Mathematics Commons^™

Uniqueness Of Solution To The Kolmogorov Forward Equation: Applications To White Noise Theory Of Filtering, Abhay G Bhatt, Rajeeva L Karandikar

Communications on Stochastic Analysis

No abstract provided.

Quasi-Exact Approximation Of Hidden Markov Chain Filters, Eckhard Platen, Renata Rendek

Communications on Stochastic Analysis

No abstract provided.

Inverse Stochastic Transfer Principle, Matthew Linn, Anna Amirdjanova

Communications on Stochastic Analysis

No abstract provided.

Risk-Based Indifference Pricing Under A Stochastic Volatility Model, Robert J Elliott, Tak Kuen Siu

Communications on Stochastic Analysis

No abstract provided.

When Is The Numerical Range Of A Nilpotent Matrix Circular?, Valentin Matache, Mihaela Teodora Matache

Mathematics Faculty Publications

The problem formulated in the title is investigated. The case of nilpotent matrices of size at most 4 allows a unitary treatment. The numerical range of a nilpotent matrix M of size at most 4 is circular if and only if the traces tr M^∗M² and tr M^∗M³ are null. The situation becomes more complicated as soon as the size is 5. The conditions under which a 5×5nilpotent matrix has circular numerical range are thoroughly discussed.

Subclinical Myocardial Necrosis And Cardiovascular Risk In Stable Patients Undergoing Elective Cardiac Evaluation, W.H. Wilson Tang, Yuping Wu, Stephen J. Nicholls, Danielle M. Brennan, Michael Pepoy, Shirley Mann, Alan Pratt, Frederick Van Lente, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Objective— The presence of subclinical myocardial necrosis as a prodrome to longer-term adverse cardiac event risk has been debated. The debate has focused predominantly within patients with acute coronary syndrome, and on issues of troponin assay variability and accuracy of detection, rather than on the clinical significance of the presence of subclinical myocardial necrosis (ie, “troponin leak”) within stable cardiac patients. Herein, we examine the relationship between different degrees of subclinical myocardial necrosis and long-term adverse clinical outcomes within a stable cardiac patient population with essentially normal renal function. Methods and Results— Sequential consenting patients (N=3828; median creatinine clearance, 100 …

Software Internationalization: A Framework Validated Against Industry Requirements For Computer Science And Software Engineering Programs, John Huân Vũ

Master's Theses

View John Huân Vũ's thesis presentation at http://youtu.be/y3bzNmkTr-c.

In 2001, the ACM and IEEE Computing Curriculum stated that it was necessary to address "the need to develop implementation models that are international in scope and could be practiced in universities around the world." With increasing connectivity through the internet, the move towards a global economy and growing use of technology places software internationalization as a more important concern for developers. However, there has been a "clear shortage in terms of numbers of trained persons applying for entry-level positions" in this area. Eric Brechner, Director of Microsoft Development Training, suggested …

Incompressibility And Global Inversion, Eduardo C. Balreira

Mathematics Faculty Research

Given a local diffeomorphism ƒ : ℝⁿ → ℝⁿ, we consider certain in- compressibility conditions on the parallelepiped Dƒ(x) ([0, 1]ⁿ) which imply that the pre-image of an affine subspace is non-empty and has trivial homotopy groups. These conditions are then used to establish criteria for ƒ to be globally invertible, generalizing in all dimensions the previous results of M. Sabatini.

Lie Algebroid Structures On Double Vector Bundles And Representation Theory Of Lie Algebroids, Alfonso Gracia-Saz, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of equivalence. In this setting, we are able to construct characteristic classes, which in special cases reproduce characteristic classes constructed by Crainic and Fernandes. We give a complete classification of regular VB-algebroids, and in the process we obtain another characteristic class of Lie algebroids that does not appear in the ordinary representation theory of Lie algebroids.

A Sharp Diameter Bound For Unipotent Groups Of Classical Type Overℤ /Pℤ, Jordan S. Ellenberg, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

The unipotent subgroup of a finite group of Lie type over a prime field Fp comes equipped with a natural set of generators; the properties of the Cayley graph associated to this set of generators have been much studied. In the present paper, we show that the diameter of this Cayley graph is bounded above and below by constant multiples of np + n2 log p, where n is the rank of the associated Lie group. This generalizes the result of Ellenberg, A sharp diameter bound for an upper triangular matrix group, Harvard University, 1993, which treated the case of …

Sequences Of Positive Integers Containing No K-Term Arithmetic Progressions And Smooth Numbers In Short Intervals., Goutam Pal Dr.

Doctoral Theses

In my thesis I have worked on two problems:1. On sequences of positive integers containing no k terms in arithmetic progressions.2. On smooth numbers in short intervals.The first two chapters of my thesis deal with the first problem and in the rest of the thesis I have focused on the 2nd problem.In the first chapter of my thesis I have considered the function rk(N) for a fixed k ≥ 3, where, by definition, rk(N) is the cardinality of a maximal subset of N consecutive natural numbers with the property that nork terms of it are in an Arithmetic Progression (A. …

Application Of Combinatorial Structures To Key Predistribution In Sensor Networks And Traitor Tracing., Sushmita Ruj Dr.

Doctoral Theses

From time immemorial people have used cryptography for secure communication. Cryptography has decided the fate of many kings and queens as well as the outcome of various wars. It has become all the more important nowadays, with the growing need of electronic communication. We now live in a society where electronic networks pervade all aspects of our professional and private lives. We all use cryptography when we do bank transfers by ATM, or SWIFT, while using the mobile phones and i-phones, SSL protocols or using password protected machines. Though electronic communication is fast and easy, it is vulnerable to security …

Doubly Connected Minimal Surfaces And Extremal Harmonic Mappings, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate …

Oxygen Regulates The Effective Diffusion Distance Of Nitric Oxide In The Aortic Wall, Xiaoping Liu, Parthasarathy Srinivasan, Eric Collard, Paula Grajdeanu, Kevin Lok, Sarah E. Boyle, Avner Friedman, Jay L. Zweier

Mathematics and Statistics Faculty Publications

Endothelium-derived nitric oxide (NO) is critical in maintaining vascular tone. Accumulating evidence shows that NO bioavailability is regulated by oxygen concentration. However, it is unclear to what extent the oxygen concentration regulates NO bioavailability in the vascular wall. In this study, a recently developed experimental setup was used to measure the NO diffusion flux across the aortic wall at various oxygen concentrations. It was observed that for a constant NO concentration at the endothelial surface, the measured NO diffusion flux out of the adventitial surface at [O2] = 0 μM is around fivefold greater than at [O2] = 150 μM, …

A Unified Theory Of Function Spaces And Hyperspaces: Local Properties, Szymon Dolecki, Frédéric D. Mynard

Mathematical Sciences: Faculty Publications

Many classically used function space structures (including the topology of pointwise convergence, the compact-open topology, the Isbell topology and the continuous convergence) are induced by a hyperspace structure counterpart. This scheme is used to study local properties of function space structures on C(X,R), such as character, tighntess, fan-tightness, strong fan-tightness, the Fr{\'e}chet property and some of its variants. Under mild conditions, local properties of C(X,R) at the zero function correspond to the same property of the associated hyperspace structure at X. The latter is often easy to characterize in terms of covering properties …

On Type Of Periodicity And Ergodicity To A Class Of Fractional Order Differential Equations, Ravi P. Agarwal, Bruno D. Andrade, Claudio Cuevas

Mathematics and System Engineering Faculty Publications

We study several types of periodicity to a class of fractional order differential equations.

Asian Spread Option Pricing Models And Computation, Sijin Chen

Theses and Dissertations

In the commodity and energy markets, there are two kinds of risk that traders and analysts are concerned a lot about: multiple underlying risk and average price risk. Spread options, swaps and swaptions are widely used to hedge multiple underlying risks and Asian (average price) options can deal with average price risk. But when those two risks are combined together, then we need to consider Asian spread options and Asian-European spread options for hedging purposes. For an Asian or Asian-European spread call option, its payoff depends on the difference of two underlyings' average price or of one average price and …

Enhanced Metric Regularity And Lipschitzian Properties Of Variational Systems, Francisco J. Aragón Artacho, Boris S. Mordukhovich

Mathematics Research Reports

This paper mainly concerns the study of a large class of variational systems governed by parametric generalized equations, which encompass variational and hemivariational inequalities, complementarity problems, first-order necessary optimality conditions, and other optimization-related models important for optimization theory and applications. An efficient approach to these issues has been developed in our preceding work [1] establishing qualitative and quantitative relationships between conventional metric regularity jsubregularity and Lipschitzian/calmness properties in the framework of parametric generalized equations in arbitrary Banach spaces. This paper provides, on one hand, significant extensions of the major results in [1] to new partial metric regularity and hemiregularity properties. …

A Stochastic Model Of Cell Cycle Desynchronization, Peter Olofsson, Thomas O. Mcdonald

Mathematics Faculty Research

A general branching process model is suggested to describe cell cycle desynchronization. Cell cycle phase times are modeled as random variables and a formula for the expected fraction of cells in S phase as a function of time is established. The model is compared to data from the literature and is also compared to previously suggested deterministic and stochastic models.

Improved Automated Monitoring And New Analysis Algorithm For Circadean Phototaxis Rhythms In Chlamydomonas, Christa Gaskill, Jennifer Forbes-Stovall, Bruce Kessler, Mike Young, Claire A. Rinehart, Sigrid Jacobshagen

Mathematics Faculty Publications

Automated monitoring of circadian rhythms is an efficient way of gaining insight into oscillation parameters like period and phase for the underlying pacemaker of the circadian clock. Measurement of the circadian rhythm of phototaxis (swimming towards light) exhibited by the green alga Chlamydomonas reinhardtii has been automated by directing a narrow and dim light beam through a culture at regular intervals and determining the decrease in light transmittance due to the accumulation of cells in the beam. In this study, the monitoring process was optimized by constructing a new computercontrolled measuring machine that limits the test beam to wavelengths reported …

Integer Functions On The Cycle Space And Edges Of A Graph, Dan Slilaty

Mathematics and Statistics Faculty Publications

A directed graph has a natural Z-module homomorphism from the underlying graph’s cycle space to Z where the image of an oriented cycle is the number of forward edges minus the number of backward edges. Such a homomorphism preserves the parity of the length of a cycle and the image of a cycle is bounded by the length of that cycle. Pretzel and Youngs (SIAM J. Discrete Math. 3(4):544–553, 1990) showed that any Z-module homomorphism of a graph’s cycle space to Z that satisfies these two properties for all cycles must be such a map induced from an edge direction …

Highway Hull Revisited, Greg Aloupis, Jean Cardinal, Sébastien Collette, Ferran Hurtado, Stefan Langerman, Joseph O'Rourke, Belén Palop

Computer Science: Faculty Publications

A highway H is a line in the plane on which one can travel at a greater speed than in the remaining plane. One can choose to enter and exit H at any point. The highway time distance between a pair of points is the minimum time required to move from one point to the other, with optional use of H. The highway hull H(S,H) of a point set S is the minimal set containing S as well as the shortest paths between all pairs of points in H(S,H), using the highway time distance. We provide a Θ(nlogn) worst-case …

Perturbed Spherical Objects In Acoustic And Fluid Flow Fields, Manmeet Kaur

Dissertations

In this study, the time averaged acoustic radiation force and drag on a small, nearly spherical object suspended freely in a stationary sound wave field in a compressible, low viscosity fluid is to be calculated. This problem has been solved for a spherical object, and it has many important engineering applications related to segregation and separation processes for particles in fluids such as water. Small but significant errors have occurred in the predicted behavior of the particles using the existing approximate solutions based on perfect spheres. The classical approach has been extended in this research to objects that deviate slightly …

The Bernstein Problem For Embedded Surfaces In The Heisenberg Group H, Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu, Scott D. Pauls

Dartmouth Scholarship

In the paper [13] we proved that the only stable C 2 minimal surfaces in the first Heisenberg group H 1 which are graphs over some plane and have empty characteristic locus must be vertical planes. This result represents a sub-Riemannian version of the celebrated theorem of Bernstein. In this paper we extend the result in [13] to C 2 complete em-bedded minimal surfaces in H 1 with empty characteristic locus. We prove that every such a surface without boundary must be a vertical plane. This result represents a sub-Riemannian coun-terpart of the classical theorems of Fischer-Colbrie and Schoen, [16], …

Modeling And Quasi-Monte Carlo Simulation Of Risk In Credit Portfolios, Bo Ren

Dissertations

Credit risk is the risk of losing contractually obligated cash flows promised by a counterparty such as a corporation, financial institution, or government due to default on its debt obligations. The need for accurate pricing and hedging of complex credit derivatives and for active management of large credit portfolios calls for an accurate assessment of the risk inherent in the underlying credit portfolios. An important challenge for modeling a credit portfolio is to capture the correlations within the credit portfolio. For very large and homogeneous portfolios, analytic and semi-analytic approaches can be used to derive limiting distributions. However, for portfolios …

Nonlinear Evolution Of Annular Layers And Liquid Threads In Electric Fields, Qiming Wang

Dissertations

The nonlinear dynamics of viscous perfectly conducting liquid jets or threads under the action of a radial electric field are studied theoretically and numerically here. The field is generated by a potential difference between the jet surface and a concentrically placed electrode of given radius. A long-wave nonlinear model that is used to predict the dynamics of the system and in particular to address the effect of the radial electric field on jet breakup is developed, Two canonical regimes are identified that depend on the size of the gap between the outer electrode and the unperturbed jet surface. For relatively …

On The Convergence Of An Implicit Iterative Process For Generalized Asymptotically Quasi-Nonexpansive Mappings, Ravi P. Agarwal, Xiaolong Qin, Shinmin Kang

Mathematics and System Engineering Faculty Publications

The purpose of this paper is to introduce and consider a general implicit iterative process which includes Schu's explicit iterative processes and Sun's implicit iterative processes as special cases for a finite family of generalized asymptotically quasi-nonexpansive mappings. Strong convergence of the purposed iterative process is obtained in the framework of real Banach spaces.

Quantification Of Artistic Style Through Sparse Coding Analysis In The Drawings Of Pieter Bruegel The Elder, James M. Hughes, Daniel J. Graham, Daniel N. Rockmore

Dartmouth Scholarship

Recently, statistical techniques have been used to assist art historians in the analysis of works of art. We present a novel technique for the quantification of artistic style that utilizes a sparse coding model. Originally developed in vision research, sparse coding models can be trained to represent any image space by maximizing the kurtosis of a representation of an arbitrarily selected image from that space. We apply such an analysis to successfully distinguish a set of authentic drawings by Pieter Bruegel the Elder from another set of well-known Bruegel imitations. We show that our approach, which involves a direct comparison …

Harmonic Mapping Problem And Affine Capacity, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

The Harmonic Mapping Problem asks when there exists a harmonic homeomorphism between two given domains. It arises in the theory of minimal surfaces and in calculus of variations, specifically in hyperelasticity theory. We investigate this problem for doubly connected domains in the plane, where it already presents considerable challenge and leads to several interesting open questions.

Cryptography: A History In Mathematics, An Application In The Classroom, Brian Olmanson

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.