On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions

AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.

Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group

2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.

Space time coding for polynomial phase modulated signals

Polynomial phase modulated (PPM) signals have been shown to provide improved error rate performance with respect to conventional modulation formats under additive white Gaussian noise and fading channels in single-input single-output (SISO) communication systems. In this dissertation, systems with two and four transmit antennas using PPM signals were presented. In both cases we employed full-rate space-time block codes in order to take advantage of the multipath channel. For two transmit antennas, we used the orthogonal space-time block code (OSTBC) proposed by Alamouti and performed symbol-wise decoding by estimating the phase coefficients of the PPM signal using three different methods: maximum-likelihood (ML), sub-optimal ML (S-ML) and the high-order ambiguity function (HAF). In the case of four transmit antennas, we used the full-rate quasi-OSTBC (QOSTBC) proposed by Jafarkhani. However, in order to ensure the best error rate performance, PPM signals were selected such as to maximize the QOSTBC’s minimum coding gain distance (CGD). Since this method does not always provide a unique solution, an additional criterion known as maximum channel interference coefficient (CIC) was proposed. Through Monte Carlo simulations it was shown that by using QOSTBCs along with the properly selected PPM constellations based on the CGD and CIC criteria, full diversity in flat fading channels and thus, low BER at high signal-to-noise ratios (SNR) can be ensured. Lastly, the performance of symbol-wise decoding for QOSTBCs was evaluated. In this case a quasi zero-forcing method was used to decouple the received signal and it was shown that although this technique reduces the decoding complexity of the system, there is a penalty to be paid in terms of error rate performance at high SNRs.

Quasi-Orthogonal Space-Time Block Coding Using Polynomial Phase Modulation

Recently, polynomial phase modulation (PPM) was shown to be a power- and bandwidth-efficient modulation format. These two characteristics are in high demand nowadays specially in mobile applications, where devices with size, weight, and power (SWaP) constraints are common. In this paper, we propose implementing a full-diversity quasiorthogonal space-time block code (QOSTBC) using polynomial phase signals as modulation format. QOSTBCs along with PPM are used in order to improve the power efficiency of communication systems with four transmit antennas. We obtain the optimal PPM constellations that ensure full diversity and maximize the QOSTBC's minimum coding gain distance. Simulation results show that by using QOSTBCs along with a properly selected PPM constellation, full diversity in flat fading channels and thus low BER at high signal-to-noise ratios (SNR) can be ensured. More importantly, it is also shown that QOSTBCs using PPM achieve a better error performance than those using conventional modulation formats.

Uncertain natural frequency analysis of composite plates including effect of noise – A polynomial neural network approach

Acknowledgement SN and SS gratefully acknowledge the financial support from Lloyd’s Register Foundation Centre during this work.

The Irish paradigm on the natural progression of hepatitis C virus infection: an investigation in a homogeneous patient population infected with HCV 1b (Review)

The aetiological agent of chronic hepatitis C is the hepatitis C virus. The hepatitis C virus is spread by parenteral transmission of body fluids, primarily blood or blood products. In 1989, after more than a decade of research, HCV was isolated and characterised. The hepatitis C viral genome is a positive-sense, single-stranded RNA molecule approximately 9.4 kb in length, which encodes a polyprotein of about 3100 amino acids. There are 6 main genotypes of HCV, each further stratified by subtype. In 1994, a cohort of women was identified in Ireland as having been iatrogenically exposed to the hepatitis C virus. The women were all young and exposed as a consequence of the receipt of HCV 1b contaminated anti-D immunoglobulin. The source of the infection was identified as an acutely infected female. As part of a voluntary serological screening programme involving 62,667 people, 704 individuals were identified as seropositive for exposure to the hepatitis C virus; 55.4% were found to be positive for the viral genome 17 years after exposure. Of these women 98% had evidence of inflammation, but suprisingly, a remarkable 49% showed no evidence of fibrosis. Clinicopathology and virological analysis has identified associations between viral load and the histological activity index for inflammation, and, between inflammation and levels of the liver enzyme alanine aminotransferase. Infection at a younger age appears to protect individuals from progression to advanced liver disease. Molecular analyses of host immunogenetic elements shows that particular class II human leukocyte associated antigen alleles are associated with clearance of the hepatitis C virus. Additional class II alleles have been identified that are associated with stable viraemia over an extended period of patient follow-up. Although, investigation of large untreated homogeneous cohorts is likely to become more difficult, as the efficacy of anti-viral therapy improves, further investigation of host and viral factors that influence disease progression will help provide an evidence based approach were realistic expectations regarding patient prognosis can be ascertained.

A polynomial algorithm for the three-machine open shop with a bottleneck machine

Abstract not available

Resistive Embedded Heating for Homogeneous Curing of Composite Damage Repair

Thesis (Ph.D.)--University of Washington, 2016-08

Motivic Decomposition of Projective Pseudo-Homogeneous Varieties

Let G be a semi-simple algebraic group over a field k. Projective G-homogeneous varieties are projective varieties over which G acts transitively. The stabilizer or the isotropy subgroup at a point on such a variety is a parabolic subgroup which is always smooth when the characteristic of k is zero. However, when k has positive characteristic, we encounter projective varieties with transitive G-action where the isotropy subgroup need not be smooth. We call these varieties projective pseudo-homogeneous varieties. To every such variety, we can associate a corresponding projective homogeneous variety. In this thesis, we extensively study the Chow motives (with coefficients from a finite connected ring) of projective pseudo-homogeneous varieties for G inner type over k and compare them to the Chow motives of the corresponding projective homogeneous varieties. This is done by proving a generic criterion for the motive of a variety to be isomorphic to the motive of a projective homogeneous variety which works for any characteristic of k. As a corollary, we give some applications and examples of Chow motives that exhibit an interesting phenomenon. We also show that the motives of projective pseudo-homogeneous varieties satisfy properties such as Rost Nilpotence and Krull-Schmidt.

On the suboptimality of the p-version interior penalty discontinuous Galerkin method

We address the question of the rates of convergence of the p-version interior penalty discontinuous Galerkin method (p-IPDG) for second order elliptic problems with non-homogeneous Dirichlet boundary conditions. It is known that the p-IPDG method admits slightly suboptimal a-priori bounds with respect to the polynomial degree (in the Hilbertian Sobolev space setting). An example for which the suboptimal rate of convergence with respect to the polynomial degree is both proven theoretically and validated in practice through numerical experiments is presented. Moreover, the performance of p- IPDG on the related problem of p-approximation of corner singularities is assessed both theoretically and numerically, witnessing an almost doubling of the convergence rate of the p-IPDG method.

Synthesis of waterborne polyurethane-urea dispersions with chain extension step in homogeneous and heterogeneous media

Hypothesis: The possibility of tailoring the final properties of environmentally friendly waterborne polyurethane and polyurethane-urea dispersions and the films they produce makes them attractive for a wide range of applications. Both the reagents content and the synthesis route contribute to the observed final properties. Experiments: A series of polyurethane-urea and polyurethane aqueous dispersions were synthesized using 1,2-ethanediamine and/or 1,4-butanediol as chain extenders. The diamine content was varied from 0 to 4.5 wt%. Its addition was carried out either by the classical heterogeneous reaction medium (after phase inversion step), or else by the alternative homogeneous medium (prior to dispersion formation). Dispersions as well as films prepared from dispersions have been later extensively characterized. Findings: 1,2-Ethanediamine addition in heterogeneous medium leads to dispersions with high particle sizes and broad distributions whereas in homogeneous medium, lower particle sizes and narrow distributions were observed, thus leading to higher uniformity and cohesiveness among particles during film formation. Thereby, stress transfer is favored adding the diamine in a homogeneous medium; and thus the obtained films presented quite higher stress and modulus values. Furthermore, the higher uniformity of films tends to hinder water molecules transport through the film, resulting, in general, in a lower water absorption capacity.

The temporal evolution of the energy flux across scales in homogeneous turbulence

A temporal study of energy transfer across length scales is performed in 3D numerical simulations of homogeneous shear flow and isotropic turbulence. The average time taken by perturbations in the energy flux to travel between scales is measured and shown to be additive. Our data suggests that the propagation of disturbances in the energy flux is independent of the forcing and that it defines a ‘velocity’ that determines the energy flux itself. These results support that the cascade is, on average, a scale-local process where energy is continuously transmitted from one scale to the next in order of decreasing size.

Direct numerical simulation of statistically stationary and homogeneous shear turbulence and its relation to other shear flows

Statistically stationary and homogeneous shear turbulence (SS-HST) is investigated by means of a new direct numerical simulation code, spectral in the two horizontal directions and compact-finite-differences in the direction of the shear. No remeshing is used to impose the shear-periodic boundary condition. The influence of the geometry of the computational box is explored. Since HST has no characteristic outer length scale and tends to fill the computational domain, long-term simulations of HST are “minimal” in the sense of containing on average only a few large-scale structures. It is found that the main limit is the spanwise box width, Lz, which sets the length and velocity scales of the turbulence, and that the two other box dimensions should be sufficiently large (Lx ≳ 2Lz, Ly ≳ Lz) to prevent other directions to be constrained as well. It is also found that very long boxes, Lx ≳ 2Ly, couple with the passing period of the shear-periodic boundary condition, and develop strong unphysical linearized bursts. Within those limits, the flow shows interesting similarities and differences with other shear flows, and in particular with the logarithmic layer of wall-bounded turbulence. They are explored in some detail. They include a self-sustaining process for large-scale streaks and quasi-periodic bursting. The bursting time scale is approximately universal, ∼20S−1, and the availability of two different bursting systems allows the growth of the bursts to be related with some confidence to the shearing of initially isotropic turbulence. It is concluded that SS-HST, conducted within the proper computational parameters, is a very promising system to study shear turbulence in general.

Spatio-temporal modeling of data imputation for daily rainfall series in homogeneous zones.

Spatio-temporal modelling is an area of increasing importance in which models and methods have often been developed to deal with specific applications. In this study, a spatio-temporal model was used to estimate daily rainfall data. Rainfall records from several weather stations, obtained from the Agritempo system for two climatic homogeneous zones, were used. Rainfall values obtained for two fixed dates (January 1 and May 1, 2012) using the spatio-temporal model were compared with the geostatisticals techniques of ordinary kriging and ordinary cokriging with altitude as auxiliary variable. The spatio-temporal model was more than 17% better at producing estimates of daily precipitation compared to kriging and cokriging in the first zone and more than 18% in the second zone. The spatio-temporal model proved to be a versatile technique, adapting to different seasons and dates.