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Study of Stochastic Differential Equation Driven by Time-Changed Levy Noise
(2020-03-24)
This dissertation is composed of two parts. The first part studies stabilities of the solution
of stochastic differential equation (SDE) driven by time-changed L´evy noise in probability,
moment, and path sense. This ...
Differential geometry on matrix groups
(2020-03-20)
In this dissertation, we study the differential geometry of the matrix groups. In literatures, many authors proposed to compute matrix means using the geodesic distance defined by an invariant Riemannian metrics on the ...
The Intersection Problem for Maximum Packings of the Complete Graph with 4-Cycles
(2020-05-11)
A maximum packing of K_n with 4-cycles may leave some edges of the graph unpacked. The size of the leave is determined by the congruence class of n modulo 8. When n ≡ 1 (mod 8) the packing coincides with a 4-cycle system ...
Products of positive definite symplectic matrices
(2020-07-15)
We show that every symplectic matrix is a product of five positive definite symplectic
matrices and five is the best in the sense that there are symplectic matrices which are not product
of less.
Estimation of Semi-parametric Functional-coefficient Panel Data Models with Fixed Effects
(2020-07-20)
We consider the problem of estimating a semiparametric varying coefficient panel data model where the unobserved individual effects are correlated with explanatory variables in an unknown arbitrary way using a local linear ...
Hopfield Neural Lattice Models
(2020-07-22)
Hopfield neural network model is a continuous deterministic model proposed by John J.
Hopfield in the early 1980’s. The model was proposed in an attempt to produced an artificial
neural network architecture that mimic ...
Semiparametric Estimation for Integral Projection Models
(2020-07-21)
Understanding the connection between variation in climate and population dynamics of plants and animals is important for predicting the impacts of future climate change. A popular approach for studying population dynamics ...
On Planar Embeddings of the Knaster V Lambda-Continuum
(2020-07-21)
A\v nusi\'c, Bruin, and \v Cin\v c have asked in \cite{Anusic2} which hereditarily decomposable chainable continua (HDCC) have uncountably many mutually inequivalent planar embeddings. It was noted, as per the embedding ...
Hardy space associated with flag-type singular integrals of three parameters
(2020-07-21)
The main purpose of this thesis is to establish a Hardy space theory associated with the flag-type singular integrals on Euclidean space. This theory is a continuation of those the classical one parameter, product setting ...
Dynamics of Chemotherapy Models with Variable Infusion and Time Delays
(2020-07-23)
Chemotherapy is a fundamental and commonly used form of cancer treatment, usually done with the application of a chemotherapy agent to the infected individual. The chemotherapy agent targets fast-growing cells including ...