For over a decade UK legislation has existed which grants powers to English Local Authorities to implement a Workplace Parking Levy (WPL). Despite positive experiences in Australia of utilising area wide parking space levies to pay for public transport improvements, only one UK local authority to date (2017), Nottingham City Council, has chosen to implement a WPL. The Nottingham WPL scheme is intended to act as a transport demand management measure as well as a core funding mechanism for transport improvements including two new tram lines. Acceptance by the public and the business community is a key barrier to implementing a WPL. The two major criticisms of the Nottingham scheme prior to its implementation were that a WPL would discourage business investment and thus damage the economy while its intended impact on traffic congestion would be minimal. Therefore, a comprehensive evaluation of the Nottingham WPL scheme s performance is essential in order to facilitate transferability of this approach to other UK and European Cities. This thesis contributes to the wider WPL evaluation project by evaluating to what extent the Nottingham WPL has met three key objectives identified for the scheme which address the impact on congestion, transport mode share and inward investment. This research utilises a theoretical evaluation approach, a Theory of Change approach strengthened by elements of Realistic Evaluation . This approach provides an appropriate framework for evaluating progress towards the three key objectives by identifying a plausible model for change and expected impacts for the Nottingham WPL and the transport improvements which it part funds. This model or Theory of Change , is then tested to understand if the scheme is achieving the desired impacts by analysing appropriate indicators to measure and attribute change to causal factors. Methods used to facilitate this research include, benchmarking indicators against similar UK Cities, questionnaire surveys to assess the reasons for mode switch, time series modelling of the impact on congestion and a consideration of the reasoning behind investment and de-investment decisions made by businesses in Nottingham. It is concluded that while the WPL and its associated transport improvements are resulting in congestion constraint and mode shift away from commuting by car, these impacts are being reduced by the presence of exogenous change notably, economic and population growth, short term disruption to the road network resulting from roadworks associated with the construction of transport improvements and suppressed demand for commuting by car. Additionally, this research shows that there is a body of evidence which demonstrates that the WPL has not negatively impacted on levels of inward investment and that there is some evidence to date that suggests the improved transport system facilitated by the WPL is attractive to potential business investors.

Path integral approaches have been widely used for long in both quantum mechanics as well as statistical mechanics. In addition to being a tool for obtaining the probability distributions of interest(wave functions in the case of quantum mechanics),these methods are very instructive and offer great insights into the problem. In this thesis, path integrals are extensively employed to study some very interesting problems in both equilibrium and non-equilibrium statistical mechanics. In the non-equilibrium regime, we have studied, using a path integral approach, a very interesting class of anomalous diffusion, viz. the L´evy flights. In equilibrium statistical mechanics, we have evaluated the partition function for a class of molecules referred to as the hindered rotors which have a barrier for internal rotation. Also, we have evaluated the exact quantum statistical mechanical propagator for a harmonic potential with a time-dependent force constant, valid under certain conditions. Diffusion processes have attracted a great amount of scientific attention because of their presence in a wide range of phenomena. Brownian motion is the most widely known class of diffusion which is usually driven by thermal noise. However ,there are other classes of diffusion which cannot be classified as Brownian motion and therefore, fall under the category of Anomalous diffusion. As the name suggests, the properties of this class of diffusion are very different from those for usual Brownian motion. We are interested in a particular class of anomalous diffusion referred to as L´evy flights in which the step sizes taken by the particle during the random walk are obtained from what is known as a L´evy distribution. The diverging mean square displacement is a very typical feature for L´evy flights as opposed to a finite mean square displacement with a linear dependence on time in the case of Brownian motion. L´evy distributions are characterized by an index α where 0 <α ≤ 2. When α =2, the distribution becomes a Gaussian and when α=1, it reduces to a Cauchy/Lorentzian distribution. In the overdamped limit of friction, the probability density or the propagator associated with L´evy flights can be described by a position space fractional Fokker-Planck equation(FFPE)[1–3]. Jespersen et al. [4]have solved the FFPE in the Fourier domain to obtain the propagator for free L´evy flight(absence of an external potential) and L´evy flights in linear and harmonic potentials. We use a path integral technique to study L´evy flights. L´evy distributions rarely have a compact analytical expression in the position space. However, their Fourier transformations are rather simple and are given by e−D │p│α where D determines the width of the distribution. Due to the absence of a simple analytical expression, attempts in the past to study L´evy flights using path integrals in the position space [5, 6] have not been very successful. In our approach, we have tried to make use of the elegant representation of the L´evy distribution in the Fourier space and therefore, we write the propagator in terms of a two-dimensional path integral –one over paths in the position space(x)and the other over paths in the Fourier space(p). We shall refer to this space as the ‘phase space’. Such a representation is similar to the Hamiltonian path integral of quantum mechanics which was introduced by Garrod[7]. If we try to perform the path integral over Fourier variables first, then what remains is the usual position space path integral for L´evy flights which is rather difficult to solve. Instead, we perform the position space path integral first which results in expressions which are rather simple to handle. Using this approach, we have obtained the propagators for free L´evy flight and L´evy flights in linear and harmonic potentials in the over damped limit [8]. The results obtained by this method are in complete agreement with those obtained by Jesepersen et al. [4]. In addition to these results, we were also able to obtain the exact propagator for L´evy flights in a harmonic potential with a time-dependent force constant which has not been reported in the literature. Another interesting problem that we have considered in the over damped limit is to obtain the probability distribution for the area under the trajectory of a L´evy particle. The distributions, again, were obtained for free L´evy flight and for L´evy flights subjected to linear and harmonic potentials. In the harmonic potential, we have considered situations where the force constant is time-dependent as well as time-independent. Like in the case of the over damped limit, the probability distribution for L´evy flights in the under damped limit of friction can also be described using a fractional Fokker-Planck equation, although in the full phase space. However, this has not yet been solved for any general value of α to obtain the complete propagator in terms of both position and velocity. Using our path integral approach, the exact full phase space propagators have been obtained for all values of α for free L´evy flights as well as in the presence of linear and harmonic potentials[8]. The results that we obtain are all exact when the potential is at the most harmonic. If the potential is higher than harmonic, like the cubic potential, we have used a semi classical evaluation where, we extremize the action using an optimal path and further, account for fluctuations around this optimal path. Such potentials are very useful in describing the problem of escape of a particle over a barrier. The barrier crossing problem is very extensively studied for Brownian motion (Kramers problem) and the associated rate constant has been calculated in a variety of methods, including the path integral approach. We are interested in its L´evy analogue where we consider the escape of a particle driven by a L´evy noise over a barrier. On extremizing the action which depends both on phase space variables, we arrived at optimal paths in both the position space as well as the space of the conjugate variable, p. The paths form an infinite hierarchy of instant on paths, all of which have to be accounted for in order to obtain the correct rate constant. Care has to be taken while accounting for fluctuations around the optimal path since these fluctuations should be independent of the time-translational mode of the instant on paths. We arrived at an ‘orthogonalization’ scheme to perform the same. Our procedure is valid in the limit when the barrier height is large(or when the diffusion constant is very small), which would ensure that there is small but a steady flux of particles over the barrier even at very large times. Unlike the traditional Kramers rate expression, the rate constant for barrier crossing assisted by L´evy noise does not have an exponential dependence on the barrier height. The rate constant for wide range of α, other than for those very close to α = 2, are proportional to Dμ where, µ ≈ 1 and D is the diffusion constant. These observations are consistent with the simulation results obtained by Chechkin et al. [9]. In addition, our approach when applied to Brownian motion, gives the correct dependence on D. In equilibrium statistical mechanics we have considered two problems. In the first one, we have evaluated the imaginary time propagator for a harmonic oscillator with a time-dependent force constant(ω2(t))exactly, when ω2(t) is of the form λ2(t) - λ˙(t)where λ(t) is any arbitrary function of t. We have made use of Hamiltonian path integrals for this. The second problem that we considered was the evaluation of the partition function for hindered rotors. Hindered rotors are molecules which have a barrier for internal rotation. The molecule behaves like free rotor when the barrier is very small in comparison with the thermal energy, and when the barrier is very high compared to thermal energy, it behaves like a harmonic oscillator. Many methods have been developed in order to obtain the partition function for a hindered rotor. However, most of them are some what ad-hoc since they interpolate between free-rotor and the harmonic oscillator limits. We have obtained the approximate partition function by writing it as the trace of the density matrix and performing a harmonic approximation around each point of the potential[10]. The density matrix for a harmonic potential is in turn obtained from a path integral approach[11]. The results that we obtain using this method are very close to the exact results for the problem obtained numerically. Also, we have devised a proper method to take the indistinguishability of particles into account in internal rotation which becomes very crucial while calculating the partition function at low temperatures.

No description available.

Doctora en Ciencias de la Ingeniería, Mención Modelación Matemática / El objetivo de este trabajo es explorar el comportamiento de los procesos de rami ficación evolucionando a tiempo y estados continuos, y encontrar representaciones para su trayectoria y su genealogía. En el primer capítulo se muestra que un proceso de ramifi cación condicionado a no extinguirse es la única solución fuerte de una ecuación diferencial estocástica conducida por un movimiento Browniano y una medida puntual de Poisson, más un subordinador que representa la inmigración, dónde estos procesos son mutuamente independientes. Para esto se usa el hecho de que es posible obtener la ley del proceso condicionado a partir del proceso original, a través de su h-transformada, y se da una manera trayectorial de construir la inmigración a partir de los saltos del proceso. En el segundo capítulo se encuentra una representación para los procesos de rami ficación con crecimiento logístico, usando ecuaciones estocásticas. En particular, usando la de finición general dada por A. Lambert, se prueba que un proceso logístico es la única solución fuerte de una ecuación estocástica conducida por un movimiento Browniano y una medida puntual de Poisson, pero con un drift negativo fruto de la competencia entre individuos. En este capítulo se encuentra además una ecuación diferencial estocástica asociada con un proceso logístico condicionado a no extinguirse, suponiendo que éste existe y que puede ser de finido a través de una h-transformada. Esta representación muestra que nuevamente el condicionamiento da origen a un término correspondiente a la inmigración, pero en este caso dependiente de la población. Por último, en el tercer capítulo se obtiene una representación de tipo Ray-Knight para los procesos de ramifi cación logísticos, lo que da una descripción de su genealogía continua. Para esto, se utiliza la construcción de árboles aleatorios continuos asociados con procesos de Lévy generales dada por J.-F. Le Gall e Y. Le Jan, y una generalización del procedimiento de poda desarrollado por R. Abraham, J.-F. Delmas. Este resultado extiende la representación de Ray-Knight para procesos de difusión logísticos dada por V. Le, E. Pardoux y A. Wakolbinger.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21534号 / 理博第4441号 / 新制||理||1638(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 矢野 孝次, 教授 重川 一郎, 教授 泉 正己 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Most critical analyses of humor in postcolonial literary settings have focused on its power to critique and subvert dominant hegemonic systems in ways that tend to divide participants according to predictable dichotomies. Yet humor theorists have long recognized laughter's equivalent potential as a bonding mechanism. An examination of the rhetorical functions of humor in Andrea Levy'sSmall Islandreveals the extent to which these affiliative forms of humor can be successfully deployed across cultural divides within a migrant context, as well as the risks and limitations inherent to such an approach. Ultimately, the novel's gentle, inviting, and accessible humor provides the basis for a convincing, character-driven appeal to reduce racial prejudice.

A space of pseudoquotients can be described as a space of either single term quotients (the injective case) or the quotient of sequences (the non-injective case) where the parent sets for the numerator and the denominator satisfy particular conditions. The first part of this project is concerned with the minimal of conditions required to have a well-defined set of pseudoquotients. We continue by adding more structure to our sets and discuss the effect on the resultant pseudoquotient. Pseudoquotients can be thought of as extensions of the parent set for the numerator since they include a natural embedding of that set. We answer some questions about the extension properties. One family of these questions involves assuming a structure (algebraic or topological) on a set and asking if the set of pseudoquotients generated has the same structure. A second family of questions looks at maps between two sets and asks if there is an extension of that map between the corresponding pseudoquotients? If so, do the properties of the original map survive the extension? The result of our investigations on the abstract setting will be compared with some well-known spaces of pseudoquotients and Boehmians (a particular case of non-injective pseudoquotients). We will show that the conditions discussed in the first part are satisfied and we will use that to reach conclusions about our extension spaces and the extension maps. The Fourier transform is one of the maps that we will continuously revisit and discuss. Finally many spaces of Boehmians have been introduced where the initial set is a particular class of functions on either locally compact groups R and or a compact group such as a sphere. The natural question is, can we generalize the construction to any locally compact group. In some previous work such construction is discussed, however here we go further; we use characters and define the Fourier transform of integrable and square integrable Boehmians on a locally compact group. Then we discuss the properties of such transform.

No description available.

This dissertation examines the performance of China's pulp and paper industry under environmental regulations, and reflects on the implementation of the regulations, and especially on market-based instruments. The dissertation includes two empirical chapters: one uses a frontier production function model to examine the impact of China's environmental policy on paper mills' environmental as well as efficiency performance; the other derives shadow prices for pollutants for the same group of mills, based on a distance function model, to examine the efficiency performance of current pollution control policy and the degree of regional variation in the policy enforcement. The basic conclusion from the first empirical chapter is that the economic instrument-pollution levy system-can be an effective tool in inducing polluting mills to abate their pollution, and there is no strong evidence that the instrument adversely affected the mills' efficiency performance. The reason that the pollution problem is not lessening over time can be largely attributed to allocative inefficiency and regional disparity in policy enforcement, as is demonstrated by the second empirical chapter. These results should point future policy in the direction of better enforcement and/or the trial of a tradable permit system. / Ph. D.

Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2011. / Imported from http://etd.sun.ac.za / ENGLISH ABSTRACT: In this thesis, we propose to use Levy processes to model the dynamics of asset prices. In the first part, we deal with single asset options and model the log stock prices with a Levy process. We employ pure jump Levy processes of infinite activity, in particular variance gamma and CGMY processes. We fit the log-returns of six stocks to variance gamma and CGMY distributions and check the goodness of fit using statistical tests. It is observed that the variance gamma and the CGMY distributions fit the financial market data much better than the normal distribution. Calibration shows that at given maturity time the two models fit into the option prices very well. In the second part, we investigate the effect of dependence structure to multivariate option pricing. We use the new concept of Levy copula introduced in the literature by Tankov [40]. Levy copulas allow us to separate the dependence structure from the behavior of the marginal components. We consider bivariate variance gamma and bivariate CGMY models. To model the dependence structure between underlying assets we use the Clayton Levy copula. The empirical results on six stocks indicate a strong dependence between two different stock prices. Subsequently, we compute bivariate option prices taking into account the dependence structure. It is observed that option prices are highly sensitive to the dependence structure between underlying assets, and neglecting tail dependence will lead to errors in option pricing. / AFRIKAANSE OPSOMMING: In hierdie proefskrif word Levy prosesse voorgestel om die bewegings van batepryse te modelleer. Levy prosesse besit die vermoe om die risiko van spronge in ag te neem, asook om die implisiete volatiliteite, wat in finansiele opsie pryse voorkom, te reproduseer. Ons gebruik suiwer–sprong Levy prosesse met oneindige aktiwiteit, in besonder die gamma– variansie (Eng. variance gamma) en CGMY–prosesse. Ons pas die log–opbrengste van ses aandele op die gamma–variansie en CGMY distribusies, en kontroleer die resultate met behulp van statistiese pasgehaltetoetse. Die resultate bevestig dat die gamma–variansie en CGMY modelle die finansiele data beter pas as die normaalverdeling. Kalibrasie toon ook aan dat vir ’n gegewe verstryktyd die twee modelle ook die opsiepryse goed pas. Ons ondersoek daarna die gebruik van Levy prosesse vir opsies op meervoudige bates. Ons gebruik die nuwe konsep van Levy copulas, wat deur Tankov[40] ingelei is. Levy copulas laat toe om die onderlinge afhanklikheid tussen bateprysspronge te skei van die randkomponente. Ons bespreek daarna die simulasie van meerveranderlike Levy prosesse met behulp van Levy copulas. Daarna bepaal ons die pryse van opsies op meervoudige bates in multi–dimensionele exponensiele Levy modelle met behulp van Monte Carlo–metodes. Ons beskou die tweeveranderlike gamma-variansie en – CGMY modelle en modelleer die afhanklikheidsstruktuur tussen onderleggende bates met ’n Levy Clayton copula. Daarna bereken ons tweeveranderlike opsiepryse. Kalibrasie toon aan dat hierdie opsiepryse baie sensitief is vir die afhanlikheidsstruktuur, en dat prysbepaling foutief is as die afhanklikheid tussen die sterte van die onderleggende verdelings verontagsaam word.