Based on the author's MA thesis (84 leaves, University of British Columbia, 1982). / Includes bibliographical references. Also issued online.

Let {Tsub(p) : q1 ≤ p ≤ q2} be a family of consistent Csub(0) semigroups on Lφ(Ω) with q1, q2 ∈ [1, ∞)and Ω ⊆ IRn open. We show that certain commutator conditions on Tφ and on the resolvent of its generator Aφ ensure the φ independence of the spectrum of Aφ for φ ∈ [q1, q2]. Applications include the case of Petrovskij correct systems with Hölder continuous coeffcients, Schrödinger operators, and certain elliptic operators in divergence form with real, but not necessarily symmetric, or complex coeffcients.

Though the arrival directions of ultra-high-energy cosmic rays (UHECRs) are distributed in a relatively isotropic manner, there is evidence of small-scale anisotropy. This, combined with the detection of cosmic rays with energies above the GZK cut-off, has motivated us to further investigate the idea that UHECRs are the result of a top-down mechanism involving the annihilation of superheavy dark matter particles in our galactic halo. To more precisely characterize the nature of dark matter, we have endeavoured to apply two different models to the leading UHECR spectra, namely those from the AGASA, High Resolution Flys Eye, and Pierre Auger Collaborations. First, we attempt a non-linear, least-squares fit of the particle physics fragmentation function to the spectra. Second, we propose that the observed cosmic ray spectrum above 3.5 × 10E+18 eV is the superposition of flux from two different sources: bottom-up acceleration via a simple power-law relation at lower energies and scattered particles from dark matter annihilation governed by fragmentation functions at higher energies. We find that while the former model does not provide a satisfactory fit to observatory data, the latter yields reduced χ2 values between 1.14 and 2.6. From the fragmentation function component of our second model, we are able to extract estimates of dark matter particle mass. We find values of (1.2 ± 0.6) 10E+21 eV, (5.0 ± 4.3) 10E+20 eV, and (2.6 ± 1.5) 10E+21 eV respectively for the AGASA, HiRes, and Pierre Auger data, which agree with earlier predictions based on a cosmological analysis of non-thermal particle production in an inflationary universe. Furthermore, we verify that the dark matter particle densities required by our two-source model are in line with current CDM theory.

FFT-based digital spectral analyzer has become more and more widely used as a result of the development of Digital Signal Processing (DSP) techniques. Modern Analog-to-Digital Converters (ADC) and processors have made it possible to make fast measurements with a limited number of hardware.   In this thesis, a design of a simple low-cost FFT-based digital spectrum analyzer was presented. The author discusses the design of each components of the system in qualitatively and quantitatively. The report presents the whole system design in detail which contains filter design, micro-controller design, UART transmission design and MATLAB GUI design. Some satisfying measurement result of the system were presented in the paper. The system can provide fast measurement with good accuracy. But the measured result has a limited range and resolution of the display is not very high. At last, the advantages and disadvantages of the system was discussed which is considered as guidelines for further work.

Cognitive radio is a low-cost communication system, which can choose the available frequencies and waveforms automatically on the premise of avoiding interfering the licensed users. The spectrum sensing is the key enabling technology in cognitive radio networks. It is able to fill voids in the wireless spectrum and can dramatically increase spectral efficiency.   In this thesis, the author use matlab to simulate the received signals from the cognitive radio networks and an energy detector to detect whether the spectrum is being used. The report also compares the theoretical value and the simulated result and then describes the relationship between the signal to noise ratio (SNR) and the detections. At last, the method, energy detection and simulation and result are discussed which is considered as the guidelines for the future work.

Spectrum sensing plays a key role for radio resource awareness in cognitive radio. To enhance the capabilities of cognitive radio nodes, exploiting the spatial resource in addition to frequency and time re-sources seems reasonable. This thesis investigates the possibility of exploiting the spatial resources during sensing and transmission using sector antennas which is also termed as directional spectrum sensing and transmission. The measured radiation patterns from fabricated antenna and radiation patterns obtained from analytical expressions representing circular array of dipole are used for performance analysis. A ray tracer tool is used for modelling the urban environment as well as for wave propagation simulation. The power angular profiles obtained at different locations are further processed in MATLAB using measured and analytical radiation patterns to evaluate the performance in terms of spatial opportunity and detection of weak primary signals. The results show that exploiting the spatial dimension in spectrum sensing using sector antennas increase the opportunities for secondary communication and also improves the detection of primary signals as compared with an omni-directional antenna. Additionally, directional sensing and trans-mission are studied together using analytical radiation patterns. The results show that the service probability as well as range of communica-tion increases with an increase in number of sectors but saturation is achieved when nine sectors are used, indicating that six sectors antenna is the optimum choice for exploring the spatial resource in cognitive radio in a typical multipath urban environment.

OFDM is a fast growing technology in the area of wireless communication due to its numerous advantages and applications. The current and future technologies in the area of wireless communications like WiMAX, WiFi, LTE, MBWA and DVB-T uses the OFDM signals. The OFDM technology is applicable to the radio communication as well as the acoustic communication. Though the licensed spectrum is intended to be used only by the spectrum owners, Cognitive radio is a concept of reusing this licensed spectrum in an unlicensed manner. Cognitive radio is motivated by the measurements of spectrum utilization . Cognitive radio must be able to detect very weak primary users signal and to keep the interference level at a maximum acceptable level. Hence spectrum sensing is an essential part of the cognitive radio. Spectrum is a scarce resource and spectrum sensing is the process of identifying the unused spectrum, without causing any harm to the existing primary user’s signal. The unused spectrum is referred to as spectrum hole or white space and this spectrum hole could be reused by the cognitive radio. This thesis work focuses on implementing primary acoustic transmitter to transmit the OFDM signals from a computer through loudspeaker and receive the signals through a microphone. Then by applying different detection methods on the received OFDM signal for detection of the spectrum hole, the performance of these detection methods is compared here. The commonly used detection methods are power spectrum estimation, energy detection and second–order statistics (GLRT approach, Autocorrelation Function (ACF) detection and cyclostationary feature detection ). The detector based on GLRT approach exploits the structure of the OFDM signal by using the second order statistics of the received data. The thesis mainly focuses on GLRT approach and ACF detectors and compare their performance.

Cognitive radio (CR) paradigm is a new radio technology proposed to solve spectrum scarcity and underutilization. Central to CR is spectrum sensing (SS), which is responsible for detecting unoccupied frequencies. Since Detection techniques differ in their performance, selecting the optimal detection method to locally perform SS has received significant attention. This research work aims to enhance the reliability of local detection decisions, under low SNR, by developing a spectrum sensing that can take advantage of multiple detection techniques. This model can either select the optimal technique or make these techniques cooperate with one another to achieve better sensing performance. The model performance is measured with respect to detection and false alarm probability as well as sensing time. To develop this model, the performance of three detection techniques is evaluated and compared. Furthermore, the voting and the maximum a posteriori probability (MAP) fusion models were developed and employed to combine spectrum sensing results obtained from the three techniques. It is concluded that the cyclostationary feature detection technique is a superior detector in low SNR situations. MAP fusion model is found to be more reliable than the voting model.

Though the arrival directions of ultra-high-energy cosmic rays (UHECRs) are distributed in a relatively isotropic manner, there is evidence of small-scale anisotropy. This, combined with the detection of cosmic rays with energies above the GZK cut-off, has motivated us to further investigate the idea that UHECRs are the result of a top-down mechanism involving the annihilation of superheavy dark matter particles in our galactic halo. To more precisely characterize the nature of dark matter, we have endeavoured to apply two different models to the leading UHECR spectra, namely those from the AGASA, High Resolution Flys Eye, and Pierre Auger Collaborations. First, we attempt a non-linear, least-squares fit of the particle physics fragmentation function to the spectra. Second, we propose that the observed cosmic ray spectrum above 3.5 × 10E+18 eV is the superposition of flux from two different sources: bottom-up acceleration via a simple power-law relation at lower energies and scattered particles from dark matter annihilation governed by fragmentation functions at higher energies. We find that while the former model does not provide a satisfactory fit to observatory data, the latter yields reduced χ2 values between 1.14 and 2.6. From the fragmentation function component of our second model, we are able to extract estimates of dark matter particle mass. We find values of (1.2 ± 0.6) 10E+21 eV, (5.0 ± 4.3) 10E+20 eV, and (2.6 ± 1.5) 10E+21 eV respectively for the AGASA, HiRes, and Pierre Auger data, which agree with earlier predictions based on a cosmological analysis of non-thermal particle production in an inflationary universe. Furthermore, we verify that the dark matter particle densities required by our two-source model are in line with current CDM theory.

It is very interesting to probe the rotational symmetry of semiconductor quantum dots for quantum information and quantum computation applications. We studied the effects of rotational symmetry in semiconductor quantum dots using configuration interaction calculation. Moreover, to compare with the experimental data, we studied the effects of hidden symmetry. The 2D single-band model and the 3D single-band model were used to generate the single-particle states. How the spectra affected by the breaking of hidden symmetry and rotational symmetry are discussed. The breaking of hidden symmetry splits the degeneracy of electron-hole single-triplet and triplet-singlet states, which can be clearly seen from the spectra. The breaking of rotational symmetry redistributes the weight percentage, due to the splitting of px and py states, and gives a small brightness to the dark transition, giving rise to asymmetry peaks. The asymmetry peaks of 4X, 5X, and 6X were analyzed numerically. In addition, Auger-like satellites of biexciton recombination were found in the calculation. There is an asymmetry peak of the biexciton Auger-like satellite for the 2D single-band model while no such asymmetry peak occurs for the 3D single-band model. Few-particle effects are needed in order to determine the energy separation of the biexciton main peak and the Auger-like satellite. From the experiments, it was confirmed that the lower emission energy peak of X2-spectrum is split. The competed splitting of the X2- spectra were revealed when temperature dependence was implemented. However, since the splitting is small, we suggest the X2- peaks are broadened in comparison with other configurations according to single-band models. Furthermore, the calculated excitonic emission patterns were compared with experiments. The 2D single-band model fails to give the correct energy order of the peaks for the few-particle spectra; on the other hand the peaks order from 3D single-band model consistent with experimental data.