This thesis shows how certain classes of binary constant weight codes can be represented geometrically using linear structures in Euclidean space. The geometric treatment is concerned mostly with codes with minimum distance 2(w - 1), that is, where any two codewords coincide in at most one entry; an algebraic generalization of parts of the theory also applies to some codes without this property. The presented theorems lead to a total of 18 improvements of the table of lower bounds on A(n,d,w) maintained by E. M. Rains and N. J. A. Sloane. Additional improvements have been made by finding new lexicographic codes.

The main part of the thesis is applications of the Strong Artin conjecture to number theory. We have two applications. One is generating number fields with extreme class numbers. The other is generating extreme positive and negative values of Euler-Kronecker constants. For a given number field $K$ of degree $n$, let $\widehat{K}$ be the normal closure of $K$ with $Gal(\widehat{K}/\Bbb Q)=G.$ Let $Gal(\widehat{K}/K)=H$ for some subgroup $H$ of $G$. Then, $$ L(s,\rho,\widehat{K}/\Bbb Q)=\frac{\zeta_K(s)}{\zeta(s)} $$ where $Ind_H^G1_H = 1_G + \rho$. When $L(s,\rho)$ is an entire function and has a zero-free region $[\alpha,1] \times [-(\log N)^2, (\log N)^2]$ where $N$ is the conductor of $L(s,\rho)$, we can estimate $\log L(1,\rho)$ and $\frac{L'}{L}(1,\rho)$ as a sum over small primes: $$ \log L(1,\rho) = \sum_{p\leq(\log N)^{k}}\lambda(p)p^{-1} + O_{l,k,\alpha}(1)$$ $$ \frac{L'}{L}(1,\rho)=-\sum_{p\leq x} \frac{\lambda(p) \log{p}}{p} +O_{l,x,\alpha}(1). $$ where $0 < k < \frac{16}{1-\alpha}$ and $(\log N)^{\frac{16}{1-\alpha}} \leq x \leq N^{\frac{1}{4}}$. With these approximations, we can study extreme values of class numbers and Euler-Kronecker constants. Let $\frak{K}$ $(n,G,r_1,r_2)$ be the set of number fields of degree $n$ with signature $(r_1,r_2)$ whose normal closures are Galois $G$ extension over $\Bbb Q$. Let $f(x,t) \in \Bbb Z[t][x]$ be a parametric polynomial whose splitting field over $\Bbb Q (t)$ is a regular $G$ extension. By Cohen's theorem, most specialization $t\in \Bbb Z$ corresponds to a number field $K_t$ in $\frak{K}$ $(n,G,r_1,r_2)$ with signature $(r_1,r_2)$ and hence we have a family of Artin L-functions $L(s,\rho,t)$. By counting zeros of L-functions over this family, we can obtain L-functions with the zero-free region above. In Chapter 1, we collect the known cases for the Strong Artin conjecture and prove it for the cases of $G=A_4$ and $S_4$. We explain how to obtain the approximations of $\log (1,\rho)$ and $\frac{L'}{L}(1,\rho)$ as a sum over small primes in detail. We review the theorem of Kowalski-Michel on counting zeros of automorphic L-functions in a family. In Chapter 2, we exhibit many parametric polynomials giving rise to regular extensions. They contain the cases when $G=C_n,$ $3\leq n \leq 6$, $D_n$, $3\leq n \leq 5$, $A_4, A_5, S_4, S_5$ and $S_n$, $n \geq 2$. In Chapter 3, we construct number fields with extreme class numbers using the parametric polynomials in Chapter 2. In Chapter 4, We construct number fields with extreme Euler-Kronecker constants also using the parametric polynomials in Chapter 2. In Chapter 5, we state the refinement of Weil's theorem on rational points of algebraic curves and prove it. The second topic in the thesis is about simple zeros of Maass L-functions. We consider a Hecke Maass form $f$ for $SL(2,\Bbb Z)$. In Chapter 6, we show that if the L-function $L(s,f)$ has a non-trivial simple zero, it has infinitely many simple zeros. This result is an extension of the result of Conrey and Ghosh.

Interval censoring arises frequently in life history data, as individuals are often only observed at a sequence of assessment times. This leads to a situation where we do not know when an event of interest occurs, only that it occurred somewhere between two assessment times. Here, the focus will be on methods of estimation for recurrent event data, current status data, and multistate data, subject to interval censoring. With recurrent event data, the focus is often on estimating the rate and mean functions. Nonparametric estimates are readily available, but are not smooth. Methods based on local likelihood and the assumption of a Poisson process are developed to obtain smooth estimates of the rate and mean functions without specifying a parametric form. Covariates and extra-Poisson variation are accommodated by using a pseudo-profile local likelihood. The methods are assessed by simulations and applied to a number of datasets, including data from a psoriatic arthritis clinic. Current status data is an extreme form of interval censoring that occurs when each individual is observed at only one assessment time. If current status data arise in clusters, this must be taken into account in order to obtain valid conclusions. Copulas offer a convenient framework for modelling the association separately from the margins. Estimating equations are developed for estimating marginal parameters as well as association parameters. Efficiency and robustness to the choice of copula are examined for first and second order estimating equations. The methods are applied to data from an orthopedic surgery study as well as data on joint damage in psoriatic arthritis. Multistate models can be used to characterize the progression of a disease as individuals move through different states. Considerable attention is given to a three-state model to characterize the development of a back condition known as spondylitis in psoriatic arthritis, along with the associated risk of mortality. Robust estimates of the state occupancy probabilities are derived based on a difference in distribution functions of the entry times. A five-state model which differentiates between left-side and right-side spondylitis is also considered, which allows us to characterize what effect spondylitis on one side of the body has on the development of spondylitis on the other side. Covariate effects are considered through multiplicative time homogeneous Markov models. The robust state occupancy probabilities are also applied to data on CMV infection in patients with HIV.

Interval censoring arises frequently in life history data, as individuals are often only observed at a sequence of assessment times. This leads to a situation where we do not know when an event of interest occurs, only that it occurred somewhere between two assessment times. Here, the focus will be on methods of estimation for recurrent event data, current status data, and multistate data, subject to interval censoring. With recurrent event data, the focus is often on estimating the rate and mean functions. Nonparametric estimates are readily available, but are not smooth. Methods based on local likelihood and the assumption of a Poisson process are developed to obtain smooth estimates of the rate and mean functions without specifying a parametric form. Covariates and extra-Poisson variation are accommodated by using a pseudo-profile local likelihood. The methods are assessed by simulations and applied to a number of datasets, including data from a psoriatic arthritis clinic. Current status data is an extreme form of interval censoring that occurs when each individual is observed at only one assessment time. If current status data arise in clusters, this must be taken into account in order to obtain valid conclusions. Copulas offer a convenient framework for modelling the association separately from the margins. Estimating equations are developed for estimating marginal parameters as well as association parameters. Efficiency and robustness to the choice of copula are examined for first and second order estimating equations. The methods are applied to data from an orthopedic surgery study as well as data on joint damage in psoriatic arthritis. Multistate models can be used to characterize the progression of a disease as individuals move through different states. Considerable attention is given to a three-state model to characterize the development of a back condition known as spondylitis in psoriatic arthritis, along with the associated risk of mortality. Robust estimates of the state occupancy probabilities are derived based on a difference in distribution functions of the entry times. A five-state model which differentiates between left-side and right-side spondylitis is also considered, which allows us to characterize what effect spondylitis on one side of the body has on the development of spondylitis on the other side. Covariate effects are considered through multiplicative time homogeneous Markov models. The robust state occupancy probabilities are also applied to data on CMV infection in patients with HIV.

During the last half century there has been a resurgence of interest in Monge's 18th century mass transportation problem, with most of the activity limited to continuous spaces. This thesis, consequently, develops techniques based on mass transportation for the purpose of obtaining tight concentration inequalities in a discrete setting. Such inequalities on n-fold products of graphs, equipped with product measures, have been well investigated using combinatorial and probabilistic techniques, the most notable being martingale techniques. The emphasis here, is instead on the analytic viewpoint, with the precise contribution being as follows. We prove that the modified log-Sobolev inequality implies the transportation inequality in the first systematic comparison of the modified log-Sobolev inequality, the Poincar inequality, the transportation inequality, and a new variance transportation inequality. The duality shown by Bobkov and Gtze of the transportation inequality and a generating function inequality is then utilized in finding the asymptotically correct value of the subgaussian constant of a cycle, regardless of the parity of the length of the cycle. This result tensorizes to give a tight concentration inequality on the discrete torus. It is interesting in light of the fact that the corresponding vertex isoperimetric problem has remained open in the case of the odd torus for a number of years. We also show that the class of bounded degree expander graphs provides an answer, in the affirmative, to the question of whether there exists an infinite family of graphs for which the spread constant and the subgaussian constant differ by an order of magnitude. Finally, a candidate notion of a discrete Ricci curvature for finite Markov chains is given in terms of the time decay of the Wasserstein distance of the chain to its stationarity. It can be interpreted as a notion arising naturally from a standard coupling of Markov chains. Because of its natural definition, ease of calculation, and tensoring property, we conclude that it deserves further investigation and development. Overall, the thesis demonstrates the utility of using the mass transportation problem in discrete isoperimetric and functional inequalities.

Managed Pressure Drilling now at the pinnacle of the 'Oil Well Drilling' evolution tree, has itself been coined in 2003. It is an umbrella term for a few new drilling techniques and some preexisting drilling techniques, all of them aiming to solve several drilling problems, including non-productive time and/or drilling flat time issues. These techniques, now sub-classifications of Managed Pressure Drilling, are referred to as 'Variations' and 'Methods' of Managed Pressure Drilling. Although using Managed Pressure Drilling for drilling wells has several benefits, not all wells that seem a potential candidate for Managed Pressure Drilling, need Managed Pressure Drilling. The drilling industry has numerous simulators and software models to perform drilling hydraulics calculations and simulations. Most of them are designed for conventional well hydraulics, while some can perform Underbalanced Drilling calculations, and a select few can perform Managed Pressure Drilling calculations. Most of the few available Managed Pressure Drilling models are modified Underbalanced Drilling versions that fit Managed Pressure Drilling needs. However, none of them focus on Managed Pressure Drilling and its candidate selection alone. An 'Managed Pressure Drilling Candidate Selection Model and software' that can act as a preliminary screen to determine the utility of Managed Pressure Drilling for potential candidate wells are developed as a part of this research dissertation. The model and a flow diagram identify the key steps in candidate selection. The software performs the basic hydraulic calculations and provides useful results in the form of tables, plots and graphs that would help in making better engineering decisions. An additional Managed Pressure Drilling worldwide wells database with basic information on a few Managed Pressure Drilling projects has also been compiled that can act as a basic guide on the Managed Pressure Drilling variation and project frequencies and aid in Managed Pressure Drilling candidate selection.

An experimental study of the effect of initial conditions on the development of Rayleigh Taylor Instabilities (RTI) at low Atwood numbers (order of 10-4) was performed in the water channel facility at TAMU. Initial conditions of the flow were generated using a controllable, highly reliable Servo motor. The uniqueness of the study is the system’s capability of generating the required initial conditions precisely as compared to the previous endeavors. Backlit photography was used for imaging and ensemble averaging of the images was performed to study mixing width characteristics in different regimes of evolution of Rayleigh-Taylor Instability (RTI). High-speed imaging of the flows was performed to provide insights into the growth of bubble and spikes in the linear and non-linear regime of instability development. RTI are observed in astrophysics, geophysics and in many instances in nature. The vital role of RTI in the feasibility and efficiency of the Inertial Confinement Fusion (ICF) experiment warrants a comprehensive study of the effect of mixing characteristics of RTI and its dependence on defining parameters. With this broader objective in perspective, the objectives of this present investigation were mainly threefold: First was the validation of the novel setup of the Water channel system. Towards this objective, validation of Servo motor, splitter plate thickness effects, density and temperature measurements and single-mode experiments were performed. The second objective was to study the mixing and growth characteristics of binary and multi-mode initial perturbations seeking an explanation of behavior of the resultant flow structures by performing the first ever set of such highly controlled experiments. The first-ever set of experiments with highly controlled multi-mode initial conditions was performed. The final objective of this study was to measure and compare the bubble and spike velocities with single-mode initial conditions with existing analytical models. The data derived from these experiments would qualitatively and quantitatively enhance the understanding of dependence of mixing width on parametric initial conditions. The knowledge would contribute towards a generalized theory for RTI mixing with specified dependence on various parameters, which has a wide range of applications. The system setup was validated to provide a reliable platform for the novel multi-modal experiments to be performed in the future. It was observed that the ensemble averaged mixing width of the binary system does not vary significantly with the phase-difference between the modes of a binary mode initial condition experiment, whereas it varies with the amplitudes of the component modes. In the exponential and non-linear regimes of evolution, growth rates of multi-mode perturbations were found to be higher than the component modes, whereas saturation growth rates correspond to the dominant wavelength. Quadratic saturation growth rate constants, alpha were found to be about 0.07 ± 0.01 for binary and multi modes whereas single-mode data measured alpha about 0.06 ± 0.01. High-speed imaging was performed to measure bubble and spike amplitudes to obtain velocities and growth rates. It was concluded that higher temporal and spatial resolution was required for accurate measurement. The knowledge gained from the above study will facilitate a better understanding of the physics underlying Rayleigh-Taylor instability. The results of this study will also help validating numerical models for simulation of this instability, thereby providing predictive capability for more complex configurations.

In this thesis, we expand the option pricing and virtual asset model system by Cheng (2005) and include new simulations and maximum likelihood estimation of the parameter of the stochastic differential equations. For easy manipulation of general users, the interface of original option pricing system is modified. In addition, in order to let the system more completely, some stochastic models and methods of pricing and estimation are added. This system can be divided into three major parts. One is an option pricing system; The second is an asset model simulation system; The last is estimation system of the parameter of the model. Finally, the analysis for the data of network are carried out. The differences of the prices between estimator of this system and real market are compared.

In this thesis, we investigate the use of adaptive antenna algorithms for OFDM systems to suppress interference in various channel conditions including narrowband and wideband interference, flat and frequency selective fading. We propose a novel frequency-domain beamformer, based on the linearly constrained modified constant modulus hybrid LMS (LCMCM-HLMS) algorithm for OFDM systems to improve the performance of interference suppression in AWGN channel with narrowband interference, Rayleigh fast fading channel with phase distortion, and the multipath environment. To verify the merits of the frequency-domain beamformer, the effect due to narrowband interference and random phase distortion are investigated. Moreover, to improve the performance of adaptive beamforming algorithm, the frequency-domain linearly constrained modified constant modulus hybrid LMS (LCMCM-HLMS) algorithm is proposed. Computer simulation results show that the proposed frequency-domain LCMCM-HLMS beamformer has good capability of interference supression in various environment, and can mitigate the phase distortion of channel. However, in the time-domain beamformer based on LMS [33], RLS ,LC-LMS and LC-FLS algorithm for OFDM systems, the performance may severely degraded under some situations. We will show that in terms of output SINR, beampatern, received signal constellation and mean square error (MSE), for narrowband interference suppression in AWGN channel, phase distortion in Rayleigh fast fading channel and the multipath environment.

<p>The rapid expansion of major cities in the west Europeancountries has accentuated the need to exploit every potentialsite for new establishments, e.g. areas over train tunnels andnear railway tracks in general. A significant impediment toexploit such areas is the structure-borne noise generated bythe train traffic, which is transmitted into buildings via theground. Reliable prediction methods and cost-effective noisecontrol measures are therefore needed and are also the objectof the present work. In this thesis, the studied buildings areconsidered as wave-guides for the sound transmitted from theground. The work is restricted to the case of hard ground suchas granite. The chosen technique permits comparison betweendifferent potential measures to reduce the transmission ofstructure-borne sound upward in buildings. It is shown that thedesign of the load-bearing structures is important in thiscontext, and a design with relocated columns has givenpromising results. It is also shown that the stiffness of theground plays an important role in the transmission process.This leads to the idea that a sand layer between the foundationof the building and the bedrock may reduce the transmission.New methods have thus been developed in the course of this workto evaluate the stiffness of the layer using approximate andexact techniques. Results are presented and a comparison ismade with previous results for a "normal" building and it isshown that the insertion of sand layer has a potential toconsiderably reduce the sound level in the building.</p><p><b>Keywords:</b>Ground-borne noise, railway noise, in-planewaves, wave-guides, scattering, propagation constant, inputmobility, elastic stratum, dual integral equations.</p>