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NUMERICAL SOLUTION OF SADDLE POINT PROBLEMS BY PROJECTION
(2017-12-04)
In this thesis, we work on iterative solutions of large linear systems of saddle
point problems of the form
A B1
T
B2 0
x
y
=
f
0
,
where A ∈ R
n×n
, B1, B2 ...
WEIGHTED UPWINDING COMPACT SCHEME FOR SHOCK CAPTURING
(2017-05-03)
The Weighted Upwinding Compact Scheme in this dissertation has been constructed due to dissipation and dispersion analysis at each stencil. The new scheme is applied to many one-dimensional typical problems involving ...
NONPARAMETRIC ADAPTIVE DISTRIBUTION-FREE PROCEDURE FOR CROSSOVER DESIGN WITH REPEATED MEASURES
(2017-05-11)
We propose to apply adaptive nonparametric procedures (Hill, Padmanabhan, & Puri, 1988) on 2x2 crossover design with repeated measures. We will derive the test-statistics (based on function of ranks) and find their ...
STATISTICAL ESTIMATION IN MULTIVARIATE NORMAL DISTRIBUTION WITH A BLOCK OF MISSING OBSERVATIONS
(2017-10-16)
Missing observations occur quite often in data analysis. We study a random sample from a multivariate normal distribution with a block of missing observations, here the observations missing is not at random. We use maximum ...
EVOKED AND SPONTANEOUS NEUROTRANSMITTER RELEASES FOR INDEPENDENT SYNAPTIC CURRENTS: MATHEMATICAL MODELING AND ANALYSIS
(2017-08-01)
Synapses play a major role in neuron communications in the brain. The synapses act through a chemical process called synaptic fusion between pre-synaptic and post-synaptic terminals. Presynaptic terminals release ...
A STUDY ON THE NONLOCAL SHALLOW-WATER MODEL ARISING FROM THE FULL WATER WAVES WITH THE CORIOLIS EFFECT
(2017-08-28)
The Equatorial Undercurrent is a significant feature of the geophysical waves near the equator, which is one of the key factors to explain El Niño phenomenon. However, based on β-plane approximation, the classical theory ...
HIGH ORDER DNS FOR VORTEX STRUCTURE IN LATE FLOW TRANSITION
(2017-08-02)
Turbulence is still a world puzzle after over one hundred years research, and the current and classical theories brim with self-contradictions. C. Liu proposed a new theory on turbulence generation and structure after 28 ...
STABILITY STUDY ON SHEAR FLOW AND VORTICES IN LATE BOUNDARY LAYER TRANSITION
(2017-08-09)
Turbulence is still an unsolved scientific problem, it has been regarded as “the most important unsolved problem of classical physics”. Dr. Liu proposed a new mechanism about turbulence generation and sustenance after ...
A study on traveling wave solutions in the shallow-water-type system
(2017-08-08)
The study of water waves reveals the physical principles of many phenomena of scientific and engineering interest. In this dissertation I consider three models: two-component Camassa-Holm system(2CH), generalized two-component ...
Image Reconstruction from Incomplete Radon Data and Generalized Principal Component Analysis
(2017-08-11)
Image reconstruction in various types of tomography requires inversion of the Radon transform and its generalizations. While there are many stable and robust algorithms for such inversions from reasonably well sampled data, ...