Current Search: Shuai, Zhisheng (x)
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 Title
 MATHEMATICAL MODELS OF MOSQUITO POPULATIONS.
 Creator

Reed, Hanna, Shuai, Zhisheng, University of Central Florida
 Abstract / Description

The intent of this thesis is to develop ordinary differential equation models to better understand the mosquito population. We first develop a framework model, where we determine the condition under which a natural mosquito population can persist in the environment. Wolbachia is a bacterium which limits the replication of viruses inside the mosquito which it infects. As a result, infecting a mosquito population with Wolbachia can decrease the transmission of viral mosquitoborne diseases,...
Show moreThe intent of this thesis is to develop ordinary differential equation models to better understand the mosquito population. We first develop a framework model, where we determine the condition under which a natural mosquito population can persist in the environment. Wolbachia is a bacterium which limits the replication of viruses inside the mosquito which it infects. As a result, infecting a mosquito population with Wolbachia can decrease the transmission of viral mosquitoborne diseases, such as dengue. We develop another ODE model to investigate the invasion of Wolbachia in a mosquito population. In a biologically feasible situation, we determine three coexisting equilibria: a stable Wolbachiafree equilibrium, an unstable coexistence equilibrium, and a complete invasion equilibrium. We establish the conditions under which a population of Wolbachia infected mosquitoes may persist in the environment via the next generation number and determine when a natural mosquito population may experience a complete invasion of Wolbachia.
Show less  Date Issued
 2018
 Identifier
 CFH2000299, ucf:45845
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFH2000299
 Title
 RIGOROUS ANALYSIS OF AN EDGEBASED NETWORK DISEASE MODEL.
 Creator

Mai, Sabrina, Shuai, Zhisheng, University of Central Florida
 Abstract / Description

Edgebased network disease models, in comparison to classic compartmental epidemiological models, better capture social factors affecting disease spread such as contact duration and social heterogeneity. We reason that there should exist infinitely many equilibria rather than only an endemic equilibrium and a diseasefree equilibrium for the edgebased network disease model commonly used in the literature, as there do not exist any changes in demographic in the model. We modify the commonly...
Show moreEdgebased network disease models, in comparison to classic compartmental epidemiological models, better capture social factors affecting disease spread such as contact duration and social heterogeneity. We reason that there should exist infinitely many equilibria rather than only an endemic equilibrium and a diseasefree equilibrium for the edgebased network disease model commonly used in the literature, as there do not exist any changes in demographic in the model. We modify the commonly used network model by relaxing some assumed conditions and factor in a dependency on initial conditions. We find that this modification still accounts for realistic dynamics of disease spread (such as the probability of contracting a disease based off your neighbors' susceptibility to the disease) based on the basic reproduction number. Specifically, if the basic reproduction number is below 1, then the infection dies out; while if the basic reproduction number is above 1, then there is possibility of an epidemic.
Show less  Date Issued
 2019
 Identifier
 CFH2000537, ucf:45651
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFH2000537
 Title
 REINFORCEMENT LEARNING FOR OPTIMAL CONTROL OF NETWORK EPIDEMIC PROCESSES.
 Creator

Kerrigan, Alec H, Enyioha, Chinwendu, Shuai, Zhisheng, University of Central Florida
 Abstract / Description

Our society is increasingly interconnected, making it easy for cascades/epidemic (diseases, disinformation etc). Current epidemic control efforts are based on approximate network epidemic models, which often ignore the unique complexity and rich information embedded in the complex interconnections of realworld networks/populations.Deep reinforcement learning (RL) is a powerful tool at learning policies for these nonlinear, complex processes in highdimension. To control an epidemic outbreak...
Show moreOur society is increasingly interconnected, making it easy for cascades/epidemic (diseases, disinformation etc). Current epidemic control efforts are based on approximate network epidemic models, which often ignore the unique complexity and rich information embedded in the complex interconnections of realworld networks/populations.Deep reinforcement learning (RL) is a powerful tool at learning policies for these nonlinear, complex processes in highdimension. To control an epidemic outbreak on a SusceptibleInfectedSusceptible network epidemic model, we design a RL framework with a custom reward structure using the node2vec embedding technique. Results indicate deep RL is able to determine and converge on an optimal intervention policy in a relatively short time.
Show less  Date Issued
 2019
 Identifier
 CFH2000580, ucf:45643
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFH2000580
 Title
 Variational inclusions with general overrelaxed proximal point and variationallike inequalities with densely pseudomonotonicity.
 Creator

Nguyen, George, Mohapatra, Ram, Han, Deguang, Shuai, Zhisheng, Xu, Mengyu, University of Central Florida
 Abstract / Description

This dissertation focuses on the existence and uniqueness of the solutions of variational inclusion and variational inequality problems and then attempts to develop efficient algorithms to estimate numerical solutions for the problems. The dissertation consists a total of five chapters. Chapter 1 is an introduction to variational inequality problems, variational inclusion problems, monotone operators, and some basic definitions and preliminaries from convex analysis. Chapter 2 is a studyof a...
Show moreThis dissertation focuses on the existence and uniqueness of the solutions of variational inclusion and variational inequality problems and then attempts to develop efficient algorithms to estimate numerical solutions for the problems. The dissertation consists a total of five chapters. Chapter 1 is an introduction to variational inequality problems, variational inclusion problems, monotone operators, and some basic definitions and preliminaries from convex analysis. Chapter 2 is a studyof a general class of nonlinear implicit inclusion problems. The objective of this study is to explore how to omit the Lipschitz continuity condition by using an alternating approach to the proximal point algorithm to estimate the numerical solution of the implicit inclusion problems. In chapter 3 we introduce generalized densely relaxed ? ? ? pseudomonotone operators and generalized relaxed ? ? ? proper quasimonotone operators as well as relaxed ? ? ? quasimonotone operators. Using these generalized monotonicity notions, we establish the existence results for the generalized variationallike inequality in the general setting of Banach spaces. In chapter 4, we use the auxiliary principle technique to introduce a general algorithm for solutions of the densely relaxed pseudomonotone variationallike inequalities. Chapter 5 is the chapter concluding remarks and scope for future work.
Show less  Date Issued
 2019
 Identifier
 CFE0007693, ucf:52410
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0007693
 Title
 Modeling Disease Impact of VibrioPhage Interactions.
 Creator

Botelho, Christopher, Shuai, Zhisheng, Nevai, A, Zhang, Teng, Teter, Kenneth, University of Central Florida
 Abstract / Description

Since the work of John Snow, scientists and medical professionals have understood that individuals develop cholera by means of consuming contaminated water. Despite the knowledge(&)nbsp;of cholera's route of infection, many countries have experienced and still experience endemic cholera. Cholera is caused by the Vibrio cholerae (V. cholerae) bacterium and presents with acute diarrhea and vomiting. If untreated, infected individuals may die due to dehydration. Cholera is a disease that most...
Show moreSince the work of John Snow, scientists and medical professionals have understood that individuals develop cholera by means of consuming contaminated water. Despite the knowledge(&)nbsp;of cholera's route of infection, many countries have experienced and still experience endemic cholera. Cholera is caused by the Vibrio cholerae (V. cholerae) bacterium and presents with acute diarrhea and vomiting. If untreated, infected individuals may die due to dehydration. Cholera is a disease that most commonly affects countries with poor infrastructure and water sanitation. Despite efforts to control cholera in such countries, the disease persists. One such example is Haiti which has been experiencing a cholera outbreak since 2010. While there has been much research in the field of microbiology to understand V. cholerae, there has been comparably less research in the field of mathematical biology to understand the dynamics of V. cholerae in the environment. A mathematical model of V. cholerae incorporating a phage population is coupled with a SIRS disease model to examine the impact of vibrio and phage interaction. It is shown that there might exist two endemic equilibria, besides the disease free equilibrium: one in which phage persist in the environment and one in which the phage fail to persist. Existence and stability of these equilibria are established. Disease control strategies based on vibrio and phage interactions are discussed.
Show less  Date Issued
 2019
 Identifier
 CFE0007604, ucf:52544
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0007604
 Title
 Analysis and Simulation for Homogeneous and Heterogeneous SIR Models.
 Creator

Wilda, Joseph, Shuai, Zhisheng, Brennan, Joseph, Nevai, A, University of Central Florida
 Abstract / Description

In mathematical epidemiology, disease transmission is commonly assumed to behave in accordance with the law of mass action; however, other disease incidence terms also exist in the literature. A homogeneous SusceptibleInfectiousRemoved (SIR) model with a generalized incidence term is presented along with analytic and numerical results concerning effects of the generalization on the global disease dynamics. The spatial heterogeneity of the metapopulation with nonrandom directed movement...
Show moreIn mathematical epidemiology, disease transmission is commonly assumed to behave in accordance with the law of mass action; however, other disease incidence terms also exist in the literature. A homogeneous SusceptibleInfectiousRemoved (SIR) model with a generalized incidence term is presented along with analytic and numerical results concerning effects of the generalization on the global disease dynamics. The spatial heterogeneity of the metapopulation with nonrandom directed movement between populations is incorporated into a heterogeneous SIR model with nonlinear incidence. The analysis of the combined effects of the spatial heterogeneity and nonlinear incidence on the disease dynamics of our model is presented along with supporting simulations. New global stability results are established for the heterogeneous model utilizing a graphtheoretic approach and Lyapunov functions. Numerical simulations confirm nonlinear incidence gives raise to rich dynamics such as synchronization and phaselock oscillations.
Show less  Date Issued
 2015
 Identifier
 CFE0005906, ucf:50872
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005906
 Title
 The Effect of Precipitation on the Spread of MosquitoBorne Diseases: A Case Study of Florida Counties.
 Creator

Osbourne, Marvin, Mohapatra, Ram, Shuai, Zhisheng, Kincaid, John, University of Central Florida
 Abstract / Description

The state of Florida is the third most populous state in the United States of America, with six (6) of its metropolitan areas dubbed as the fastest growing in the entire country. A mosquito bite may mean the transmission of a virus or disease which might be fatal. Hence, there is a need for the state to control mosquitoes through the various Departments of Mosquito Control in each of its sixtyseven (67) counties. Six locally acquired mosquitoborne viruses which affect humans and animals in...
Show moreThe state of Florida is the third most populous state in the United States of America, with six (6) of its metropolitan areas dubbed as the fastest growing in the entire country. A mosquito bite may mean the transmission of a virus or disease which might be fatal. Hence, there is a need for the state to control mosquitoes through the various Departments of Mosquito Control in each of its sixtyseven (67) counties. Six locally acquired mosquitoborne viruses which affect humans and animals in the state of Florida were considered. This thesis used statistical methods to examine data for rainfall, population estimate, as well as, the data on six (6) arboviruses, over the course of thirteen (13) years, namely 2002 to 2014. The first hypothesis that was tested, was that greater precipitation increased the likelihood of a greater number of arbovirus cases. It was important to also examine the relationship that this growing human population had with mosquitoborne diseases, and so the second hypothesis that was tested, was that, an increase in the human population would increase the likelihood of a greater number of arbovirus cases. Subsequently, an analysis was done for eleven (11) of Florida's 67 counties with the greatest cumulative occurrence of human and animal arbovirus cases combined. Of the eleven counties, seven exhibited a weak associated between the size of the human population and the spread of animal and human arbovirus cases; three exhibited a somewhat moderate association; and one () Osceola County () had a strong negative association. This indicated that, as the size of the human population increased in Osceola County, the combined number of human and animal arbovirus cases decreased, which refuted the second hypothesis of this thesis. A linear regression model for the data for Osceola County was derived and that model was used to simulate what will occur in future years with the use of population projection data. In each simulated year, the number of combined human and arbovirus cases was negative. This prediction meant that, as the projected population increased from year to year, then the number of cases should be zero in each year. The reliability of these predictions are questionable, since Osceola County does not exist in a vacuum and it cannot be isolated from the surrounding counties which may be experiencing an outbreak of arboviruses.
Show less  Date Issued
 2015
 Identifier
 CFE0005859, ucf:50926
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005859
 Title
 Modeling Network Worm Outbreaks.
 Creator

Foley, Evan, Shuai, Zhisheng, Kaup, David, Nevai, A, University of Central Florida
 Abstract / Description

Due to their convenience, computers have become a standard in society and therefore, need the utmost care. It is convenient and useful to model the behavior of digital virus outbreaks that occur, globally or locally. Compartmental models will be used to analyze the mannerisms and behaviors of computer malware. This paper will focus on a computer worm, a type of malware, spread within a business network. A mathematical model is proposed consisting of four compartments labeled as Susceptible,...
Show moreDue to their convenience, computers have become a standard in society and therefore, need the utmost care. It is convenient and useful to model the behavior of digital virus outbreaks that occur, globally or locally. Compartmental models will be used to analyze the mannerisms and behaviors of computer malware. This paper will focus on a computer worm, a type of malware, spread within a business network. A mathematical model is proposed consisting of four compartments labeled as Susceptible, Infectious, Treatment, and Antidotal. We shall show that allocating resources into treating infectious computers leads to a reduced peak of infections across the infection period, while pouring resources into treating susceptible computers decreases the total amount of infections throughout the infection period. This is assuming both methods are receiving resources without loss. This result reveals an interesting notion of balance between protecting computers and removing computers from infections, ultimately depending on the business executives' goals and/or preferences.
Show less  Date Issued
 2015
 Identifier
 CFE0005948, ucf:50816
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005948
 Title
 computational study of traveling wave solutions and global stability of predatorprey models.
 Creator

Zhu, Yi, Qi, Yuanwei, Rollins, David, Shuai, Zhisheng, Zhai, Lei, University of Central Florida
 Abstract / Description

In this thesis, we study two types of reactiondiffusion systems which have direct applications in understanding wide range of phenomena in chemical reaction, biological pattern formation and theoretical ecology.The first part of this thesis is on propagating traveling waves in a class of reactiondiffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two...
Show moreIn this thesis, we study two types of reactiondiffusion systems which have direct applications in understanding wide range of phenomena in chemical reaction, biological pattern formation and theoretical ecology.The first part of this thesis is on propagating traveling waves in a class of reactiondiffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two different cases will bestudied. The first is autocatalytic chemical reaction of order $m$ without decay. The second is chemical reaction of order $m$ with a decay of order $l$, where $m$ and $l$ are positive integers and $m(>)l\ge1$. A typical system is $A + 2B \rightarrow3B$ and $B\rightarrow C$ involving three chemical species, a reactant A and an autocatalyst B and C an inert chemical species.We use numerical computation to give more accurate estimates on minimum speed of traveling waves for autocatalytic reaction without decay, providing useful insight in the study of stability of traveling waves. For autocatalytic reaction of order $m = 2$ with linear decay $l = 1$, which hasa particular important role in biological pattern formation, it is shown numerically that there exist multiple traveling waves with 1, 2 and 3 peaks with certain choices of parameters.The second part of this thesis is on the global stability of diffusive predatorprey system of Leslie Type and HollingTanner Type in a bounded domain $\Omega\subset R^N$ with noflux boundary condition. By using a new approach, we establish much improved global asymptotic stability of a unique positiveequilibrium solution. We also show the result can be extended to more general type of systems with heterogeneous environment and/or other kind of kinetic terms.
Show less  Date Issued
 2016
 Identifier
 CFE0006519, ucf:51359
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006519
 Title
 Mathematical Modeling of Infectious Diseases with Latency: Homogeneous Mixing and Contact Network.
 Creator

Carlson, Keith, Shuai, Zhisheng, Mohapatra, Ram, Guha, Ratan, University of Central Florida
 Abstract / Description

In mathematical epidemiology, the standard compartmental models assume homogeneous mixingin the host population, in contrast to the disease spread process over a real host contact network. One approach to incorporating heterogeneous mixing is to consider the population to be a networkof individuals whose contacts follow a given probability distribution. In this thesis we investigate in analogy both homogeneous mixing and contact network models for infectious diseases that admit latency...
Show moreIn mathematical epidemiology, the standard compartmental models assume homogeneous mixingin the host population, in contrast to the disease spread process over a real host contact network. One approach to incorporating heterogeneous mixing is to consider the population to be a networkof individuals whose contacts follow a given probability distribution. In this thesis we investigate in analogy both homogeneous mixing and contact network models for infectious diseases that admit latency periods, such as dengue fever, Ebola, and HIV. We consider the mathematics of thecompartmental model as well as the network model, including the dynamics of their equations from the beginning of disease outbreak until the disease dies out. After considering the mathematical models we perform software simulations of the disease models. We consider epidemic simulationsof the network model for three different values of R0 and compare the peak infection numbers and times as well as disease outbreak sizes and durations. We examine averages of these numbers for one thousand simulation runs for three values of R0. Finally we summarize results and consider avenues for further investigation.
Show less  Date Issued
 2016
 Identifier
 CFE0006276, ucf:51054
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006276
 Title
 Optimization problem in single period markets.
 Creator

Jiang, Tian, Yong, Jiongmin, Qi, Yuanwei, Shuai, Zhisheng, University of Central Florida
 Abstract / Description

There had been a number of researches that investigated on the security market without transactioncosts. The focus of this research is in the area that when the security market with transaction costsis fair and in such fair market how one chooses a suitable portfolio to optimize the financial goal.The research approach adopted in this thesis includes linear algebra and elementary probability.The thesis provides evidence that we can maximize expected utility function to achieve our goal...
Show moreThere had been a number of researches that investigated on the security market without transactioncosts. The focus of this research is in the area that when the security market with transaction costsis fair and in such fair market how one chooses a suitable portfolio to optimize the financial goal.The research approach adopted in this thesis includes linear algebra and elementary probability.The thesis provides evidence that we can maximize expected utility function to achieve our goal(maximize expected return under certain risk tolerance). The main conclusions drawn from thisstudy are under certain conditions the security market is arbitragefree, and we can always find anoptimal portfolio maximizing certain expected utility function.
Show less  Date Issued
 2013
 Identifier
 CFE0004696, ucf:49875
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004696
 Title
 Mathematical Investigation of the Spatial Spread of an Infectious Disease in a Heterogeneous Environment.
 Creator

Gaudiello, Arielle, Shuai, Zhisheng, Nevai, A, Song, Zixia, Mohapatra, Ram, QuintanaAscencio, Pedro, University of Central Florida
 Abstract / Description

Outbreaks of infectious diseases can devastate a population. Researchers thus study the spread of an infection in a habitat to learn methods of control. In mathematical epidemiology, disease transmission is often assumed to adhere to the law of mass action, yet there are numerous other incidence terms existing in the literature. With recent global outbreaks and epidemics, spatial heterogeneity has been at the forefront of these epidemiological models.We formulate and analyze a model for...
Show moreOutbreaks of infectious diseases can devastate a population. Researchers thus study the spread of an infection in a habitat to learn methods of control. In mathematical epidemiology, disease transmission is often assumed to adhere to the law of mass action, yet there are numerous other incidence terms existing in the literature. With recent global outbreaks and epidemics, spatial heterogeneity has been at the forefront of these epidemiological models.We formulate and analyze a model for humans in a homogeneous population with a nonlinear incidence function and demographics of birth and death. We allow for the combination of host immunity after recovery from infection or host susceptibility once the infection has run its course in the individual. We compute the basic reproduction number, R0, for the system and determine the global stability of the equilibrium states. If R0(<)= 1, the population tends towards a diseasefree state. If R0 (>)1, an endemic equilibrium exists, and the disease is persistent in the population. This work provides the framework needed for a spatially heterogeneous model. The model is then expanded to include a set of cities (or patches), each of which is structured from the homogeneous model. Movement is introduced, allowing travel between the cities at different rates. We assume there always exists a potentially nondirect route between two cities, and the movement need not be symmetric between two patches. Further, each city has its own nonlinear incidence function, demographics, and recovery rates, allowing for realistic interpretations of countrywide network structures. New global stability results are established for the diseasefree equilibrium and endemic equilibrium, the latter utilizing a graph theoretic approach and Lyapunov functions. Asymptotic profiles are determined for both the diseasefree equilibrium and basic reproduction number as the diffusion of human individuals is faster than the disease dynamics. A numerical investigation is performed on a star network, emulating a ruralurban society with a center city and surrounding suburbs. Numerical simulations give rise to similar and contrasting behavior for symmetric movement to the proposed asymmetric movement. Conjectures are made for the monotonicty of the basic reproduction number in terms of the diffusion of susceptible and infectious individuals. The limiting behavior of the system as the diffusion of susceptibles halts is shown to experience varying behavior based on the location of hot spots and biased movement.
Show less  Date Issued
 2019
 Identifier
 CFE0007637, ucf:52463
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0007637
 Title
 A mathematical model for feral cat ecology with application to disease.
 Creator

Sharpe, Jeff, Nevai, A, Shuai, Zhisheng, Qi, Yuanwei, QuintanaAscencio, Pedro, University of Central Florida
 Abstract / Description

We formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to LotkaVolterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also...
Show moreWe formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to LotkaVolterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also considered, including additional competition and abandonment into the feral population. Control measures are also modeled in the form of percapita removal rates. We compute the net reproduction number (R_0) for the colony and consider its influence. In the absence of abandonment, if R_0(>)1, the population always persists at a positive equilibrium and if R_0 (<)= 1, the population always tends toward local extinction. This work will be referred to as the core model.The model is then expanded to include a set of colonies (patches) such as those in the core model (this time neglecting the effect of abandonment). Adult females and kittens remain in their native patch while adult males spend a fixed proportion of their time in each patch. Adult females experience competition from both the adult females living in the same patch as well as the visiting adult males. The proportion of adult males in patch j suffer competition from both adult females resident to that patch as well the proportion of adult males also in the patch. We formulate a net reproduction number for each patch (a patch reproduction number) R_j. If R_j(>)1 for at least one patch, then the collective population always persists at some nontrivial (but possibly semitrivial) steady state. We consider the number of possible steady states and their properties. This work will be referred to as the patch model.Finally, the core model is expanded to include the introduction of the feline leukemia virus. Since this disease has many modes of transmission, each of which depends on the host's gender and lifestage, we regard this as a model disease. A basic reproduction number R_0 for the disease is defined and analyzed. Vaccination terms are included and their role in disease propagation is analyzed. Necessary and sufficient conditions are given under which the diseasefree equilibrium is stable.
Show less  Date Issued
 2016
 Identifier
 CFE0006502, ucf:51389
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006502
 Title
 HJB Equation and Statistical Arbitrage applied to High Frequency Trading.
 Creator

Park, Yonggi, Yong, Jiongmin, Swanson, Jason, Richardson, Gary, Shuai, Zhisheng, University of Central Florida
 Abstract / Description

In this thesis we investigate some properties of market making and statistical arbitrage applied to High Frequency Trading (HFT). Using the HamiltonJacobiBellman(HJB) model developed by Guilbaud, Fabien and Pham, Huyen in 2012, we studied how market making works to obtain optimal strategy during limit order and market order. Also we develop the best investment strategy through Moving Average, Exponential Moving Average, Relative Strength Index, Sharpe Ratio.
 Date Issued
 2013
 Identifier
 CFE0004907, ucf:49628
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004907
 Title
 Analytical solutions to nonlinear differential equations arising in physical problems.
 Creator

Baxter, Mathew, Vajravelu, Kuppalapalle, Li, Xin, Mohapatra, Ram, Shuai, Zhisheng, Kassab, Alain, University of Central Florida
 Abstract / Description

Nonlinear partial differential equations are difficult to solve, with many of the approximate solutions in the literature being numerical in nature. In this work, we apply the Homotopy Analysis Method to give approximate analytical solutions to nonlinear ordinary and partial differential equations. The main goal is to apply different linear operators, which can be chosen, to solve nonlinear problems. In the first three chapters, we study ordinary differential equations (ODEs) with one or two...
Show moreNonlinear partial differential equations are difficult to solve, with many of the approximate solutions in the literature being numerical in nature. In this work, we apply the Homotopy Analysis Method to give approximate analytical solutions to nonlinear ordinary and partial differential equations. The main goal is to apply different linear operators, which can be chosen, to solve nonlinear problems. In the first three chapters, we study ordinary differential equations (ODEs) with one or two linear operators. As we progress, we apply the method to partial differential equations (PDEs) and use several linear operators. The results are all purely analytical, meaning these are approximate solutions that we can evaluate at points and take their derivatives.Another main focus is error analysis, where we test how good our approximations are. The method will always produce approximations, but we use residual errors on the domain of the problem to find a measure of error.In the last two chapters, we apply similarity transforms to PDEs to transform them into ODEs. We then use the Homotopy Analysis Method on one, but are able to find exact solutions to both equations.
Show less  Date Issued
 2014
 Identifier
 CFE0005303, ucf:50527
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005303