Two models of a self-stabilizing hydrofoil system is developed where the effects from the struts and hydrofoil give torques for angular rotations. Lifting line theory for the hydrofoil which can twist is used. Nonlinear versions of the models are also developed and compared to find that the linear models use valid approximations. Backward Differentiation Formula is used to get numerical solutions, and eigenvalues of linear system matrices are used to get stability regions. The models did not accurately capture what has been seen in testing. / Två modeller för ett självstabiliserande bärplanssystem utvecklas där effekter från stöttor och bärplan ger vridmoment för vinkelrotationer. Lyftande linjeteori för det skevande bärplanet används. Icke-linjära versioner av modellerna tas också fram och jämförs för att finna att de linjära modellerna använder giltiga approximationer. Backward Differentiation Formula används för att fram numeriska lösningar, och egenvärden i det linjära systemetsmatriser används för att hitta stabilitetsregioner. Modellerna fångade inte korrekt vad som har setts i testning.

This doctoral thesis is concerned with some theoretical and practical questions related to backward stochastic differential equations (BSDEs) and more specifically their connection with some parabolic partial differential equations (PDEs). The thesis is made of three parts. In the first part, we study the probabilistic representation for a class of multidimensional PDEs with quadratic nonlinearities of a special form. We obtain a representation formula for the PDE solution in terms of the solutions to a Lipschitz BSDE. We then use this representation to obtain an estimate on the gradient of the PDE solutions by probabilistic means. In the course of our analysis, we are led to prove some results for the associated multidimensional quadratic BSDEs, namely an existence result and a partial uniqueness result. In the second part, we study the well-posedness of a very general quadratic reflected BSDE driven by a continuous martingale. We obtain the comparison theorem, the special comparison theorem for reflected BSDEs (which allows to compare the increasing processes of two solutions), the uniqueness and existence of solutions, as well as a stability result. The comparison theorem (from which uniqueness follows) and the special comparison theorem are obtained through natural techniques and minimal assumptions. The existence is based on a perturbative procedure, and holds for a driver whis is Lipschitz, or slightly-superlinear, or monotone with arbitrary growth in y. Finally, we obtain a stability result, which gives in particular a local Lipschitz estimate in BMO for the martingale part of the solution. In the third and last part, we study the time-discretization of BSDEs having nonlinearities that are monotone but with polynomial growth in the primary variable. We show that in that case, the explicit Euler scheme is likely to diverge, while the implicit scheme converges. In fact, by studying the family of θ-schemes, which are mixed explicit-implicit, θ characterizing the degree of implicitness, we find that the scheme converges when the implicit component is dominant (θ ≥ 1/2 ). We then propose a tamed explicit scheme, which converges. We show that the implicit-dominant schemes with θ > 1/2 and our tamed explicit scheme converge with order 1/2 , while the trapezoidal scheme (θ = 1/2) converges with order 7/4.

Existing low-voltage networks may not accommodate high penetrations of low-carbon technologies. The topic of this thesis is unbalance, which if minimised can delay or avoid the constraining of these technologies or the replacing of still-useful network assets. Most of the discussion on unbalance, as seen in the standards and the literature, centres on the effects of voltage unbalance on consumer equipment. Its effects on the network are not equally reported. This thesis recognises fundamental differences between the consumer and network perspectives. It can inform distribution network operators on the interpretation of measurements taken on low-voltage networks and guide research on unbalance due to high penetrations of low-carbon technologies. Much of the work involved simulations of LV networks. Initially, existing 3 x 3 or 5 x 5 approaches to the forward-backward sweep method were thought suitable. After a review of these approaches however, there were doubts as to how accurately they accounted for the shared neutral-earth return path on which the out-of-balance current flows. This led to the derivation of a new 5 x 5 approach using only Kirchhoff s voltage (KVL) and current laws (KCL). Its results are validated thoroughly in the thesis. In addition to satisfying KVL and KCL, they match Matlab SimPowerSystems exactly and are in close agreement with measurements taken on a very unbalanced rural feeder. This thesis also investigates the mitigation of unbalance using the static balancer. This is a transformer with a single interconnected-star winding. It was used in 1930-1950s to correct unbalance. Contributions are made for its possible re-introduction as a retrofit option. They include a model for use in the forward-backward sweep method, validated by laboratory and field measurements, and the quantification of the static balancer s strengths and weaknesses as this can help identify when it should be used.

In this thesis, first we study the unique classical solution of quasi-linear second order parabolic partial differential equations (PDEs). For this, we study the existence and uniqueness of the $L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{d}) \otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k})\otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k\times d})$ valued solution of forward backward stochastic differential equations (FBSDEs) with finite horizon, the regularity property of the solution of FBSDEs and the connection between the solution of FBSDEs and the solution of quasi-linear parabolic PDEs. Then we establish their connection in the Sobolev weak sense, in order to give the weak solution of the quasi-linear parabolic PDEs. Finally, we study the unique weak solution of quasi-linear second order elliptic PDEs through the stationary solution of the FBSDEs with infinite horizon.

Problemas provenientes de química atmosférica, possuem uma característica especial denominada stiffness, indicando que as soluções dos sistemas de equações diferenciais ordinárias envolvidos variam em diferentes ordens de grandeza. Isso faz com que métodos numéricos adequados devam ser aplicados no intuito de obter soluções numéricas convergentes e estáveis. Os métodos mais eficazes para tratar este tipo de problema são os métodos implícitos, pois possuem uma região de estabilidade ilimitada que permite grandes variações no tamanho do passo, mantendo o erro de discretização dentro de uma dada tolerância. Mais precisamente, estes métodos possuem a propriedade de A-estabilidade ou A(alpha)-estabilidade. Neste trabalho, comparamos dois métodos numéricos com estas características: o método de Rosenbrock e a fórmula de diferenciação regressiva (métodos BDF). O primeiro é usado no módulo de Química do modelo CCATT-BRAMS do Centro de Previsão de Tempo e Estudos Climáticos (CPTEC), sendo incluído na previsão numérica de regiões com intensas fontes de poluição. Este é um método de passo simples implícito com um controle de passo adaptativo. Aqui empregamos também o segundo, um método de passo múltiplo que dispõe de uma fórmula que permite variação no tamanho do passo e na ordem, empregando o pacote LSODE. Os resultados de nossas comparações indicam que os métodos BDF podem se constituir em interessante alternativa para uso no CCATT-BRAMS. / Problems from atmospheric chemistry have a special characteristic denominated stiffness, indicating that the solutions of the involved ordinary differential equations systems vary in different scales. This means that appropriate methods should be applied in order to get convergent and stable numerical solutions. The most powerful methods to treat problems like this are implicit schemes, since they have unlimited stabity regions, allowing large variations in step size, keeping the discretization error within a given tolerance. More precisely, these methods have the A-stability or A(alpha)-stability properties. In this work, we compared two numerical methods with those characteristics: the Rosenbrock method and the backward differentiation formula (BDF). The first one is employed in the Chemistry package within CCATT-BRAMS local weather model of CPTEC (Center for Weather Forecasts and Climate Studies), which is mainly used for the numerical forecasting of regions with intense pollution. This is a implicit one-step method with an adaptative stepsize control. We compare it with the second method, a multistep method with a formula that allows variations in step size and order, with the help of the LSODE package. The results of our comparisons indicate that BDF methods are an interesting alternative to be used within CCATT-BRAMS.

Dans la première partie de cette thèse, on présente des inégalités de concentration convexe pour des intégrales stochastiques. Ces résultats sont obtenus par calcul stochastique e tpar calcul de Malliavin forward/backward. On présente également des inégalités de déviation pour les exponentielles martingales à saut.Dans une deuxième partie on présente des théorèmes limites pour le conditionnement du mouvement brownien.

Spatial decision making is a process of providing an effective solution for a problem that encompasses semi-structured spatial data. It is a challenging task which involves various factors to consider. For example, in order to build a new industry, an appropriate site must be selected for which several factors have to be taken into consideration. Some of the factors, which can affect the decision in this particular case, are air pollution, noise pollution, and distance from living areas, which makes the decision difficult. The geographic information systems (GIS) and the expert systems (ES) have many advantages in solving problems in their prospective areas. Integrating these two systems will benefit in solving spatial decision making problems. In the past, many researchers have proposed integrating systems which extracts the data from the GIS and saves it in the database for decision making. Most of the frameworks which have been developed were system dependent and are not properly structured. So it is difficult to search the data. This thesis proposes a framework which extracts the GIS data and processes it with the help of ES decision making capabilities to solve the spatial decision making problem. This framework is named GeoFilter. This research classifies various types of mechanisms that can be used to integrate these two systems.

Protection of groundwater sources has become an important issue in Canada. Over the last decade many approaches to the protection of groundwater sources have evolved. Some approaches provide qualitative information while others give quantitative values with respect to protection measures. The objective of the thesis is to examine the existing approaches of source water protection (SWP) using a complex geological setting, and introduce new methodologies towards the quantitative measurement of the various steps of SWP. The information obtained from the studies can be used to set up future guidelines for SWP. The first step in SWP is to assess the vulnerability of an aquifer. In this thesis, we compare three approaches for evaluating aquifer vulnerability: the Index Approach (Intrinsic Susceptibility Index, or ISI), the Hydraulic Resistance (HR) Approach (similar to the Aquifer Vulnerability Index, or AVI) and the Travel Time Approach (Surface to Aquifer Advective Time, or SAAT). The ISI approach uses the thickness and vertical hydraulic conductivity of the layers overlying an aquifer, and the vulnerability is expressed as a numerical score which is related to these parameters but is not physically based. The HR approach is physically based, uses the same parameters as ISI with the addition of porosity, and results are in the form of travel time under a unit gradient. SAAT extends the physically based approach by including the unsaturated zone and using the actual downward gradient; results are given in terms of advective travel time from surface to aquifer. These three approaches are compared, using two different aquifer systems. The second step in SWP is the delineation of wellhead protection areas (WHPAs). The WHPA delineates the area within which a source of contamination could have an impact on the well. The actual impact on the well depends not only on the source, but also on the characteristics of the groundwater system. Important considerations include the dimensionality of the system, the uncertainty in the system characteristics, and the physical processes that could affect the impact. The conventional approach is to define different time of travel (TOT) zones based on backward advective particle tracking. An alternative approach is to apply backward advective-dispersive solute transport modelling, in which dispersion can be taken as representing the uncertainty in defining the hydrogeologic characteristics (e.g. hydraulic conductivity) of the aquifer. The outlines of the TOT zones in the backward advective particle tracking approach is obtained by drawing an envelope around the respective tracks, which may require considerable guesswork. In the backward-in-time transport modelling, the outline of the TOT zones are developed using mass balance principles. The third step is the assessment of well vulnerability. Well vulnerability is based on the source-pathway-receptor concept which analyses the transport and fate of the contaminants along its path from the source to the receptor, and the interaction of the well itself with the flow system, and thus determines the actual impact on the well. The impact can be expressed in terms of the contaminant concentration in the well water. The mapping of the impact can be carried out by using a standard advective-dispersive transport model in either a forward-in-time mode (for a known contaminant source) or in a backward-in-time mode (for unknown sources). Thus, the well vulnerability concept goes beyond the conventional approach of WHPA, which is based solely on advective transport, neglecting dispersion and chemical processes. For any known point or non-point time-varying contaminant sources located arbitrarily within the well capture zone, the expected concentration at the well can simply be evaluated by convoluting the source mass with the results of the well vulnerability without further use of the model. Convolution is a well-known and effective superposition method to deal with arbitrary inputs in time and space for linear systems. The information of the contaminant concentration in the well water can be used to quantify the risk of a well becoming contaminated. Risk can be expressed in terms of the exposure value of the contaminant concentration exceeding the allowable limit and the time frame within which the well becomes contaminated. The exposure value can be integrated with the time element to set up a ranking of priorities, or to calculate the investment that must be made today in order to have the required funds available for remediation at the time it becomes necessary. The concept is applied to a well using hypothetical contaminant sources located arbitrarily within the capture zone. Well vulnerability maps can be used as a powerful tool to identify the optimal locations for Beneficial Management Practices (BMPs). A case study addressing the problem of elevated nitrate levels in a drinking water supply well is used to demonstrate the principle. The reduction of nitrate input concentration within the most vulnerable areas shows the largest impact at the well.

Protection of groundwater sources has become an important issue in Canada. Over the last decade many approaches to the protection of groundwater sources have evolved. Some approaches provide qualitative information while others give quantitative values with respect to protection measures. The objective of the thesis is to examine the existing approaches of source water protection (SWP) using a complex geological setting, and introduce new methodologies towards the quantitative measurement of the various steps of SWP. The information obtained from the studies can be used to set up future guidelines for SWP. The first step in SWP is to assess the vulnerability of an aquifer. In this thesis, we compare three approaches for evaluating aquifer vulnerability: the Index Approach (Intrinsic Susceptibility Index, or ISI), the Hydraulic Resistance (HR) Approach (similar to the Aquifer Vulnerability Index, or AVI) and the Travel Time Approach (Surface to Aquifer Advective Time, or SAAT). The ISI approach uses the thickness and vertical hydraulic conductivity of the layers overlying an aquifer, and the vulnerability is expressed as a numerical score which is related to these parameters but is not physically based. The HR approach is physically based, uses the same parameters as ISI with the addition of porosity, and results are in the form of travel time under a unit gradient. SAAT extends the physically based approach by including the unsaturated zone and using the actual downward gradient; results are given in terms of advective travel time from surface to aquifer. These three approaches are compared, using two different aquifer systems. The second step in SWP is the delineation of wellhead protection areas (WHPAs). The WHPA delineates the area within which a source of contamination could have an impact on the well. The actual impact on the well depends not only on the source, but also on the characteristics of the groundwater system. Important considerations include the dimensionality of the system, the uncertainty in the system characteristics, and the physical processes that could affect the impact. The conventional approach is to define different time of travel (TOT) zones based on backward advective particle tracking. An alternative approach is to apply backward advective-dispersive solute transport modelling, in which dispersion can be taken as representing the uncertainty in defining the hydrogeologic characteristics (e.g. hydraulic conductivity) of the aquifer. The outlines of the TOT zones in the backward advective particle tracking approach is obtained by drawing an envelope around the respective tracks, which may require considerable guesswork. In the backward-in-time transport modelling, the outline of the TOT zones are developed using mass balance principles. The third step is the assessment of well vulnerability. Well vulnerability is based on the source-pathway-receptor concept which analyses the transport and fate of the contaminants along its path from the source to the receptor, and the interaction of the well itself with the flow system, and thus determines the actual impact on the well. The impact can be expressed in terms of the contaminant concentration in the well water. The mapping of the impact can be carried out by using a standard advective-dispersive transport model in either a forward-in-time mode (for a known contaminant source) or in a backward-in-time mode (for unknown sources). Thus, the well vulnerability concept goes beyond the conventional approach of WHPA, which is based solely on advective transport, neglecting dispersion and chemical processes. For any known point or non-point time-varying contaminant sources located arbitrarily within the well capture zone, the expected concentration at the well can simply be evaluated by convoluting the source mass with the results of the well vulnerability without further use of the model. Convolution is a well-known and effective superposition method to deal with arbitrary inputs in time and space for linear systems. The information of the contaminant concentration in the well water can be used to quantify the risk of a well becoming contaminated. Risk can be expressed in terms of the exposure value of the contaminant concentration exceeding the allowable limit and the time frame within which the well becomes contaminated. The exposure value can be integrated with the time element to set up a ranking of priorities, or to calculate the investment that must be made today in order to have the required funds available for remediation at the time it becomes necessary. The concept is applied to a well using hypothetical contaminant sources located arbitrarily within the capture zone. Well vulnerability maps can be used as a powerful tool to identify the optimal locations for Beneficial Management Practices (BMPs). A case study addressing the problem of elevated nitrate levels in a drinking water supply well is used to demonstrate the principle. The reduction of nitrate input concentration within the most vulnerable areas shows the largest impact at the well.

A digital signature technique has evolved into varies digital signature schemes in different application environments. In general, a digital signature consists of a random number and a hash function in addition to signing function. The random number can be used to provide the randomization of digital signatures. The hash function can be used for generating a message digest that has a fix length and is convenient for signing. The random number that hides in the digital signature is a useful factor. If we can use this factor well, then the digital signature can carry the other secret messages. On the basis of the concept of a subliminal channel proposed by Simmon, we have proposed multiple subliminal channels that can carry more than one subliminal message to different subliminal receivers. Furthermore, by using the concept of a subliminal channel, we can use the random number as another secure parameter of the digital signature. This concept leads to a forward-secure digital signature with backward-secure detection when the subliminal channel is embedded in the signature. We have proposed a forward-backward secure digital signature. A hash function is an important tool for generating a message digest. The hash function used in a signature must be one-way and collision resistant. A signing message will map to a message digest via a hash function. In recent years, several chameleon hash functions have been proposed. A chameleon hash function is a trapdoor one-way hash function that prevents everyone except the holder of the trapdoor key from computing the collisions for a randomly given input. There are various studies that apply the chameleon hash function to online/offline digital signatures and sterilization signatures. In this thesis, we apply this concept to a network secure gateway. We have achieved fast blind verification for an application gateway, such as a firewall. Further, we propose triple-trapdoor chameleon hash function and apply to vehicle owenship identification scheme. We have achieved the fast identification for vehicle ownership without connect to online database. We also have proposed threshold chameleon hash function and achieved that the collision will control under the threshold value. The trapdoor information will be exposed after the number of collision has accomplished.