Mais que fenômenos exóticos, oscilações de corrente e potencial são bastante comuns em vários sistemas eletroquímicos. Ainda que conhecidos há muito tempo, processos oscilatórios na interface sólido/líquido eletrificada são relativamente pouco investigados sob o ponto de vista teórico. São apresentados nessa Tese dois trabalhos, o primeiro relacionado às instabilidades cinéticas observadas em tais sistemas, por meio de um modelo formado por três equações diferenciais não-lineares ordinárias acopladas, que representam um protótipo mínimo do comportamento complexo observado em reações eletrocatalíticas. Especificamente, este protótipo reproduz as características gerais de osciladores eletroquímicos caracterizados por uma resistência diferencial negativa parcialmente escondida em uma curva de corrente/potencial em forma de N. O modelo foi abordado utilizando as análises convencionais e os diagramas de estabilidade, de Lyapunov e de período. A partir dos diagramas de estabilidade foi possível descrever o comportamento do sistema levando em consideração a condição homoclínica de Shilnikov. Já os diagramas de Lyapunov e período mostraram de forma detalhada o comportamento caótico e periódico do modelo, em que se pode observar a existência de estruturas auto-organizadas nos domínios de periodicidade em um fundo caótico, onde tais estruturas são chamadas de shrimps. A observação de tais estruturas que também são encontradas em outros sistemas reforçando a hipótese da universalidade estrutural para fenômenos de codimensão dois. A segunda parte dessa Tese consiste num estudo do drift observado em séries experimentais aplicando técnicas de análise multivariada a uma série temporal experimental obtida para eletro-oxidação da molécula do metanol em Pt policristalina. O resultado mostrou que podemos descrever a influência do drift no comportamento oscilatório por meio de três variáveis relacionados aos processos superficiais. / More than just an exotic phenomenon, oscillations of potential and current are often found in several electrochemical systems. Although oscillatory processes at solid/liquid electrified interfaces have been reported a long time ago, just few theoretical studies have been done so far. This Thesis comprises two parts: the first one analyzes kinetic instabilities observed in electrochemical systems by using a model consisting of three non-linear coupled ordinary differential equations that represent a prototype of the complex behavior observed in electrocatalytic systems. Specifically, this prototype captures the general characteristics of electrochemical oscillators that display a negative differential resistance partially hidden for an N-shaped current/potential curve. The model was studied using conventional analyses and stability diagrams, Lyapunov exponents and the evaluation of the period of oscillations. From the stability diagrams it was possible to describe the behavior of the system taking into consideration the homoclinic Shilnikov condition. The Lyapunov and period analyses showed in a very detailed manner the chaotic and periodic behavior of the model, where it is observed the existence of self-organized structures in the domains of periodicity on a chaotic background. Those structures are known as shrimps. The observation of such structures that are also found in other systems reinforces the idea of structural universality for codimension two phenomena. The second part of the Thesis deals with the analysis of the oscillatory drift by using multivariate analysis techniques to an experimental time series obtained for the electroxidation of methanol on polycrystalline Pt. The results showed that it is possible to describe the influence of the drift during the oscillatory behavior by means of three variables that act on the surface of the electrode.

O processo de conformação de chapas planas, estampagem, consiste na obtenção de peças conforme o projeto do processo e do produto. Faz-se necessária uma margem de segurança para que as variações de processo e do material possam ser absorvidas e o sucesso seja alcançado no processo de produção do componente. O presente trabalho mostra aspectos de estampabilidade de uma chapa de aço de baixo teor de carbono, o material mais utilizado no processo de estampagem. Estes aspectos são descritos e demonstrados como influenciam no processo de estampagem. No caso prático apresentado, evidencia-se que com a aplicação dos conhecimentos científicos de comportamento mecânico do material obtém-se uma melhoria no desempenho do processo e, conseqüentemente, na redução de custos e no aumento de competitividade. Como objetivo principal, tem o presente trabalho estudar a influência da redução a frio de acabamento do processo de relaminação no coeficiente de encruamento e mostrar como este estudo teve participação na solução e aplicação de uma peça-exemplo. Conseqüentemente há como objetivos secundários o estudo da influencia do tamanho de grão no coeficiente de encruamento, o desenvolvimento da textura cristalográfica antes e após a conformação da peça-exemplo e demonstrar a importância da utilização do método de elementos finitos no processo de conformação por estampagem para determinação dos tipos de conformação predominante no processo. Para realização do trabalho foram utilizados dois aços de baixo teor de carbono com composição química semelhantes porem com processos de fabricação diferenciados. Atenção especial foi dada a redução aplicada na laminação de acabamento de ambos os aços, através do uso de medidores de espessura e redução através de raios-X. Os aços foram caracterizados antes da conformação da peça-exemplo quanto a orientação cristalográfica através de difração de raios-X e EBSD, quanto as propriedades mecânicas através de ensaios mecânicos de tração e quanto a microestrutura e tamanho de grão através de metalografia. Foi realizada uma simulação de estampagem da peça-exemplo através de elementos finitos afim de determinar o tipo de conformação predominante na região mais solicitada da peça-exemplo. A peça exemplo foi conformada na pratica e caracterizada a distribuição das deformações através da medições da rede circulo previamente impressa na superfície da chapa na região mais solicitada conforme previamente determinado através da simulação. A orientação cristalográfica da região mais solicitada também foi caracterizada. Os resultados mostram a influencia de uma pequena variação na redução, 0,73% e 0,34%, aplicada na laminação de acabamento no coeficiente de encruamento. Para confirmação de que a redução aplicada foi a principal influenciadora no resultado o coeficiente de encruamento foi calculado através de equações disponíveis na literatura que correlacionam composição e tamanho de grão com o coeficiente de encruamento. A textura preferencial dos dois aços também foi avaliada através de figuras de função de orientação da distribuição e o comportamento dos dois aços foi relativamente semelhante, onde o aço com melhor desempenho demonstrou um aumento na componente {223} também conhecida como γ'. O estudo através de elementos finitos mostra que região mais solicitada da peça tem conformação predominada por estiramento. Por fim é mostrada a melhor distribuição das deformações na peça-exemplo produzida com aço de maior coeficiente de encruamento. Concluindo o trabalho permitiu a avaliação da influencia da redução aplicada na laminação de acabamento de aços de baixo teor de carbono nas propriedades mecânicas do aço e também o resultado deste comportamento mecânico na peça-exemplo adotada.Também permitiu avaliar a evolução da textura cristalográfica dos dois aços escolhidos antes e após a conformação da peça-exemplo. / The forming process of plain sheets, stamping, consists on the obtainment of parts according to the project of the process and the product. A safety margin becomes necessary so that the process variations and of the material can be absorbed and the success is reached in the process of production of the component. The present paper shows aspects of formability of a steel sheet of low carbon content, the most used material in the stamping process. These aspects are described and demonstrated how they influence the stamping process. In the presented case, it is proven that with the application of the scientific knowledge of mechanical behavior of the material an improvement in the performance of the process is reached and, consequently, the reduction of costs and the increase of competitiveness. As main objective, the present work study the influence of the cold reduction applied on skin pass of the cold rolling process on the strain hardening coefficient and to show how this study had participated on the solution and application of an part. Consequently it has as secondary objective the study of influences of the size of grain in the coefficient of strain hardening, the development of texture before and after forming of the part and to demonstrate the importance of the use of the method of finite elements in the forming process for determination of the predominant types of forming in the stamping process. For accomplishment of this paper two steel of low carbon content had been used with similar chemical composition but with differentiated rolling processes of manufacture. Special attention was given to the reduction applied in the skin pass of both steel, through the use of measurers of thickness and reduction through x-ray. The steel had been characterized before the stamping of the part above crystallographic texture through x-ray diffraction and EBSD, above mechanical properties through mechanical tensile tests and above microstructure and size of grain through metallography. A simulation of stamping process of the part through finite elements was carried out with the objective of determine the type of predominant forming in the most requested region of the part. The part was formed in mechanical presses and characterized the distribution of the deformations through the measurements circle grids, previously printed in the surface of the sheet, in the region most requested as previously determined through the simulation. The crystallographic orientation of the most requested region was also characterized. The results show influence of a small variation in the rolling reduction, 0.73% and 0.34%, applied in the skin pass on the strain hardening coefficient. For confirmation that the pplied skin pass was the main influence in the strain hardening coefficient result, was calculated hrough available equations in literature that correlate composition and grain size with the strain hardening coefficient. The preferential texture of two steel was also evaluated through figures of orientation function distribution and the behavior of two steel was relatively similar, where the steel with better performance demonstrated an increase in the {223} component also known as γ'. The study through finite elements shows that the more requested region of the part has forming predominated for stretching. Finally the best distribution of the deformations in the part produced with steel of higher coefficient of train hardening is shown. Concluding the work allowed the evaluation of influences of the skin pass on the rolling of steel of low carbon content in the mechanical properties of the steel and the result of this mechanical behavior in the adopted part. Also it allowed to evaluate the evolution of the crystallographic texture of two steel chosen before and after.

Please read the abstract in the section 00front of this document / Thesis (PhD)--University of Pretoria, 2008. / Materials Science and Metallurgical Engineering / PhD / Unrestricted

La poursuite de l'intégration de fonctions toujours plus complexes au sein d'un même circuit constitue un des principaux enjeux de la microélectronique. L'intégration tridimensionnelle par empilement de circuits (3D stacking) constitue une voie prometteuse pour y parvenir. Elle permet notamment de dépasser certaines limitations atteintes par les circuits actuels, plus particulièrement dans les circuits pour lesquelles les données sont distribuées et qui nécessitent des bandes passantes importantes. Néanmoins, à ce jour, très peu de travaux ont montré les avantages de l'intégration 3D, en particulier ceux s'appuyant sur des résultats expérimentaux et de circuits concrets notamment dans le domaine des imageurs. Le présent travail de thèse a eu pour objectif d'exploiter la technologie 3D dans le cadre des capteurs d'images et dépasser la preuve de concept présentée dans l'état de l'art afin d'apporter une analyse concrète des apports de cette technologie dans le domaine des imageurs visibles. Nous avons identifié, d'une part l'extension de dynamique qui requiert un traitement proche pixel, d'autre part la compression locale, destinée à adresser les problèmes d'intégrité du signal, bande passante et consommation qui deviennent critiques avec l'augmentation des formats des imageurs. Ce choix permet d'apporter une réponse à la limitation de la dynamique des capteurs d'images 2D actuels, tout en gardant une architecture classique des pixels et en adressant le problème de la réduction de la quantité de données à transmettre. Une nouvelle méthode de codage flottant par groupe de pixels a été proposée et implémentée. Le principe s'appuie sur l'adaptation du temps d'intégration par groupe de pixels via l'application d'un exposant commun au groupe. Le temps d'intégration est ajusté à l'image suivante. Un premier niveau de compression est ainsi réalisé par le codage mantisse-exposant proposé. L'implémentation de cette technique a été validée sur un démonstrateur 2D au détriment de pixels sacrifiés aveugles de chaque groupe de pixels, comportant l'électronique de génération des signaux de commande de la HDR. La technique d'extension de dynamique proposée est suivie d'une compression à base de DCT (Discrete Cosine Transform} permettant de réduire le flux de données en sortie de la puce imageur. Les deux niveaux de compression permettent d'atteindre des taux de compression élevés allant jusqu'à 93% en maintenant un PSNR de 30dB et une qualité d'image acceptable pour des post-traitements. Une étude théorique de l'apport de l'intégration 3D en termes de consommation a été élaborée. Enfin, un démonstrateur 2D a été réalisé en technologie CMOS 180 nm en vue de valider l'architecture grande dynamique proposée. L'utilisation de la technologie 3D, dans la suite des travaux, permet l'implémentation d'une boucle courte, devenue possible grâce aux interconnexions verticales sans sacrifier des pixels morts. Le traitement local proche du pixel et la réduction de la latence, du flux de données et de la consommation sont les apports majeurs de l'intégration 3D étudiés dans ce travail / With the increase of systems complexity, integrating different technologies together has become a major challenge. Another challenge has traditionally been the limitation on the throughout between different part of the system coming from the interconnections. If traditional two dimensional integration solutions like System In a Package (SIP) bring heterogonous technologies together there is still limitations coming from the restricted number and lengths of interconnections between the different system components. Three Dimensional stacking (3D), by exploiting short vertical interconnections between different circuits of mixed technologies, has the potential to overcome these limitations. Still, despite strong interests for the 3D concepts, there is no advanced analysis of 3D integration benefits, especially in the field of imagers and smart image sensors. This thesis study the potential benefits of 3D integration, with local processing and short feedback loops, for the realisation of a High Dynamic Range (HDR) image sensor. The dense vertical interconnections are used to locally adapt the integration time by group of pixels, called macro-pixels, while keeping a classic pixel architecture and hence a high fill factor. Stacking the pixel section and circuit section enables a compact pixel and the integration of flexible and versatile functions. High Dynamic Range values producing an important quantity of data, the choice has been made to implement data compression to reduce the circuit throughout. A first level of compression is produced by coding the pixel value using a floating format with a common exponent shared among the macro-pixel. A second level of compression is proposed based on a simplified version of the Discrete Cosine Transform (DCT). Using this two level scheme, a compression of 93% can be obtained with a typical PSNR of 30 dB. A validation of the architecture was carried out by the development; fabrication and test of a prototype on a 2D, 180 nm, CMOS technology. A few pixels of each macro-pixel had to be sacrificed to implement the high dynamic range control signals and emulate the 3D integration. The test results are very promising proving the benefits that will bring the 3D integration in term of power consumption and image quality compared to a classic 2D integration. Future realisations of this architecture, done using a real 3D technology, separating sensing and processing on different circuits communicating by vertical interconnection will not need the sacrifice of any pixel to adjust the integration time, improving power consumption, image quality and latency

Cette thèse concerne l'étude de l'exposant critique associé à un groupe de surface dans deux cas. Le premier fait l'étude de l'action diagonale par deux représentations de l'espace de Teichmüller sur le produit de plans hyperboliques. Le second correspond à l'action quasi-Fuchsienne sur l'espace hyperbolique de dimension 3. Elle contient un chapitre de préliminaires détaillées introduisant les différents outils mathématiques nécessaires à la compréhension générale des énoncés et des preuves. L'étude de l'exposant critique sur H2*H2 correspond aux chapitre 2 et 3. Dans le second on y fait l'étude approfondie de la courbe de Manhattan, telle que définie par M. Burger, et des invariants qui lui sont associés (exposant critique, exposant critique directionnel, coefficient de corrélation). Dans le troisième, on y prouve le résultat principal de la première partie, un théorème d'isolation, précisant un résultat de rigidité de Bishop-Steger. Le dernier chapitre correspond à l'étude de l'exposant critique des groupes quasi-Fuchsiens. On y prouve deux inégalités entre l'entropie volumiques des surfaces plongées et l'exposant critique. On précise les cas d'égalités ce qui permet d'obtenir deux théorèmes de rigidité de l'exposant critique. / This aim of this thesis is the study of the critical exponent associated to a surface group acting on two different spaces. First we study the diagonal action of two teichmuller representations on the product of hyperbolic planes. Then we study quasi-Fuchsian action on the hyperbolic 3-space. The first chapter is dedicated to introduce the basic notions we need to understand the different theorems and proofs in the thesis. The study of critical exponent on H2*H2 is made in chapters 2 and 3. In chapter 2 we study the Manhattan curve, as defined by M. Burger, and more or less classical invariants as critical exponent, critical exponent with given slope, correlation coefficient. In chapter 3, we survey some results on geometric Teichmüller theory, as geodesic currents and earthquakes. We conclude this Chapter by the principal theorem of this first part, that is to say, an isolation result, improving a rigidity result of Bishop-Steger. In the last chapter, we study quasi-Fuchsian representations. The main result is an inequality between critical exponent and volume entropy of embedded surfaces. Moreover we precise the equality case, which gives a theorem of rigidity for the critical exponent.

L'objectif de cette thèse est de traiter de deux aspects différents de la théorie de l'exposant de Lyapunov de cocycles de Schrödinger définis par une dynamique ergodique. Dans la première partie, on s'intéresse aux estimées de grandes déviations de type Bourgain & Goldstein pour des cocycles quasi-périodiques, puis pour ceux définis par le doublement de l'angle. Après avoir montré que seule une estimée par dessus sur une bande complexe est nécessaire pour avoir la minoration, on redémontre cette inégalité pour une dynamique quasi-périodique en utilisant des techniques de mouvement brownien en lien avec des fonctions sous-harmoniques. Ensuite on adapte la méthode au cas du doublement de l'angle pour lequel on prouve des estimées de grandes déviations sur les branches inverses de cette dynamique. Dans la deuxième partie sont étudiés des cocycles de Schrödinger dont la dynamique est une somme de dynamiques quasi-périodique et aléatoire. On démontre que, dans le régime perturbatif, les développements asymptotiques de l'exposant de Lyapunov attaché à ces cocycles sont similaires à ceux déjà démontrés dans le cas aléatoire par Figotin & Pastur ou Sadel & Schulz-Baldes. L'analyse se fait en fonction du caractère diophantien ou résonant de l'énergie par rapport à la fréquence diophantienne de la partie quasi-périodique du potentiel. / In this thesis we are interested in the Lyapunov exponent of ergodic Schrödinger cocycles. These cocycles occur in the analysis of solutions to the Schrödinger equation where the potential is defined with ergodic dynamics. We study two distinct aspects related to the the Lyapunov exponent for different kinds of dynamics. First we focus on a large deviation theorem for quasi-periodic cocycles and then for potentials defined by the doubling map. We prove that estimates of Bourgain & Goldstein type are granted if an upper estimate involved in the theorem is true on a strip of the complex plane. Then we establish a new technique to prove this upper bound in the quasi-periodic setting, based on subharmonic arguments suggested by Avila, Jitomirskaya & Sadel. We adapt afterwards the method to the doubling map and prove a large deviation theorem for the inverse branches of this dynamics. In the second part, we establish an asymptotic development similar to the results of Figotin & Pastur and Sadel & Schulz-Baldes for the Lyapunov exponent of Schrödinger cocycles at small coupling when the potential is a mixture of quasi-periodic and random. The analysis distinguishes the cases when the energy is either diophantine or resonant with respect to the frequency of the quasi-periodic part of the potential.

PhD (Statistics) / Department of Statistics / There has been a growing interest in investment opportunities in Africa. The net foreign direct investment (FDI) to Sub-Saharan Africa has increased from $13 billion in 2004 to about $54 billion in 2015. Investing on the stock markets is one of such investment opportunities. Stock markets in Africa have realised growth in market capitalization, membership, value and volume traded due to an increase in investments. This level of growth in African stock markets has raised questions about their efficiency. This thesis examined the weak-form informational efficiency of African stock markets. The aim therefore of this thesis is to test the efficiency of African stock markets in the weak-form of the Efficient Market Hypothesis (EMH) for eight countries, namely, Botswana, Egypt, Kenya, Mauritius, Morocco, Nigeria, South Africa and Tunisia. Since, the researcher will be testing the weak-form of the EMH, the data to be used is on past price information on the markets of the eight countries. Data for the eight countries were obtained from DataStream for the period between August 28, 2000 to August 28, 2015. The data is for a period of 180 months which resulted in 3915 data points. Although there have been studies on the weak-form market efficiency of African stock markets, the efficiency conclusions on the markets have been mixed. This problem might be due to the methods used in the analyses. First, most of the methods used were linear in nature although the data generating process of stock market data is nonlinear and hence nonlinear methods maybe more appropriate in its analysis. Also these linear methods tested the efficiency of African markets in absolute form, however, an efficiency conclusion relying solely on absolute efficiency might be misleading because, stock markets become efficient with time due to improvements in the quality of information processing from reforms on the markets. The researcher solved this problem of using absolute frequency by comparing the results when the presence of long-memory in frequency and time domains of the markets were examined. The researcher used a semi-parametric estimator, the Local Whittle estimator to test for long-memory in frequency domain and the Detrended Fluctuation Analysis (DFA) to test for long-memory in time domain. The DFA method is suitable for both stationary and nonstationary time series which makes it to have more power over methods like the rescaled range analysis (R/S) in the estimation of Hurst exponent. Second, the researcher examined whether the markets were predictable under the Adaptive Market Hypothesis (AMH). The researcher employed the Generalised Spectral (GS) test to examine the Martingale difference hypothesis (MDH) of the markets. The Generalised spectral (GS) test is a non-parametric ii test designed to detect the presence of linear and nonlinear dependencies in a stationary time series. The GS test considers dependence at all lags. Third, because of the nonlinear nature in the data-generating process on the markets, the stationarity of the market returns under a nonlinear Exponential Smooth Threshold Autoregressive (ESTAR) model was examined. A nonlinear ADF unit root test against ESTAR and a modified Wald-type test against ESTAR in the analysis were employed. Fourth, the self-exciting threshold Autoregressive (SETAR) method was employed to model the returns when non-linear patterns were observed as a result of nonlinear data generating process on the markets. The literature on market efficiency of African stock markets has shown that variations exist in the study characteristics. There are variations in the method of analysis, type of test, type of data employed, time period chosen and the scope of analysis for the studies. The researcher therefore quantitatively reviewed previous studies by means of meta-analysis to identify which study characteristics affects efficiency conclusions of African markets using the mixed effects model. The findings showed the presence of long-memory in the returns of the stock markets when the whole sample was used. This made the markets weak-form inefficient, however, when the researcher tested for the persistence of long-memory through time, there were periods the markets were efficient in the weak-form. The memory effect was low in the South African market but high in the Mauritian market. Furthermore, it was observed that, the returns for Egypt, which were highly predictable when the whole data was analysed became not highly predictable when the rolling window approach of the GS test was used. Egypt had one of the lowest percentages of the windows that had a p-value less than 0.05 after South Africa. The results obtained from using the non-linear unit root tests on the logarithmic price series of the markets under study showed that, the markets were non-stationary and hence weak-form efficient under an ESTAR framework but for Botswana. Thus the markets were weak-form efficient when analysed using a non-linear method. This observation means that Africa’s foreign direct investment would have been increased over the years if the appropriate methods are used. This is because, over the years, studies on the weak-form efficiency African stock markets have ended with mixed conclusions with most of the markets being concluded to be weak-form inefficient as a result of the use of linear methods in the analysis. This finding, to us, has had an effect on investors commitments to Africa because the right methodology was not employed. iii The findings from modelling the returns under the non-linear SETAR model showed that, the SETAR model performs better than the standard AR(1) and AR(2) model for all the markets under study after the non-linear patterns were identified in the returns series. The SETAR (2,2,2) model is a threshold model, therefore, investors are able to move freely in search of higher opportunities between the low and high regimes. Investors main aim is to make profits, hence, the threshold model of SETAR gives them the freedom to move to a regime where the rate of returns is increasing unlike the standard AR(1) and AR(2) linear models where there are no switching of regimes. Finally, none of the study characteristics in the market efficiency studies was found to be significant in efficiency conclusions of African stock markets but the indicator for publication bias was significant. This means that there has been a change in attitude in recent years towards studies on informational market efficiency whose results do not support the Efficient Market Hypothesis (EMH), unlike the earlier years when the EMH was formulated and acclaimed to be one of the best propositions in economics. It was therefore concluded that when time-varying methods are used in analysing weak-form efficiency, the dynamics of the markets become known to investors for proper decision-making. Also, nonlinear methods should be used in order to reflect the nonlinear nature of data capturing on the stock markets / NRF

The first part of this work gives an introduction into aperiodic order in general and the lines of research pursued. The second part consists of eight manuscripts.

The research performed in this thesis aims to improve our understanding about one of the most malignant tumors of the human brain – glioma. From the early stages of my career I was confronted with the cruel reality of losing patients due to this devastating disease. The studies performed over the last four years involve extensive data analysis in different clinical and laboratory settings. The direct application of different analysis methods and tools in order to investigate the glioma infiltration delineation has potentially lead to direct applications of our results in the clinical setting. The overall approach of the study is based on three primary outcome measures, i.e., neuronal, electrophysiological and genetic/molecular features for distinguishing infiltrated and non-infiltrated zones within specifically peritumoral tissue (PT) and, more extensively, across the radiologically-defined boundaries of healthy, peritumoral and tumoral tissues. As such, we propose for the first time an objective demarcation and characterization of the PT and we detail how the genetic and epigenetic alterations within the tumoral and peritumoral area are linked with macroscopic functional MRI results. We also describe scale-free features (power law exponent) as well as distinct spectral features and reactivity to external stimulus in the tumoral and adjacent tissue of patients and provide novel insights in terms of glioma’s electrophysiology. The insights gained from these empirical studies further improve our understanding about the pathophysiology of this disease at micro- and macroscopic scales allowing us to envisage novel management methods for patients affected by glioma.

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.