Mathematics Commons^™

On The Fundamental Theorem Of Asset Pricing, Abhay G Bhatt, Rajeeva L Karandikar

Communications on Stochastic Analysis

No abstract provided.

Periodic Solutions Of Discrete Generalized Schrödinger Equations On Cayley Trees, Fumio Hiroshima, József Lörinczi, Utkir Rozikov

Communications on Stochastic Analysis

No abstract provided.

Almost-Sure Explosive Solutions Of Some Nonlinear Parabolic Itô Equations, Pao-Liu Chow, Rafail Khasminskii

Communications on Stochastic Analysis

No abstract provided.

Invariant Basis Number And Basis Types For C*-Algebras, Philip M. Gipson

Department of Mathematics: Dissertations, Theses, and Student Research

We develop the property of Invariant Basis Number (IBN) in the context of C*-algebras and their Hilbert modules. A complete K-theoretic characterization of C*- algebras with IBN is given. A scheme for classifying C*-algebras which do not have IBN is given and we prove that all such classes are realized. We investigate the invariance of IBN, or lack thereof, under common C*-algebraic construction and perturbation techniques. Finally, applications of Invariant Basis Number to the study of C*-dynamical systems and the classification program are investigated.

Adviser: David Pitts

Averaged Instrumental Variables Estimators, Yoonseok Lee, Yu Zhou

Center for Policy Research

We develop averaged instrumental variables estimators as a way to deal with many weak instruments. We propose a weighted average of the preliminary k-class estimators, where each estimator is obtained using different subsets of the available instrumental variables. The averaged estimators are shown to be consistent and to satisfy asymptotic normality. Furthermore, its approximate mean squared error reveals that using a small number of instruments for each preliminary k-class estimator reduces the finite sample bias, while averaging prevents the variance from inflating. Monte Carlo simulations find that the averaged estimators compare favorably with alternative instrumental-variable-selection approaches when the strength levels …

Modeling The Diffusion Of Heat Energy Within Composites Of Homogeneous Materials Using The Uncertainty Principle, Elyse M. Garon

Honors Theses

The purpose of this project is to model the diffusion of heat energy in one space dimension, such as within a rod, in the case where the heat flow is through a medium consisting of two or more homogeneous materials. The challenge of creating such a mathematical model is that the diffusivity will be represented using a piecewise constant function, because the diffusivity changes based on the material. The resulting model cannot be solved using analytical methods, and is impractical to solve using existing numerical methods, thus necessitating a novel approach.

The approach presented in this thesis is to represent …

Time Integration Methods Of Fundamental Solutions And Approximate Fundamental Solutions For Nonlinear Elliptic Partial Differential Equations, Corey Leon Jones

Dissertations

A time-dependent method is coupled with the Method of Approximate Particular Solutions (MAPS) of Delta-shaped basis functions, the Method of Fundamental Solutions (MFS), and the Method of Approximate Fundamental Solutions (MAFS) to solve a second order nonlinear elliptic partial differential equation (PDE) on regular and irregular shaped domains. The nonlinear PDE boundary value problem is first transformed into a time-dependent quasilinear problem by introducing a fictitious time. Forward Euler integration is then used to ultimately convert the problem into a sequence of time-dependent linear nonhomogeneous modified Helmholtz boundary value problems on which the superposition principle is applied to split the …

Revised Model For Antibiotic Resistance In A Hospital, Ruhang Pei

Electronic Theses and Dissertations

In this thesis we modify an existing model for the spread of resistant bacteria in a hospital. The existing model does not account for some of the trends seen in the data found in literature. The new model takes some of these trends into account. For the new model, we examine issues relating to identifiability, sensitivity analysis, parameter estimation, uncertainty analysis, and equilibrium stability.

Multivariate Statistical Methodologies Applied In Biomedical Raman Spectroscopy: Assessing The Validity Of Partial Least Squares Regression Using Simulated Model Datasets., Mark Keating

Articles

Raman spectroscopy is fast becoming a valuable analytical tool in a number of biomedical scenarios, most notably disease diagnostics. Importantly, the technique has also shown increasing promise in the assessment of drug interactions on a cellular and subcellular level, particularly when coupled with multivariate statistical analysis. However, an important consideration, both with Raman spectroscopy and the associated statistical methodologies, is the accuracy of these techniques and more specifically the sensitivities which can be achieved and ultimately the limits of detection of the various methods. The purpose of this study is thus the construction of a model simulated data set with …

Mathematical Modeling Of Trending Topics On Twitter, Jonathan S. Skaza

Honors Projects in Mathematics

Created in 2006, Twitter is an online social networking service in which users share and read 140-character messages called Tweets. The site has approximately 288 million monthly active users who produce about 500 million Tweets per day. This study applies dynamical and statistical modeling strategies to quantify the spread of information on Twitter. Parameter estimates for the rates of infection and recovery are obtained using Bayesian Markov Chain Monte Carlo (MCMC) methods. The methodological strategy employed is an extension of techniques traditionally used in an epidemiological and biomedical context (particularly in the spread of infectious disease). This study, which addresses …

Development Of Analytical Sensitivity Analysis For Ahp Applications, Marie L. Ivanco

Mechanical & Aerospace Engineering Theses & Dissertations

Decision makers often face complex problems, which can seldom be addressed without the use of structured analytical models. Mathematical models have been developed over the last 50 years to streamline and facilitate decision making activities. The Analytic Hierarchy Process constitutes one of the most utilized Multi-Criteria Decision Analysis Methods. While AHP has been thoroughly researched and applied, the method still shows limitations in terms of integrating profile disparities of Subject Matter Experts (SMEs). This thesis develops an analytical sensitivity analysis method for AHP based on local partial derivatives to address these limitations. Four examples are presented to demonstrate and validate …

Estimating The Extreme Low-Temperature Event Using Nonparametric Methods, Anisha D'Silva

Master's Theses (2009 -)

This thesis presents a new method of estimating the one-in-N low temperature threshold using a non-parametric statistical method called kernel density estimation applied to daily average wind-adjusted temperatures. We apply our One-in-N Algorithm to local gas distribution companies (LDCs), as they have to forecast the daily natural gas needs of their consumers. In winter, demand for natural gas is high. Extreme low temperature events are not directly related to an LDCs gas demand forecasting, but knowledge of extreme low temperatures is important to ensure that an LDC has enough capacity to meet customer demands when extreme low temperatures are experienced. …

Analysing Systemic Risk Contribution Using A Closed Formula For Conditional Value At Risk Through Copula, Brice Hakwa, Manfred Jäger-Ambrożewicz, Barbara Rüdiger

Communications on Stochastic Analysis

No abstract provided.

Mathematical Formulation Of An Optimal Execution Problem With Uncertain Market Impact, Kensuke Ishitani, Takashi Kato

Communications on Stochastic Analysis

No abstract provided.

On A Nonsymmetric Ornstein-Uhlenbeck Semigroup And Its Generator, Yong Chen

Communications on Stochastic Analysis

No abstract provided.

Existence Of Lévy's Area And Pathwise Integration, Peter Imkeller, David J Prömel

Communications on Stochastic Analysis

No abstract provided.

Branching Particle Systems And Compound Poisson Processes Related To Pólya-Aeppli Distributions, Richard B Paris, Vladimir Vinogradov

Communications on Stochastic Analysis

No abstract provided.

Hitting Times For Bessel Processes, Gerardo Hernández-Del-Valle, Carlos G Pacheco

Communications on Stochastic Analysis

No abstract provided.

Comparing The G-Normal Distribution To Its Classical Counterpart, Erhan Bayraktar, Alexander Munk

Communications on Stochastic Analysis

No abstract provided.

Convergence Of Scheme For Decoupled Forward Backward Stochastic Differential Equation, Hani Abidi, Habib Ouerdiane

Communications on Stochastic Analysis

No abstract provided.

My Finite Field, Matthew Schroeder

Journal of Humanistic Mathematics

A love poem written in the language of mathematics.

Solutions Of A Logistic Equation On Varying Time Scales: A Quantitative And Qualitative Analysis, Alexandria Amity Amorim

Theses, Dissertations and Capstones

Time Scale Calculus, introduced by Dr. Stefan Hilger in 1988, combines the study of differential and difference equations into a single topic. We begin with an introduction of sets used in this field, time scales, and build up to the definition of the exponential function on a time scale. The main focus of this work is a study of the solutions of a particular logistic dynamic equation on varying time scales. We study both the analytical and graphical solutions of this equation. Analytical solutions are worked out using theorems from Time Scale Calculus, including properties of the exponential function. Graphical …

Quantization Of Analysis, Kelvin K. Lui

Honors Theses

In quantum mechanics the replacement of complex vectors with operators is essential to “quantizing” space. Nonetheless, in many physics textbooks there is no justification for this action. Therefore in this thesis I will attempt to understand the mathematical formalism that allows for such a “replacement” to be rigorous. I will approach this topic by first defining a vector spaces and its dual space, a Hilbert space and a conjugate Hilbert space, and an operator space. Next, I will look at the algebraic tensor product of two vector spaces, two Hilbert spaces, and finally two operator spaces. Ultimately we will look …

Formality And Informality In Cost-Benefit Analysis, Amy Sinden

Utah Law Review

Cost-benefit analysis (CBA) is usually treated as a monolith. In fact, the term can refer to a broad variety of decisionmaking practices, ranging from a qualitative comparison of pros and cons to a highly formalized and technical method grounded in economic theory that monetizes both costs and benefits, discounts to present net value, and locates the point at which the marginal benefits curve crosses the marginal costs curve. This article develops a typology that helps to conceptualize the multiple varieties of CBA along a formality-informality spectrum. It then uses this typology to analyze the treatment of CBA by the academic …

Techno-Art Of Selariu Supermathematics Functions, 2nd Volume, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

An ALBUM, according to the dictionary, is defined as "notebook for storing photos, postcards, stamps, lyrics, quotes etc.", which, in other words, means gatherings of "pieces" of the same "species". Or, in the new Techno-Art of Selariu SuperMathematics Functions ALBUM (the second book of Selariu SuperMathematics Functions), one contemplates a unique COMPOSITION, INTER-, INTRA- and TRANS-DISCIPLINARY. (Capitalizing here is not a futility, but a harmony with the TRUTH.) One caveat I am indebted to do, as a consequent "reader" – over time, I received the ALBUM, chapter by chapter, pace by pace, which gave me the time to analyze / …

Neutrosophic Axiomatic System, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we introduce for the first time the notions of Neutrosophic Axiom, Neutrosophic Axiomatic System, Neutrosophic Deducibility and Neutrosophic Inference, Neutrosophic Proof, Neutrosophic Tautologies, Neutrosophic Quantifiers, Neutrosophic Propositional Logic, Neutrosophic Axiomatic Space, Degree of Contradiction (Dissimilarity) of Two Neutrosophic Axioms, and Neutrosophic Model. A class of neutrosophic implications is also introduced. A comparison between these innovatory neutrosophic notions and their corresponding classical notions is made. Then, three concrete examples of neutrosophic axiomatic systems, describing the same neutrosophic geometrical model, are presented at the end of the paper.

Special Type Of Topological Spaces Using [0, N), Florentin Smarandache, W.B Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of special type of topological spaces using the interval [0, n). They are very different from the usual topological spaces. Algebraic structure using the interval [0, n) have been systemically dealt by the authors. Now using those algebraic structures in this book authors introduce the notion of special type of topological spaces. Using the super subset interval semigroup special type of super interval topological spaces are built. Several interesting results in this direction are obtained. Next six types of topological spaces using subset interval pseudo ring semiring of type …

Infinite Quaternion Pseudo Rings Using [0, N), Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors study the properties of finite real quaternion ring which was introduced in [2000]. Here a complete study of these finite quaternion rings are made. Also polynomial quaternion rings are defined, they happen to behave in a very different way. In the first place the fundamental theorem of algebra, “a nth degree polynomial has n and only n roots”, n is untrue in case of polynomial in polynomial quaternion rings in general. Further the very concept of derivative and integrals of these polynomials are untrue. Finally interval pseudo quaternion rings also behave in an erratic way. Not …

Algebraic Structures On Mod Planes, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

Study of MOD planes happens to a very recent one. Authors have studied several properties of MOD real planes Rn(m); 2 ≤ m ≤ ∞. In fact unlike the real plane R × R which is unique MOD real planes are infinite in number. Likewise MOD complex planes Cn(m); 2 ≤ m ≤ ∞, are infinitely many. The MOD neutrosophic planes RnI(m); 2 ≤ m ≤ ∞ are infinite in number where as we have only one neutrosophic plane R(I) = 〈R ∪ I〉 = {a + bI | I2 = I; a, b ∈ R}. Further three other new …

Mod Functions: A New Approach To Function Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the notion of MOD functions are defined on MOD planes. This new concept of MOD functions behaves in a very different way. Even very simple functions like y = nx has several zeros in MOD planes where as they are nice single line graphs with only (0, 0) as the only zero. Further polynomials in MOD planes do not in general follows the usual or classical laws of differentiation or integration. Even finding roots of MOD polynomials happens to be very difficult as they do not follow the fundamental theorem of algebra, viz a nth degree polynomial …