In this thesis, we study some problems on the Navier-Stokes equations and Boltzmann- Enskog equation which are in the active research area of applied mathematics. The system of Navier-Stokes equations is a typical example of the conservation laws. In the first part of the thesis, we study the global existence and convergence rates of solutions to the three-dimensional compressible Navier-Stokes equations without heat conductivity.
Math Projects
Mathematics (Maths) is the study of quantity, structure, space, and change. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity. This section is dedicated to mathematics project ideas, math projects, sample report, mathematics projects topic, maths project list, math research projects, mathematics project titles.
Baseline Adjustment for Ordinal Covariates by Inducing a Partial Ordering in Randomized Clinical Trials
In two-armed randomized clinical trials (RCTs) designed to compare a new treatment with a control, a key endpoint is often measured and analyzed both at baseline and after treatment for two groups. More powerful and precise statistical inferences are possible once the between-group comparisons have been adjusted for covariates.
On Stratified Algebras and Lie Superalgebras
This thesis, consisting of three papers and a summary, studies properties of stratified algebras and representations of Lie super algebras.In Paper I we give a characterization when the Ringel dual of an SSS-algebra is properly stratified.We show that for an SSS-algebra, whose Ringel dual is properly stratified, there is a (generalized) tilting module which allows one to compute the finitistic dimension of the SSS-algebra, and moreover, it gives rise to a new covariant Ringel-type duality.
Definitions of Chaos
Vapnik Chervonenkis dimension is a basic combinatorial notion with applications in machine learning, stability theory, and statistics. We explore what effect model theoretic structure has on the VC dimension of formulas, considered as parameterized families of sets, with respect to long disjunctions and conjunctions.
Global Shape Description of Digital Objects
New methods for global shape description of three-dimensional digital objects are presented. The shape of an object is first represented by a digital surface where the faces are either triangles or quadrilaterals. Information regarding the worldwide shape is going to be captured through the coefficients in the spherical harmonics expansions.
Computation of Parameters in some Mathematical Models
In computational science it is common to describe dynamic systems by mathematical models in forms of differential or integral equations. These models may contain parameters that have to be computed for the model to be complete. A formula, named the modified Kaufman algorithm, is proposed also it takes the separability into consideration.
Investigation into Solvable Quintics
This paper focuses on two families of quintics that pose different challenges for solving them. The 1st family is a popular group of quintics which are known as Emma Lehmer’s Quintics. These quintics are known to have the cyclic group of order 5 as their Galois group and one might hope that expressing the roots [...]
Stochastic Volatility with Levy Processes: Calibration and Pricing
In this thesis, stochastic volatility models with Levy processes are treated in parameter calibration by the Carr-Madan fast Fourier transform (FFT) method and pricing through the partial integro-differential equation (PIDE) approach. First, different models where the underlying log stock price or volatility driven by either a Brownian motion or a Levy… Contents 1 Introduction 1.1 [...]
Some problems on a class of fluid dynamical systems
In this MPhil thesis, we consider the solutions for a class of fluid dynamical systems, such as the isentropic Euler-Poisson, Navier-Stokes-Poisson, Navier-Stokes, Euler systems. As these systems share some similar mathematical structures, we would like to find the relationship between them, such as some blowup and stability phenomena… Contents 1 Introduction 2 Blowup Solutions I [...]
Factor Analysis of Cross-Classified Data
This thesis introduces a model hierarchy related to Principal Component Analysis and Factor Analysis, in which vector measurements are linearly decomposed into a relatively small set of hypothetical principal directions, for purposes of dimension reduction. The mathematical specification of unknown parameters in the models is unified… Contents 1 Introduction 1.1 Principal Component Analysis 1.2 Factor [...]