Matroidal networks are useful tools in furthering research in network coding. They have been used to show the limitations of linear coding solutions. In this paper we examine the basic information on network coding and matroid theory. We then go over the method of creating matroidal networks. Finally we construct matroidal networks from the dual of the fano matroid and the dual of the non-fano matroid, and breifly discuss some coding solutions.

We investigate conditions for the ergodicity of threshold autoregressive time series by embedding the time series in a general state Markov chain and apply a FosterLyapunov drift condition to demonstrate ergodicity of the Markov chain. We are particularly interested in demonstrating V uniform ergodicity where the test function V () is a function of a norm on the statespace. In this dissertation we provide conditions under which the general state space chain may be approximated by a simpler system, whether deterministic or stochastic, and provide conditions on the simpler system which imply V uniform ergodicity of the general state space Markov chain and thus the threshold autoregressive time series embedded in it. We also examine conditions under which the general state space chain may be classified as transient. Finally, in some cases we provide conditions under which central limit theorems will exist for the V uniformly ergodic general state space chain.

This thesis investigates a horizontal water turbine blade designed to suit the periodical ocean current in Penghu sea region. Blade element momentum theory is exploited to design blade profiles. Then, CFD software, Fluent, is used to obtain such simulation result for torque, power, and efficiency. Firstly, performance of turbines with various cross-sectional profiles is discussed. Then, we use quasi-steady method to simulate power output of turbines from periodical ocean current and estimate how much ocean current energy we can obtain per day. Further, the performance of a turbine installed for different immersed depth from the surface is investigated. Our studies show that airfoil profile NACA6409 can outperform others in terms of high lift/drag ratio under low Reynolds number, and better hydrodynamic properties help the water turbine obtain higher torque and power output. A water turbine designed by using NACA6409, at R=1 m, at uniform velocity=2 m/s is estimated to generate 5KW output power. On condition of periodical current flow, the ebb tidal current can rotate water turbine, but power output is only 0.54 times of flood tidal current. The water turbine can generate more power when it is sited in deeper water, and less torque when it is sited near the water surface.

Uniform lying helix(ULH) is a cholesteric LC structure with helical axix lying on the substrate. This structure has a periodic refractive index profile characteristics, so that it can be used as a phase grating. The ULH period can be tuned with different electric fields which provide with various applications. However, ULH is not a steady state in general, once the electric field shutdown, ULH texture will transform to planar texture. Generally, the ULH exist only under a few conditions: well homogeneous alignment and cell the ratio of gap to pitch smaller than 2 , in case the ratio more than 2, the ULH won¡¦t align well. We use two methods to make ULH align well at large cell gap pitch ratio; cooling down from isotropic temperature under electric field and putting mechanical stress on the sample, therefore we can get a well alignment and more stable ULH. We discuss the influence of different boundary conditions to the stability of ULH, and we discover that when d/p large than 10, the stability of ULH improved significantly. Then we study the influence in different alignment anchoring, we find stronger anchoring energy makes ULH transform to planar easily. So we use photo alignment to get weaker anchoring energy, and the ULH using photo alignment stable more than 24 hours. Finally we use a large d/p ULH as tunable phase grating, the pitch length can be tuned about 380nm with low power consumption, and it still have grating function when the field shutdown . Keyword: cholesteric liquid crystal¡Buniform lying helix¡Bgrating

The study aims to explore flow-induced vibration of shear flow past a circular cylinder. The major parameters in the experiment are the natural frequency of the cylinder, and the velocity and velocity gradient of the shear flow approaching the cylinder. The vibration of the cylinder in a water tunnel were measured by two accelerometers to simultaneously obtain the vibration amplitudes in both the streamwise and cross-stream directions. The experimental results show that in the shear flow the cylinder tends of vibrate the orbits of the cylinder vibration become in the streamwise direction while in uniform flow the cylinder vibrates in all directions in the X-Y plane the tendency is obvious for the cylinder with high natural frequency (13Hz). The orbits of the cylinder with low natural frequency (9Hz) are basically similar in shear flow and in uniform flow.

Due to most studies on vibration of pre-loaded rectangular plate being subject to uniform loading, this thesis will investigate vibration of plate under preloading with sine functional distributions. The approach behind this study is using first-order shear deformation plate theory and finite element method to analyze vibration frequency. Study results show that, when a plate¡¦s boundary condition is CCCC, SSSS, CFCF, or SFSF with sine functional pre-loading, its vibration frequency will increase to an extent with little difference when the number of modes increases. Vibration frequency will increase shortly then decrease when increasing the number of sine waves. Vibration frequency will also increase when increasing stress parameters. However, obvious frequency changes are observed only at lower modes with SFSF boundary condition.

In this paper we present the results of a first empirical investigation on how the quality of non-uniform variates is influenced by the underlying uniform RNG and the transformation method used. We use well known standard RNGs and transformation methods to the normal distribution as examples. We find that except for transformed density rejection methods, which do not seem to introduce any additional defects, the quality of the underlying uniform RNG can be both increased and decreased by transformations to non-uniform distributions. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

We investigate conditions for the ergodicity of threshold autoregressive time series by embedding the time series in a general state Markov chain and apply a FosterLyapunov drift condition to demonstrate ergodicity of the Markov chain. We are particularly interested in demonstrating V uniform ergodicity where the test function V () is a function of a norm on the statespace. In this dissertation we provide conditions under which the general state space chain may be approximated by a simpler system, whether deterministic or stochastic, and provide conditions on the simpler system which imply V uniform ergodicity of the general state space Markov chain and thus the threshold autoregressive time series embedded in it. We also examine conditions under which the general state space chain may be classified as transient. Finally, in some cases we provide conditions under which central limit theorems will exist for the V uniformly ergodic general state space chain.

The design of two-dimensional signal constellations for the transmission of binary non-uniform memoryless sources over additive white Gaussian noise channels is investigated. The main application of this problem is the implementation of improved constellations where transmitted data is highly non-uniform. A simple algorithm, which optimizes a constellation by re-arranging its points in a pairwise fashion (i.e., two points are modified at a time, with all other points remaining fixed), is presented. In general, the optimized constellations depend on both the source statistics and the signal-to-noise ratio (SNR) in the channel. We show that constellations designed with source statistics considered can yield symbol error rate performance that is substantially better than rectangular quadrature amplitude modulation signal sets used with either Gray mapping or more recently developed maps. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2009-10-06 22:22:40.096

We present three criteria for compactness in the context of apartness spaces and Bishop-style constructive mathematics. Each of our three criteria can be summarised as requiring that there is a positive distance between any two disjoint closed sets. Neat locatedness and the product apartness give us three variations on this theme. We investigate how our three criteria relate to one another and to several existing compactness criteria, namely classical compactness, completeness, total boundedness, the anti-Specker property, and Diener's neat compactness.