Denna uppsats undersöker effekten av oljepriser på inflation i Tyskland under 2000-talet. Under denna tid har många viktiga makroekonomiska händelser ägt rum och oljepriser har fluktuerat. Tyskland har valts att undersökas eftersom det är en stor europeisk ekonomi som är beroende av energiimport. En multipel linjär regression baserad på den nya Keynesianska Phillipskurvan har konstruerats. Resultaten visar att oljepriser har en statistiskt signifikant effekt på inflation; 1% ökning av oljepriser resulterar i en inflationsökning om 0,011%. Resultatet visar en positiv relation som ligger i linje med det teoretiska ramverket, men effekten är relativt liten vilket tyder på att oljepriser har en begränsad effekt på inflation under 2000-talet jämfört med tidigare tidsperiod. / This essay examines the effects of oil prices on inflation in Germany during the twenty-first century. At this time, many important macroeconomic events have occurred and oil prices have fluctuated. Germany was chosen as it is a strong European economy dependent on energy imports. A multiple regression analysis based on the theory of the new Keynesian Phillips curve has been constructed. The results show that oil prices have a statistically significant effect on inflation; a 1% increase in oil prices results in an inflation increase of 0,011%. The result of this positive relationship is in accordance with the theory, but the effect is relatively small thus suggesting that oil prices are not the primary cause of inflation. Oil prices seem to have a more limited effect on inflation in the twenty-first century compared to earlier time periods.

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In the first part I discuss ancestors of NURBS curves and surfaces, rather Ferguson, Beziere, Coons and B-spline curves and surfaces and furthermore B-spline functions. In the second part I devote to NURBS curves and surfaces, their description as a linear combination of B-spline functions in the projective space. I specify conical arcs more detailed, their submit in the projective space and NURBS surfasec given as tensor product of NURBS curves. Last part is devote to describtion programs for modeling conicals and NURBS surface.

Cryptography algorithms like the Advanced Encryption Standard, Elliptic Curve Cryptography algorithms etc are designed using algebraic properties of finite fields. Thus performance of these algorithms depend on performance of the underneath field operations. Moreover, different algorithms use finite fields of widely varying order. In order to cater to these finite fields of different orders in an area efficient manner, it is necessary to design solutions in the form of hardware-consolidations, keeping the performance requirements in mind. Due to their small area occupancy and high utilization, such circuits are less likely to stay idle and therefore are less prone to loss of energy due to leakage power dissipation. There is another class of applications that rely on finite field algebra namely the various error detection and correction techniques. Most of the classical block codes used for detection of bit-error in communications over noisy communication channels apply the algebraic properties of finite fields. Cyclic redundancy check is one such algorithm used for detection of error in data in computer network. Reed-Solomon code is most notable among classical block codes because of its widespread use in storage devices like CD, DVD, HDD etc. In this work we present the architecture of a polymorphic multiplier for operations over various extensions of GF(2). We evolved the architecture of a textbook shift-and-add multiplier to arrive at the architecture of the polymorphic multiplier through a generalized mathematical formulation. The polymorphic multiplier is capable of morphing itself in runtime to create data-paths for multiplications of various orders. In order to optimally exploit the resources, we also introduced the capability of sub-word parallel execution in the polymorphic multiplier. The synthesis results of an instance of such a polymorphic multipliershowsabout41% savings in area with 21% degradation in maximum operating frequency compared to a collection of dedicated multipliers with equivalent functionality. We introduced the multiplier as an accelerator unit for field operations in the coarse grained runtime reconfigurable platform called REDEFINE. We observed about 40-50% improvement in performance of the AES algorithm and about 52×improvement in performance of Karatsuba-Ofman multiplication algorithm.

Les problèmes d'interpolation ont été largement étudiés dans la Conception Géométrique Assistée par Ordinateur. Ces problèmes consistent en la construction de courbes et de surfaces qui passent exactement par un ensemble de données. Dans ce cadre, l'objectif principal de cette thèse est de présenter des méthodes d'interpolation de données 2D et 3D au moyen de courbes Algébriques Trigonométriques à Hodographe Pythagorien (ATPH). Celles-ci sont utilisables pour la conception de modèles géométriques dans de nombreuses applications. En particulier, nous nous intéressons à la modélisation géométrique d'objets odontologiques. À cette fin, nous utilisons les courbes spatiales ATPH pour la construction de surfaces développables dans des volumes odontologiques. Initialement, nous considérons la construction de courbes planes ATPH avec continuité C² qui interpolent une séquence ordonnée de points. Nous employons deux méthodes pour résoudre ce problème et trouver la « bonne » solution. Nous étendons les courbes ATPH planes à l'espace tridimensionnel. Cette caractérisation 3D est utilisée pour résoudre le problème d'interpolation Hermite de premier ordre. Nous utilisons ces splines ATPH spatiales C¹ continues pour guider des facettes développables, qui sont déployées à l'intérieur de volumes tomodensitométriques odontologiques, afin de visualiser des informations d'intérêt pour le professionnel de santé. Cette information peut être utile dans l'évaluation clinique, diagnostic et/ou plan de traitement. / Interpolation problems have been widely studied in Computer Aided Geometric Design (CAGD). They consist in the construction of curves and surfaces that pass exactly through a given data set, such as point clouds, tangents, curvatures, lines/planes, etc. In general, these curves and surfaces are represented in a parametrized form. This representation is independent of the coordinate system, it adapts itself well to geometric transformations and the differential geometric properties of curves and surfaces are invariant under reparametrization. In this context, the main goal of this thesis is to present 2D and 3D data interpolation schemes by means of Algebraic-Trigonometric Pythagorean-Hodograph (ATPH) curves. The latter are parametric curves defined in a mixed algebraic-trigonometric space, whose hodograph satisfies a Pythagorean condition. This representation allows to analytically calculate the curve's arc-length as well as the rational-trigonometric parametrization of the offsets curves. These properties are usable for the design of geometric models in many applications including manufacturing, architectural design, shipbuilding, computer graphics, and many more. In particular, we are interested in the geometric modeling of odontological objects. To this end, we use the spatial ATPH curves for the construction of developable patches within 3D odontological volumes. This may be a useful tool for extracting information of interest along dental structures. We give an overview of how some similar interpolating problems have been addressed by the scientific community. Then in chapter 2, we consider the construction of planar C2 ATPH spline curves that interpolate an ordered sequence of points. This problem has many solutions, its number depends on the number of interpolating points. Therefore, we employ two methods to find them. Firstly, we calculate all solutions by a homotopy method. However, it is empirically observed that only one solution does not have any self-intersections. Hence, the Newton-Raphson iteration method is used to directly compute this \good" solution. Note that C2 ATPH spline curves depend on several free parameters, which allow to obtain a diversity of interpolants. Thanks to these shape parameters, the ATPH curves prove to be more exible and versatile than their polynomial counterpart, the well known Pythagorean-Hodograph (PH) quintic curves and polynomial curves in general. These parameters are optimally chosen through a minimization process of fairness measures. We design ATPH curves that closely agree with well-known trigonometric curves by adjusting the shape parameters. We extend the planar ATPH curves to the case of spatial ATPH curves in chapter 3. This characterization is given in terms of quaternions, because this allows to properly analyze their properties and simplify the calculations. We employ the spatial ATPH curves to solve the first-order Hermite interpolation problem. The obtained ATPH interpolants depend on three free angular values. As in the planar case, we optimally choose these parameters by the minimization of integral shape measures. This process is also used to calculate the C1 interpolating ATPH curves that closely approximate well-known 3D parametric curves. To illustrate this performance, we present the process for some kind of helices. In chapter 4 we then use these C1 ATPH splines for guiding developable surface patches, which are deployed within odontological computed tomography (CT) volumes, in order to visualize information of interest for the medical professional. Particularly, we construct piecewise conical surfaces along smooth ATPH curves to display information related to the anatomical structure of human jawbones. This information may be useful in clinical assessment, diagnosis and/or treatment plan. Finally, the obtained results are analyzed and conclusions are drawn in chapter 5.

Geothermal energy is an important source of clean and renewable energy. This project deals with the study of deep geothermal power plants for the generation of electricity. The design involves the extraction of heat from the Earth and its conversion into electricity. This is performed by allowing fluid deep into the Earth where it gets heated due to the surrounding rock. The fluid gets vaporized and returns to the surface in a heat pipe. Finally, the energy of the fluid is converted into electricity using turbine or organic rankine cycle (ORC). The main feature of the system is the employment of side channels to increase the amount of thermal energy extracted. A finite difference computer model is developed to solve the heat transport equation. The numerical model was employed to evaluate the performance of the design. The major goal was to optimize the output power as a function of parameters such as thermal diffusivity of the rock, depth of the main well, number and length of lateral channels. The sustainable lifetime of the system for a target output power of 2 MW has been calculated for deep geothermal systems with drilling depths of 8000 and 10000 meters, and a financial analysis has been performed to evaluate the economic feasibility of the system for a practical range of geothermal parameters. Results show promising an outlook for deep geothermal systems for practical applications.

This master thesis is about Elliptic Curve Digital Signature Algorithm or ECDSA and two of the known attacks on this security system. The purpose of this thesis is to find points that are likely to be points of high order on an elliptic curve. If we have a point P of high order and if Q = mP, then we have a large set of possible values of m. Therefore it is hard to solve the Elliptic Curve Discrete Logarithm Problem or ECDLP. We have investigated on the time of finding the solution of ECDLP for a certain amount of elliptic curves based on the order of the point which is used to create the digital signatures by those elliptic curves. Method: Algebraic Structure of elliptic curves over finite fields and Discrete logarithms. This has been done by two types of attacks namely Baby Step, Giant Step and Pollard’s Rho and all of the programming parts has been done by means of Mathematica. Conclusion: We have come into a conclusion of having the probable good points which are the points of high order on elliptic curves through the mentioned attacks in which solving the ECDLP is harder if these points have been used in generating the digital signature. These probable good points can be estimated by means of a function we have come up with. The input of this function is the order of the point and the output is the time of finding the answer of ECDLP.

In present work we study the algorithms for point counting on elliptic and hy- perelliptic curves. At the beginning we describe a few simple and ineffective al- gorithms. Then we introduce more complex and effective ways to determine the point count. These algorithms(especially the Schoof's algorithm) are important for the cryptography based on discrete logarithm in the group of points of an el- liptic or hyperelliptic curve. The point count is important to avoid the undesirable cases where the cryptosystem is easy to attack. 1

Made available in DSpace on 2017-07-21T19:26:10Z (GMT). No. of bitstreams: 1 Jocenei Antonio Oliveira.pdf: 2309316 bytes, checksum: 8527d62e93fbe03d332c4ffaa65aedda (MD5) Previous issue date: 2014-06-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Soil water retention properties can be described by so-called soil-water characteristic curve (SWCC) or retention curve (WRC). This curve expresses the relationship between matric potential and soil moisture based on weight or volume. Through the attainment and subsequent analytical interpolation of the WRC, it’s possible the indirect estimative of the pore-size distribution (PSD) curve of any porous system. Sometimes, obtaining the WRC may be a time-consuming process or involve the use of equipment not available in some laboratories. Thus the development of an alternative method to obtain the WRC and after the PSD becomes desirable, since these are properties of extreme importance to characterize porous media. The main objective of this study is to create and adapt methodology for obtaining PSD using computer simulation in tomographic images with micrometer resolution. In this study, there were used samples of sand and glass beads of different grain sizes for the generation of the PSD curve using a Haines’ funnel on balance. After WRC achievement, these were adjusted through an analytical model and then there were built experimental PSD curve. PSD were also determined by adaptation of a computer program using tomographic images of these samples. The results of obtained WRC associated with geometric models to predict the entry point of air have only revealed the idea about how may occur drying of the samples, showing only morphological considerations are not sufficient to describe this situation. The investigated porous systems homogeneity was able to be visualized by comparing the PSD curves in terms of their widths. / Propriedades de retenção da água no solo podem ser descritas pela chamada curva característica de água no solo ou curva de retenção (CR). Esta curva exprime a relação entre potencial mátrico e a umidade do solo à base de massa ou volume. Mediante o levantamento da CR e posterior interpolação analítica, pode-se estimar indiretamente a curva de distribuição de poros (CDP) de um sistema poroso qualquer. Algumas vezes, a obtenção da CR pode ser um processo demorado ou envolver a utilização de equipamentos não disponíveis em alguns laboratórios. Desta forma, o desenvolvimento de uma metodologia alternativa para a obtenção da CR e posteriormente da CDP se faz desejável, uma vez que se trata de propriedade de extrema importância para a caracterização de um meio poroso. O objetivo principal deste trabalho é criar e adaptar metodologia para a obtenção de CDPs utilizando simulação computacional em imagens tomográficas com resolução micrométrica. No presente estudo, foram utilizadas amostras de areias e esferas de vidro de diferentes granulometrias para o levantamento das CRs usando um funil de Haines adaptado. Depois de obtidas as CRs, essas foram ajustadas através do modelo de ajuste de van Genuchten e obtidas as CDPs (primeira derivada da CR). Também foram obtidas CDPs mediante a adaptação de um programa computacional que utiliza informações de imagens tomográficas dessas amostras. Os resultados das CDPs levantadas pelos dois métodos mostram alguma concordância. Verificou-se, no entanto, que apenas considerações sobre a morfologia dos poros não são suficientes para descrever a forma com que as amostras são drenadas.

Objective: The objective of the present study was to evaluate the performance of the monothermal caloric screening test in a large sample of patients. Design: A retrospective analysis of the medical records of 1002 consecutive patients who had undergone vestibular assessment at the Mayo Clinic during the years 1989 and 1990 was conducted. Patients with incomplete alternate binaural bithermal (ABB) caloric testing, congenital or periodic alternating nystagmus, or bilateral vestibular loss were excluded from the study. Clinical decision theory analyses (relative operating characteristic curves) were used to determine the accuracy with which the monothermal warm (MWST) and monothermal cool (MCST) caloric screening tests predicted the results of the ABB caloric test. Cumulative distributions were constructed as a function of the cutoff points for monothermal interear difference (IED) to select the cutoff point associated with any combination of true-positive and false-positive rates. Results: Both MWST and MCST performed well above chance level. The test performance for the MWST was significantly better than that of the MCST for three of the four ABB gold standards. A 10% IED cutoff point for the MWST yielded a false-negative rate of either 1% (UW ≥25%) or 3% (UW ≥20%). The use of a 10% IED (UW ≥25%) for the MWST would have resulted in a 40% reduction (N = 294) in the number of ABB caloric tests performed on patients without a unilateral weakness. Conclusions: The results of this study indicated that the MWST decreases test time without sacrificing the sensitivity of the ABB caloric test.