Abstract The main emphasis in modern RF power amplifier (PA) research is on improving linearity while at the same time maintaining reasonably good efficiency, for which purpose external linearization in the form of feedforward or predistortion is often used. Linearity and linearization can be considered from both a fundamental signal (amplitude and phase conversions, AM-AM & AM-PM) and an intermodulation distortion (IMD) regeneration point of view, and since a study of intermodulation gives more information on the behaviour of an amplifier, linearity is studied in this thesis by analysing the amplitude and phase of IM components under varying signal conditions, i.e. as functions of temperature, modulation bandwidth and amplitude. To study the behaviour of IM components analytically, a Volterra model including electro-thermal distortion mechanisms is developed and a simulation technique is introduced to determine how easily the amplifier can be linearized. An S-parameter characterization method for extracting the Volterra model and the simulation model is developed, and the amplitude and phase dependences of the IM components are shown by means of measurements performed by a novel technique developed here. The results show that the behaviour of IM components is more complicated than had commonly been expected. Three techniques are developed for eliminating the frequency dependence of IM components, impedance optimization, envelope filtering and envelope injection. In the envelope injection technique, a low frequency envelope signal is added to the input of the amplifier in order to improve both the bandwidth and amplitude range of the memoryless predistortion. The functionality of envelope injection is demonstrated by Volterra calculations, simulations and measurements, and the technique is applied to 1W, 1.8 GHz common-emitter BJT and common-source MESFET amplifiers. IM cancellation better than 20 dB is achieved over a wide range of bandwidths and amplitudes. It is concluded that an inherently linear amplifier is not necessarily easy to linearize any further using external techniques, but that the part of the distortion that varies with bandwidth and amplitude can be cancelled out using envelope injection and the remaining memoryless distortion by means of a simple polynomial RF predistorter. This results in good cancellation of distortion, and since both envelope injection and RF predistortion consume little power, both good efficiency and linearity can be achieved.

We study diffusion-reaction-advection models describing population dynamics of aquatic organisms subject to a constant drift, with reflecting upstream and outflow downstream boundary conditions. We consider three different models: single logistically growing species, two and three competing species. In the case of a single population, we determine conditions for existence, uniqueness and stability of non-trivial steady-state solutions. We analyze the dependence of such solutions on advection speed, growth rate and length of the habitat. Such analysis offers a possible explanation of the "drift paradox" in our context. We also introduce a spatially implicit ODE (nonspatial approximation) model which captures the essential behavior of the original PDE model. In the case of two competing species, we use a diffusion-advection version of the Lotka-Volterra competition model. Combining numerical and analytical techniques, in both the spatial and nonspatial approximation settings, we describe the effect of advection on competitive outcomes. Finally, in the case of three species, we use the nonspatial approximation approach to analyze and classify the possible scenarios as we change the flow speed in the habitat.

We extend the recently developed rough path theory to the case of more rough noise and/or more singular Volterra kernels. It was already observed that the Volterra rough path introduced there did not satisfy any geometric relation, similar to that observed in classical rough path theory. Thus, an extension of the theory to more irregular driving signals requires a deeper understanding of the specific algebraic structure arising in the Volterra rough path. Inspired by the elements of "non-geometric rough paths" developed, we provide a simple description of the Volterra rough path and the controlled Volterra process in terms of rooted trees, and with this description we are able to solve rough Volterra equations driven by more irregular signals.

This thesis studies the decision-making of agents exhibiting time-inconsistent preferences and its implications in the context of contract theory. We take a probabilistic approach to continuous-time non-Markovian time-inconsistent stochastic control problems for sophisticated agents. By introducing a refinement of the notion of equilibrium, an extended dynamic programming principle is established. In turn, this leads to consider an infinite family of BSDEs analogous to the classical Hamilton–Jacobi–Bellman equation. This system is fundamental in the sense that its well-posedness is both necessary and sufficient to characterise equilibria and its associated value function. In addition, under modest assumptions, the existence and uniqueness of a solution is established. With the previous results in mind, we then study a new general class of multidimensional type-I backward stochastic Volterra integral equations. Towards this goal, the well-posedness of a system of an infinite family of standard backward stochastic differential equations is established. Interestingly, its well-posedness is equivalent to that of the type-I backward stochastic Volterra integral equation. This result yields a representation formula in terms of semilinear partial differential equation of Hamilton–Jacobi–Bellman type. In perfect analogy to the theory of backward stochastic differential equations, the case of Lipschitz continuous generators is addressed first and subsequently the quadratic case. In particular, our results show the equivalence of the probabilistic and analytic approaches to time-inconsistent stochastic control problems. Finally, this thesis studies the contracting problem between a standard utility maximiser principal and a sophisticated time-inconsistent agent. We show that the contracting problem faced by the principal can be reformulated as a novel class of control problems exposing the complications of the agent’s preferences. This corresponds to the control of a forward Volterra equation via constrained Volterra type controls. The structure of this problem is inherently related to the representation of the agent’s value function via extended type-I backward stochastic differential equations. Despite the inherent challenges of this class of problems, our reformulation allows us to study the solution for different specifications of preferences for the principal and the agent. This allows us to discuss the qualitative and methodological implications of our results in the context of contract theory: (i) from a methodological point of view, unlike in the time-consistent case, the solution to the moral hazard problem does not reduce, in general, to a standard stochastic control problem; (ii) our analysis shows that slight deviations of seminal models in contracting theory seem to challenge the virtues attributed to linear contracts and suggests that such contracts would typically cease to be optimal in general for time-inconsistent agents; (iii) in line with some recent developments in the time-consistent literature, we find that the optimal contract in the time-inconsistent scenario is, in general, non-Markovian in the state process X.

>Magister Scientiae - MSc / In principle, an enrichment of resources in predator-prey systems show prompts destabilisation of a framework, accordingly, falling trophic communication, a phenomenon known to as the \Paradox of Enrichment" [54]. After it was rst genius postured by Rosenzweig [48], various resulting examines, including recently those of Mougi-Nishimura [43] as well as that of Bohannan-Lenski [8], were completed on this problem over numerous decades. Nonetheless, there has been a universal none acceptance of the \paradox" word within an ecological eld due to diverse interpretations [51]. In this dissertation, some theoretical exploratory works are being surveyed in line with giving a concise outline proposed responses to the paradox. Consequently, a quantity of di usion-driven models in mathematical ecology are evaluated and analysed. Accordingly, piloting the way for the spatial structured pattern (we denote it by SSP) formation in nonlinear systems of partial di erential equations [36, 40]. The central point of attention is on enrichment consequences which results toward a paradoxical state. For this purpose, evaluating a number of compartmental models in ecology similar to those of [48] will be of great assistance. Such displays have greater in uence in pattern formations due to diversity in meta-population. Studying the outcomes of initiating an enrichment into [9] of Braverman's model, with a nutrient density (denoted by n) and bacteria compactness (denoted by b) respectively, suits the purpose. The main objective behind being able to transform [9]'s system (2.16) into a new model as a result of enrichment. Accordingly, n has a logistic- type growth with linear di usion, while b poses a Holling Type II and nonlinear di usion r2 nb2 [9, 40]. Five fundamental questions are imposed in order to address and guide the study in accordance with the following sequence: (a) What will be the outcomes of introducing enrichment into [9]'s model? (b) How will such a process in (i) be done in order to change the system (2.16)'s stability state [50]? (c) Whether the paradox does exist in a particular situation or not [51]? Lastly, (d) If an absurdity in (d) does exist, is it reversible [8, 16, 54]? Based on the problem statement above, the investigation will include various matlab simulations. Therefore, being able to give analysis on a local asymptotic stability state when a small perturbation has been introduced [40]. It is for this reason that a bifurcation relevance comes into e ect [58]. There are principal de nitions that are undertaken as the research evolves around them. A study of quantitative response is presented in predator-prey systems in order to establish its stability properties. Due to tradeo s, there is a great likelihood that the growth rate, attack abilities and defense capacities of species have to be examined in line with reviewing parameters which favor stability conditions. Accordingly, an investigation must also re ect chances that leads to extinction or coexistence [7]. Nature is much more complex than scienti c models and laboratories [39]. Therefore, di erent mechanisms have to be integrated in order to establish stability even when a system has been under enrichment [51]. As a result, SSP system is modeled by way of reaction-di usion di erential equations simulated both spatially and temporally. The outcomes of such a system will be best suitable for real-world life situations which control similar behaviors in the future. Comparable models are used in the main compilation phase of dissertation and truly re ected in the literature. The SSP model can be regarded as between (2018-2011), with a stability control study which is of an original.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19108号 / 情博第554号 / 新制||情||98(附属図書館) / 32059 / 京都大学大学院情報学研究科知能情報学専攻 / (主査)教授 阿久津 達也, 教授 西田 豊明, 教授 山本 章博 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

The need for high spectral efficiency and data rate drives the modulation schemes like OFDM and QAM. The resulting signal is a complex signal with high peak to average power ratio. This property causes signal sensitivity to the non-linearity of power amplifiers. Power amplifiers create out-of-band distortion, in band distortion and spectral re-growth. The spectral re-growth affects the adjacent channels and cause Adjacent Channel Interference (ACI). So linearization techniques should be used to remove the skirts produced by the amplifier in the adjacent frequencies. The objective of this thesis is to figure out a pre distortion method that is simple enough to implement with an analog circuit. We are proposing a novel method to model the non linearity and use the same model as post-distorter and pre-distorter to invert non linearity so linear gain is maintained. The implementation is generic to all the non linear systems and can be implemented to invert the non linearity of any such system.

Total pressure non-uniformities in an axial flow compressor can contribute to losses in aerodynamic operability through a reduction in stall margin, pressure rise and mass flow, and to loss of structural integrity through means of high cycle fatigue (HCF). HCF is a primary mechanism of blade failure caused by vibrations at levels exceeding material endurance limits. Previous research has shown total pressure distortions to be the dominant HCF driver in aero engines, and has demonstrated the damaging results of total pressure distortion induced HCF on first stage fan and compressor blade rows [Manwaring et al., 1997]. It is, however, also of interest to know how these distortion patterns propagate through a rotor stage and impact subsequent downstream stages and engine components. With current modeling techniques, total pressure distortion magnitudes can be directly correlated to induced blade vibratory levels and modes. The ability to predict downstream distortion patterns then allows for the inference of blade vibratory response of downstream blades to inlet distortion patterns. Given a total pressure distortion excitation entering a blade row, the nonlinear Volterra series can serve as a predictor of the downstream total pressure profile and therefore provide insight into the potential for HCF in downstream blade rows. This report presents the adaption of nonlinear Volterra theory to the prediction of the transport of non-uniform total pressure distortions through an axial flow compressor. The use of Volterra theory in nonlinear system modeling relies on the knowledge of Volterra kernels, which capture the behavior of a system's response characteristics. Here an empirical method is illustrated for identifying these kernels based on total pressure distortion patterns measured both upstream and downstream of a transonic rotor of modern design. A Volterra model based on these kernels has been applied to the prediction of distortion transfer at new operating points of the same rotor with promising results. Methods for improving Volterra predictions by training Volterra kernels along individual streamlines and normalizing total pressure data sets by physics-based parameters are also investigated. / Master of Science

The applications of differential equations are many. However, many differential equations modelling real-world scenarios are very complex and it can be of great difficulty to find an exact solution if one even exists. Thus, it is of importance to be able to approximate solutions of differential equations. Here, a method using neural networks is explored and its performance is compared to that of a numerical method. To illustrate the method, two first order, two second order and two first order systems of ordinary differential equations are explored. The systems are the Lotka-Volterra system and the SEIR (Susceptible, Exposed, Infected, Removed) epidemiological model. The first four examples have exact solutions to compare to and the observations are then used as a basis when discussing the results of the systems. The results of the thesis show that while the neural network method takes longer to deliver an approximation, it continuously gives better approximations than the implicit Euler method used for comparison. The main contribution of this thesis is the comparison done of the performances of the neural network method and the implicit Euler method. / Det finns många användningsområden för differentialekvationer. Däremot är många differentialekvationer som modellerar verkligheten komplexa och det kan vara svårt, om inte omöjligt, att hitta en exakt lösning. På grund av detta är det viktigt att ha metoder som kan approximera lösningar till differentialekvationer. Därför undersöks här en metod som använder sig av neurala nätverk. Dess resultat blir sedan jämförda med en numerisk metod. För att illustrera metoden presenteras två ekvationer av första ordningen, två ekvationer av andra ordningen och två system av differentialekvationer. Systemen som undersöks är Lotka-Volterra ekvationerna samt SEIR (Susceptible, Exposed, Infected, Removed) modellen. De första fyra exemplen som undersöks har exakta lösningar att jämföra med och dessa observationer används sedan vid diskussionerna gällande systemen. Resultaten visar att medan metoden som använder neurala nätverkar tar längre tid att exekvera, så ger metoden bättre approximationer än den implicita Euler metoden som användes som jämförelse. Det huvudsakliga bidraget med det här examensarbetet är jämförelsen av hur de två metoderna presterar.

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