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A light scattering study of dilute solutions consisting of poly(4-vinylpyridine) dissolved in chloroform has been carried out. Chloroform is a good solvent for P4VP. Dynamic light scattering measurements show only a diffusion mode in the intensity autocorrelation function for freshly prepared solutions, but two modes are present as the solution ages. The two modes found in P4VP/CHCl3 solution both show a clear q dependence, q being the magnitude of the scattering wave vector, thus indicating that both are diffusive modes. For this system, the diffusion coefficient is found to be mainly determined by the osmotic modulus, with the solution stress modulus making a negligible contribution. A decrease of mutual diffusion coefficient with increasing polymer concentration is observed. As the temperature of the solution is lowered, the mutual diffusion coefficient decreases linearly. Extrapolation of the mutual diffusion coefficient to zero yields the critical temperature, at which the P4VP/CHCl3 solution undergoes a phase transition.

It¡¦s not easy to keep photographs clean in every day. A photograph is liable to be polluted by accumulating defects such as dusts, which can degrade the imaging quality. In the thesis, a method of image restoration is proposed for image polluted by multiplicative transmittance noise. The method is based on estimating the approximate autocorrelation function of the unpolluted image. This autocorrelation function is obtained by analyzing the relationship among the autocorrelation function for polluted image, unpolluted image and noise. Further more, the noisy image is restored by the property of the autocorrelation function. A polluted photograph in imaging system is modeled by a thin random screen against the original image. In this model, defects are Poisson-distribution and may be overlapped. Since transmittance effect of each defect is multiplicative, the transmittance of random screen is computed as a product of Poisson-distribution-centered random function. Then, the statistical autocorrelation function of random screen is accordingly computed. More specifically, we should rearrange image data as periodic signal to avoid insufficient data in computing the process autocorrelation function. The simulated polluted image is restored by the amplitude information from the estimated autocorrelation function of the original image. Simulating results is demonstrated that the RMS of the restored image computed with the polluted image is improved.

The profilogramms are interpreted as realization of casual static function with normal distribution,so the parameters of profilogramms are treated as characteristic of normal process. In this work we assessed the autocorrelation function of profilogramms, and then using the analytic form of these functions we modeled the static process.

In this thesis, identification of periodically varying orders of univariate Periodic Autoregressive Moving-Average (PARMA) processes is mainly studied. The identification of the varying orders of PARMA process is carried out by generalizing the well-known Box-Jenkins techniques to a seasonwise manner. The identification of pure periodic moving-average (PMA) and pure periodic autoregressive (PAR) models are considered only. For PARMA model identification, the Periodic Autocorrelation Function (PeACF) and Periodic Partial Autocorrelation Function (PePACF), which play the same role as their ARMA counterparts, are employed. For parameter estimation, which is considered only to refine model identification, the conditional least squares estimation (LSE) method is used which is applicable to PAR models. Estimation becomes very complicated, difficult and may give unsatisfactory results when a moving-average (MA) component exists in the model. On account of overcoming this difficulty, seasons following PMA processes are tried to be modeled as PAR processes with reasonable orders in order to employ LSE. Diagnostic checking, through residuals of the fitted model, is also performed stating its reasons and methods. The last part of the study demonstrates application of identification techniques through analysis of two seasonal hydrologic time series, which consist of average monthly streamflows. For this purpose, computer programs were developed specially for PARMA model identification.

In the thesis, we study the data collected from twelve-note music of Webern and Schoenberg, including opus 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 and opus 31 of Webern and opus 25, 33a and opus 37 of Schoenberg. The data consists of the following two kinds. The data of the first kind consists of the four basic forms of the twelve-tone music. And the data of the second kind consists of the twelve-tone derived from the matrix of the twelve-note music. We will introduce the twelve-note music first and then study two main topics about twelve-note music in this thesis. In the first part, we consider the Markov properties of the first kind data. We compare the sample autocorrelation function and autocorrelation function of the fitted model to determine the fitness of the Markovian model. In the second part, we build the time series model for the second kind data. Sample autocorrelation function¡Bpartial autocorrelation function and extended autocorrelation function are used to determine the orders of the models. The best model is selected based on the AICC. Finally, we check the fitness of the models using sample autocorrelation function and partial autocorrelation function of the residuals.

The first part of this work deals with open dynamical systems. A natural question of how the survival probability depends upon a position of a hole was seemingly never addresses in the theory of open dynamical systems. We found that this dependency could be very essential. The main results are related to the holes with equal sizes (measure) in the phase space of strongly chaotic maps. Take in each hole a periodic point of minimal period. Then the faster escape occurs through the hole where this minimal period assumes its maximal value. The results are valid for all finite times (starting with the minimal period), which is unusual in dynamical systems theory where typically statements are asymptotic when time tends to infinity. It seems obvious that the bigger the hole is the bigger is the escape through that hole. Our results demonstrate that generally it is not true, and that specific features of the dynamics may play a role comparable to the size of the hole. In the second part we consider some classes of cellular automata called Deterministic Walks in Random Environments on Z^1. At first we deal with the system with constant rigidity and Markovian distribution of scatterers on Z^1. It is shown that these systems have essentially the same properties as DWRE on Z^1 with constant rigidity and independently distributed scatterers. Lastly, we consider a system with non-constant rigidity (so called process of aging) and independent distribution of scatterers. Asymptotic laws for the dynamics of perturbations propagating in such environments with aging are obtained.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this study is propose a new mathematical expression to describe the observed meandering autocorrelation functions in low-wind speed. The analysis utilizes a large number of the data to show that the new proposed theoretical function reproduces the experimental behavior of the fit curves, well as the negative lobes that characterizing the autocorrelation function for meandering condition. Furthermore, the good agreement of the measured autocorrelation curves with the proposed algebraic autocorrelation function allows to calculate the magnitudes of the meandering period and of the loop parameter. In adition, the parameters founded in this study can be used to simulate the dispersion of contaminant during low wind episodes. The results agree with the values presented and discussed in the literature. / O presente estudo propõe uma nova expressão matemática para descrever as funções de autocorrelação observadas sob condições de meandro do vento horizontal. A análise utiliza um grande número de dados para demonstrar que a função proposta reproduz o comportamento da curva experimental, bem como os lóbulos negativo que caracterizam a função de autocorrelação para a situação de meandro. Além disso, a boa concordância entre as curvas de autocorrelação observadas e a nova função de autocorrelação algébrica, proposta neste trabalho, permitiu realizar o cálculo de grandezas físicas como o parâmetro de oscilação e o período de meandro. Um resultado adicional, foi empregar os valores médios encontrados para os parâmetros do meandro na simulação da dispersão de contaminante durante episódios de vento fraco. Os resultados encontrados estão de acordo com os valores apresentados e discutidos na literatura.

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The motivation for this research is to leverage the increasing deployment of the phasor measurement unit (PMU) technology by electric utilities in order to improve situational awareness in power systems. PMUs provide unprecedentedly fast and synchronized voltage and current measurements across the system. Analyzing the big data provided by PMUs may prove helpful in reducing the risk of blackouts, such as the Northeast blackout in August 2003, which have resulted in huge costs in past decades. In order to provide deeper insight into early warning signs (EWS) of catastrophic events in power systems, this dissertation studies changes in statistical properties of high-resolution measurements as a power system approaches a critical transition. The EWS under study are increases in variance and autocorrelation of state variables, which are generic signs of a phenomenon known as critical slowing down (CSD). Critical slowing down is the result of slower recovery of a dynamical system from perturbations when the system approaches a critical transition. CSD has been observed in many stochastic nonlinear dynamical systems such as ecosystem, human body and power system. Although CSD signs can be useful as indicators of proximity to critical transitions, their characteristics vary for different systems and different variables within a system. The dissertation provides evidence for the occurrence of CSD in power systems using a comprehensive analytical and numerical study of this phenomenon in several power system test cases. Together, the results show that it is possible extract information regarding not only the proximity of a power system to critical transitions but also the location of the stress in the system from autocorrelation and variance of measurements. Also, a semi-analytical method for fast computation of expected variance and autocorrelation of state variables in large power systems is presented, which allows one to quickly identify locations and variables that are reliable indicators of proximity to instability.