In this thesis we study a scalar uniform and non-uniform quantization of random processes (or signals) in average case setting. Quantization (or discretization) of a signal is a standard task in all nalog/digital devices (e.g., digital recorders, remote sensors etc.). We evaluate the necessary memory capacity (or quantization rate) needed for quantized process realizations by exploiting the correlation structure of the model random process. The thesis consists of an introductory survey of the subject and related theory followed by four included papers (A-D). In Paper A we develop a quantization coding method when quantization levels crossings by a process realization are used for its coding. Asymptotical behavior of mean quantization rate is investigated in terms of the correlation structure of the original process. For uniform and non-uniform quantization, we assume that the quantization cellwidth tends to zero and the number of quantization levels tends to infinity, respectively. In Papers B and C we focus on an additive noise model for a quantized random process. Stochastic structures of asymptotic quantization errors are derived for some bounded and unbounded non-uniform quantizers when the number of quantization levels tends to infinity. The obtained results can be applied, for instance, to some optimization design problems for quantization levels. Random signals are quantized at sampling points with further compression. In Paper D the concern is statistical inference for run-length encoding (RLE) method, one of the compression techniques, applied to quantized stationary Gaussian sequences. This compression method is widely used, for instance, in digital signal and image processing. First, we deal with mean RLE quantization rates for various probabilistic models. For a time series with unknown stochastic structure, we investigate asymptotic properties (e.g., asymptotic normality) of two estimates for the mean RLE quantization rate based on an observed sample when the sample size tends to infinity. These results can be used in communication theory, signal processing, coding, and compression applications. Some examples and numerical experiments demonstrating applications of the obtained results for synthetic and real data are presented.

Thickened tailings production and disposal continue to grow in importance in the mining industry. In particular, the transport of oil sands tailings is of interest in this study. These tailings must be in a homogeneous state (non-segregating) during pipeline flow and subsequent discharge. Tailings are often transported in an open channel or flume. Slurries containing both clay and coarse sand particles typically exhibit non-Newtonian rheological behaviour. The prediction of the flow behaviour of these slurries is complicated by the limited research activity in this area. As a result, the underlying mechanisms of solids transport in these slurries are not well understood. To address this deficiency, experimental studies were conducted with kaolin clay slurries containing coarse sand in an open circular channel.<p> A numerical model has been developed to predict the behaviour of coarse solid particles in laminar, open channel, non-Newtonian flows. The model involves the simultaneous solution of the Navier-Stokes equations and a scalar concentration equation describing the behaviour of coarse particles within the flow. The model uses the theory of shear-induced particle diffusion (Phillips et al., 1992) to provide a number of relationships to describe the diffusive flux of coarse particles within laminar flows. A sedimentation flux has been developed and incorporated into the Phillips et al. (1992) model to account for gravitational flux of particles within the flow. Previous researchers (Gillies et al., 1999) have shown that this is a significant mechanism of particle migration.<p> The momentum and concentration partial differential equations have been solved numerically by applying the finite volume method. The differential equations are non-linear, stiff and tightly coupled which requires a novel means of analysis. Specific no-flux, no-slip and no-shear boundary conditions have been applied to the channel walls and free surface to produce simulated velocity and concentration distributions. The results show that the model is capable of predicting coarse particle settling in laminar, non-Newtonian, open channel flows. The results of the numerical simulations have been compared to the experimental results obtained in this study, as well as the experimental results of previous studies in the literature.

In dieser Arbeit werden zwei Klassen von Evolutionsgleichungen in einem Matrixraum-Setting studiert: Hyperbolische Erhaltungsgleichungen und aktive skalare Gleichungen. Für erstere wird untersucht, wann man Oszillationen mit Hilfe polykonvexen Maßen ausschließen kann; für Zweitere wird mit Hilfe von Oszillationen gezeigt, dass es unendlich viele periodische schwache Lösungen gibt.

Thickened tailings production and disposal continue to grow in importance in the mining industry. In particular, the transport of oil sands tailings is of interest in this study. These tailings must be in a homogeneous state (non-segregating) during pipeline flow and subsequent discharge. Tailings are often transported in an open channel or flume. Slurries containing both clay and coarse sand particles typically exhibit non-Newtonian rheological behaviour. The prediction of the flow behaviour of these slurries is complicated by the limited research activity in this area. As a result, the underlying mechanisms of solids transport in these slurries are not well understood. To address this deficiency, experimental studies were conducted with kaolin clay slurries containing coarse sand in an open circular channel.<p> A numerical model has been developed to predict the behaviour of coarse solid particles in laminar, open channel, non-Newtonian flows. The model involves the simultaneous solution of the Navier-Stokes equations and a scalar concentration equation describing the behaviour of coarse particles within the flow. The model uses the theory of shear-induced particle diffusion (Phillips et al., 1992) to provide a number of relationships to describe the diffusive flux of coarse particles within laminar flows. A sedimentation flux has been developed and incorporated into the Phillips et al. (1992) model to account for gravitational flux of particles within the flow. Previous researchers (Gillies et al., 1999) have shown that this is a significant mechanism of particle migration.<p> The momentum and concentration partial differential equations have been solved numerically by applying the finite volume method. The differential equations are non-linear, stiff and tightly coupled which requires a novel means of analysis. Specific no-flux, no-slip and no-shear boundary conditions have been applied to the channel walls and free surface to produce simulated velocity and concentration distributions. The results show that the model is capable of predicting coarse particle settling in laminar, non-Newtonian, open channel flows. The results of the numerical simulations have been compared to the experimental results obtained in this study, as well as the experimental results of previous studies in the literature.

In this study nano-patterning was carried out using two different nano-optic devices namely- the NSOM and Fresnel zone plate. In the first study, NSOM was used to generate nano-patterns on selected semiconducting (Si and Ge) and metallic (Cr, Cu and Ag) targets under different laser pulse durations, laser energies and number of laser pulses. Based on the experimental results, femtosecond laser pulses, provided lower pattern generation thresholds on targets but higher damage thresholds to the NSOM probes at the wavelength (~400-410 nm) studied, compared with nanosecond laser pulses. Three different mechanisms were identified as the dominant processes for pattern generation under different conditions, namely nano-scale laser ablation, nano-scale thermal oxidation and nano-scale melting/recrystallization of the targets. Furthermore, the resulting nano-patterns also showed a significant dependence on the optical properties (i.e., absorption coefficient and surface reflectivity) of the target material. By comparing the obtained experimental results, it was concluded that the optical energy transport from the NSOM probe to the target dominates the pattern generation when femtosecond laser is applied to the NSOM system. When nanosecond laser is applied, both the thermal and optical energy transported from the NSOM probe to the targets attribute to the obtained morphology of nano-patterns on different targets under the experimental conditions studied. In the second study, a traditional Fresnel zone plate with a focus length of 3 micrometres was fabricated with a novel lift-off process in e-beam lithography. The fabrication process involved, using a HSQ/PMMA bi-layer in a negative tone lift-off process with a layer of conducting polyaniline for charge dissipation. HSQ was used as the high resolution negative resist for e-beam patterning and the PMMA under-layer was used to enable a HSQ lift-off process. The fabricated Fresnel zone plate was used to generate nano-patterns on a UV sensitive photoresist using nanosecond laser light with lamda~409nm. The smallest pattern sizes generated was close to the diffraction limit. Nano-pattern sizes generated on the photoresist were comparable with a numerically calculated intensity distribution at the focus spot of the designed Fresnel zone plate obtained from Scalar Diffraction Theory.

In this dissertation we first consider a parallel linear model with correlated dual responses on a symmetric compact design region and construct locally optimal designs for estimating the location-shift parameter. These locally optimal designs are variant under linear transformation of the design space and depend on the correlation between the dual responses in an interesting and sensitive way. Subsequently, minimax and maximin efficient designs for estimating the location-shift parameter are derived. A comparison of the behavior of efficiencies between the minimax and maximin efficient designs relative to locally optimal designs is also provided. Both minimax or maximin efficient designs have advantage in terms of estimating efficiencies in different situations. Thirdly, we consider a linear regression model with a one-dimensional control variable x and an m-dimensional response variable y=(y_1,...,y_m). The components of y are correlated with a known covariance matrix. The calibration problem discussed here is based on the assumed regression model. It is of interest to obtain a suitable estimation of the corresponding x for a given target T=(T_1,...,T_m) on the expected responses. Due to the fact that there is more than one target value to be achieved in the multiresponse case, the m expected responses may meet their target values at different respective control values. Consideration includes the deviation of the expected response E(y_i) from its corresponding target value T_i for each component and the optimal value of calibration point x, say x_0, is considered to be the one which minimizes the weighted sum of squares of such deviations within the range of x. The objective of this study is to find a locally optimal design for estimating x_0, which minimizes the mean square error of the difference between x_0 and its estimator. It shows the optimality criterion is approximately equivalent to a c-criterion under certain conditions and explicit solutions with dual responses under linear and quadratic polynomial regressions are obtained.

The role of $f_{0}(980)$ and $a_{0}(980)$ scalar meson intermediate states in the mechanism of radiative $phi (1020)$ meson decay into two charged $K (494)$ mesons and a photon $phirightarrow K^{+} + K^{-} + gamma$ is investigated. For the contribution of scalar meson intermediate state two models are considered. In the kaon-loop model, the scalar meson intermediate state couples the final state to the initial $phi$ meson through a charged kaon-loop. The second model, called no-structure model, consist of point-like coupling of intermediate scalar meson state to the initial state. It is found that in the kaon-loop model, scalar meson intermediate state results in a considerable modification of the pure Bremsstrahlung photon spectrum.

The first explored area in this thesis is the proposed data hiding method, TCQ-IS. The method is based on Trellis Coded Quantization (TCQ), whose initial state selection is arbitrary. TCQ-IS exploits this fact to hide data. It is a practical multi-dimensional that eliminates the prohibitive task of designing high dimensional quantizers. The strength and weaknesses of the method are stated by various experiments. The second contribution is the proposed data hiding method, Forbidden Zone Data Hiding (FZDH), which relies on the concept of &ldquo / forbidden zone&rdquo / , where host signal is not altered. The main motive of FZDH is to introduce distortion as much as needed, while keeping a range of host signal intact depending on the desired level of robustness. FZDH is compared against Quantization Index Modulation (QIM) as well as DC-QIM and ST-QIM. FZDH outperforms QIM even in 1-D and DC-QIM in higher dimensions. Furthermore, FZDH is comparable with ST-QIM for certain operation regimes. The final contribution is the video data hiding framework that includes FZDH, selective embedding and Repeat Accumulate (RA) codes. De-synchronization due to selective embedding is handled with RA codes. By means of simple rules applied to the embedded frame markers, certain level of robustness against temporal attacks is introduced. Selected coefficients are used to embed message bits by employing multi-dimensional FZDH. The framework is tested with typical broadcast material against common video processing attacks. The results indicate that the framework can be utilized in real life applications.

In the present work some hadronic properties of the scalar &kappa / meson are studied. Using the QCD sum rules approach, which is a nonperturbative method, the mass and the overlap amplitude of this meson are calculated. As well as the mass and the overlap amplitude, &kappa / &rarr / K^+&pi / ^&minus / decay is also studied. For this decay the coupling constant g_&kappa / K^+&pi / ^&minus / is obtained using light cone QCD sum rules which is an extension of the QCD sum rules method. Moreover, the coupling constant is calculated using the experimental decay width and it is compared with the value obtained in light cone QCD sum rules approach. The result of the calculation of g_&kappa / K^+&pi / ^&minus / , the one obtained from light cone QCD sum rules approach, is also applied to acquire the f_0 &minus / &sigma / scalar mixing angle, &theta / s, using the ratio g^2 (&kappa / &rarr / K^+&pi / ^&minus / )/g^2 (&sigma / &rarr / &pi / &pi / ) obtained from experimental decay width. The value of scalar mixing angle is also compared with its experimental results.

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