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ON SOME PROBLEMS IN SPARSE HYBRID IMAGING, NON-STANDARD FINITE DIFFERENCE METHODS, AND FOKKER-PLANCK FRAMEWORKS IN ESOPHAGEAL CANCER
(2022-08-16)
In this thesis, we first discuss nonlinear optimization frameworks for the sparsity-
based on nonlinear reconstruction of parameters in hybrid imaging modalities such as
current density impedance imaging (CDII) and two-photon ...
Decomposition of Modules and Tensor Products over Principal Subalgebras of Truncated Polynomial Rings
(2022-08-15)
The topic of my dissertation is to investigate the behavior of modules and tensor products over a truncated polynomial ring with prime characteristic. This investigation utilizes principal subalgebras of the truncated ...
Exponential Tensor Modules
(2022-06-02)
Representation theory of Lie algebra of a finite dimensional reductive Lie algebra g is a long-standing problem. The ultimate goal is to classify all representations of g. However. the only case only case when a complete ...
HIGHER-ORDER NONSTANDARD FINITE DIFFERENCE METHODS FOR AUTONOMOUS DIFFERENTIAL EQUATIONS WITH APPLICATIONS IN MATHEMATICAL ECOLOGY
(2022-08-08)
Nonstandard finite difference (NSFD) methods have been widely used to numerically solve various problems in biology. In recent years, NSFD methods have been proposed that preserve essential properties of the solutions of ...
Twisting Systems and some Quantum P³s with Point Scheme a Rank-2 Quadric
(2022-05-18)
In 1996, J. J. Zhang introduced the concept of twisting a graded algebra by a twisting system, which generalizes the concept of twisting a graded algebra by an automorphism (the latter concept having been introduced in an ...
Abrading the enigma of the wound healing process: Modeling the inflammation, proliferation, and maturation stage
(2022-08-17)
Wound healing encompasses a group of processes categorized into overlapping stages known as the inflammation, proliferation, and maturation/remodeling stage. The dynamics of these processes are important in studying outcomes ...
Quantized Enveloping Superalgebra of Type P
(2022-05-09)
We introduce a new quantized enveloping superalgebra $\mathfrak{U}_q\mathfrak{p}_n$ attached to the Lie superalgebra $\mathfrak{p}_n$ of type P. The superalgebra $\mathfrak{U}_q\mathfrak{p}_n$ is a quantization of a Lie ...
ACADEMIC INTEGRATION AND SELF-REGULATION STRATEGIES IN PRECALCULUS AND CALCULUS I
(2022-08-15)
This case study examines the self-regulation strategies and academic integration of first-semester undergraduate students enrolled in precalculus and first-semester calculus at a large urban university in the southwestern ...
Performance of Density Estimators in Additive Measurement Error Models Based on Right Censored Data
(2022-05-09)
In the deconvolution problem for right censored data, one is interested in estimating the density of a contaminated variable X when X satisfies Z= X+ E, where E is a measurement error with a known distribution, and the ...
A Necessary and Sufficient Condition for the Asymptotic Normality of the Quantile Estimator in the Deconvolution Problem
(2022-05-16)
In this study, we examine the estimation of a quantile function when we have n observations coming from the convolution model contaminated by additive measurement errors. Under certain assumptions, a kernel type deconvolution ...