Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The purpose of this work is to study the relationships between admissible pairs, systems admissible and bialgebras in the category of Yetter-Drinfeld modules, as well as some properties of the Hopf algebra associated (via bosonization) to an admissible pair. We end this dissertation with a family of examples of admissible pairs. / O objetivo deste trabalho é estudar as relações entre pares admissíveis, sistemas admissíveis e biálgebras na categoria dos módulos de Yetter-Drinfeld, bem como algumas propriedades da álgebra de Hopf associada (via bosonização) a um par admissível. Finalizamos esta dissertação com uma família de exemplos de pares admissíveis.

No abstract available / Jurisprudence / LL.M.

Thesis (LLM)--University of Stellenbosch, 2005. / ENGLISH ABSTRACT: The law regarding the admissibility of unconstitutionally obtained evidence for impeaching the accused's testimony is still undeveloped. This work discusses three of the options available to South African courts and the difficulties inherent in each. The first is to follow the approach of the Supreme Court of the United States. The American approach regarding the exclusion of evidence from the case in chief is strict. Courts are not bestowed with a discretion to admit unconstitutionally obtained evidence: Unless one of the accepted exceptions exist, a court must exclude unconstitutionally obtained evidence in order to deter unconstitutional behaviour by the authorities. Deterrence of unconstitutional police behaviour is however no longer considered controlling when cross-examining the accused. Unconstitutionally obtained evidence - both real and testimonial communications - is therefore admissible for impeachment purposes despite being excluded from the case in chief. The rationale is to prevent the accused giving perjurious testimony in the face of the prosecution's inability to impeach the accused's veracity in the usual manner. The application of the American approach in South Africa has however already been rejected in S v Makhathini.1 The second possibility is for South African courts to follow the position of the Supreme Court of Canada in R v Calder.2 The admissibility of impeachment evidence in Canada - as with evidence in chief - is based on the effect of its admission of the repute of the administration of justice. However, evidence excluded from the case in chief will only in very rare circumstances be admitted in cross-examination of the accused. Finally, the option suggested by this thesis, is to continue the trend started by s 35(5) of the South African Constitution, which has already been applied with great success in cases where the admissibility of unconstitutionally obtained evidence in the case in chief is in issue. Section 35(5), like the Canadian s 24(2) it bears some resemblance to, gives courts a discretion to exclude unconstitutionally obtained evidence on the basis of unfairness to the accused or the effect admission will have on the administration of justice. It is submitted in this thesis that, because of the interlocutory nature of a ruling on admissibility, this approach adapts easily to the admission of limited purpose evidence such as impeachment evidence: If the admission of the unconstitutionally obtained evidence, regardless of whether it was previously excluded from the case in chief, renders the trial unfair or would otherwise be detrimental to the administration of justice it must be excluded. / AFRIKAANSE OPSOMMING: Die reg in verband met die toelaatbaarheid van ongrondwetlik verkree getuienis vir 'n geloofwaardigheidsaanval op die beskuldigde is nog in 'n vroee stadium van ontwikkeling. Hierdie tesis bespreek drie moontlikhede beskikbaar aan Suid-Afrikaanse howe en die probleme inherent aan elkeen. Die eerste is om die posisie van die Amerikaanse Hooggeregshof te volg. Die Amerikaanse posisie betreffende die toelaatbaarheid van getuienis tydens die staat se saak is streng. Howe het geen diskresie om ongrondwetlik verkree getuienis toe te laat nie: Behalwe in gevalle waar aanvaarde uitsonderings bestaan, moet 'n hof dus ongrondwetlik verkree getuienis uitsluit om ongrondwetlike optrede deur die owerhede te voorkom. Voorkoming van ongrondwetlike optrede aan die kant van die polisie is egter nie meer die beherende oorweging wanneer die beskuldigde in kruis-ondervraging geneem word nie. Ongrondwetlik verkree getuienins - beide reel en verklarend van aard - is gevolglik toelaatbaar vir doeleindes van 'n geloofwaardigheidsaanval, ten spyte daarvan dat dit moontlik ontoelaatbaar was tydens die staat se saak. Die rede is om te voorkom dat die beskuldigde meinedige getuienis lewer terwyl die staat verhoed word om the bekuldigde se geloofwaardigheid op die gewone manier te toets. Hierdie posisie is egter al verwerp in S v Makhathini. 3 Die tweede moontlikheid is om die posisie soos uitgele deur die Hooggeregshof van Kanada, in R v Calder 4 te volg. In Kanada word die toelaatbaarheid van getuienis rakende geloofwaardigheid - sowel as getuienis rakende skuld - bepaal deur die invloed wat die toelating daarvan op die reputasie van die regspleging het. Getuienis wat ontoelaatbaar is tydens die staat se saak sal egter slegs in baie beperkte omstandighed toegalaat word tydens kruisondervraging van die beskuldigde. Laastens, die opsie wat voorgestel word deur hierdie tesis, is om voort te gaan met die patroon wat ontwikkel is deur art. 35(5) van die Grondwet van Suid-Afrika, wat alreeds met groot sukses toegepas is in sake waar die toelaatbaarheid van ongrondwetlik verkree getuienis in die staat se saak ter sprake was. Artikel 35(5), soos Kanada se art 24(2) waarmee dit tot 'n mate ooreenstem, gee howe 'n diskresie om ongrondwetlik verkree getuienis uit te sluit op grond van onregverdigheid teenoor die beskuldigde of indien die toelating daarvan 'n negatiewe invloed op die regspleging sal he. Omdat 'n beslissing oor die toelaatbaarheid van getuienis tussenstyds van aard is, pas dit goed aan by die verdere ondersoek na die toelaatbaarheid van getuienis wat slegs VIr 'n beperkte doel aangebied word: Indien die toelating van ongrondwetlik verkree getuienis, ongeag of dit voorheen uitgesluit was uit die staat se saak, die verhoor onregverdig maak of die regspleging negatiefbeinvloed, moet sulke getuienis uitgesluit word.

In the presented work we define non-commutative Gröbner bases including the necessary basis of non- commutative algebra theory and notion admissible ordering. We present non-commutative variant of the Buchberger algorithm and study how the algorithm can be improved. Analogous to the Gebauer-Möller criteria lead us to detect almost all unnecessary obstructions in the non-commutative case. The obstructions are graphically ilustrated. The Buchberger algorithm can be improved within redundant polynomials. This work is a summary and its specification of the results of some known authors engaged in this field. Presented definitions are ilustrated on examples. We perform proves of some of the statements which have been proven differently by other authors. Powered by TCPDF (www.tcpdf.org)

No abstract available / Jurisprudence / LL.M.

La simulation numérique est devenue un outil omniprésent dans les milieux industriels. En particulier, dans le domaine de l’ingénierie mécanique où l’objectif est de prévoir la réponse d'une structure à des sollicitations. La simulation est dans ce cas une aide au dimensionnement qui permet de réduire le développement de prototypes coûteux. Les systèmes étudiés en bureau d’études étant de plus en plus complexes, il est courant de traiter des structures comportant plusieurs composants déformables en interaction. Le contexte d’étude repose donc sur les équations de la mécanique des milieux continus avec prise en compte du contact. Cependant, l’obtention des solutions exactes de ce système d’équation aux dérivées partielles n’est en général pas envisageable. L’obtention d’une solution passe par l'utilisation d’une discrétisation du modèle. Ainsi le résultat obtenu est une approximation de la solution exacte du problème traité. En situation industrielle il est nécessaire de pouvoir contrôler la qualité de ce résultat approché, c’est à dire mesurer l’écart entre la solution exacte (inconnue) et la solution approchée (disponible), ce sont des outils de vérification. Il existe de nombreux travaux sur l’estimation d’erreur permettant d’évaluer l’écart entre les solutions exactes et approchées. Malgré cela, l’utilisation des outils de vérification (estimateur de l’erreur commise) reste encore peu répandue dans l’industrie (disponibilité dans les codes de calculs, fiabilité, coûts de calcul, difficulté d’utilisation …) Dans ce travail, nous proposons une méthode d’estimation d’erreur, basée sur le concept d’erreur en relation de comportement, parallélisable et permettant s’adapter aux contraintes industrielles (pertes d’information, problèmes mal connus …). De plus, afin de la rendre l’outil rapidement disponible en bureau d’étude, le choix a été fait de développer la méthode directement dans le code de calcul industriel SAMCEF lors du projet ANR ROMMA. / In the field of mechanical engineering, numerical simulation has become an indispensable tool to predict the response of a structure to mechanical load.The simulation allows to reduce conception costs using numerical models instead of costly prototypes.Engineers use increasingly complex structures; it is now common to treat structures composed of several deformable components interacting. The studies carried out in this work are based on the equations of continuum mechanics with contact.However, these numerical simulations involve a discretized version of a continuous mathematical model (finite element analysis). Therefore, they lead only to an approximation of the exact solution of the reference problem.In an industrial context, the results of a finite element calculation must satisfy certain quality requirements. The purpose of an error estimation is to evaluate the distance between the exact solution and an approximate solution of the problem.Methods for evaluating the global error due to the problem's discretization have been studied for several years. However the use of error estimation tools is still not widespread in industry (availability in industrial softwares , reliability, calculation costs, difficulty of use ...)The objective of this work is to propose a parallelized estimation method based on the concept of constitutive relation error, adapted to industrial constraints. Furthermore, to make it quickly available for design office, the choice was made to develop the method directly in the industrial software SAMCEF during the ANR project ROMMA.

Establishing dynamic characteristics of structures is a challenging area of research. The dynamic characteristics of structures, such as natural frequencies, modeshapes, response levels and damping characteristics play an important role in identifying the condition of the structures. The assumed modes method is a particular analytical method used to estimate the dynamic characteristics of a structure. However, the eigenfunctions used in the assumed mode method often led to ill-conditioning due to the presence of hyperbolic functions. Furthermore, a change in the boundary conditions of the system usually necessitates a change in the choice of assumed mode. In this thesis, a set of Alternative Admissible Functions (AAF), along with penalty functions, are used to obtain closed form solutions for an Euler-Bernoulli beam with various boundary conditions. A key advantage of the proposed approach is that the choice of AAF does not depend on the boundary conditions since the boundary conditions are modelled via penalty functions. The mathematical formulation is validated with different boundary conditions, Clamped-Free (CF), Simply-Supported (SS), and Clamped-Clamped (CC). A specific relation between the penalty function and the system parameters are established for CF, SS and CC boundary conditions to obtain appropriate values of penalties. Validation of results with the reported literature indicates excellent agreement when compared with closed-form Euler-Bernoulli beam values. The AAF approach with penalties is extended to a beam with a shallow crack to estimate the dynamic characteristics. The crack is modelled as a penalty function via a massless rotational spring. This model has the advantage of simplifying parametric studies, because of its discrete nature, allowing easy modification in the crack position and depth of the crack. Therefore, once the model is established, various practical applications may be performed without reformulation of the problem. Validation of results with the reported literature on beams with shallow cracks indicates the suitability of the proposed approach.

In this thesis we study radial weights on Rn. We study two radial weights with different exponent sets. We show that they are both 1-admissible by utilizing a previously shown sufficient condition, for radial weights to be 1-admissible, together with some results connecting exponent sets and Ap weights. Furthermore applying a similar method on a more general radial weight, we manage to improve the previously shown sufficient condition for radial weights to be 1-admissible. Finally we show for one of these two weights that even though it is 1-admissible, whether or not it belongs to some class Ap depends both on the value of p and on the dimension n. Additionally, both of these weights as well as another simple weight are, at least in some dimensions n, not A1 even though they are 1-admissible.

Kapaciteter kan vara till stor nytta, bland annat då partiella differentialekvationer ska lösas. Kapaciteter är dock i många fall väldigt svåra att beräkna exakt, speciellt i viktade rum. Vad som istället kan göras är att försöka uppskatta kapaciteterna, vilket för ringar runt en fix punkt kan utföras med hjälp av fyra olika exponentmängder, \underline{Q}_0, \underline{S}_0, \overline{S}_0 och \overline{Q}_0, som beskriver hur vikten beter sig i närheten av denna punkt och i viss mån ger rummets lokala dimension. För att kunna dra nytta av exponentmängderna är det bra att veta vilka kombinationer av dessa som kan förekomma. För att få fram nya kombinationer använder vi olika sätt att mäta volym av klot med varierande radier. Dessa mått är definierade genom olika vikter. Det har tidigare funnits ett fåtal exempel på hur olika kombinationer av exponentmängderna kan se ut. Variationerna består av hur avstånden är i förhållande till varandra och om ändpunkterna tillhör mängderna eller inte. I denna rapport har vi tagit fram ytterligare fem nya kombinationer av mängderna, bland annat en där \underline{Q}_0 är öppen. / Capacities can be of great benefit, for instance when solving partial differential equations. In most cases, capacities can be difficult to calculate exactly, in particular on weighted spaces. In these cases, it can be sufficient with an estimation of the capacity instead. For annuli around a given point, the estimation can be done using four exponent sets \underline{Q}_0, \underline{S}_0, \overline{S}_0 and \overline{Q}_0, which describe how the weight behaves in a neighbourhood of that point and in some sense define the local dimension of the space. To be able to use the exponent sets, it is useful to know which combinations of them can exist. For this we use various measures, which are a way to measure volumes of balls with varying radii in Rn. These measures are defined by different weights. Earlier, there existed a few examples giving different combinations of exponent sets. The variations consist in their relationship to each other and if their endpoints belong to the set or not. In this thesis we present five new combinations of the exponent sets, amongst them one where \underline{Q}_0 is open.

Thesis (LLM)--University of Stellenbosch, 2002. / ENGLISH ABSTRACT: The permanent International Criminal Court (ICC) will come into operation after the 60th ratification of the Rome Statute of the International Criminal Court of 1998. The ICC will have jurisdiction over the most serious international crimes, namely war crimes, genocide and crimes against humanity. The focus of this thesis is the difficulties surrounding the admissibility of a case before the ICC. There are basically two legs to this analysis: jurisdiction and complementarity .. Jurisdiction of the ICC is analysed in historical and theoretical context. This comprises an overview of the international tribunals since the First World War, and more specifically their impact on the development of jurisdiction in international criminal law. Secondly, the thesis is examining the jurisdiction of the ICC in terms of the specific provisions of the Rome Statute. This analysis comprises a detailed analysis of all the provisions of the Rome Statute that have an impact on the exercise of the ICC's jurisdiction. The relationship between the ICC and national courts is a difficult relationship based on a compromise at the Rome Conference in 1998. The principle underlying this relationship is known as "complementarity". This : means that the ICC will only exercise its jurisdiction if a national court is "unwilling" or "unable" to exercise its jurisdiction. A detailed analysis of the different provisions of the Rome Statute, as well as some references to other international tribunals, serve to analyse the impact of complementarity on the eventual ambit of the ICC's jurisdiction. In conclusion, some suggestions regarding the admissibility of cases and the difficult relationship between the ICC and national courts are made. / AFRIKAANSE OPSOMMING: Die permanente Internasionale Strafhof (ISH) sal met sy werksaamhede begin na die 60ste ratifikasie van die Statuut van Rome van 1998. Die ISH sal jurisdiksie uitoefen oor die ernstigste internasionale misdade, tewete oorlogsmisdade, volksmoord en misdade teen die mensdom. Hierdie tesis fokus op die probleme rondom die toelaatbaarheid van 'n saak voor die ISH. Hierdie ontleding het basies twee bene: jurisdiksie en komplementariteit. Die jurisdiksie van die ISH word in historiese en teoretiese konteks ontleed. Dit behels 'n oorsig van die internasionale tribunale sedert die Eerste Wêreldoorlog, en meer spesifiek die impak wat hierdie tribunale op die ontwikkeling van jurisdiksie in die internasionale strafreg gehad het. In die tweede plek word jurisdiksie ontleed aan die hand van die spesifieke bepalings van die Statuut van Rome. Hierdie ontleding behels 'n gedetaileerde ontleding van al die bepalings van die Statuut van Rome wat 'n impak het op die uitoefening van die ISH se jurisdiksie. Die verhouding tussen die ISH en nasionale howe is 'n komplekse verhouding, gebaseer op 'n kompromie wat by die Rome Konferensie van 1998 aangegaan is. Die beginselonderliggend aan hierdie verhouding staan bekend as "komplementariteit". Dit beteken dat die ISH slegs sy jurisdiksie sal uitoefen indien 'n nasionale hof "onwillig" of "nie in staat is" om jurisdiksie uit te oefen nie. 'n Gedetaileerde ontleding van die verskillende bepalings van die Statuut van Rome, sowel as verwysings na ander internasionale tribunale, dien om die impak van komplementariteit op die omvang van die ISH se jurisdiksie, te ontleed. Ten slotte word sekere voorstelle aangaande die toelaatbaarheid van sake en die verhouding tussen die ISH en nasionale howe gemaak.