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Articles 1  30 of 1078
FullText Articles in Analysis
Symmetric Rigidity For Circle Endomorphisms With Bounded Geometry And Their Dual Maps, John Adamski
Symmetric Rigidity For Circle Endomorphisms With Bounded Geometry And Their Dual Maps, John Adamski
All Dissertations, Theses, and Capstone Projects
Let $f$ be a circle endomorphism of degree $d\geq2$ that generates a sequence of Markov partitions that either has bounded nearby geometry and bounded geometry, or else just has bounded geometry, with respect to normalized Lebesgue measure. We define the dual symbolic space $\S^*$ and the dual circle endomorphism $f^*=\tilde{h}\circ f\circ{h}^{1}$, which is topologically conjugate to $f$. We describe some properties of the topological conjugacy $\tilde{h}$. We also describe an algorithm for generating arbitrary circle endomorphisms $f$ with bounded geometry that preserve Lebesgue measure and their corresponding dual circle endomorphisms $f^*$ as ...
Nonlocal Helmholtz Decompositions And Connections To Classical Counterparts, Andrew Haar, Petronela Radu
Nonlocal Helmholtz Decompositions And Connections To Classical Counterparts, Andrew Haar, Petronela Radu
UCARE Research Products
In recent years nonlocal models have been successfully introduced in a variety of applications, such as dynamic fracture, nonlocal diffusion, flocking, and image processing. Thus, the development of a nonlocal calculus theory, together with the study of nonlocal operators has become the focus of many theoretical investigations. Our work focuses on a Helmholtz decomposition in the nonlocal (integral) framework. In the classical (differential) setting the Helmholtz decomposition states that we can decompose a three dimensional vector field as a sum of an irrotational function and a solenoidal function. We will define new nonlocal gradient and curl operators that allow us ...
Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences, Walter Mcfarland Bridges
Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences, Walter Mcfarland Bridges
LSU Doctoral Dissertations
Our main results are asymptotic zeroone laws satisfied by the diagrams of unimodal sequences of positive integers. These diagrams consist of columns of squares in the plane; the upper boundary is called the shape. For various types of unimodal sequences, we show that, as the number of squares tends to infinity, 100% of shapes are near a certain curvethat is, there is a single limit shape. Similar phenomena have been wellstudied for integer partitions, but several technical difficulties arise in the extension of such asymptotic statistical laws to unimodal sequences. We develop a widely applicable method for obtaining these limit ...
Gait Characterization Using Computer Vision Video Analysis, Martha T. Gizaw
Gait Characterization Using Computer Vision Video Analysis, Martha T. Gizaw
Undergraduate Honors Theses
The World Health Organization reports that falls are the secondleading cause of accidental death among senior adults around the world. Currently, a research team at William & Mary’s Department of Kinesiology & Health Sciences attempts to recognize and correct agingrelated factors that can result in falling. To meet this goal, the members of that team videotape walking tests to examine individual gait parameters of older subjects. However, they undergo a slow, laborious process of analyzing video frame by video frame to obtain such parameters. This project uses computer vision software to reconstruct walking models from residents of an independent living retirement ...
On Quantum Effects Of Vector Potentials And Generalizations Of Functional Analysis, Ismael L. Paiva
On Quantum Effects Of Vector Potentials And Generalizations Of Functional Analysis, Ismael L. Paiva
Computational and Data Sciences (PhD) Dissertations
This is a dissertation in two parts. In the first one, the AharonovBohm effect is investigated. It is shown that solenoids (or flux lines) can be seen as barriers for quantum charges. In particular, a charge can be trapped in a sector of a long cavity by two flux lines. Also, grids of flux lines can approximate the force associated with continuous twodimensional distributions of magnetic fields. More, if it is assumed that the lines can be as close to each other as desirable, it is explained how the classical magnetic force can emerge from the AharonovBohm effect. Continuing, the ...
An Analysis Of The First Passage To The Origin (Fpo) Distribution, Aradhana Soni
An Analysis Of The First Passage To The Origin (Fpo) Distribution, Aradhana Soni
Electronic Theses and Dissertations
What is the probability that in a fair coin toss game (a simple random walk) we go bankrupt in n steps when there is an initial lead of some known or unknown quantity $m? What is the distribution of the number of steps N that it takes for the lead to vanish? This thesis explores some of the features of this ﬁrst passage to the origin (FPO) distribution. First, we explore the distribution of N when m is known. Next, we compute the maximum likelihood estimators of m for a ﬁxed n and also the posterior distribution of m when ...
On The Application Of Multidimensional Logarithmic Residue To Systems Of NonAlgebraic Equations, Barlikbay Prenov
On The Application Of Multidimensional Logarithmic Residue To Systems Of NonAlgebraic Equations, Barlikbay Prenov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this paper, the residue integrals over cycles associated with a system of nonalgebraic equations and formulas for their calculation are given. Their connection with the power sums of the roots of the system is established. Some examples are considered.
Investigations Into D'Alembert's Definition Of Limit (Real Analysis Version), Dave Ruch
Investigations Into D'Alembert's Definition Of Limit (Real Analysis Version), Dave Ruch
Analysis
No abstract provided.
MemoryModulated Cir Process With Discrete Delay Coefficients, Pathiranage Lochana Siriwardena, Harry Randolph Hughes, D. G. Wilathgamuwa
MemoryModulated Cir Process With Discrete Delay Coefficients, Pathiranage Lochana Siriwardena, Harry Randolph Hughes, D. G. Wilathgamuwa
Journal of Stochastic Analysis
No abstract provided.
Some Exit Time Estimates For SuperBrownian Motion And FlemingViot Process, Parisa Fatheddin
Some Exit Time Estimates For SuperBrownian Motion And FlemingViot Process, Parisa Fatheddin
Journal of Stochastic Analysis
No abstract provided.
An Improved Uniqueness Result For A System Of Sde Related To The Stochastic Wave Equation, Carl Mueller, Eyal Neuman, Michael Salins, Giang Truong
An Improved Uniqueness Result For A System Of Sde Related To The Stochastic Wave Equation, Carl Mueller, Eyal Neuman, Michael Salins, Giang Truong
Journal of Stochastic Analysis
No abstract provided.
Collaboration (Reacting To The Past/Math/History/Writing), James Hayashi
Collaboration (Reacting To The Past/Math/History/Writing), James Hayashi
Q2S Enhancing Pedagogy
This is an assignment for a Freshman level course in the College of Natural Science. By the end students will have an understanding of valid research, collaboration and communication skills. Faculty that chooses to use this assignment will be preparing students for an active learning environment, and understanding a “Big Idea”, valid research, technology and communication skills.
Faculty should give an example of what is valid research. As students are completing this assignment mini deadlines (checkins) shall be set. With the checkins for this assignment focus on how the group will communicate the check point and the collaboration.
The focus ...
Large And Moderate Deviation Principles For Recursive Kernel Estimators For Spatial Data, Salim Bouzebda, Yousri Slaoui
Large And Moderate Deviation Principles For Recursive Kernel Estimators For Spatial Data, Salim Bouzebda, Yousri Slaoui
Journal of Stochastic Analysis
No abstract provided.
Closed Quantum BlackScholes: Quantum Drift And The Heisenberg Equation Of Motion, Will Hicks
Closed Quantum BlackScholes: Quantum Drift And The Heisenberg Equation Of Motion, Will Hicks
Journal of Stochastic Analysis
No abstract provided.
Jump Theorems For The BochnerMartinelli Integral In Domains With A Piecewise Smooth Boundary, Alexander Kytmanov, Davlatbay Dzhumabaev, Bayrambay Utemuratov, Barlikbay Prenov
Jump Theorems For The BochnerMartinelli Integral In Domains With A Piecewise Smooth Boundary, Alexander Kytmanov, Davlatbay Dzhumabaev, Bayrambay Utemuratov, Barlikbay Prenov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
Jump theorems for the BochnerMartinelli integral in domains with a piecewise smooth boundary are obtained. Moreover, theorem for the BochnerMartinelli integral in domains with a piecewise smooth boundary is proved for continuous functions and also for functions from the class 𝓛^{p}.
Exit Problems For JumpDiffusion Processes With Uniform Jumps, Mario Lefebvre
Exit Problems For JumpDiffusion Processes With Uniform Jumps, Mario Lefebvre
Journal of Stochastic Analysis
No abstract provided.
Ogawa Integrability And A Condition For Convergence In The Multidimensional Case, Nicolò Cangiotti, Sonia Mazzucchi
Ogawa Integrability And A Condition For Convergence In The Multidimensional Case, Nicolò Cangiotti, Sonia Mazzucchi
Journal of Stochastic Analysis
No abstract provided.
Mixing Coefficient For DiscreteTime Stochastic Flow, E.V. Glinyanaya
Mixing Coefficient For DiscreteTime Stochastic Flow, E.V. Glinyanaya
Journal of Stochastic Analysis
No abstract provided.
On A Class Of Average Preserving SemiMartingale Laws Optimization Problems, Rémi Lassalle
On A Class Of Average Preserving SemiMartingale Laws Optimization Problems, Rémi Lassalle
Journal of Stochastic Analysis
No abstract provided.
The Semimartingale Dynamics And Generator Of A Continuous Time SemiMarkov Chain, Robert J. Elliott
The Semimartingale Dynamics And Generator Of A Continuous Time SemiMarkov Chain, Robert J. Elliott
Journal of Stochastic Analysis
No abstract provided.
The Isoperimetric Inequality: Proofs By Convex And Differential Geometry, Penelope Gehring
The Isoperimetric Inequality: Proofs By Convex And Differential Geometry, Penelope Gehring
RoseHulman Undergraduate Mathematics Journal
The Isoperimetric Inequality has many different proofs using methods from diverse mathematical fields. In the paper, two methods to prove this inequality will be shown and compared. First the 2dimensional case will be proven by tools of elementary differential geometry and Fourier analysis. Afterwards the theory of convex geometry will briefly be introduced and will be used to prove the BrunnMinkowskiInequality. Using this inequality, the Isoperimetric Inquality in n dimensions will be shown.
Quantitative Analysis Of A Stochastic Seitr Epidemic Model With Multiple Stages Of Infection And Treatment, Olusegun M. Otunuga, Mobolaji O. Ogunsolu
Quantitative Analysis Of A Stochastic Seitr Epidemic Model With Multiple Stages Of Infection And Treatment, Olusegun M. Otunuga, Mobolaji O. Ogunsolu
Mathematics Faculty Research
We present a mathematical analysis of the transmission of certain diseases using a stochastic susceptibleexposedinfectioustreatedrecovered (SEITR) model with multiple stages of infection and treatment and explore the effects of treatments and external ﬂuctuations in the transmission, treatment and recovery rates. We assume external ﬂuctuations are caused by variability in the number of contacts between infected and susceptible individuals. It is shown that the expected number of secondary infections produced (in the absence of noise) reduces as treatment is introduced into the population. By deﬁning R_{T}_{,n} and ℛ_{T}_{,n} as the basic deterministic and stochastic reproduction numbers, respectively ...
Elementary Hyperreal Analysis, Logan Cebula
Elementary Hyperreal Analysis, Logan Cebula
Williams Honors College, Honors Research Projects
This text explores elementary analysis through the lens of nonstandard analysis. The hyperreals will be proven to be implied by the existence of the reals via the axiom of choice. The notion of a hyperextension will be defined, and the socalled Transfer Principle will be proved. This principle establishes equivalence between results in real and hyperreal analysis. Sequences, subsequences, and limit suprema/infima will then be explored. Finally, integration will be considered.
Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, Martin Keagan Wynne Brown
Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, Martin Keagan Wynne Brown
Murray State Theses and Dissertations
Data and algorithmic modeling are two diﬀerent approaches used in predictive analytics. The models discussed from these two approaches include the proportional odds logit model (POLR), the vector generalized linear model (VGLM), the classiﬁcation and regression tree model (CART), and the random forests model (RF). Patterns in the data were analyzed using trigonometric polynomial approximations and Fast Fourier Transforms. Predictive modeling is used frequently in statistics and data science to ﬁnd the relationship between the explanatory (input) variables and a response (output) variable. Both approaches prove advantageous in diﬀerent cases depending on the data set. In our case, the data ...
Eigenvalue Statistics And Localization For Random Band Matrices With Fixed Width And Wegner Orbital Model, Benjamin Brodie
Eigenvalue Statistics And Localization For Random Band Matrices With Fixed Width And Wegner Orbital Model, Benjamin Brodie
Theses and DissertationsMathematics
We discuss two models from the study of disordered quantum systems. The first is the Random Band Matrix with a fixed band width and Gaussian or more general disorder. The second is the Wegner $n$orbital model. We establish that the point process constructed from the eigenvalues of finite size matrices converge to a Poisson Point Process in the limit as the matrix size goes to infinity.
The proof is based on the method of Minami for the Anderson tightbinding model. As a first step, we expand upon the localization results by Schenker and PeledSchenkerShamisSodin to account for complex energies ...
Theory Of Lexicographic Differentiation In The Banach Space Setting, Jaeho Choi
Theory Of Lexicographic Differentiation In The Banach Space Setting, Jaeho Choi
Electronic Theses and Dissertations
Derivative information is useful for many problems found in science and engineering that require equation solving or optimization. Driven by its utility and mathematical curiosity, researchers over the years have developed a variety of generalized derivatives. In this thesis, we will first take a look at Clarke’s generalized derivative for locally Lipschitz continuous functions between Euclidean spaces, which roughly is the smallest convex set containing all nearby derivatives of a domain point of interest. Clarke’s generalized derivative in this setting possesses a strong theoretical and numerical toolkit, which is analogous to that of the classical derivative. It includes ...
A Generalization Of Schroter's Formula To George Andrews, On His 80th Birthday, James Mclaughlin
A Generalization Of Schroter's Formula To George Andrews, On His 80th Birthday, James Mclaughlin
Mathematics Faculty Publications
We prove a generalization of Schroter's formula to a product of an arbitrary number of Jacobi triple products. It is then shown that many of the wellknown identities involving Jacobi triple products (for example the Quintuple Product Identity, the Septuple Product Identity, and Winquist's Identity) all then follow as special cases of this general identity. Various other general identities, for example certain expansions of (q; q)(infinity) and (q; q)(infinity)(k), k >= 3, as combinations of Jacobi triple products, are also proved.
Stochastic Process And Its Role In The Development Of The Financial Market: Celebrating Professor Chow's Long And Successful Career, Xisuo L. Liu
Communications on Stochastic Analysis
No abstract provided.
Stochastic Partial Differential Equation Sis Epidemic Models: Modeling And Analysis, Nhu N. Nguyen, George Yin
Stochastic Partial Differential Equation Sis Epidemic Models: Modeling And Analysis, Nhu N. Nguyen, George Yin
Communications on Stochastic Analysis
No abstract provided.
Action Functionals For Stochastic Differential Equations With Lévy Noise, Shenglan Yuan, Jinqiao Duan
Action Functionals For Stochastic Differential Equations With Lévy Noise, Shenglan Yuan, Jinqiao Duan
Communications on Stochastic Analysis
No abstract provided.