De nos jours, la compression de l'image médicale est un processus essentiel dans les systèmes de cybersanté. Compresser des images médicales de haute qualité est une exigence vitale pour éviter de mal diagnostiquer les examens médicaux par les radiologues. WAAVES est un algorithme de compression d'images médicales prometteur basé sur la transformée en ondelettes discrètes (DWT) qui permet d'obtenir une performance de compression élevée par rapport à l'état de la technique. Les principaux objectifs de ce travail sont d'améliorer la qualité d'image lors de la compression à l'aide de WAAVES et de fournir une architecture DWT haute vitesse pour la compression d'image sur des systèmes embarqués. En ce qui concerne l'amélioration de la qualité, les systèmes de nombres logarithmiques (LNS) ont été explorés pour être utilisés comme une alternative à l'arithmétique linéaire dans les calculs de DWT. Une nouvelle bibliothèque LNS a été développée et validée pour réaliser le DWT logarithmique. En outre, une nouvelle méthode de quantification appelée (LNS-Q) basée sur l'arithmétique logarithmique a été proposée. Un nouveau schéma de compression (LNS-WAAVES) basé sur l'intégration de la méthode Hybrid-DWT et de la méthode LNS-Q avec WAAVES a été développé. Hybrid-DWT combine les avantages des domaines logarithmique et linéaire conduisant à l'amélioration de la qualité d'image et du taux de compression. Les résultats montrent que LNS-WAAVES est capable d'obtenir une amélioration de la qualité d'un pourcentage de 8% et de 34% par rapport aux WAAVES en fonction des paramètres de configuration de compression et des modalités d'image. Pour la compression sur les systèmes embarqués, le défi majeur consistait à concevoir une architecture 2D DWT qui permet d'obtenir un débit de 100 trames full HD. Une nouvelle architecture unifiée de calcul 2D DWT a été proposée. Cette nouvelle architecture effectue à la fois des transformations horizontale et verticale simultanément et élimine le problème des accès de pixel d'image en colonne à partir de la RAM DDR hors-puce. Tous ces facteurs ont conduit à une réduction de la largeur de bande DDR RAM requise de plus de 2X. Le concept proposé utilise des tampons de ligne à 4 ports conduisant à quatre opérations en parallèle pipeline: la DWT verticale, la transformée DWT horizontale et les opérations de lecture / écriture vers la mémoire externe. L'architecture proposée a seulement 1/8 de cycles par pixel (CPP) lui permettant de traiter plus de 100fps Full HD et est considérée comme une solution prometteuse pour le futur traitement vidéo 4K et 8K. Enfin, l'architecture développée est hautement évolutive, surperforme l'état de l'art des travaux connexes existants, et est actuellement déployé dans un prototype médical EEG vidéo. / Nowadays, medical image compression is an essential process in eHealth systems. Compressing medical images in high quality is a vital demand to avoid misdiagnosing medical exams by radiologists. WAAVES is a promising medical images compression algorithm based on the discrete wavelet transform (DWT) that achieves a high compression performance compared to the state of the art. The main aims of this work are to enhance image quality when compressing using WAAVES and to provide a high-speed DWT architecture for image compression on embedded systems. Regarding the quality improvement, the logarithmic number systems (LNS) was explored to be used as an alternative to the linear arithmetic in DWT computations. A new LNS library was developed and validated to realize the logarithmic DWT. In addition, a new quantization method called (LNS-Q) based on logarithmic arithmetic was proposed. A novel compression scheme (LNS-WAAVES) based on integrating the Hybrid-DWT and the LNS-Q method with WAAVES was developed. Hybrid-DWT combines the advantages of both the logarithmic and the linear domains leading to enhancement of the image quality and the compression ratio. The results showed that LNS-WAAVES is able to achieve an improvement in the quality by a percentage of 8% and up to 34% compared to WAAVES depending on the compression configuration parameters and the image modalities. For compression on embedded systems, the major challenge was to design a 2D DWT architecture that achieves a throughput of 100 full HD frame/s. A novel unified 2D DWT computation architecture was proposed. This new architecture performs both horizontal and vertical transform simultaneously and eliminates the problem of column-wise image pixel accesses to/from the off-chip DDR RAM. All of these factors have led to a reduction of the required off-chip DDR RAM bandwidth by more than 2X. The proposed concept uses 4-port line buffers leading to pipelined parallel four operations: the vertical DWT, the horizontal DWT transform, and the read/write operations to the external memory. The proposed architecture has only 1/8 cycles per pixel (CPP) enabling it to process more than 100fps Full HD and it is considered a promising solution for future 4K and 8K video processing. Finally, the developed architecture is highly scalable, outperforms the state of the art existing related work, and currently is deployed in a video EEG medical prototype.

Mit dieser Arbeit liegt eine ausführliche Studie zu den Integralverfahren der Grenzschichttheorie vor. Der Schwerpunkt liegt dabei auf den Dissipationsintegralverfahren. Im Vergleich zu anderen Grenzschichtverfahren bestehen die generellen Vorteile der Integralverfahren in ihrer Robustheit, ihrer hohen Praktikabilität sowie den im Sinne der aufzuwendenden Computerkapazität geringen Kosten. Ein spezieller Vorteil der Dissipationsintegralverfahren ist es zudem, das komplette Schubspannungsprofil der Grenzschicht zu berücksichtigen. Über eine entsprechende Ableitung der Dissipationsintegrale kann die Vorgeschichte der Grenzschicht erfassen werden. Ausgangspunkt der Arbeit ist eine Literaturanalyse, welche aufzeigt, dass Integralverfahren weit verbreitet sind und für vielfältige Typen von Grenzschichten Anwendung finden. Ausgehend von den Navier-Stokes-Gleichungen wird über die Grenzschichtgleichungen die allgemeine Form der Dissipationsintegralgleichungen hergeleitet. Auf der Basis dieser Gleichungen werden Berechnungsalgorithmen für zwei- und dreidimensionale Grenzschichten entworfen und ausführlich diskutiert. Die zur Komplettierung der Berechnungsalgorithmen benötigten Parameterzusammenhänge werden aus expliziten Geschwindigkeitsprofilen hergeleitet. Hierzu werden beruhend auf dem Zweischichtenmodell turbulenter Grenzschichten Geschwindigkeitsprofile turbulenter Grenzschichten diskutiert. Drei Kombinationen von Haupt- und Querströmungsprofil werden für den dreidimensionalen Fall ausgewählt und algorithmisch umgesetzt. Die Algorithmen für zweidimensionale Grenzschichten beruhen auf einem Geschwindigkeitsprofil. Dem Aufbau der Algorithmen schließen sich ausführliche Testrechnungen sowie eine Bewertung der Verfahren an. Es wird festgestellt, dass Dissipationsintegralverfahren für zwei- und dreidimensionale Grenzschichten mit gutem Erfolg angewandt werden können. Vergleiche der Rechenergebnisse für zweidimensionale Grenzschichten zeigen die zumindest Gleichwertigkeit mit Zweigleichungsmodellen an. / Calculation and prediction of turbulent boundary layers are among the most challenging tasks of present fluid mechanics. A strong demand exists for robust, easy-to-handle and in terms of computing effort cheap algorithms which can be used for technical applications. From an engineering point of view zonal methods and RANS are the most useful tools for solution of fluid mechanical problems. It is known that zonal methods which use integral approaches for the description of the boundary layer can be used successfully in manifold forms. One way to improve zonal methods further is the Basically three different types of integral algorithms - entrainment, momentum of momentum and dissipation integral method - can be derived from the three-dimensional boundary layer equations. If one compares the usual entrainment integral method with the dissipation integral method it turns out that the latter has the following physical advantages. While the entrainment method considers information about the shear stress distribution only at the outer edge of the boundary layer, the dissipation integral method uses the whole distribution. This work gives an overview over dissipation integral method and extends them to three-dimensional boundary layers. The general integral equations for the three-dimensional case are derived. Using two different sets of mean velocity profiles the hyperbolical character of a dissipation integral method is shown. Apart from the integral momentum balance, the dissipation integral method satisfies a second major balance with the integral balance of mechanical energy. It is found that for a practical calculation the integral momentum equation and the integral energy equation are most useful. Sixteen two-dimensional experimental test cases with none-zero pressure gradients were computed. It was found that the averaged relative deviation between measured and computed values for the skin friction coefficient is about 5 % and about 3 % for the shape parameter. Two three-dimensional fully turbulent boundary layers approaching an obstacle where computed. The agreement between experimental results and the calculation is reasonably good. The calculation allows the prediction of the velocity distributions. Flow angle and flow gradient angle distributions being additional results.

Creep is defined as deformation that takes place under constant load after an initial elastic response. This thesis focuses on a material property problem area that concerns stress analysis. Focus is on stress development considering creep deformations occurring when a concrete structure is under load, i.e. stress analysis with viscoelastic properties of the material.From laboratory tests, both elastic modulus and deformations over time are estimated in an evaluation process. Usually, deformations of moist sealed samples are denoted basic creep. At Luleå Technical University creep measurements are evaluated according to the theory and methodology in Larson and Jonasson (2003a, 2003b). The model is denoted Linear Logarithmic Model, used for moist sealed concrete samples. This thesis involves an investigation of the evaluation procedure for basic creep performed in Thysell laboratory at LTU, to examine how sensitive the evaluation process is for the outcome from stress calculations. The calculations are performed in the Finite Element Method software ConTeSt Pro.The aim of the thesis is to analyze the sensitivity of evaluation of basic creep and of the Linear Logarithmic Model (LLM) by making changes in the evaluation process to see how different parameters sets effect calculated stresses/strains during through crack analysis. The changes are solely done in the relaxation spectra.The purpose is also to analyze how sensitive the changes made in the evaluation process are when typical cases are studied. The typical cases are defined with a structure of a newly cast wall on a mature slab, where various thickness of the wall during different temperature conditions are analyzed. The temperature conditions are named standard, winter and summer. With this, concrete is tested and evaluated to yield two material parameter sets useful for temperature - and stress calculations for young concrete.The material parameter sets were analyzed and their creep values were converted into relaxation values, i.e. relaxation spectra, according to Maxwell-chain formulation for LLM. ConTeSt calculations generate temperature development for the walls and slabs. Colour maps and values of the strain ratio for each studied case are also obtained.It can be established that the evaluation process of basic creep is sensitive. A conclusion to be drawn is that small changes in the relaxation spectra, gives changes in the results of stress calculations for the typical cases. As soon as we deviate from the temperature development for the test performed in the laboratory, either by changing the thickness of the wall or by testing different temperature conditions we get a different temperature development than the tested one. With the deviation in the calculated temperature development compared to the measured one, a difference in the calculated strain ratios for the two different material parameter sets created are found.The main discovery in this work is that when a geometry of the wall that is identical to the geometry of the concrete tested at the laboratory is analyzed, a small deviation in the calculations of strain is obtained. This is expected since the temperature development in the created wall will follow the temperature development of the tested concrete. When differing from this geometry and temperature case, differences in calculated strain ratios are observed. / Krypning är deformation som sker under en konstant belastning och i detta examensarbete är det fokus på deformationer av fuktförseglade betongprover. Detta examensarbete är inriktat på olika materialparametersuppsättningar som berör spänningsanalyser. Det är fokus på spänningsutveckling med avseende på krypdeformationer som uppstår när en betongstruktur är under belastning. Detta gällande spänningsanalyser med viskoelastiska egenskaper hos betongmaterialet. Från laboratorietester bestäms både elasticitetsmodulen och deformationer över tid i en utvärderingsprocess. På Luleå tekniska universitet, utvärderas krypningsmätningarna enligt teorin och metodiken som finns beskriven i Larson och Jonasson (2003a, 2003b). Modellen är benämnd Linjär Logaritmisk Modell (LLM), som används för fuktförseglade betongprover. Examensarbetet innehåller en undersökning av utvärderingsprocessen för krypning utförda i Thysell laboratoriet vid LTU. Detta för att undersöka hur känslig utvärderingsprocessen är för resultatet av spänningsberäkningar. Beräkningarna utförs i Finita Elementprogrammet ConTeSt. Syftet med detta arbete är att analysera känsligheten i utvärderingen av krypning för fuktförseglade betongprover och för den Linjära Logaritmiska modellen genom att göra ändringar i utvärderingsprocessen för att se hur olika materialparametersuppsättningar påverkar beräknade spänningar under analys av genomgående sprickor. Ändringar görs endast i relaxationsspektra. Syftet är också att analysera hur känsliga förändringarna i utvärderingsprocessen är när olika typfall studeras. Typfallen definieras av ny gjuten vägg på en mogen betongplatta, där olika väggtjocklekar under olika temperaturförhållanden analyseras. Temperaturförhållandena benämns standard, vinter och sommar. Därvid testas och utvärderas betongen för att ge två materialparameteruppsättningar som är användbara för temperatur- och spänningsberäkningar för ung betong.Materialparameteruppsättningarna analyserades och deras krypvärden konverterades till relaxationsvärden, så kallade relaxations spektra, genom att använda Maxwell element för LLM. Från ConTeSt beräkningar erhålls värden för temperaturutveckling i vägg samt platta. Värmeutvecklingskarta tillsammans med värden på töjningskvoten för väggarna under varje studerat temperaturfall erhålls också från ConTeSt programmet. Det kan fastställas att den studerade utvärderingsprocessen för krypning är känslig. Små ändringar i relaxationsspektra ger variationer i resultatet av spänningsberäkningar för de olika typfallen. Så fort vi varierar den beräknade väggens temperaturutveckling från temperaturutvecklingen för testet som utförts i laboratoriet, antingen genom att ändra väggtjocklek eller genom att testa olika temperaturförhållanden, så erhålls en annorlunda temperaturutveckling än den som togs fram från laboratoriet. Med avvikelser i de beräknade temperaturutvecklingarna jämfört med den erhållna temperaturutvecklingen från den testade betongen i laboratoriet beräknas och analyseras skillnaden i töjningskvot. Den huvudsakliga upptäckten i detta arbete är att när den beräknade geometrin på väggen är identisk med den geometri som används för testriggen i laboratoriet, erhålls små variationer i de beräknade töjningskvoten. Detta är förväntat eftersom temperaturutvecklingen i den beräknade väggen är densamma som för betongen i testriggen i laboratoriet. När man avviker från den geometri eller de temperaturförhållandena som är identiska till dem i laboratoriet så erhålls större avvikelser i värden för den beräknade töjningskvoten.

<p>In this thesis we discuss in detail the density-matrix renormalization group (DMRG) for simulating low-energy properties of quantum spin models. We implement an original DMRG routine on the S=1/2 antiferromagnetic Heisenberg chain and benchmark its efficiency against exact results (energies, correlation functions, etc.) as well as conformal field-theoretical calculations due to finite-size scaling (ground-state energy and spin gap logarithmic corrections). Moreover, we apply the DMRG to a two-leg square ladder system, where in addition to bilinear exchange terms, we also consider an additional cyclic four-spin ring-exchange. The transposition of four spins gives rise to biquadratic exchange terms which are non-trivial to implement in the DMRG. Intermediate results of the ring-exchange are presented along with the difficulties presently encountered.</p> / Master of Science (MSc)

Biologically inspired logarithmic CMOS sensors offer high dynamic range imaging capabilities without the difficulties faced by linear imagers. By compressing dynamic range while encoding contrast information, they mimic the human visual system’s response to photo stimuli in fewer bits than those used in linear sensors. Despite this prospect, logarithmic sensors suffer poor image quality due to illumination dependent fixed pattern noise (FPN), making individual pixels appear up to 100 times brighter or darker. This thesis is primarily concerned with alleviating FPN in logarithmic imagers in a simple and convenient way while undertaking a system approach to its origin, distribution and effect on the quality of monochrome and colour images, after FPN correction. Using the properties of the Human visual system, I propose to characterise the errors arising from FPN in a perceptually significant manner by proposing an error measure, never used before. Logarithmic operation over a wide dynamic range is first characterised using a new model; yi j =aj +bj ln(exp sqrt(cj +djxi)−1), where yi j is the response of the sensor to a light stimulus xi and aj, bj, cj and dj are pixel dependent parameters. Using a proposed correction procedure, pixel data from a monochromatic sensor array is FPN corrected to approximately 4% error over 5 decades of illumination even after digitisation - accuracy equivalent to four times the human eyes ability to just notice an illumination difference against a uniform background. By evaluating how error affects colour, the possibility of indiscernible residual colour error after FPN correction, is analytically explored using a standard set of munsell colours. After simulating the simple FPN correction procedure, colour quality is analysed using a Delta E76 perceptual metric, to check for perceptual discrepancies in image colour. It is shown that, after quantisation, the FPN correction process yields 1−2 Delta E76 error units over approximately 5 decades of illumination; colour quality being imperceptibly uniform in this range. Finally, tone-mapping techniques, required to compress high dynamic range images onto the low range of standard screens, have a predominantly logarithmic operation during brightness compression. A new Logr'Gb' colour representation is presented in this thesis, significantly reducing computational complexity, while encoding contrast information. Using a well-known tone mapping technique, images represented in this new format are shown to maintain colour accuracy when the green colour channel is compressed to the standard display range, instead of the traditional luminance channel. The trade off between colour accuracy and computation in this tone mapping approach is also demonstrated, offering a low cost alternative for applications with low display specifications.

Este trabalho descreve uma abordagem do método primal-dual barreira logarítmica (MPDBL) associado ao método de Newton modificado para a resolução do problema de fluxo de potência para sistemas de distribuição radial. Também foi realizado um estudo comparativo com duas técnicas clássicas de solução do problema de fluxo potência para redes de distribuição radial. São os métodos: Backward/Forward Sweep e o método proposto por M. Baran e F. Wu, que é baseado na técnica de Newton-Raphson. Este método utiliza uma matriz Jacobiana modificada que atende a característica radial dos sistemas de distribuição. Nos testes comparativos serão considerados todos os parâmetros do sistema. Os algoritmos de solução serão analisados em suas propriedades de convergência e será realizado um teste de robustez. Os resultados dos testes realizados em 4 sistemas (4, 10, 34 e 70 barras) e o teste comparativo entre os métodos evidenciam a melhor metodologia na solução do problema de fluxo de potência para sistemas radiais / This work describes an approach on primal-dual logarithmic barrier method (PDLBM) associate to the method of Newton modified for the resolution of the problem of power flow for radial distribution systems. Also a comparative study with two classic techniques of solution of the flow problem was carried through power for nets of radial distribution. They are the methods: Backward/Forward Sweep and the method considered for M. Baran and F. Wu, that is based on the technique of Newton-Raphson. This method uses modified Jacobiana matrix that takes care of the radial characteristic of the distribution systems. In the comparative tests all will be considered the parameters of the system. The solution algorithms will be analyzed in its properties of convergence and will be carried through a robustness test. The results of the tests carried through in 4 systems (4, 10, 34 and 70 bus) and the comparative test between the methods evidence the best methodology in the solution of the problem of power flow for radial systems

Este trabalho tem como objetivo realizar um estudo de alocação de unidades termoelétricas em sistemas elétricos de potência (SEP). O fluxo de potencia ótimo (FPO) foi utilizado para se obter o ponto ótimo de operação para o sistema e os multiplicadores de Lagrange associados às restrições. Os multiplicadores de Lagrange indicam a sensibilidade entre a função objetivo e a restrição a ele associada. Esta sensibilidade indica, quais as barras do sistema, são candidatas à alocação de novas usinas termoelétricas. Testes nos sistemas de 5 barras, IEEE 14 barras, IEEE 30 barras, equivalente CESP 440 kV de 53 barras e IEEE 118 barras comprovam a eficiência da abordagem, a qual poderá ser utilizada em estudos de planejamento da expansão do sistema. / The aim of this paper is to present a study of thermoelectrical generation allocation in electric power systems. The optimal power flow (OPF) was used to evaluate the optimal operation point for the power system and also Lagrange multipliers associated with the constraints. The Lagrange multipliers are the sensitivity between the objective function and its constraints. This sensitivity is used to verify in a power system where is the best place to incentive the allocation of new thermoelectrical power plants. Tests on the systems: 5 buses, IEEE 14 buses, IEEE 30 buses, equivalent CESP 440kV 53 buses and IEEE 118 buses showed the efficiency of the presented approach. This method of analyzing the system can be used in study of expansion planning system.

Este trabalho propõe estudos de casos em sistemas de energia elétrica por meio do Fluxo de Potência Ótimo (FPO) e da Análise de Sensibilidade em diferentes cenários de operação. Para isso, foram obtidos dados teóricos, a partir de levantamento bibliográfico, que explicitaram os conceitos de otimização aplicados ao sistema estático de energia elétrica. A pesquisa fundamentou-se metodologicamente no método primal-dual barreira logarítmica e nas condições necessárias de primeira-ordem de Karush-Kuhn-Tucker (KKT) para o problema de FPO, e no teorema proposto por Fiacco (1976) para a Análise de Sensibilidade. Os sistemas de equações resultantes das condições de estacionaridade, da função Lagrangiana, foram resolvidos pelo método de Newton. Na implementação computacional foram usadas técnicas de esparsidade. Estudos de casos foram realizados nos sistemas 3, IEEE 14, 30, 118, 300 barras e no equivalente CESP 440 kV com 53 barras, em que foi verificada a eficiência das técnicas apresentadas. / This work proposes a study of cases in power systems by Optimal Power Flow (OPF) and Sensitivity Analysis in different operation scenarios. For this purpose, theoretical data were obtained, starting from a bibliographical review, which enlightened the optimization concepts applied to the static system of electrical energy. The research was methodologically based on the primal-dual logarithmic barrier method and in the first-order necessary Karush-Kuhn-Tucker conditions to the OPF problem and in the theorem proposed by Fiacco (1976) to the Sensitivity Analysis. The equation sets generated by the first-order necessary conditions of the Lagrangian function, were solved by Newton\'s method. In the computational implementation, sparsity techniques were used. Studies of cases were carried out in the 3, IEEE 14, 30, 118, 300 buses and in the equivalent CESP 440 kV 53 bus, where the efficiency of the presented techniques was verified.

Made available in DSpace on 2016-04-27T16:58:14Z (GMT). No. of bitstreams: 1 Maria Sueli Gomes Saldanha.pdf: 608041 bytes, checksum: 1bdc94c03284d28bbaa8e5048a8c11dd (MD5) Previous issue date: 2007-05-22 / The purpose of this research, done according to the qualitative approach, was to analyze the teaching-learning process, involving the teacher, the student and the mathematical knowledge in the solving of problems, focusing on inequalities and logarithmic inequations. In order to reach this goal, six didactic situations were elaborated, based on the dialectic notion tool-object of the researcher Régina Douady. These same notions were used in the data analysis. The target-public was constituted by students and a teacher-researcher from the 10th grade of a private school in the city of São Paulo. The main instruments used in the data collection were recordings on tape of the dialogues among the teacher-researcher and the group of students, dialogues among teacher-researcher and classmatesgroup and the written work of the students in the solving of the proposed problems. The conclusion obtained was the approach developed by the proposed didactic sequence that favored the learning of inequalities and logarithmic inequations and, also, made possible to reflect about the teaching practice of the teacherresearcher / Esta pesquisa realizada na abordagem qualitativa, teve como objetivo analisar o processo ensino-aprendizagem, envolvendo professor, aluno e saber matemático na resolução de problemas, enfocando as desigualdades e inequações logarítmicas. Para atingir este objetivo, foram elaboradas seis situações didáticas, com base na noção dialética-ferramenta-objeto da pesquisadora francesa Régine Douady. Essas mesmas noções foram utilizadas nas análises dos dados. O público-alvo constitui-se de alunos e professora-pesquisadora de uma classe da 2ª série do Ensino Médio de uma escola particular de Vila Nova Conceição da cidade de São Paulo. Os principais instrumentos utilizados na coleta dos dados foram gravações em fita cassete dos diálogos entre professora-pesquisadora e o grupo de alunos, professora-pesquisadora e o grupo sala e produções escritas dos alunos na resolução dos problemas propostos. A conclusão obtida foi que a abordagem desenvolvida pela seqüência didática proposta favoreceu a aprendizagem das desigualdades e inequações logarítmicas e, também, oportunizou uma reflexão sobre a prática de ensino da professora-pesquisadora

Le but principal de cette thèse de doctorat est l'étude de l'anneau de cohomologie du complément d'une courbe algébrique réduite dans le plan projectif pondéré complexe dont les composantes irréductibles sont des courbes rationnelles (avec ou sans points singuliers). En particulier, des représentants holomorphes (rationnels) sont obtenus pour les classes de cohomologie. Pour atteindre notre objectif, il est nécessaire de développer une théorie algébrique des courbes sur des surfaces avec des singularités quotient et d'étudier des techniques pour calculer certains invariants particulièrement utiles à travers des Q-résolutions plongées. / The main goal of this PhD thesis is the study of the cohomology ring of the complement of a reduced algebraic curve in the complex weighted projective plane whose irreducible components are all rational (possibly singular) curves. In particular, holomorphic (rational) representatives are found for the cohomology classes. In order to achieve our purpose one needs to develop an algebraic theory of curves on surfaces with quotient singularities and study techniques to compute some particularly useful invariants by means of embedded Q-resolutions.