Applied Mathematics Commons^™

On Directionally Dependent Subdifferentials, Ivan Ginchev, Boris S. Mordukhovich

Mathematics Research Reports

In this paper directionally contextual concepts of variational analysis, based on dual-space constructions similar to those in [4, 5], are introduced and studied. As an illustration of their usefulness, necessary and also sufficient optimality conditions in terms of directioual subdifferentials are established, and it is shown that they can be effective in the situations where known optimality conditions in terms of nondirectional subdifferentials fail.

Analyzing Fractals, Kara Mesznik

Renée Crown University Honors Thesis Projects - All

For my capstone project, I analyzed fractals. A fractal is a picture that is composed of smaller images of the larger picture. Each smaller picture is self- similar, meaning that each of these smaller pictures is actually the larger image just contracted in size through the use of the Contraction Mapping Theorem and shifted using linear and affine transformations.

Fractals live in something called a metric space. A metric space, denoted (X, d), is a space along with a distance formula used to measure the distance between elements in the space. When producing fractals …

Neutrosophic Physics: More Problems, More Solutions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

When considering the laws of theoretical physics, one of the physicists says that these laws – the actual expressions of the laws of mathematics and logics being applied to physical phenomena – should be limited according to the physical meaning we attribute to the phenomena. In other word, there is an opinion that a theoretical physicist should put some limitations onto mathematics, in order to “reduce” it to the observed reality. No doubt, we can do it. However, if following this way, we would arrive at only mathematical models of already known physical phenomena. Of course, this might be useful …

The Steiner Linear Ordering Problem: Application To Resource-Constrained Scheduling Problems, Mariah Magagnotti

All Theses

When examined through polyhedral study, the resource-constrained scheduling problems have always dealt with processes which have the same priority. With the Steiner Linear Ordering problem, we can address systems where the elements involved have different levels of priority, either high or low. This allows us greater flexibility in modeling different resource-constrained scheduling problems. In this paper, we address both the linear ordering problem and its application to scheduling problems, and provide a polyhedral study of the associated polytopes.

Increased Accuracy And Efficiency In Finite Element Computations Of The Leray-Deconvolution Model Of Turbulence, Abigail Bowers

All Theses

This thesis develops, analyzes and tests a finite element method for approximating solutions to the Leray–deconvolution regularization of the Navier–Stokes equations. The scheme combines three ideas in order to create an accurate and effective algorithm: the use of an incompressible filter, a linearization that decouples the velocity–pressure system from the filtering and deconvolution operations, and a stabilization that works well with the linearization. A rigorous and complete numerical analysis of the scheme is given, and numerical experiments are presented that show clear advantages of the scheme.

Source Optimization In Abstract Function Spaces For Maximizing Distinguishability: Applications To The Optical Tomography Inverse Problem, Bonnie Jacob

All Dissertations

The focus of this thesis is to formulate an optimal source problem for the medical imaging technique of optical tomography by maximizing certain distinguishability criteria. We extend the concept of distinguishability in electrical impedance tomography to the frequency-domain diffusion approximation model used in optical tomography.
We consider the dependence of the optimal source on the choice of appropriate function spaces, which can be chosen from certain Sobolev or Lp spaces. All of the spaces we consider are Hilbert spaces; we therefore exploit the inner product in several ways. First, we define and use throughout an inner product on the Sobolev …

Improved Accuracy For Fluid Flow Problems Via Enhanced Physics, Michael Case

All Dissertations

This thesis is an investigation of numerical methods for approximating solutions to fluid flow problems, specifically the Navier-Stokes equations (NSE) and magnetohydrodynamic equations (MHD), with an overriding theme of enforcing more physical behavior in discrete solutions. It is well documented that numerical methods with more physical accuracy exhibit better long-time behavior than comparable methods that enforce less physics in their solutions. This work develops, analyzes and tests finite element methods that better enforce mass conservation in discrete velocity solutions to the NSE and MHD, helicity conservation for NSE, cross-helicity conservation in MHD, and magnetic field incompressibility in MHD.

The Postsecret Phenomenon: A Contemporary Application Of Existential Psychotherapy, Dan Martin

Senior Honors Projects

In November 2004, as a whimsical break from his monotonous job, Frank Warren decided he would start a small art project in his community. This idea, which he entitled “PostSecret,” involved leaving blank post cards in various public locations that simply asked to “Share a Secret” and listed a few guidelines. Frank’s goal was to “create this non-judgmental, safe place where people could feel comfortable sharing parts of their lives that they've never told a soul.” What he expected to be a small result became a weekly blog, five published books, a traveling art gallery, and a lecture series given …

The Four-Color Theorem And Chromatic Numbers Of Graphs, Sarah E. Cates

Undergraduate Theses and Capstone Projects

We study graph colorings of the form made popular by the four-color theorem. Proved by Appel and Haken in 1976, the Four-Color Theorem states that all planar graphs can be vertex-colored with at most four colors. We consider an alternate way to prove the Four-Color Theorem, introduced by Hadwiger in 1943 and commonly know as Hadwiger’s Conjecture. In addition, we examine the chromatic number of graphs which are not planar. More specifically, we explore adding edges to a planar graph to create a non-planar graph which has the same chromatic number as the planar graph which we started from.

Mathematical Modeling Of Optimal Seasonal Reproductive Strategies And A Comparison Of Long-Term Viabilities Of Annuals And Perennials, Anthony Delegge

Department of Mathematics: Dissertations, Theses, and Student Research

In 1954, Lamont Cole posed a question which has motivated much ecological work in the past 50 years: When is the life history strategy of semelparity (organisms reproduce once, then die) favored, via evolution, over iteroparity (organisms may reproduce multiple times in their lifetime)? Although common sense should dictate that iteroparity would always be favored, we can observe that this is not always the case, since annual plants are not only prevalent, but can dominate an area. Also, certain plant species may be perennial in one region, but annual in another. Thus, in these areas, certain characteristics must be present …

Codes From Riemann-Roch Spaces For Y2 = Xp - X Over Gf(P), Darren B. Glass, David Joyner, Amy Ksir

Math Faculty Publications

Let Χ denote the hyperelliptic curve y2 = xp - x over a field F of characteristic p. The automorphism group of Χ is G = PSL(2, p). Let D be a G-invariant divisor on Χ(F). We compute explicit F-bases for the Riemann-Roch space of D in many cases as well as G-module decompositions. AG codes with good parameters and large automorphism group are constructed as a result. Numerical examples using GAP and SAGE are also given.

Switching Exponent Scaling Near Bifurcation Points For Non-Gaussian Noise, Lora Billings, Ira Schwartz, Mary Mccrary, A. Korotkrov, M. Dykman

Department of Mathematics Faculty Scholarship and Creative Works

We study noise-induced switching of a system close to bifurcation parameter values where the number of stable states changes. For non-Gaussian noise, the switching exponent, which gives the logarithm of the switching rate, displays a non-power-law dependence on the distance to the bifurcation point. This dependence is found for Poisson noise. Even weak additional Gaussian noise dominates switching sufficiently close to the bifurcation point, leading to a crossover in the behavior of the switching exponent.

On Construction Of The Smallest One-Sided Confidence Interval For The Difference Of Two Proportions, Weizhen Wang

Mathematics and Statistics Faculty Publications

For my class of one-sided 1 - α confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then applied to identify the minimum effective dose (MED) for binary data in dose-response studies, and a multiple test procedure that controls the familywise error rate at …

Accurate And Stable Numerical Methods For Solving Micro Heat Transfer Models In An N-Carrier System In Spherical Coordinates, Di Zhao

Doctoral Dissertations

Energy exchange between electrons and phonons in metal provides the best example in describing non-equilibrium heating during the ultrafast transient. In times comparable to the thermalization and relaxation time of electrons and phonons, which are in the range of a few to several tens of picoseconds, heat continuously flows from hot electrons to cold phonons through mutual collisions. Consequently, electron temperature continuously decreases whereas phonon temperature continuously increases until thermal equilibrium is reached. Tien developed the well-known parabolic two-step model for describing the non-equilibrium heating in the electron-phonon system in 1992, and Tzou developed the parabolic model for the non-equilibrium …

Seducing The Single Ticket Buyer: Converting Single Ticket Buyers To Subscribers At The Binghamton Philharmonic, Lauren F. Elicks

MPA Capstone Projects 2006 - 2015

Declining interests in classical music have left many performances based organizations scrambling to maintain subscriptions rates, ticket revenue and attendance. The Binghamton Philharmonic has a substantial single ticket buyer base which if converted to subscribers, would secure revenue and attendance to each season. This study explores the motivations and attendance levels of Binghamton Philharmonic single ticket buyer population. Using frequency distribution charts, cross-tabular analysis and independent samples t-tests, variables of motivation were compared to the single ticket and subscriber population.This project discusses the factors affecting single ticket buyer motivations for attendance, effective methods for encouraging greater attendance, and provides an …

An Empirical Likelihood-Based Method For Comparison Of Treatment Effects-Test Of Equality Of Coefficients In Linear Models, Haiyan Su, Hua Liang

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

To compare two treatment effects, which can be described as the difference of the parameters in two linear models, we propose an empirical likelihood-based method to make inference for the difference. Our method is free of the assumptions of normally distributed and homogeneous errors, and equal sample sizes. The empirical likelihood ratio for the difference of the parameters of interest is shown to be asymptotically chi-squared. Simulation experiments illustrate that our method outperforms the published ones. Our method is used to analyze a data set from a drug study.

Applying Metric Regularity To Compute Condition Measure Of Smoothing Algorithm For Matrix Games, Boris S. Mordukhovich, Javier Peña, Vera Roshchina

Mathematics Research Reports

Abstract. We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the smoothing first-order algorithm proposed in (4] and the exact bound of metric regularity for an associated set-valued mapping. In this way we compute the aforementioned condition measure in terms of the initial matrix game data.

High Order Finite Elements For Lagrangian Computational Fluid Dynamics, Truman Everett Ellis

Master's Theses

A general finite element method is presented to solve the Euler equations in a Lagrangian reference frame. This FEM framework allows for separate arbitrarily high order representation of kinematic and thermodynamic variables. An accompanying hydrodynamics code written in Matlab is presented as a test-bed to experiment with various basis function choices. A wide range of basis function pairs are postulated and a few choices are developed further, including the bi-quadratic Q2-Q1d and Q2-Q2d elements. These are compared with a corresponding pair of low order bi-linear elements, traditional Q1-Q0 and sub-zonal pressure Q1-Q1d. Several test problems are considered including static convergence …

Measuring Balkanization In Wikipedia, Colin Welch

Mathematics, Statistics, and Computer Science Honors Projects

Modern society has become increasingly balkanized, or ideologically polarized and socially fragmented. Political parties interact with each other over divisive issues by using polarizing rhetoric. Internet users create small, opinionated communities like dKosapedia and Conservapedia, Wikipedia-like websites written from positions of left-leaning and right-leaning bias. Even Wikipedia may not be immune to balkanization. As a free encyclopedia written by users from an unbiased point of view, it is in the interest of the general public to keep Wikipedia as free of balkanization and polarization as possible. If Wikipedia authors are free to express their conflicting points of view, the quality …

Morphological Evolution Of Single-Crystal Ultrathin Solid Films, Mikhail Khenner

Mathematics Faculty Publications

An introduction to mathematical modeling of ultrathin solid films and the role of such modeling in nanotechnologies: Educational presentation for senior physics majors