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Integral graded homology of Reeb chord complex of Legendrian knots in R^3
(2014-07)
The main work of this thesis concerns the classification of Legendrian knots up to Legendrian isotopy in R^3 with standard contact structure. In the thesis, we construct a topological invariant of Legendrian knots: the ...
On the existence and smoothness problem of the magnetohydrodynamics system
(2014-05)
Fluid mechanics plays a pivotal role in engineering application to daily lives. The prominently famous fluid dynamics partial differential equations (PDE) due to its remarkable utility is the Navier-Stokes equations of ...
Study on the global well-posedness for the two-dimensional Boussinesq and Lans-alpha magnetohydrodynamics equations
(2014-07)
We investigate the global (in time) regularity problem for two different models; generalized two-dimensional Boussinesq and Lans-alpha magnetohydrodynamics system. First, the global regularity of 2D incompressible generalized ...
Exploration of mathematics graduate teaching assistants' teaching philosophies: A case study
(2014-08)
This multi-case study is an exploration of mathematics graduate teaching assistants' teaching philosophies. It focused on the cases of four purposefully selected beginning mathematics graduate teaching assistants (MGTAs) ...
Systolic freedom of 3-manifolds
(2014-05)
In this thesis, we study the Z2-coefficient homology (1, 2)-systolic freedom of 3-manifolds. In 1994, Bearard-Bergery and Katz proved the Z-coefficient homology (1, 2)-systolic freedom of S2 x S1. More generally, compact ...