## Search

Now showing items 11-20 of 90

#### Short-time asymptotics of heat kernels of hypoelliptic Laplacians on Lie groups

(2011-10-11)

This thesis suggests an approach to compute the short-time behaviour of the hypoelliptic heat kernel corresponding to sub-Riemannian structures on unimodular Lie groups of type I, without previously holding a closed form ...

#### Bifurcations of Periodic Solutions of Functional Differential Equations with Spatio-Temporal Symmetries

(2012-04-30)

We study bifurcations of periodic solutions with spatio-temporal symmetries of functional differential equations (FDEs). The two main results are: (1) a centre manifold reduction around a periodic solution of FDEs with ...

#### Generalization of Ruderman's Problem to Imaginary Quadratic Fields

(2012-04-13)

In 1974, H. Ruderman posed the following question: If $(2^m-2^n)|(3^m-3^n)$, then does it follow that $(2^m-2^n)|(x^m-x^n)$ for every integer $x$? This problem is still open. However, in 2011, M. R. Murty and V. K. Murty ...

#### Variations of Li's criterion for an extension of the Selberg class

(2012-08-09)

In 1997, Xian-Jin Li gave an equivalence to the classical Riemann hypothesis,
now referred to as Li's criterion, in terms of the non-negativity of a particular
infinite sequence of real numbers. We formulate the analogue ...

#### On the Reduced Operator Algebras of Free Quantum Groups

(2012-08-03)

In this thesis, we study the operator algebraic structure of various classes of unimodular free quantum groups, including thefree orthogonal quantum groups $O_n^+$, free unitary quantum groups $U_n^+$, and trace-preserving ...

#### Joint Modelling of Longitudinal Quality of Life Measurements and Survival Data in Cancer Clinical Trials

(2013-01-23)

In cancer clinical trials, longitudinal Quality of Life (QoL)
measurements on a patient may be analyzed by classical linear
mixed models but some patients may drop out of study due to
recurrence or death, which causes ...

#### Statistical Methods for Testing Treatment-Covariate Interactions in Cancer Clinical Trials

(2011-09-27)

Treatment–covariate interaction is often used in clinical trials to assess the homogeneity of treatment effects over these subgroups defined by a baseline covariate, which is frequently conducted after primary analysis ...

#### Measuring Dependence via Mutual Information

(2011-10-03)

Considerable research has been done on measuring dependence between random variables. The correlation coefficient is the most widely studied linear measure of dependence. However, the limitation of linearity limits its ...

#### Inclusive Fitness on Evolutionary Graphs

(2012-10-04)

The evolution of cooperative behaviours has received a large amount of attention in the literature. A recurrent result is that a spatial population structure often aids the evolution of cooperation. One such possible ...

#### Management and Sensing of Spectrum in Cognitive Radio

(2013-06-04)

Under the contemporary spectrum usage regulations, radio frequency bands are allocated statically to licensed users in a large geographical area and over a long period of time. Recent investigations have revealed that such ...