitz’s piano style, can be interpreted as postmodern as well as Romantic. If the reader holds Andreas Huyssen’s and John Butt’s view that Postmodernism’s recycling of historical styles due to the lapse of time will be new in essence and consequently postmodern, Lang Lang’s piano style and the present day piano tradition can be viewed as postmodern. If the reader, following Linda Hutcheon’s views, feels that postmodern recycling should inevitably be ironic and therefore in nature political, Lang Lang’s piano style and the contemporary piano tradition can be considered Romantic. / Thesis (DMus)--University of Pretoria, 2011. / Music / unrestricted

<p>Vi undersöker huruvida redovisningsharmoniseringen inom EU har ökat jämförbarheten av företags finansiella information. Detta har gjorts genom en replikastudie på en undersökning genomförd av Joos och Lang publicerad 1994 där de fann att någon konvergens mellan Frankrike, Storbritannien och Tyskland ej kunde konstateras.</p><p>Länderna som undersöks är Frankrike, Storbritannien, Sverige och Tyskland under perioden 1995 - 2005. Genom att ta reda på hur ROE, E/P- och B/M-kvoterna utvecklat sig kan vi dra slutsatsen att viss konvergens har skett mellan länderna.</p><p>En pris- och en avkastningsregression har även utförts men resultaten av dessa kan ej bevisa att konvergens mellan länderna har skett under vår undersökningsperiod.</p>

In the nineteenth century, as society in Victorian Britain adjusted to the effects of urbanization and industrialization, social roles began to shift, changes that were reflected in the children’s book illustrations of Randolph Caldecott, Henry J. Ford, and Beatrix Potter. This time period was considered the golden age of children’s book illustrations due to a large boom in both number and quality available. These children’s books illustrators had a lasting impact on culture and aesthetics and reinforced the social constructions of the new urban middle class. Randolph Caldecott’s illustrations of nursery rhymes gave new interpretations to familiar texts, some of which furthered shifts in gender roles for both males and females. Andrew Lang’s fairy tale series, illustrated by H. J. Ford, walked a fine line between high art ideals and consumerism. Ford’s illustrations referenced the Pre-Raphaelite aesthetic. The fairytale genre has emphasized female roles from its inception, and Lang's and Ford's focus on an essentially English femininity added complexities to messages about the ideal woman. Beatrix Potter’s subversive work can be seen as the culmination of the Victorian period. She satirized the ideal woman at home, illuminating the anxieties and pressures of the domestic sphere and exploring the Victorians' fixation with the etiquettes of social rank. In an attempt to further the scope of traditional art history, this dissertation shows that, even in consumerist-driven visual culture, even in seemingly inconsequential children’s book illustration, we can see the impact of key social changes and values.

Vi undersöker huruvida redovisningsharmoniseringen inom EU har ökat jämförbarheten av företags finansiella information. Detta har gjorts genom en replikastudie på en undersökning genomförd av Joos och Lang publicerad 1994 där de fann att någon konvergens mellan Frankrike, Storbritannien och Tyskland ej kunde konstateras. Länderna som undersöks är Frankrike, Storbritannien, Sverige och Tyskland under perioden 1995 - 2005. Genom att ta reda på hur ROE, E/P- och B/M-kvoterna utvecklat sig kan vi dra slutsatsen att viss konvergens har skett mellan länderna. En pris- och en avkastningsregression har även utförts men resultaten av dessa kan ej bevisa att konvergens mellan länderna har skett under vår undersökningsperiod.

Compared to the solo percussion works, little academic work has been done in the research and analysis of percussion ensemble compositions. David Lang, a Pulitzer Prize winning composer, has written many prominent works for percussion in both the solo and chamber setting. His work, The So-Called Laws of Nature for percussion quartet, written in 2001, has quickly become standard repertoire. Lang composed the piece with many overlapping processes, patterns that are affected in a pre-defined manner, in line with his totalist style. Using traditional analytical methods would not accurately represent the complexity the work has to offer to the performer. This paper will attempt to find musical significance by breaking down the individual processes.The conclusions from this research are mostly open-ended and, to some extent, subjective. The most effective performers will take the objective analytical information and use it to create an informed, well-intentioned, subjective experience. In this study of The So-Called Laws of Nature the analysis attempts to connect the objective--the data--and the subjective--the analysis of that data--to work together to aid the performer to create the best possible musical and ultimately artistic interpretation.

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