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- 5Frei, Christoph (Mathematical and Statistical Sciences)
- 5Mizera, Ivan (Mathematical and Statistical Sciences)
- 4Kong, Linglong (Mathematical and Statistical Sciences)
- 4Lau, Anthony To-Ming (Mathematical and Statistical Sciences)
- 4Lele, Subhash (Mathematical and Statistical Sciences)
- 4Lewis, Mark (Mathematical and Statistical Sciences)
In this thesis we study operator ideals on ordered Banach spaces such as Banach lattices, $C^*$-algebras, and noncommutative function spaces. The first part of this work is concerned with the domination problem: the relationship between order and algebraic ideals of operators. Fremlin, Dodds...
We introduce two kinds of particle filters, one is weighted particle filter and the other is resampling particle filter. We prove the Strong Law of Large Numbers and Central Limit Theorem for both particle filters. Then, we show that the resampling particle filter is better than the weighted one.
One main goal of this thesis is to bring forth a systematic and simple construction of a multiwavelet basis on a bounded interval. The construction that we present possesses orthogonality in the derivatives of the multiwavelet basis among all scale levels. Since we are mainly interested in Riesz...
A graph-theoretic approach to the construction of Lyapunov functions for coupled systems on networksDownload
For coupled systems of differential equations on networks, a graph-theoretic approach to the construction of Lyapunov functions is systematically developed in this thesis. Kirchhoff’s Matrix-Tree Theorem in graph theory plays an essential role in the approach’s development. The approach is...
This thesis is concerned with the analysis of the control design to the nonlinear networked control systems (NCSs). Ignoring the network connection and cascading actuators, the plant and sensors together, a sampled-data system is obtained. The stabilization problem of nonlinear sampled-data...
Exponential Random Graph Models (ERGMs) have been developed for fitting social network data on both static and dynamic levels. However, the lack of large sample asymptotic properties makes it inadequate in assessing the goodness-of-fit of these ERGMs. Simulation-based goodness-of-fit plots were...
After the scientific problem of interest is defined, collecting data is the first stage of any statistical analyses. The question of how large the sample should be is thus of great interest. In this thesis we demonstrate that in a geostatistical experiment determining the minimum sample size to...
Given a conformal superalgebra A over an algebraically closed field k of characteristic zero, a twisted loop conformal superalgebra L based on A has a differential conformal superalgebra structure over the differential Laurent polynomial ring D. In this context, L is a D_m/D–form of A \otimes D...
Abstract harmonic analysis is well established on compact Hausdorff admissible right topological (CHART) groups. Specifically these groups are one-sided analogues of topological groups, where the elements that multiply continuously on the other side are dense in the group. The analytic theory of...
Formation of singularities in physical phenomena has always fascinated scientists and stimulated both development of mathematical theories accounting for observations and further experimental scrutiny of the governing physics with the goal to resolve the singular behavior. The underlying theme of...