For random waves the free surface elevation can be described by a number of individual wave parameters. The main objective of this work has been to study the statistical properties of individual parameters in successive waves; the wave crest height, the wave height and the wave period. In severe sea states the wave crest heights exhibit a nonlinear behavior, which must be reflected in the models. An existing marginal distribution that uses second order Stokes-type nonlinearity is transformed to a two-dimensional distribution by use of the two–dimensional Rayleigh distribution. This model only includes sum frequency effects. A two-dimensional distribution is also established by transforming a second order model including both sum and different frequency effects. Both models are based on the narrow-band assumption, and the effect of finite water depth is included. A parametric wave crest height distribution proposed by Forristall (2000) has been extended to two dimensions by transformation of the two-dimensional Weibull distribution. Two successive wave heights are modeled by a Gaussian copula, which is referred to as the Nataf model. Results with two initial distributions for the transformation are presented, the Næss (1985) model and a two-parameter Weibull distribution, where the latter is in best agreement with data. The results are compared with existing models. The Nataf model has also been used for modeling three successive wave heights. Results show that the Nataf transformation of three successive wave heights can be approximated by a first order autoregression model. This means that the distribution of the wave height given the previous wave height is independent of the wave heights prior to the previous wave height. The simulation of successive wave heights can be done directly without simulating the time series of the complete surface elevation. Successive wave periods are modeled with the Nataf transformation by using a two-parameter Weibull distribution and a generalized Gamma distribution as the initial distribution, where the latter is in best agreement with data. Results for the marginal and two-dimensional distributions are compared with existing models. In practical applications, it is often of interest to consider successive wave periods with corresponding wave heights exceeding a certain threshold. Results show that the distribution for successive wave periods when the corresponding wave heights exceed the root-mean-square value of the wave heights can be approximated by a multivariate Gaussian distribution. When comparing the results with data, a long time series is needed in order to obtain enough data cases. Results for three successive wave periods are also presented. The models are compared with field data from the Draupner field and the Japan Sea, and with laboratory data from experiments at HR Wallingford. In addition, data from numerical simulations based on second order wave theory, including both sum and frequency effects, are included.

La tesi analizza se e a quali condizioni le società possano distribuire ai propri azionisti dividendi con mezzi diversi dal denaro. La soluzione proposta è positiva e attribuisce alla società un margine di scelta sul valore dei beni. / The research analyzes if and according with which conditions corporations can distribute to their shareholders not through a sum of money but though different assets. The answer is positive and it grants to company a choose on assets' value.

Interindustry transactions recorded at a macro level are simply summations of commodity shipment decisions taken at a micro level. The resulting statistical problem is to obtain minimally biased estimates of commodity flow distributions at the disaggregated level, given various forms of aggregated information. This study demonstrates the application of the entropy-maximizing paradigm in its traditional form, together with recent adaptations emerging from information theory, to the area of spatial and non-spatial input-output analysis. A clear distinction between the behavioural and statistical aspects of entropy modelling is suggested. The discussion of non-spatial input-output analysis emphasizes the rectangular and dynamic extensions of Leontief's original model, and also outlines a scheme for simple aggregation, based on a criterion of minimum loss of information. In the chapters on spatial analysis, three complementary approaches to the estimation of interregional flows are proposed. Since the static formulations cannot provide an accurate picture of the gross interregional flows between any two sectors, Leontief's dynamic framework is adapted to the problem. The study concludes by describing a hierarchical system of models to analyse feasible paths of economic development over space and time. / digitalisering@umu

The species–area relationship (SAR) has been applied to predict species richness declines as area is converted to human-dominated land covers.In many areas of the world, however, many species persist in human-dominated areas, including threatened species. Because SARs are decelerating nonlinear, small extents of natural habitat can be converted to human use with little expected loss of associated species, but with the addition of more species that are associated with human land uses. Decelerating SARs suggest that, as area is converted to human-dominated forms, more species will be added to the rare habitat than are lost from the common one. This should lead to a peaked relationship between richness and natural area. I found that the effect of natural area on avian richness across Ontario was consistent with the sum of SARs for natural habitat species and human-dominated habitat species, suggesting that almost half the natural area can be converted to human-dominated forms before richness declines. However, I found that this spatial relationship did not remain consistent through time: bird richness increased when natural cover was removed (up to 4%), irrespective of its original extent. The inclusion of metapopulation processes in predictive models of species presence improves predictions of diversity change through time dramatically. Variability in site occupancy was common among bird species evaluated in this study, likely resulting from local extinction-colonization dynamics. Likelihood of species presence declined when few neighbouring sites were previously occupied by the species. Site occupancy was also less likely when little suitable habitat was present. Consistent with expectations that larger habitats are easier targets for colonists, habitat area was more important for more isolated sites. Accounting for the effect of metapopulation dynamics on site occupancy predicted change in richness better than land cover change and increased the strength of the regional richness–natural area relationship to levels observed for continental richness–environment relationships suggesting that these metapopulation processes “scale up” to modify regional species richness patterns making them more difficult to predict. It is the existence of absences in otherwise suitable habitat within species’ ranges that appears to weaken regional richness–environment relationships.

Unconventional resources will play an important role in filling the gap between supply and demand for future world energy. In North America, the impact of unconventional resources on energy supplies is growing continuously. However, around the world they have yet to serve as a major contributor to the energy supply, partly due to the scarcity of information about the exploration and development technologies required to produce them. Basin analogy can be used to estimate the undiscovered petroleum potential in a target basin by finding a geological analog that has been explored enough that its resource potential is fully understood. In 2006, Singh developed a basin analog system BASIN (Basin Analog Systems INvestigation) in detail that could rapidly and consistently identify analogous reference basins for a target basin. My research focused on continuing that work, comprehensively improving the basin analog system in four areas: the basin analog method; the database; the software functionality; and the validation methods. The updated system compares basins in terms of probability distributions of geological parameters. It compensates for data that are sparse or that do not represent basin-level geological parameters, and it expands the system's ability to compare widely varying quantitative parameters. Because the updated BASIN database contains more geologic and petroleum systems information on reference (existing) basins, it identifies analog basins more accurately and efficiently. The updated BASIN software was developed by using component-based design and data visualization techniques that help users better manage large volumes of information to understand various data objects and their complicated relationships among various data objects. Validation of the improved BASIN software confirms its accuracy: if a basin selected as the target basin appears in the reference basin list with other basins, the target basin is 100% analogous only to itself. Furthermore, when a target basin is analyzed by both BASIN and PRISE (Petroleum Resources Investigation and Summary Evaluation) software, results of the improved BASIN closely matched the PRISE results, which provides important support for using BASIN and PRISE together to quantitatively estimate the resource potential in frontier basins.

University of Macau / Faculty of Science and Technology / Department of Mathematics

The species–area relationship (SAR) has been applied to predict species richness declines as area is converted to human-dominated land covers.In many areas of the world, however, many species persist in human-dominated areas, including threatened species. Because SARs are decelerating nonlinear, small extents of natural habitat can be converted to human use with little expected loss of associated species, but with the addition of more species that are associated with human land uses. Decelerating SARs suggest that, as area is converted to human-dominated forms, more species will be added to the rare habitat than are lost from the common one. This should lead to a peaked relationship between richness and natural area. I found that the effect of natural area on avian richness across Ontario was consistent with the sum of SARs for natural habitat species and human-dominated habitat species, suggesting that almost half the natural area can be converted to human-dominated forms before richness declines. However, I found that this spatial relationship did not remain consistent through time: bird richness increased when natural cover was removed (up to 4%), irrespective of its original extent. The inclusion of metapopulation processes in predictive models of species presence improves predictions of diversity change through time dramatically. Variability in site occupancy was common among bird species evaluated in this study, likely resulting from local extinction-colonization dynamics. Likelihood of species presence declined when few neighbouring sites were previously occupied by the species. Site occupancy was also less likely when little suitable habitat was present. Consistent with expectations that larger habitats are easier targets for colonists, habitat area was more important for more isolated sites. Accounting for the effect of metapopulation dynamics on site occupancy predicted change in richness better than land cover change and increased the strength of the regional richness–natural area relationship to levels observed for continental richness–environment relationships suggesting that these metapopulation processes “scale up” to modify regional species richness patterns making them more difficult to predict. It is the existence of absences in otherwise suitable habitat within species’ ranges that appears to weaken regional richness–environment relationships.

Analyses are addressed for a number of problems in queueing systems and stochastic modeling that arose due to an investigation into techniques that could be used to approximate general closed networks. In Chapter II, a method is presented to calculate the system size distribution at an arbitrary point in time and at departures for a (n)/G/1/N queue. The analysis is carried out using an embedded Markov chain approach. An algorithm is also developed that combines our analysis with the recursive method of Gupta and Rao. This algorithm compares favorably with that of Gupta and Rao and will solve some situations when Gupta and Rao's method fails or becomes intractable. In Chapter III, an approach is developed for generating exact solutions of the time-dependent conditional joint probability distributions for a phase-type renewal process. Closed-form expressions are derived when a class of Coxian distributions are used for the inter-renewal distribution. The class of Coxian distributions was chosen so that solutions could be obtained for any mean and variance desired in the inter-renewal times. In Chapter IV, an algorithm is developed to generate numerical solutions for the steady-state system size probabilities and waiting time distribution functions of the SM/PH/1/N queue by using the matrix-analytic method. Closed form results are also obtained for particular situations of the preceding queue. In addition, it is demonstrated that the SM/PH/1/N model can be implemented to the analysis of a sequential two-queue system. This is an extension to the work by Neuts and Chakravarthy. In Chapter V, principal results developed in the preceding chapters are employed for approximate analysis of the closed network of queues with arbitrary service times. Specifically, the (n)/G/1/N queue is applied to closed networks of a general topology, and a sequential two-queue model consisting of the (n)/G/1/N and SM/PH/1/N queues is proposed for tandem queueing networks.

狄氏分配(Dirichlet distribution)可視為高維度的貝他分配，其應用範圍包括貝氏分析的共軛先驗分配，多變量資料建模。當狄氏分配參數α_1=⋯=α_(n+1)=1時，可視為在n維空間的單體(simplex)均勻分配。高維度空間的不規則區域均勻分配有很多的應用，例如：在不規則區域中物種調查的方區抽樣和蒙地卡羅模擬(Monte Carlo Simulation)常需要多面體的均勻亂數，利用狄氏分配可更迅速的生成不規則區域的均勻亂數。本論文主要是評估由Cheng et al. (2012) 設計的R統計軟體套件“rBeta2009” [8]，並探討如何利用此套件中的狄氏分配演算法來生成其他多變量分配，如：(i)反狄氏分配(Inverted Dirichlet distribution) (ii) Liouville分配，以及(iii)由線性限制式所圍成的多面體空間之均勻分配。本文也利用電腦模擬的方式驗證本文介紹之方法比現有的電腦軟體中的演算法有效率(以電腦執行時間來看)。 / Dirichlet distributions can be taken as a high-dimensioned version of beta distributions, and it has many applications, such as conjugate prior distribution in bayesian Inference and construction of the model of multivariate data. When the parameters of Dirichlet distributions are α_1=⋯=α_(n+1)=1, it can be regarded as uniform distribution within a n-dimensioned simplex. High-dimensioned uniform distribution in irregular domains has various applications, such as species surveys in quadrats sampling and Monte Carlo simulation, which often need to generate uniform random vectors over polyhedrons. With Dirichlet distributions, it is more efficient to generate uniform random vectors in irregular domain. This article evaluated the module in R, “rBeta2009” [8], originally designed by Cheng et al. (2012), and discusses how to generate other multivariate distributions by using the Dirichlet algorithm in the package, including generation of (i) Inverted Dirichlet random vectors (ii) Liouville random vectors, and (iii) uniform random vectors over polyhedrons with linear constraints. The article also verified that the method is more efficient than the older package in R. (by comparing the CPU time.)

Spray models are increasingly becoming the principal tools in the design and development of gas turbine combustors. Spray modeling requires a knowledge of the liquid atomization process, and the sizes and velocities of subsequently formed droplets as initial conditions. In order to have a better understanding of the liquid atomization process,the breakup characteristics of plane liquid sheets in co-flowing gas streams are investigated by means of linear and nonlinear hydrodynamic instability analyses. The liquid sheet breakup process is studied for initial sinuous and varicose modes of disturbance. It is observed that the sheet breakup occurs at half-wavelength intervals for an initial sinuous disturbance and at full-wavelength intervals for an initial varicose disturbance. It is also found that under certain operating conditions, the breakup process is dictated by the initial varicose disturbance compare to its sinuous counterpart. Further, the breakup process is studied for the combined mode and it is found that the sheet breakup occurs at half- or full-wavelength intervals depending on the proportion of the individual sinuous and varicose disturbances. In general, the breakup length decreases with the increase in the Weber number, gas-to-liquid velocity and density ratios. A predictive model of the initial droplet size and velocity distributions for the subsequently formed spray is also formulated here. The present model incorporates the deterministic aspect of spray formation by calculating the breakup length and the mass-mean diameter and the stochastic aspect by statistical means through the maximum entropy principle based on Bayesian entropy. The two sub-models are coupled together by the various source terms signifying the liquid-gas interaction and a prior distribution based on instability analysis, which provides information regarding the unstable wave elements on the two liquid-gas interfaces. Experimental investigation of the breakup characteristics of the liquid sheet is performed by a high speed CCD camera and the measurement of the initial droplet size and distributions is conducted by phase-Doppler interferometry. Good agreement of the theoretical breakup length with the experiment is obtained for a planar, an annular and a gas turbine nozzle. The predicted initial droplet size and velocity distributions show reasonably satisfactory agreement with experimental data for all the three types of nozzles. Hence this spray model can be utilized to predict the initial droplet size and velocity distributions in sprays, which can then be implemented as a front-end subroutine to the existing computer codes.