No description available.

<p> In this thesis, a variety of topics are investigated. Part I discusses asymptotic giant branch (AGB) stars. We review their evolution and their contribution to the galactic chemical evolution. We particularly pay attention to the nucleosynthesis in different layers of the AGB stars, and discuss diverse chains of reactions that can happen under different circumstances. </p> <p> Out of many of such reactions, three are the subjects of our special attention. The 23Na(p,α)20Ne, 23Na(p, γ)24Mg and 26YAl(p, γ)27Si reactions are important reactions that are part of the NeNa and MgAl cycles. Their reaction rates used to be uncertain by orders of magnitude, and thus have been subjects of investigation. Recently, there has been new experimental information released on these reactions. In this project, we have used this new information, and have calculated the new reaction rates for those reactions. The results show less uncertainty range in all three reaction rates compared to the prior measurements. </p> <p> We then have used these new less uncertain rates to calculate the AGB yields of hydrogen through to 62Ni. However, these reaction rates only affect the yields of Ne to Si isotopes noticeably, which are presented in Appendix A. Dr. Karakas has calculated the AGB yields by computing stellar evolution and nucleosynthesis models for a 6 M (symbol) AGB star with three different metallicities (Z = 0.02, 0.004 and 0.008) using the new reaction rates. The results show that the changes in the yields due to individually using the updated 23Na(p, γ)24Mg or 23Na(p,α)20Ne reaction rate are noticeable for some isotopes. However, these new reaction rates result in completely opposite changes in most of the yields; moreover, the updated 26gAl(p, γ)27Si reaction rate has no effect on any of the stellar yields except on the yield of 28 Si obtained by the Z = 0.02 model. Thus, by using all three new reaction rates simultaneously in the nucleosynthesis network, we only see major changes for a few isotopes, e.g. significant destruction of 20Ne and considerable production of 23 Na, 24Mg and 28Si. There is no noticeable effect on any of the remaining AGB yields. </p> <p> Part II of this project discusses the significance of studying the nuclear structure of 26Si and 30S, which are not yet well understood. We discuss classical novae and their nucleosynthesis. We pay attention to some reactions, whose rates are still uncertain, e.g. the 25 Al(p, γ)26 Si, and 29 P(p, γ)30S reactions. To lower the uncertainty range in such reaction rates, the structure of 26Si and 30S should be better understood. </p> <p> We have carried out an experiment at Wright Nuclear Structure Laboratory (WNSL) at Yale University to be able to determine whether or not further studies of the structure of 26Si and 308 can be pursued by the (12C,6He) reaction mechanism. We investigated the 20 NeC2C,6He)26 Si and 12C(24 Mg,6He)30 S reactions. The time for collecting the data for the whole experiment was only about five days. Taking into consideration the number of experiments that were done in five days, some of them resulted in low statistics. The 20 NeC2C,6He)26 Si experiment gave a null result. This is due to the fact that the target that was used was old, and the 20 Ne in that target has been diffused out. Thus, we could not determine whether the (12C,6He) reaction mechanism proves to be a good method to study the structure of 26 Si. As for the nuclear structure of 30 8, we could see the ground state and the first excited state. The time was not enough to collect enough data to be able to determine this structure; however, the (12C,6He) reaction mechanism for studying the structure of 30 S looks promising. </p> / Thesis / Master of Science (MSc)

In this project, we study an asymptotic expansion method for solving stochastic volatility European option pricing problems. We explain the backgrounds and details associated with the method. Specifically, we present in full detail the arguments behind the derivation of the pricing PDEs and detailed calculation in deriving asymptotic option pricing formulas using our own model specifications. Finally, we discuss potential difficulties and problems in the implementation of the methods.

In this dissertation, we study the behavior of microscopic organisms utilizing lateral and spiral bending waves to swim in a fluid. More specifically, spermatozoa encounter different fluid environments filled with mucus, cells, hormones, and other large proteins. These networks of proteins and cells are assumed to be stationary and of low volume fraction. They act as friction, possibly preventing or enhancing forward progression of the swimmers. The flow in the medium is described as a viscous fluid with a resistance term known as a Brinkman fluid. It depends on the Darcy permeability parameter affecting the swimming patterns of the flagella. To further understand these effects we study the asymptotic swimming speeds of an infinite-length swimmer propagating planar or spiral bending waves in a Brinkman fluid. We find that, up to the second order expansion, the swimming speeds are enhanced as the resistance increases. The work to maintain the planar bending and the torque exerted on the fluid are also examined. The Stokes limits of the swimming speeds, the work and the torque are recovered as resistance goes to zero. The analytical solutions are compared with numerical results of finite-length swimmers obtained from the method of Regularized Brinkmanlets (MRB). The study gives insight on the effects of the permeability, the length and the radius of the cylinder on the performance of the swimmers. In addition, we develop a grid-free numerical method to study the bend and twist of an elastic rod immersed in a Brinkman fluid. The rod is discretized using a Kirchhoff Rod (KR) model. The linear and angular velocity of the rod are derived using the MRB. The method is validated through a couple of benchmark examples including the dynamics of an elastic rod, and the planar bending of a flagellum in a Brinkman fluid. The studies show how the permeability and stiffness coefficients affect the waveforms, the energy, and the swimming speeds of the swimmers. Also, the beating pattern of the spermatozoa flagellum depends on the intracellular concentrations of calcium ([Ca2+]). An increase of [Ca2+] is linked to hyperactivated motility. This is characterized by highly asymmetrical beating, which allows spermatozoa to reach the oocyte (egg) or navigate along the female reproductive tract. Here, we couple the [Ca2+] to the bending model of a swimmer in a Brinkman fluid. This computational framework is used to understand how internal flagellar [Ca2+] and fluid resistance in a Brinkman fluid alter swimming trajectories and flagellar bending.

For discretization method, which provides an effective way to handle the problem, we focus on constructing a discretized version of continuous failure times. The major observation is that discrete failure times with finite values will attain their exact values although only ranks are given, as long as sample size is large enough. The score function can be asymptotically approximated by a sum of independent random variables. Consistency, asymptotic normality and efficiency of estimator can be obtained by using standard results for estimating equations, given some milder and more feasible conditions than those of martingale method. / In this thesis, some finite sample properties of marginal likelihood will be established. We prove under some regular conditions the score function of the marginal likelihood is a martingale, and prove the marginal likelihood satisfies some properties enjoyed by the standard likelihood method, although only use the relative ranks to make inference of the parameter instead of the full information. / In this thesis, the author studies some asymptotic properties of the marginal maximum likelihood estimate (marginal MLE) for general transformation models. The general transformation model is an important class of models for survival times and is nontrivially more general model than the linear transformation model (Gu, Sun and Zuo, 2005). By using marginal likelihood, we obtain estimator of regression parameter which does not depend on its baseline survival function, a property enjoyed by the Cox regression model. The major obstacle for the general transformation models is the resulting estimation function is complicated and usually has no closed analytic expression. Gu etc. (2005) proposed Markov chain Monte Carlo (MCMC) stochastic approximation algorithm to solve the marginal MLE. / Moreover, a discussion is given for the question of asymptotic properties for the proposed marginal MLE based on two different methods: martingale method and discretization method. For martingale method, emphasis is given to the role of martingale limit theory and results presented are primarily theoretical. / We also demonstrate some important transformation models do satisfy our conditions and thus show their consistency, asymptotic normality and efficiency for the first time. / Huang Bin. / "Dec 2005." / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6484. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 63-69). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Doctor of Philosophy (PhD) / We undertake an asymptotic study of a second Painlevé hierarchy based on the Jimbo-Miwa Lax pair in the limit as the independent variable approaches infinity. The hierarchy is defined by an infinite sequence of non-linear ordinary differential equations, indexed by order, with the classical second Painlevé equation as the first member. We investigate general and special asymptotic behaviours admitted by each equation in the hierarchy. We show that the general asymptotic behaviour is described by two related hyperelliptic functions, where the genus of the functions increases with each member of the hierarchy, and we prove that there exist special families of solutions which are represented by algebraic formal power series. For specific values of the constants which appear in the higher-order second Painlevé equations, exact solutions are also constructed. Particular attention is given to the fourth-order analogue of the classical second Painlevé equation. In this case, the general asymptotic behaviour is given to leading-order by two related genus-2 hyperelliptic functions. These functions are characterised by four complex parameters which depend on the independent variable through the perturbation terms of the leading-order equations, and we investigate how these parameters change with respect to this variable. We also show that the fourth-order equation admits two classes of algebraic formal power series and that there exist families of true solutions with these behaviours in specified sectors of the complex plane, as well as unique solutions in extended sectors. To complement our asymptotic study of higher-order Painlevé equations, we consider a new setting in which classical Painlevé equations arise. We study reaction-diffusion equations with quadratic and cubic source terms, with a spatio-temporal dependence included in those terms, and show that solutions of these equations are given by first and second Painlevé transcendents.

Film blowing is a highly complex industrial process used to manufacture thin plastic films for uses in a wide range of applications; for example, plastic bags. The mathematical modelling of this process involves the analysis of highly nonlinear differential equations describing the complex phenomena arising in the film blowing process, and requires a sophisticated mathematical approach. This dissertation applies an innovative combination of tools, namely analytic, numerical and heuristic mathematical techniques to the analysis of the film blowing process. The research undertaken examines, in particular, a two-point boundary value problem arising from the modelling of the radial profile of the polymer film. For even the simplest modelling of this process, namely the isothermal Newtonian model, the resulting differential equation is a highly nonlinear, second order one, with an extra degree of difficulty due to the presence of a small parameter multiplying the highest derivative. Thus, the problem falls into the category of a nonlinear singular perturbation problem. Analytic techniques are applied to the isothermal Newtonian blown film model to obtain a closed form explicit approximation to the film bubble radius. This is then used as a base approximation for an iterative numerical scheme to obtain an improved numerical solution of the problem. The process is extended to include temperature variations, varying viscosity (Power law model) and viscoelastic effects (Maxwell model). As before, closed form approximations are constructed for these models which are used to launch numerical schemes, whose solutions display good accuracy. The results compare well with results obtained by purely numerical solutions in the literature.

Mixed linear models are a time honored method of analyzing correlated data. However, there is still no method of calculating exact confidence intervals or p-values for an arbitrary parameter in any mixed linear model. Instead, researchers must use either specialized approximate and exact tests that have been developed for particular models or rely on likelihood based approximate tests and confidence intervals which may be unreliable in problems with small sample sizes. This thesis develops procedures to improve small sample likelihood based inference in these important models. The first manuscript develops I.M. Skovgaard's modified directed likelihood for mixed linear models and shows how it is a general, accurate, and easy to apply method of improving inference in mixed linear models. In the second manuscript, O.E. Barndorff-Nielsen's approximate modified profile likelihood is applied to mixed linear models. This modified profile likelihood is a sensible generalization of the commonly used residual likelihood and can be applied if either a fixed or a covariance parameter is of interest. The final manuscript discusses how the design of a mixed linear model effects the accuracy of Skovgaard's modified likelihood and suggests a useful decomposition of that statistic. / Graduation date: 1998

No description available.

No description available.