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Articles 121 - 150 of 551
Full-Text Articles in Mathematics
Numerical Methods For Spontaneous And Evoked Glutamate Release, Justin Shane Blackwell
Numerical Methods For Spontaneous And Evoked Glutamate Release, Justin Shane Blackwell
Mathematics Dissertations - Archive
As synapses are responsible for the majority of neuron communications in the brain, the events of evoked and spontaneous synaptic vesicle release/fusion are key features of all synaptic current. These release events typically activate receptors within a single postsynaptic site and give rise to miniature postsynaptic currents through activations of $N$-methyl-$D$-asparate (NMDA) and $\alpha$-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors, and therefore, they have been extremely instrumental in neurotransmissions. In this paper we will use a mathematical model to simulate spontaneous and evoked neurotransmission resulted from glutamate release within a synapse. Among several issues that modeling can provide quantitative assessment, the issue of …
Advancements And Applications Of Nonstandard Finite Difference Methods, Daniel Wood
Advancements And Applications Of Nonstandard Finite Difference Methods, Daniel Wood
Mathematics Dissertations - Archive
A class of dynamically consistent numerical methods are analyzed for general n-dimensional productive-destructive systems (PDS). Using this analysis, a methodology for constructing positive and elementary stable nonstandard numerical methods is established. The nonstandard approach results in qualitatively superior numerical methods when compared to the standard ones. PDS model a wide range of dynamical systems, including ones with biological, chemical and physical interactions. Building upon this, a nonstandard finite difference method for solving autonomous dynamical systems with positive solutions is constructed. The proposed numerical methods are computationally efficient and easy to implement. Several examples are given which show that the numerical …
On Solving Finitely Reflected Backward Stochastic Differential Equations, Wilber Alexander Ventura
On Solving Finitely Reflected Backward Stochastic Differential Equations, Wilber Alexander Ventura
Mathematics Dissertations - Archive
Classical theory gives a closed form representation of the density p(t,x), a solution to a linear parabolic PDE, via the Feynman-Kac Formula of the underlying diffusion process. In the non-linear PDE case there is no closed form representation for p(t,x) and instead one solves a SDE running back in time whose initial (deterministic value) coincides with p(t,x). This method of solving semi-linear parabolic PDEs is an effective alternative to known numerical schemes. Furthermore, the FBSDE approach allows for treatment of non-smooth coefficients in the PDE that cannot be handled by classical deterministic methods. One of the most important extensions of …
The Influence Of Dynamic Visualization On Undergraduate Calculus Learning, Julie Marie Skinner Sutton
The Influence Of Dynamic Visualization On Undergraduate Calculus Learning, Julie Marie Skinner Sutton
Mathematics Dissertations - Archive
The urgent need in the United States to produce an additional one million graduates in the areas of science, technology, engineering and mathematics and previous research into why students choose to abandon their quest to earn such degrees motivates exploration of the appropriate use of technology that engages students in the first-year calculus classroom. Technology enhances our capacity to incorporate visualization into the teaching of mathematics, yet research suggests that high school mathematics students who prefer to visualize when solving mathematics tasks are not the “super stars” of their classrooms. In this qualitative study, nine students, five of whom prefer …
A Modeling Study In The Regulation Of Stress On Neuronal Plasticity, Pengcheng Xiao
A Modeling Study In The Regulation Of Stress On Neuronal Plasticity, Pengcheng Xiao
Mathematics Dissertations - Archive
How stress can affect human cognitive functions has been a very popular topic for researchers from different fields including physiology, psychology, biology, neuroscience, and applied mathematics. Hypothalamic−pituitary−adrenal (HPA) axis plays an important role in response to stress by releasing hormones, and level of glucocorticoid has been widely considered to be one key factor to distinguish people with different stress disorder. Emerging evidence has shown that glucocorticoid act on glutamate neurotransmission system and consequently influences neuronal activities’s cognitive function. It changes in the glutamate release and induces synapse plasticity change. Spike-Timing Dependent Plasticity (STDP) is one of the important neuroscience foundations …
Nilpotent Lie Algebras And Nilmanifolds Constructed From Graphs, Allie Denise Ray
Nilpotent Lie Algebras And Nilmanifolds Constructed From Graphs, Allie Denise Ray
Mathematics Dissertations - Archive
The interaction between graph theory and differential geometry has been studied previously, but S. Dani and M. Mainkar brought a new approach to this study by associating a two-step nilpotent Lie algebra (and thereby a two-step nilmanifold) with a simple graph. We prsesent a new construction that associates a two-step nilpotent Lie algebra to an arbitrary (not necessarily simple) directed edge-labeled graph. We then use properties of a Schreier graph to determine necessary and sufficient conditions for this Lie algebra to extend to a three-step nilpotent Lie algebra.After considering the curvature of the two-step nilmanifolds associated with the graphs, we …
Comparative Analysis Of Various Continuous-Time Deterministic Models Of Tumor-Immune Interactions, Robert Paul Childress
Comparative Analysis Of Various Continuous-Time Deterministic Models Of Tumor-Immune Interactions, Robert Paul Childress
Mathematics Theses - Archive
Cancer is historically a leading cause of death in the United States. In 2013,cancer was the second leading cause of death with 584,881 deaths \cite{CDC}.Having solely been responsible for 22.5\% of all deaths in 2013 alone \cite{CDC},obtaining as complete an understanding as possible of cancer is obviously necessitated.I investigate deterministic ordinary differential equation models of increasingcomplexity simulating avascular tumor growth and interactions with the innate immuneresponse. After first establishing a baseline of tumor growth limited only by theavailability of local nutrients, I compare the effects on said growth of the nativeimmune system response, chemotherapy, immunotherapy, and various combinations ofthe aforementioned …
Some Multivariate Process Capability Indices, Rachel Lee Goodwin
Some Multivariate Process Capability Indices, Rachel Lee Goodwin
Mathematics Dissertations - Archive
Process capability indices (PCIs) play an important role in the field of Statistical Process Control. Prior to the last 25 years, PCIs had been formulated to assess the quality of a single product characteristic. Product quality, however, is typically dependent on several related variables. Therefore, there is a great need for multivariate process capability indices (MPCIs). The quality of a product is almost always determined from sample data. Thus, it is imperative that an MPCI has a corresponding confidence interval. In that way, conclusions may be drawn regarding the capability of the process that makes that product. Of the MPCIs …
Modeling Colony Collapse Disorder In Honeybees As A Contagion, Christopher Kribs, Christopher Mitchell
Modeling Colony Collapse Disorder In Honeybees As A Contagion, Christopher Kribs, Christopher Mitchell
Mathematics Faculty Publications - Archive
Honeybee pollination accounts annually for over $14 billion in United States agriculture alone. Within the past decade there has been a mysterious mass die-off of honeybees, an estimated 10 million beehives and sometimes as much as 90% of an apiary. There is still no consensus on what causes this phenomenon, called Colony Collapse Disorder, or CCD. Several mathematical models have studied CCD by only focusing on infection dynamics. We created a model to account for both healthy hive dynamics and hive extinction due to CCD, modeling CCD via a transmissible infection brought to the hive by foragers. The system of …
A Metapopulation Model For Sylvatic T. Cruzi Transmission With Vector Migration, Christopher Kribs, Britnee Crawford
A Metapopulation Model For Sylvatic T. Cruzi Transmission With Vector Migration, Christopher Kribs, Britnee Crawford
Mathematics Faculty Publications - Archive
This study presents a metapopulation model for the sylvatic transmission of Trypanosoma cruzi, the etiological agent of Chagas' disease, across multiple geographical regions and multiple overlapping host-vector transmission cycles. Classical qualitative analysis of the model and several submodels focuses on the parasite's basic reproductive number, illustrating how vector migration across patches and multiple transmission routes to hosts (including vertical transmission) determine the infection's persistence in each cycle. Numerical results focus on trends in endemic [equilibrium] persistence levels as functions of vector migration rates, and highlight the significance of the different epidemiological characteristics of transmission in each of the three regions.
A Generalized Approach To Darboux Transformations For Differential Equations, Mehmet Unlu
A Generalized Approach To Darboux Transformations For Differential Equations, Mehmet Unlu
Mathematics Dissertations - Archive
A Darboux transformation is a mathematical procedure to produce a solution to a differential equation when the solution to a related differential equation is known. The basic idea behind a Darboux transformation is to change the discrete spectrum of a linear differential operator in a controlled way without changing its continuous spectrum. For example, by using a Darboux transformation one can describe the change in a quantum mechanical system when some of its quantum levels are removed or some extra quantum levels are added. Darboux transformation formulas for various differential equations have been developed, but such formulas seem to be …
Properties Of The Pinched Tensor Product, Yousuf Alkhezi
Properties Of The Pinched Tensor Product, Yousuf Alkhezi
Mathematics Dissertations - Archive
For complexes of modules we study a new construction, called the pinched tensor product, which was introduced by Lars Winther Christensen and David A. Jorgensen to study Tate homology. We explore properties of the pinched tensor product and their comparison to properties of the ordinary tensor product. For example; we show some isomorphisms no longer holds for the pinched tensor product. Although if we change isomorphism to quasi-isomorphism the pinched version holds. Plus if f is a map from C to D and g is a map from A to B are morphisms of complexes of R-modules with f homotopic …
Representation Theory Of Totally Reflexive Modules Over Non-Gorenstein Rings, Denise Amanda Rangel
Representation Theory Of Totally Reflexive Modules Over Non-Gorenstein Rings, Denise Amanda Rangel
Mathematics Dissertations - Archive
In the late 1960's Auslander and Bridger published Stable Module Theory, in whichthe idea of totally reflexive modules first appeared. These modules have been studiedby many. However, a bulk of the information known about them is when they are overa Gorenstein ring, since in that case they are exactly the maximal Cohen-Macaulaymodules. Much is already known about maximal Cohen-Macaulay modules, that is,totally reflexive modules over a Gorenstein ring. Therefore, we investigate the existence and abundance of totally reflexive modules over non-Gorenstein rings.It is known that if there exist one non-trivial totally reflexive module over a non-Gorenstein ring, then there exists …
A Method For Exact Solutions To Integrable Evolution Equations In 2+1 Dimensions, Alicia Machuca
A Method For Exact Solutions To Integrable Evolution Equations In 2+1 Dimensions, Alicia Machuca
Mathematics Dissertations - Archive
A systematic method is developed to obtain solution formulas for certain explicit solutions to integrable nonlinear partial differential equations in two spatial variables and one time variable. The method utilizes an underlying Marchenko integral equation that arises in the corresponding inverse scattering problem. The method is demonstrated for the Kadomtsev-Petviashvili and the generalized Davey-Stewartson II system. A derivation and analysis of the solution formulas to these two nonlinear partial differential equations are given, and an independent verification of the solution formulas is presented. Such solution formulas are expressed in a compact form in terms of matrix exponentials, by using a …
Estimation Of Variance In Bivariate Normal Distribution After Preliminary Test Of Homogeneity, Juan Manuel Romero Padilla
Estimation Of Variance In Bivariate Normal Distribution After Preliminary Test Of Homogeneity, Juan Manuel Romero Padilla
Mathematics Dissertations - Archive
A preliminary test estimator of variance in the bivariate normal distribution is proposed after Pitman-Morgan test of homogeneity of two variances. We propose one estimator of variance after preliminary test of two tails and another one for one tail test. The biases and mean square errors of both estimators are derived. The relative efficiency (RE) of the preliminary test estimator is studied. Computations and 3D graphs of RE for different parameters are analyzed. In order to get the maximum RE, recommendations of the significance level for the preliminary test are given for various sample sizes by using the max-min criterion.
Weight Modules Of Orthosymplectic Lie Superalgebras, Thomas Lynn Ferguson
Weight Modules Of Orthosymplectic Lie Superalgebras, Thomas Lynn Ferguson
Mathematics Dissertations - Archive
A long-standing problem in representation theory is the classification of all simple weight modules of the classical Lie superalgebras. This problem was reduced to the classification of simple bounded highest weight modules. The latter classification has been accomplished for all classical Lie superalgebras except for the orthosymplectic series osp(m|2n) where m = 1, 3, 4, 5, 6. In this thesis, we complete the classification of the simple bounded highest weight modules of osp(1|2n) (i.e., for m = 1). The classification is obtained by developing constraints on primitive vectors in tensor products of bounded (Weyl) and finite-dimensional osp(1|2n)-modules.
Differential Equation Models Of Foreign Body Fibrotic Reactions For Assessing Roles Of Macrophage Phenotypes And Mesenchymal Stem Cells, Larrissa Owens
Differential Equation Models Of Foreign Body Fibrotic Reactions For Assessing Roles Of Macrophage Phenotypes And Mesenchymal Stem Cells, Larrissa Owens
Mathematics Dissertations - Archive
Implant failure due to fibrotic encapsulation is an ongoing challenge in the bio-medical field. We develop two mathematical models based on partial differential equations in two spatial dimensions, and use them to gain quantitative insights regarding the dynamics of immune cells and proteins following the insertion of a foreign body. We focus heavily on incorporating a distinction between varied phenotypes of macrophage cells and analyzing their effects on healing processes. We extend our research to a new model that incorporates mesenchymal stem cells that influence the chemical reactions of immune regulators. Stability analysis is conducted on a family of equilibria …
Numerical Les For Mvg Controlled Supersonic Ramp Flow, Xiao Wang
Numerical Les For Mvg Controlled Supersonic Ramp Flow, Xiao Wang
Mathematics Dissertations - Archive
An implicitly implemented large eddy simulation by using the fifth order bandwidth-optimized WENO scheme is applied to make comprehensive studies on ramp flows with micro-ramp vortex generators (MVG) at Mach 2.5 and Re=5760. Detailed mechanism and topology of flow structure after MVG was studied to make better understanding. A series of new findings are obtained about the MVG-ramp flow including the three-dimensional vortex structure generated by MVG. The mechanism about the formation of vortex ring structure and momentum deficit after MVG is deeply studied. Small scale vortical structures in the rear separation and wake near the trailing edge of MVG …
Applications Of Cubical Arrays In The Study Of Finite Semifields, Kelly Casimir Aman
Applications Of Cubical Arrays In The Study Of Finite Semifields, Kelly Casimir Aman
Mathematics Dissertations - Archive
It is well known that any finite semifield, S, can be viewed as an n-dimensional vector space over a finite field or prime order, Fp, and that the multiplication in S defines and can be defined by an n x n x n cubical array of scalars, A. For any element a E S, the matrix, La, corresponding to left multiplication by a can be determined from A. In this paper we show that there exists a unique monic polynomial of minimal degree, f E Fp[x], such that f(a) = 0, and which divides the minimal polynomial of La. Furthermore, …
Smooth Quantile Processes For Right Censored Data, Katsuhiro Uechi
Smooth Quantile Processes For Right Censored Data, Katsuhiro Uechi
Mathematics Dissertations - Archive
The development of an estimator of a quantile function Q(p) is discussed. The smooth nonparametric estimator Qn(p) of a quantile function Q(p) is defined as the solution to Fn(Qn(p)) = p, where Fn is a smooth Kaplan-Meier estimator of an unknown continuous distribution function F(x). The asymptotic properties of the smooth quantile process, n(Qn(p) - Q(p)) , based on right censored lifetimes are studied. The asymptotic properties of the bootstrap quantile process, n(Q n(p) - Q(p)) are also investigated and shown to have the same limiting distribution as the smooth quantile process. The bootstrap method to approximate the sampling distribution …
The Generalized Two-Component Hunter-Saxton System, Byungsoo Moon
The Generalized Two-Component Hunter-Saxton System, Byungsoo Moon
Mathematics Dissertations - Archive
This thesis is concerned with the generalized two-component Hunter-Saxton system. In the periodic setting, we study the wave-breaking phenomenon and global existence for the generalized two-component Hunter-Saxton system. We obtain a brief derivation of the model. We also briefly sketch a standard local well-posednessresult using Kato's semigroup approach. We establish a wave-breaking criterion for solutions and some interesting results of wave-breaking solutions with certain initial profiles. We demonstrate the exact blow-up rate of strong solutions. Finally, we give a sufficient condition for global solutions.
Numerical Integration Of Matrix Riccati Differential Equations With Solution Singularities, Charles K. Garrett
Numerical Integration Of Matrix Riccati Differential Equations With Solution Singularities, Charles K. Garrett
Mathematics Dissertations - Archive
A matrix Riccati differential equation (MRDE) is a quadratic ODE of the form X' = A₂₁ + A₂₂X - XA₁₁ - XA₁₂X ; where X is a function of t with X : R Rnxm and the Aij's are constant or functions of t with matrix sizes to respect the size of X. It is well known that MRDEs may have singularities in their solution even if all the Aij are constant. In this dissertation, several di erent ideas for the meaning of the solution of an MRDE past a solution singularity are analyzed and it is shown how all …
Influence Of Vectors' Risk-Spreading Strategies And Environmental Stochasticity On The Epidemiology And Evolution Of Vector-Borne Diseaes: The Example Of Chagas' Disease, Christopher Kribs, Perrine Pelosse, Marine Ginoux, Jorge E. Rabinovich, Sebastien Gourbiere, Frederic Menu
Influence Of Vectors' Risk-Spreading Strategies And Environmental Stochasticity On The Epidemiology And Evolution Of Vector-Borne Diseaes: The Example Of Chagas' Disease, Christopher Kribs, Perrine Pelosse, Marine Ginoux, Jorge E. Rabinovich, Sebastien Gourbiere, Frederic Menu
Mathematics Faculty Publications - Archive
Insects are known to display strategies that spread the risk of encountering unfavorable conditions, thereby decreasing the extinction probability of genetic lineages in unpredictable environments. To what extent these strategies influence the epidemiology and evolution of vector-borne diseases in stochastic environments is largely unknown. In triatomines, the vectors of the parasite Trypanosoma cruzi, the etiological agent of Chagas’ disease, juvenile development time varies between individuals and such variation most likely decreases the extinction risk of vector populations in stochastic environments. We developed a simplified multi-stage vector-borne SI epidemiological model to investigate how vector riskspreading strategies and environmental stochasticity influence the …
Solving The Optimization Control Problem For Lunar Soft Landing Using Minimization Technique, Lizeth Patricia Ocampo
Solving The Optimization Control Problem For Lunar Soft Landing Using Minimization Technique, Lizeth Patricia Ocampo
Mathematics Theses - Archive
Minimizing fuel consumption in lunar missions has been a well studied and documented optimization problem. In this paper two cases of the lunar Lander are studied. The first case is the one dimensional problem where the objective is to make a vertical soft landing using the minimum amount of fuel. The second case has the same objective but an initial tangential velocity greater than zero is given making it a two dimensional problem. The first case is solved using Newton's shooting method, finite difference method (using MATLAB's embedded function bvp4c), and solving it explicitly. For the second case, a minimization …
Point Modules Over Regular Graded Skew Clifford Algebras, Padmini Pillay Veerapen
Point Modules Over Regular Graded Skew Clifford Algebras, Padmini Pillay Veerapen
Mathematics Dissertations - Archive
In this thesis, I consider point modules over regular graded skew Clifford algebras.First, I define a notion of rank (called μ-rank) on noncommutative quadratic forms. To every (commutative) quadratic form is associated a symmetric matrix, and one has the standard notions of rank and determinant function defined on the matrix, and, thus, on the quadratic form. In 2010, in [15], the notion of quadratic form was extended to the noncommutative setting and a one-to-one correspondence was established between these quadratic forms and certain matrices. Using this generalization, I define a notion of rank (called μ-rank) for such noncommutative quadratic forms, …
Applications And Adaptations Of A Globally Convergent Numerical Method In Inverse Problems, Aubrey Rhoden
Applications And Adaptations Of A Globally Convergent Numerical Method In Inverse Problems, Aubrey Rhoden
Mathematics Dissertations - Archive
In our terminology "globally convergent numerical method" means a numerical method whose convergence to a good approximation of the correct solution is independent of the initial approximation in inverse problems. A numerical imaging algorithm has been proposed to solve a coecient inverse problem for an elliptic equation and then the algorithm is validated with the data generated by computer simulation. Previouswork in this eld was focused on the steady-state optical problem with multiple source positions moving along a straight line as well as the frequency domain problem with sweeping frequency. This work includes the steady-state thermal tomography problem with multiple …
Optimal Stopping For Markov Modulated Ito-Diffusion With Applications To Finance, Thomas William Seaquist
Optimal Stopping For Markov Modulated Ito-Diffusion With Applications To Finance, Thomas William Seaquist
Mathematics Dissertations - Archive
Despite the outstanding success of the Black-Scholes model, it relies on the assumption that drift and volatility of the underlying equity remain constant throughout time. This inaccuracy has motivated a number of interesting and innovative refinements, one of the most natural being Markov modulation. In this dissertation we analyze a variety of financially motivated optimal stopping problems under Markov modulated Ito-Diffusions. In Chapter 3, we generalize and refine a technique developed in [13] pricing an infinite time horizon American put option and we present a rigorous proof of optimality. In Chapter 3 we use this generalized technique to discover an …
Mathematical Models Of Nutrient Recycling And Toxin Production In A Gradostat, Xiaoyang Dong
Mathematical Models Of Nutrient Recycling And Toxin Production In A Gradostat, Xiaoyang Dong
Mathematics Dissertations - Archive
We discuss several gradostat models in which a microbial population excretes a biochemical that can get recycled back into the system as a nutrient source. Each mathematical model consists of six ordinary differential equations and represents the dynamics of harmful algal blooms in lakes with fringing coves. We examine three different situations of biochemical production which is based on the algal growth rate, mortality, and nutrient concentration, respectively. Local and global stability analysis of the equilibria predicts that algal abundance and biochemical concentration can be both washed out or persistent under different environmental conditions. All theoretical results are supported by …
High Order Numerical Schemes For Pdes And Applications To Cfd, Huankun Fu
High Order Numerical Schemes For Pdes And Applications To Cfd, Huankun Fu
Mathematics Dissertations - Archive
In the past two decades, many efforts have been made in developing high-order schemes with high resolution, such as compact scheme, essentially non-oscillatory scheme (ENO), weighted essentially non-oscillatory scheme (WENO).The present dissertation comprises the analysis and numerical testing of two high order methods. The first one refers to the modification of pseudo spectral method which can be used to partial differential equations(PDEs) with non-periodic boundary conditions. The second one is in high order finite difference class and is the mixing of weighted non-oscillatory scheme and compact scheme (MWCS) with using global weights instead of local ones. Numerical tests are performed …
Effects Of Discrete Time Delays And Parameters Variation On Dynamical Systems, Ibrahim Oumar Diakite
Effects Of Discrete Time Delays And Parameters Variation On Dynamical Systems, Ibrahim Oumar Diakite
Mathematics Dissertations - Archive
To understand the effects of discrete time delays and of parameters variation on certain biological system models, we first consider a Delay Differential Equation model of human immunodeficiency virus (HIV). We investigate the effects of the discrete time on the virulence of the HIV strain, and present sufficient and necessary condition for the virulence of the pathogen to change as the time delay changes. We also consider the same delay differential model for HIV infection, and we investigate analytically and numerically the stability of the endemically infected equilibrium. Our analysis shows that certain key parameters, such as the rate of …