Analysis Commons^™

Quantum Theories Associated To Increasing Hilbert Space Filtrations And Generalized Jacobi 3–Diagonal Relation, Luigi Accardi, Yun Gang Lu

Journal of Stochastic Analysis

No abstract provided.

Rate Of Convergence In The Central Limit Theorem For Iid Pareto Variables, Claas Becker, Manuel Bohnet, Sarah Kummert

Journal of Stochastic Analysis

No abstract provided.

Noncentral Limit Theorem For Large Wishart Matrices With Hermite Entries, Charles-Philippe Diez, Ciprian A. Tudor

Journal of Stochastic Analysis

No abstract provided.

Fuzzy P-Value Of Hypotheses Tests With Crisp Data Using Non-Asymptotic Fuzzy Estimators, Nikos Mylonas, Basil K. Papadopoulos

Journal of Stochastic Analysis

No abstract provided.

Total Differentiability And Monogenicity For Functions In Algebras Of Order 4, I. Sabadini, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.

A Gentle Introduction To Inequalities: A Casebook From The Fullerton Mathematical Circle, Adam Glesser, Matt Rathbun, Bogdan Suceavă

Journal of Math Circles

Run for nearly a decade, the Fullerton Mathematical Circle at California State University, Fullerton prepares middle and high school students for mathematical research by exposing them to difficult problems whose solutions require only age-appropriate techniques and background. This work highlights one of the avenues of study, namely inequalities. We cover Engel's lemma, the Cauchy--Schwartz inequality, and the AM-GM inequality, as well as providing a wealth of problems where these results can be applied. Full solutions or hints, several written by Math Circle students, are given for all of the problems, as well as some commentary on how or when to …

Numerical Integration Through Concavity Analysis, Daniel J. Pietz

Rose-Hulman Undergraduate Mathematics Journal

We introduce a relationship between the concavity of a C2 func- tion and the area bounded by its graph and secant line. We utilize this relationship to develop a method of numerical integration. We then bound the error of the approximation, and compare to known methods, finding an improvement in error bound over methods of comparable computational complexity.

On The Evolution Equation For Modelling The Covid-19 Pandemic, Jonathan Blackledge

Books/Book chapters

The paper introduces and discusses the evolution equation, and, based exclusively on this equation, considers random walk models for the time series available on the daily confirmed Covid-19 cases for different countries. It is shown that a conventional random walk model is not consistent with the current global pandemic time series data, which exhibits non-ergodic properties. A self-affine random walk field model is investigated, derived from the evolutionary equation for a specified memory function which provides the non-ergodic fields evident in the available Covid-19 data. This is based on using a spectral scaling relationship of the type 1/ωα where ω …

Radial Singular Solutions To Semilinear Partial Differential Equations, Marcelo A. Almora Rios

HMC Senior Theses

We show the existence of countably many non-degenerate continua of singular radial solutions to a p-subcritical, p-Laplacian Dirichlet problem on the unit ball in R^N. This result generalizes those for the 2-Laplacian to any value p and extends recent work on the p-Laplacian by considering solutions both radial and singular.

Using Semialgebraic Parametric Analysis By Metaprogramming In Portfolio Optimization, Philip Blaine Meersman

Lewis Honors College Capstone Collection

One classic problem in quantitative finance is portfolio optimization, which consists of assigning weights to assets in a portfolio to maximize one’s expected return while keeping the level of risk at a desired level. This problem can be modeled as a linear program (LP), using a risk aversion parameter mu. For a given single value of mu, the LP can be solved using any standard LP solver. In this work, however, the problem is considered parametrically: the optimal solution is sought for every possible value of mu. This describes how weights to the portfolio assets would be assigned from the …

A Generalized Polar-Coordinate Integration Formula, Oscillatory Integral Techniques, And Applications To Convolution Powers Of Complex-Valued Functions On $\Mathbb{Z}^D$, Huan Q. Bui

Honors Theses

In this thesis, we consider a class of function on $\mathbb{R}^d$, called positive homogeneous functions, which interact well with certain continuous one-parameter groups of (generally anisotropic) dilations. Generalizing the Euclidean norm, positive homogeneous functions appear naturally in the study of convolution powers of complex-valued functions on $\mathbb{Z}^d$. As the spherical measure is a Radon measure on the unit sphere which is invariant under the symmetry group of the Euclidean norm, to each positive homogeneous function $P$, we construct a Radon measure $\sigma_P$ on $S=\{\eta \in \mathbb{R}^d:P(\eta)=1\}$ which is invariant under the symmetry group of $P$. With this measure, we prove …

Cross-Model Parameter Estimation In Epidemiology, Julia R. Fitzgibbons

Honors Theses and Capstones

No abstract provided.

Question Answering By Bert, Suman Karanjit

Student Academic Conference

No abstract provided.

Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman

Pitzer Senior Theses

This thesis investigates the unique interactions between pregnancy, substance involvement, and race as they relate to the War on Drugs and the hyper-incarceration of women. Using ordinary least square regression analyses and data from the Bureau of Justice Statistics’ 2016 Survey of Prison Inmates, I examine if (and how) pregnancy status, drug use, race, and their interactions influence two length of incarceration outcomes: sentence length and amount of time spent in jail between arrest and imprisonment. The results collectively indicate that pregnancy decreases length of incarceration outcomes for those offenders who are not substance-involved but not evenhandedly -- benefitting white …

Some Proofs Regarding Minami Estimates And Local Eigenvalue Statistics For Some Random Schrödinger Operator Models, Samuel Herschenfeld

Theses and Dissertations--Mathematics

We provide three proofs on different, but related models in the field of random Schrödinger operators. All three results are motivated by the desire to extend results and techniques on eigenvalue statistics or Minami estimates (an essential ingredient Poisson eigenvalue statistics).

Chapters 2 and 4 are explorations of the only two known techniques for proving Minami estimates for continuum Minami estimates. In Chapter 2, we provide an alternative and simplified proof of Klopp that holds in d = 1. Chapter 4 is an application of the techniques of Dietlein and Elgart to prove a Minami estimate for finite rank lattice …

Transitioning To An Active Learning Environment For Calculus At The University Of Florida, Darryl Chamberlain, Amy Grady, Scott Keeran, Kevin Knudson, Ian Manly, Melissa Shabazz, Corey Stone

Publications

In this note, we describe a large-scale transition to an active learning format in first-semester calculus at the University of Florida. Student performance and attitudes are compared across traditional lecture and flipped sections.

A Mathematical Analysis Of The Wind Triangle Problem And An Inquiry Of True Airspeed Calculations In Supersonic Flight, Leonard T. Huang, Lisa I. Cummings

International Journal of Aviation, Aeronautics, and Aerospace

In the first half of this paper, we present a fresh perspective toward the Wind Triangle Problem in aerial navigation by deriving necessary and sufficient conditions, which we call "go/no-go conditions", for the existence/non-existence of a solution of the problem. Although our derivation is based on simple trigonometry and basic properties of quadratic functions, it is mathematically rigorous. We also offer examples to demonstrate how easy it is to check these conditions graphically. In the second half of this paper, we use function theory to re-examine another problem in aerial navigation, namely, that of computing true airspeed — even in …

Stable And Convergent Difference Schemes For Weakly Singular Convolution Integrals, Wesley Davis, Richard D. Noren

Mathematics & Statistics Faculty Publications

We obtain new numerical schemes for weakly singular integrals of convolution type called Caputo fractional order integrals using Taylor and fractional Taylor series expansions and grouping terms in a novel manner. A fractional Taylor series expansion argument is utilized to provide fractional-order approximations for functions with minimal regularity. The resulting schemes allow for the approximation of functions in C^γ [0, T], where 0 < γ <= 5. A mild invertibility criterion is provided for the implicit schemes. Consistency and stability are proven separately for the whole-number-order approximations and the fractional-order approximations. The rate of convergence in the time variable is shown …

Solving Neutrosophic Linear Equations Systems Using Symbolic Computation (Resolucion De Sistemas De Ecuaciones Lineales Neutrosóficas Mediante Computación Simbólica), Maykel Leyva-Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we apply the concept of neutrosophic numbers to solve a systems of neutrophic linear equations using symbolic computation. Also, we utilize Jupyter, which is supported in Google Colaboratory for performing symbolic computation. The sympy library of Python is used to perform the process of neutrosophic computation. Systems of neutrosophic linear equations are solved through symbolic computation in Python. A case study was developed for the determination of vehicular traffic with indeterminacy. This king of computation opens new ways to deal with indeterminacy in real-world problems.

Multivariate Distributions Of Correlated Binary Variables Generated By Pair-Copulas, Huihui Lin, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Correlated binary data are prevalent in a wide range of scientific disciplines, including healthcare and medicine. The generalized estimating equations (GEEs) and the multivariate probit (MP) model are two of the popular methods for analyzing such data. However, both methods have some significant drawbacks. The GEEs may not have an underlying likelihood and the MP model may fail to generate a multivariate binary distribution with specified marginals and bivariate correlations. In this paper, we study multivariate binary distributions that are based on D-vine pair-copula models as a superior alternative to these methods. We elucidate the construction of these binary distributions …