Low income proportion (LIP), Lorenz curve (LC) and generalized Lorenz curve (GLC) are important indexes in describing the inequality of income distribution. They have been widely used for measuring social stability by governments around the world. The accuracy of estimating those indexes is essential to quantify the economics of a country. Established statistical inferential methods for these indexes are based on an asymptotic normal distribution, which may have poor performance when the real income data is skewed or has outliers. Recent applications of nonparametric methods, though, allow researchers to utilize techniques without giving data the parametric distribution assumption. For example, existing research proposes the plug-in empirical likelihood (EL)-based inferences for LIP, LC and GLC. However, this method becomes computationally intensive and mathematically complex because of the presence of nonlinear constraints in the underlying optimization problem. Meanwhile, the limiting distribution of the log empirical likelihood ratio is a scaled Chi-square distribution. The estimation of the scale constant will affect the overall performance of the plug-in EL method. To improve the efficiency of the existing inferential methods, this dissertation first proposes kernel estimators for LIP, LC and GLC, respectively. Then the cross-validation method is proposed to choose bandwidth for the kernel estimators. These kernel estimators are proved to have asymptotic normality. The smoothed jackknife empirical likelihood (SJEL) for LIP, LC and GLC are defined. Then the log-jackknife empirical likelihood ratio statistics are proved to follow the standard Chi-square distribution. Extensive simulation studies are conducted to evaluate the kernel estimators in terms of Mean Square Error and Asymptotic Relative Efficiency. Next, the SJEL-based confidence intervals and the smoothed bootstrap-based confidence intervals are proposed. The coverage probability and interval length for the proposed confidence intervals are calculated and compared with the normal approximation-based intervals. The proposed kernel estimators are found to be competitive estimators, and the proposed inferential methods are observed to have better finite-sample performance. All inferential methods are illustrated through real examples.

The computer and microelectronics technologies are developing very quickly nowadays. In the mean time, the modern integrated avionics systems are burgeoning unceasingly. The modern integrated modular architecture more and more requires the low-latency and reliable communication databus with the high bandwidth. The traditional avionics databus technology, such as ARINC429, can not provide enough high speed and size for data communication, and it is a problem to achieve transmission mission successfully between the advanced avionic devices with the sufficient bandwidth. AFDX(Avionics Full Duplex Switched Ethernet) is a good solution for this problem, which is the high-speed full duplex switched avionic databus, on the basis of the Ethernet technology. AFDX can not only avoid Ethernet conflicts and collisions, but also increase transmission rate with a lower weigh of the databus. AFDX is now adopted by A380,B787 aircraft successfully. The avionics data must be delivered punctualy and reliablely, so it is very essential to validate the real-time performance of AFDX during the design process. The simulation is a good method to acquire the network performance, but it only happends in some given set of scenarios, and it is impossible to consider every case. So a sophisticatd network performance method for the worst-case scenario with the pessimistic upper bound requires to be deduced. The avionic design engineers have launched many researches in the AFDX simulation and methods study. That is the goal that this thesis is aimming for. The development of this project can been planned in the following two steps. In the first step, a communication platform plans to be implemented to simulate the AFDX network in two versions – the RTAI realtime framework and Linux user space framework. Ultimately, these frameworks need to be integrated into net-ASS, which is an integrated simulation and assessment platform in the cranfield’s lab.The second step deduces an effective method to evaluate network performance, including three bounds(delay,backlog and output flow), based on the NC. It is called Network Calculus. It is an internet theory keeping the network system in determistic way. It is also used in communication queue management. This mathematics method is planed to be verified with simulation results from the AFDX simuation communication platform, in order to assure its validity and applicability. All in all, the project aims to assess the performance of different network topologies in different avionic architectures, through the simulation and the mathematical assessment. The technologies used in this thesis benefit to find problems and faults in the beginning stage of the avionics architecture design in the industrial project, especially, in terms of guarantee the lossless service in avionics databus.

Elliptic curve cryptography (ECC) has been introduced as a public-key cryptosystem, which offers smaller key sizes than the other known public-key systems at equivalent security level. The key size advantage of ECC provides faster computations, less memory consumption, less processing power and efficient bandwidth usage. These properties make ECC attractive especially for the next generation public-key cryptosystems. The implementation of ECC involves so many arithmetic operations / one of them is the elliptic curve point multiplication operation, which has a great influence on the performance of ECC protocols. In this thesis work, we have studied on elliptic curve point multiplication methods which are proposed by many researchers. The software implementations of these methods are developed in C programming language on Pentium 4 at 3 GHz. We have used NIST-recommended elliptic curves over prime and binary fields, by using efficient finite field arithmetic. We have then applied our elliptic curve point multiplication implementations to Elliptic Curve Digital Signature Algorithm (ECDSA), and compared different methods. The timing results are presented and comparisons with recent studies have been done.

One of the most important design issues for phase change materials is to engineer the phase transition process. The challenge of accurately predicting a phase transition is estimating the true value of transition rate, which is determined by the saddle point with the minimum energy barrier between stable states on the potential energy surface (PES). In this thesis, a new algorithm for searching the minimum energy path (MEP) is presented. The new algorithm is able to locate both the saddle point and local minima simultaneously. Therefore no prior knowledge of the precise positions for the reactant and product on the PES is needed. Unlike existing pathway search methods, the algorithm is able to search multiple transition paths on the PES simultaneously, which gives us a more comprehensive view of the energy landscape than searching individual ones. In this method, a Bézier curve is used to represent each transition path. During the searching process, the reactant and product states are located by minimizing the two end control points of the curve, while the shape of the transition pathway is refined by moving the intermediate control points of the curve in the conjugate directions. A curve subdivision scheme is developed so that multiple transitions paths can be located. The algorithm is demonstrated by examples of LEPS potential, LEPS plus harmonic oscillator potential, and PESs defined by Rastrigin function and Schwefel function.

The scope of this study is to estimate the zero-coupon yield curve of tomorrow by using Vasicek yield curve model with the zero-coupon bond yield data of today. The raw data of this study is the yearly simple spot rates of the Turkish zero-coupon bonds with different maturities of each day from July 1, 1999 to March 17, 2004. We completed the missing data by using Nelson-Siegel yield curve model and we estimated tomorrow yield cuve with the discretized Vasicek yield curve model.

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A determinação das principais propriedades magnéticas de um ímã permanente geralmente requer sistemas de medição sofisticados e custosos. Este trabalho analisa e propõe um sistema de caracterização de ímãs permanentes de Terras Raras à temperatura ambiente de baixo custo e de implementação mais simples e rápida. Ele consiste de um circuito magnético formado pelo ímã permanente sob caracterização, uma culatra de aço, um entreferro variável e uma sonda de efeito Hall com seu respectivo gaussímetro para a medição da intensidade do campo magnético no entreferro. Como introdução se apresenta o estado da arte da caracterização dos ímãs permanentes, conceitos básicos de magnetismo e em relação aos ímãs permanentes, sua história, os principais tipos, sua importância e suas aplicações principais. Os resultados teóricos e experimentais são comparados a resultados certificados, validando o método como proposto. / Determining the main magnetic properties of a permanent magnet usually requires sophisticated and expensive measurement setups. This work analyses and proposes a low-cost system to characterize Rare Earth permanent magnets at ambient temperature with easy and fast implementation. It consists of a magnetic circuit with the permanent magnet under test, appropriate pole pieces, a variable air gap and a Hall Effect probe with its respective Gaussmeter. As an introduction, it is presented the state of the art of permanent magnets characterization, basic concepts of magnetism and its history, the main types of permanent magnets, their importance and applications. The theoretical and experimental results are compared to certified ones, validating so the method as proposed.

A determinação das principais propriedades magnéticas de um ímã permanente geralmente requer sistemas de medição sofisticados e custosos. Este trabalho analisa e propõe um sistema de caracterização de ímãs permanentes de Terras Raras à temperatura ambiente de baixo custo e de implementação mais simples e rápida. Ele consiste de um circuito magnético formado pelo ímã permanente sob caracterização, uma culatra de aço, um entreferro variável e uma sonda de efeito Hall com seu respectivo gaussímetro para a medição da intensidade do campo magnético no entreferro. Como introdução se apresenta o estado da arte da caracterização dos ímãs permanentes, conceitos básicos de magnetismo e em relação aos ímãs permanentes, sua história, os principais tipos, sua importância e suas aplicações principais. Os resultados teóricos e experimentais são comparados a resultados certificados, validando o método como proposto. / Determining the main magnetic properties of a permanent magnet usually requires sophisticated and expensive measurement setups. This work analyses and proposes a low-cost system to characterize Rare Earth permanent magnets at ambient temperature with easy and fast implementation. It consists of a magnetic circuit with the permanent magnet under test, appropriate pole pieces, a variable air gap and a Hall Effect probe with its respective Gaussmeter. As an introduction, it is presented the state of the art of permanent magnets characterization, basic concepts of magnetism and its history, the main types of permanent magnets, their importance and applications. The theoretical and experimental results are compared to certified ones, validating so the method as proposed.

It always exists different methods/models to build a yield curve from a set of observed market rates even when the curve completely reproduces the price of the given instruments. To create an accurate and smooth interest rate curve has been a challenging all the time. The purpose of this thesis is to use the real market data to construct the yield curves by the bootstrapping method and the Smith Wilson model in order to observe and compare the performance ability between the models. Furthermore, the extended Nelson Siegel model is introduced without implementation. Instead of implementation I compare the ENS model and the traditional bootstrapping method from a more theoretical perspective in order to perceive the performance capabilities of them.

This thesis introduces new algorithms for solving curve/curve and ray/surface intersections. These algorithms introduce the concept of a geometric interval to extend the technique of Bézier clipping. A geometric interval is used to tightly bound a curve or surface or to contain a point on a curve or surface. Our algorithms retain the desirable characteristics of the Bézier clipping technique such as ease of implementation and the guarantee that all intersections over a given interval will be found. However, these new algorithms generally exhibit cubic convergence, improving on the observed quadratic convergence rate of Bézier clipping. This is achieved without significantly increasing computational complexity at each iteration. Timing tests show that the geometric interval algorithm is generally about 40-60% faster than Bézier clipping for curve/curve intersections. Ray tracing tests suggest that the geometric interval method is faster than the Bézier clipping technique by at least 25% when finding ray/surface intersections.