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Inverse source problem and inverse diffusion coefficient problem for parabolic equations with applications in geology
(2017-07-26)
This dissertation deals with inverse problems for parabolic partial differential equations with an integral constraint and their applications in geology. We employ analytical and numerical methods to analyze and approximate ...
On the Independence Number of Some Hypergraph
(2018-07-10)
For integers 1 =< m < n and a prime p (we require 2 =< m when p = 2), a subset
I(p^n; p^m) ={0,...,p^n-1} is described which contains no pm-term cyclic arithmetic progression
modulo p^n, and which is maximal among subsets ...
Existence of TP(d,k,n)
(2019-04-24)
Given a square grid of land, which has n rows and n columns. It is required to plant trees on the land so that there are k trees in every row and column and there is at most 1 tree in any small square part of the land with ...
Generalized LASSO Problem with Equality and Inequality Constraints Using ADMM
(2019-12-05)
With the development of technology, the volume of the data has gradually become much larger and attracting much more attention in data science. Statisticians nowadays need to consider the case when the dataset is extremely ...
Advanced Statistical Learning Approaches to Healthcare
(2019-06-03)
In this dissertation, we propose a novel statistical modeling methodology that effectively analyzes and extracts information from large datasets. Two real datasets were employed to validate the proposed methodology: breast ...
A Distribution-Free Control Chart for Retrospective Location Analysis of Subgrouped Multivariate Data
(2011-09-08)
In multivariate quality control, a proper Phase I analysis is essential to the success of Phase II monitoring. Even self-starting methods, which seek to minimize the Phase I process, usually recommend a single retrospective ...
On The Lattice Boltzmann Method: Implementation and Applications
(2008-09-09)
We studied the development and different types of the Lattice Boltzmann method. We gave several implementations. Then we presented two moving boundary treatments for the Lattice Boltzmann method, the second one is new. We ...
Defining Chaos
(2017-07-18)
This thesis is a study of the paper “Defining Chaos” by Brian Hunt and Edward Ott [1] with added details to make arguments easier to follow. They introduced a new entropy based definition of chaos called expansion entropy. ...
Edge-Regular Graphs with Lambda=2
(2019-07-23)
A graph G is edge-regular with parameters n, d, and λ if V(G)=n, the degree of every vertex of G is d, and for any pair of adjacent vertices u and v, N_G(u)∩N_G(v)=λ. We say such graphs are in ER(n,d,λ). In this dissertation ...
Analysis of stochastic vector-host epidemic models
(2017-07-25)
In this dissertation, deterministic and stochastic mathematical models are proposed to study vector-host epidemic models with direct transmission. The total population of the host and the vector is divided into different ...