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Articles 1 - 12 of 12
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A Mathematical Study Of Malaria Models Of Ross And Ngwa, William Plemmons
A Mathematical Study Of Malaria Models Of Ross And Ngwa, William Plemmons
Electronic Theses and Dissertations
Malaria is a vector borne disease that has been plaguing mankind since before recorded history. The disease is carried by three subspecies of mosquitoes Anopheles gambiae, Anopheles arabiensis and Anopheles funestu. These mosquitoes carry one of four type of Plasmodium specifically: P. falciparum, P. vivax, P. malariae or P. ovale. The disease is a killer; the World Health Organization (WHO) estimates that about 40% of the world's total populations live in areas where malaria is an endemic disease and as global warming occurs, endemic malaria will spread to more areas. The malaria parasite kills a child every 30 seconds. In …
On Modeling Hiv Infection Of Cd4+ T Cells, Amy Comerford
On Modeling Hiv Infection Of Cd4+ T Cells, Amy Comerford
Electronic Theses and Dissertations
We examine an early model for the interaction of HIV with CD4+ T cells in vivo and define possible parameters and effects of said parameters on the model. We then examine a newer, more simplified model for the interaction of HIV with CD4+ T cells that also considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. The stability of both the disease free steady state and the endemically infected steady state are examined utilizing standard methods and the Routh-Hurwitz criteria. We show that if N, the number of infectious virions produced per …
Frames In Hilbert C*-Modules, Wu Jing
Frames In Hilbert C*-Modules, Wu Jing
Electronic Theses and Dissertations
Since the discovery in the early 1950's, frames have emerged as an important tool in signal processing, image processing, data compression and sampling theory etc. Today, powerful tools from operator theory and Banach space theory are being introduced to the study of frames producing deep results in frame theory. In recent years, many mathematicians generalized the frame theory from Hilbert spaces to Hilbert C*-modules and got significant results which enrich the theory of frames. Also there is growing evidence that Hilbert C*-modules theory and the theory of wavelets and frames are tightly related to each other in many aspects. Both …
Mathematical Modeling Of Smallpox Withoptimal Intervention Policy, Niwas Lawot
Mathematical Modeling Of Smallpox Withoptimal Intervention Policy, Niwas Lawot
Electronic Theses and Dissertations
In this work, two differential equation models for smallpox are numerically solved to find the optimal intervention policy. In each model we look for the range of values of the parameters that give rise to the worst case scenarios. Since the scale of an epidemic is determined by the number of people infected, and eventually dead, as a result of infection, we attempt to quantify the scale of the epidemic and recommend the optimum intervention policy. In the first case study, we mimic a densely populated city with comparatively big tourist population, and heavily used mass transportation system. A mathematical …
Modeling Inter-Plant Interactions, Jessica Larson
Modeling Inter-Plant Interactions, Jessica Larson
Electronic Theses and Dissertations
The purpose of this paper is to examine the interactions between two plant species endemic to Florida and develop a model for the growth of one of the plant species. An equation for the growth of Hypericum cumulicola is developed through analyzing how the distance to and the height of the nearest Ceratiola ericoides (Florida rosemary) affects the growth of Hypericum cumulicola. The hypericums were separated into five separate regions according to the distance to the nearest rosemary plant. The parameters for a basic growth equation were obtained in each of the five regions and compared to each other along …
Application Of The Empirical Likelihood Method In Proportional Hazards Model, Bin He
Application Of The Empirical Likelihood Method In Proportional Hazards Model, Bin He
Electronic Theses and Dissertations
In survival analysis, proportional hazards model is the most commonly used and the Cox model is the most popular. These models are developed to facilitate statistical analysis frequently encountered in medical research or reliability studies. In analyzing real data sets, checking the validity of the model assumptions is a key component. However, the presence of complicated types of censoring such as double censoring and partly interval-censoring in survival data makes model assessment difficult, and the existing tests for goodness-of-fit do not have direct extension to these complicated types of censored data. In this work, we use empirical likelihood (Owen, 1988) …
A Comparative Study Of Ant Colony Optimization, Matthew Becker
A Comparative Study Of Ant Colony Optimization, Matthew Becker
Electronic Theses and Dissertations
Ant Colony Optimization (ACO) belongs to a class of biologically-motivated approaches to computing that includes such metaheuristics as artificial neural networks, evolutionary algorithms, and artificial immune systems, among others. Emulating to varying degrees the particular biological phenomena from which their inspiration is drawn, these alternative computational systems have succeeded in finding solutions to complex problems that had heretofore eluded more traditional techniques. Often, the resulting algorithm bears little resemblance to its biological progenitor, evolving instead into a mathematical abstraction of a singularly useful quality of the phenomenon. In such cases, these abstract computational models may be termed biological metaphors. Mindful …
On The Use Of Gaussian Filter Functions For Adaptive Optics, Merfit Assad
On The Use Of Gaussian Filter Functions For Adaptive Optics, Merfit Assad
Electronic Theses and Dissertations
For adaptive optic systems, the use of aperture filter functions calculated using various Zernike modes can be useful in removing lower-order aberrations caused by atmospheric turbulence. Traditionally, these filter functions are calculated using the step function depicting a hard aperture that introduces integrals that are sometimes difficult to integrate and must be done numerically. The Gaussian method can be used in place of the conventional method for calculating the aperture filter functions. Evaluation of the Gaussian approximation for modeling a finite receiver aperture can be made by comparison of reduction in phase variance with results achieved using the conventional method. …
Epidemiological Models For Mutating Pathogens With Temporary Immunity, Neeta Singh
Epidemiological Models For Mutating Pathogens With Temporary Immunity, Neeta Singh
Electronic Theses and Dissertations
Significant progress has been made in understanding different scenarios for disease transmissions and behavior of epidemics in recent years. A considerable amount of work has been done in modeling the dynamics of diseases by systems of ordinary differential equations. But there are very few mathematical models that deal with the genetic mutations of a pathogen. In-fact, not much has been done to model the dynamics of mutations of pathogen explaining its effort to escape the host's immune defense system after it has infected the host. In this dissertation we develop an SIR model with variable infection age for the transmission …
Effects Of Atmospheric Turbulence On The Propagation Of Flattened Gaussian Optical Beams, Doris Cowan
Effects Of Atmospheric Turbulence On The Propagation Of Flattened Gaussian Optical Beams, Doris Cowan
Electronic Theses and Dissertations
In an attempt to mitigate the effects of the atmosphere on the coherence of an optical (laser) beam, interest has recently been shown in changing the beam shape to determine if a different power distribution at the transmitter will reduce the effects of the random fluctuations in the refractive index. Here, a model is developed for the field of a flattened Gaussian beam as it propagates through atmospheric turbulence, and the resulting effects upon the scintillation of the beam and upon beam wander are determined. A comparison of these results is made with the like effects on a standard TEM00 …
Fade Statistics For A Lasercom System And The Joint Pdf Of A Gamma-Gamma Distributed Irradiance And Its Time Derivative, Frida Stromqvist Vetelino
Fade Statistics For A Lasercom System And The Joint Pdf Of A Gamma-Gamma Distributed Irradiance And Its Time Derivative, Frida Stromqvist Vetelino
Electronic Theses and Dissertations
The performance of lasercom systems operating in the atmosphere is reduced by optical turbulence, which causes irradiance fluctuations in the received signal. The result is a randomly fading signal. Fade statistics for lasercom systems are determined from the probability density function (PDF) of the irradiance fluctuations. The expected number of fades per second and their mean fade time require the joint PDF of the fluctuating irradiance and its time derivative. Theoretical integral expressions, as well as closed form, analytical approximations, were developed for the joint PDF of a gamma-gamma distributed irradiance and its time derivative, and the corresponding expression for …
On Prime Generation Through Primitive Divisors Of Recurrence Sequences, Richard Russell
On Prime Generation Through Primitive Divisors Of Recurrence Sequences, Richard Russell
Electronic Theses and Dissertations
We examine results concerning the generation of primes in certain types of integer sequences. The sequences discussed all have a connection in that each satisfies a recurrence relation. Mathematicians have speculated over many centuries that these sequences contain an infinite number of prime terms, however no proof has been given as such. We examine a less direct method of showing an infinitude of primes in each sequence by showing that the sequences contain an infinite number of terms with primitive divisors.