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Yes / New orthogonal wavelet transforms can be designed by changing the wavelet basis functions or by constructing new low-pass filters (LPF). One family of wavelet may appeal, in use, to a particular application than another. In this study, the wavelet transform based on raisedcosine spectrum is used as an independent orthogonal wavelet to study multicarrier modulation behaviour over multipath channel environment. Then, the raised-cosine wavelet is compared with other well-known orthogonal wavelets that are used, also, to build multicarrier modulation systems. Traditional orthogonal wavelets do not have side-lobes, while the raised-cosine wavelets have lots of side-lobes; these characteristics influence the wavelet behaviour. It will be shown that the raised-cosine wavelet transform, as an orthogonal wavelet, does not support the design of multicarrier application well like the existing well-known orthogonal wavelets.

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Nonlinear structures, when subjected to multiple ground motion records that are scaled to consistent ground motion intensity show significant variation in their response. This effect of ground motion randomness on the variation of structural response is defined as Record-to-Record (RTR) Variability. Ground motion characteristics that contribute to this variability in response includes the variation of signal composition (frequency content) with time (spectral nonstationarity).The phenomenon of moving resonance which occurs when the frequency content of the ground motion shifts in a similar manner as the natural frequencies of the structural response, is likely a contributor to variability. This brings the need to further understand the sources of variability due to moving resonance. The present study was carried out to develop a method to analyze the time-frequency content of a ground motion to assess the occurrence of moving resonance and to quantify its potential in effecting the structural systems. Bilinear elastic and elastoplastic hysteretic behavior was considered. Detailed analysis is done to quantify the effect of moving resonance on structural systems due to 22 far field ground motion records. The wavelet coefficient plots gave very good detail of the characteristics of the ground motions that were not clear from the acceleration time histories and response spectra plots. Instances of moving resonance were found out to be significant. Amplification due to moving resonance was found to be quite large. One instance studied in detail (accelerogram of Northridge earthquake at Beverly Hills) had peak displacement amplified by 6 times compared to the amount of peak displacement expected if the system did not exhibit moving resonance. Based on the analyses results, the characteristics of the ground motion records that don't cause significant moving resonance effect on structural systems were observed. Similarly, the characteristics of the ground motions that do cause moving resonance effect on structural systems were examined. / Master of Science

Yes / This paper demonstrates a non-Fourier prediction methodology of triple-layer human skin tissue for determining skin burn injury with non-ideal properties of tissue, metabolism and blood perfusion. The dual-phase lag (DPL) bioheat model is employed and solved using joint integral transform (JIT) through Laplace and Fourier transforms methods. Parametric studies on the effects of skin tissue properties, initial temperature, blood perfusion rate and heat transfer parameters for the thermal response and exposure time of the layers of the skin tissue are carried out. The study demonstrates that the initial tissue temperature, the thermal conductivity of the epidermis and dermis, relaxation time, thermalisation time and convective heat transfer coefficient are critical parameters to examine skin burn injury threshold. The study also shows that thermal conductivity and the blood perfusion rate exhibits negligible effects on the burn injury threshold. The objective of the present study is to support the accurate quantification and assessment of skin burn injury for reliable experimentation, design and optimisation of thermal therapy delivery.

This thesis is divided into three parts. In the first part we study mixed norm estimates for Riesz transforms associated with various differential operators. First we prove the mixed norm estimates for the Riesz transforms associated with Dunkl harmonic oscillator by means of vector valued inequalities for sequences of operators defined in terms of Laguerre function expansions. In certain cases, the result can be deduced from the corresponding result for Hermite Riesz transforms, for which we give a simple and an independent proof. The mixed norm estimates for Riesz transforms associated with other operators, namely the sub-Laplacian on Heisenberg group, special Hermite operator on C^d and Laplace-Beltrami operator on the group SU(2) are obtained using their L^pestimates and by making use of a lemma of Herz and Riviere along with an idea of Rubio de Francia. Applying these results to functions expanded in terms of spherical harmonics, we deduce certain vector valued inequalities for sequences of operators defined in terms of radial parts of the corresponding operators. In the second part, we study the chaotic behavior of the heat semigroup generated by the Dunkl-Laplacian ∆_κ on weighted L^P-spaces. In the general case, for the chaotic behavior of the Dunkl-heat semigroup on weighted L^p-spaces, we only have partial results, but in the case of the heat semigroup generated by the standard Laplacian, a complete picture of the chaotic behavior is obtained on the spaces L^p ( R^d,〖 (φ_iρ (x ))〗^2 dx) where φ_iρ the Euclidean spherical function is. The behavior is very similar to the case of the Laplace-Beltrami operator on non-compact Riemannian symmetric spaces studied by Pramanik and Sarkar. In the last part, we study mixed norm estimates for the Cesáro means associated with Dunkl-Hermite expansions on〖 R〗^d. These expansions arise when one considers the Dunkl-Hermite operator (or Dunkl harmonic oscillator)〖 H〗_κ:=-Δ_κ+|x|^2. It is shown that the desired mixed norm estimates are equivalent to vector-valued inequalities for a sequence of Cesáro means for Laguerre expansions with shifted parameter. In order to obtain the latter, we develop an argument to extend these operators for complex values of the parameters involved and apply a version of Three Lines Lemma.

Thesis (DSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2009. / The replacement of the standard discrete cosine transform (DCT) of JPEG with the windowed modifed DCT (MDCT) is investigated to determine whether improvements in numerical quality can be achieved. To this end, we employ an existing algorithm for optimal quantisation, for which we also propose improvements. This involves the modelling and prediction of quantisation tables to initialise the algorithm, a strategy that is also thoroughly tested. Furthermore, the effects of various window functions on the coding results are investigated, and we find that improved quality can indeed be achieved by modifying JPEG in this fashion.