Mathematics Commons^™

Estimating Correlation Under Interval And Fuzzy Uncertainty: Case Of Hierarchical Estimation, Ali Jalal-Kamali

Departmental Technical Reports (CS)

In many situations, we are interested in finding the correlation ρ between different quantities x and y based on the values x_i and y_i of these quantities measured in different situations i. The correlation is easy to compute when we know the exact sample values x_i and y_i. In practice, the sample values come from measurements or from expert estimates; in both cases, the values are not exact. Sometimes, we know the probabilities of different values of measurement errors, but in many cases, we only know the upper bounds Δ_xi and Δ_yi on …

Semi-Heuristic Target-Based Fuzzy Decision Procedures: Towards A New Interval Justification, Christian Servin, Van-Nam Huynh, Yoshiteru Nakamori

Departmental Technical Reports (CS)

To more adequately describe human decision making, V.-N. Nuynh, Y. Nakamori, and others proposed a special semi-heuristic target-based fuzzy decision procedure. A usual justification for this procedure is based on the selection of the simplest possible membership functions and "and"- and "or"-operations; if we use more complex membership functions and "and"- and "or"-operations, we get different results. Interestingly, in practical applications, the procedure based on the simplest choices most adequately describes human preferences. It is therefore desirable to come up with a justification that explains this empirical fact. Such a justification is proposed in this paper

Function Estimation Of Irregularly Spaced Data With Long Memory Dependence, Rosalie Michelle Wheeler

Dissertations

We examine the problem of estimating an underlying function from collected data. The methods considered include parametric regression, density estimation, kernel estimation, wavelet regression, and specific results from when our underlying function f\left(x\right) is a member of the Besov or the Triebel spaces. Then we consider the problem of long memory error in several settings, including data which is equally spaced, data which is unequally spaced, and data which is a member of the Holder class and several other spaces. Ultimately we focus on three different problems. The first involves using linear interpolation or local averaging to account for the …

When Is A Trigonometric Polynomial Not A Trigonometric Polynomial?, Joseph E. Borzellino, Morgan Sherman

Mathematics

No abstract provided.

Resonant Solutions And Turning Points In An Elliptic Problem With Oscillatory Boundary Conditions, Alfonso Castro, Rosa Pardo

All HMC Faculty Publications and Research

We consider the elliptic equation -Δu + u = 0 with nonlinear boundary conditions ∂u/∂n = λu + g(λ,x,u), where the nonlinear term g is oscillatory and satisfies g(λ,x,s)/s→0 as |s|→0. We provide sufficient conditions on g for the existence of sequences of resonant solutions and turning points accumulating to zero.

Continued Radicals And Cantor Sets, Thomas Tyler Clark

Masters Theses & Specialist Projects

We examine the formation of sets homeomorphic to the ternary Cantor set by continued radicals. We determine properties of bridges and gaps and calculate the thickness of the Cantor set. From this we apply information from continued fractions to continued radicals to obtain new results. We also consider the measure of several Cantor sets.

Scientific Notebook At Pace University: Technology For 21st Century Mathematics And Science, Brian Evans, Demos Athanasopoulos

Cornerstone 3 Reports : Interdisciplinary Informatics

No abstract provided.

How To Define Average Class Size (And Deviations From The Average Class Size) In A Way Which Is Most Adequate For Teaching Effectiveness, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When students select a university, one of the important parameters is the average class size. This average is usually estimated as an arithmetic average of all the class sizes. However, it has been recently shown that to more adequately describe students' perception of a class size, it makes more sense to average not over classes, but over all students -- which leads to a different characteristics of the average class size. In this paper, we analyze which characteristic is most adequate from the viewpoint of efficient learning. Somewhat surprisingly, it turns out that the arithmetic average is the most adequate …

Behavioral Economics And Physician Behavior, Allyssa S. Ward

Honors Theses

This study seeks to answer whether the availability heuristic leads physicians to utilize more medical care than is economically efficient. Do rare, salient events alter physicians' perceptions about the probability of patient harm? Do these events lead physicians to overutilize certain medical procedures? This study uses Pennsylvania inpatient hospital admissions data from 2009 aggregated at the physician level to investigate these questions. The data come from the 2009 Pennsylvania Health Care Cost Containment Council (PHC4).

The study is divided into two parts. In Part I, we examine whether bad outcomes during childbirth (defined as maternal mortality, an obstetric fistula or …

The Deepwater Horizon Oil Spill Disaster: A Graphical Assessment Of Its Impact On Wildlife, Anvar Suyundikov

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The Deepwater Horizon oil spill occurred in the Gulf of Mexico on April 20, 2010. Considered the largest accidental marine oil spill in history, oil flowed for three months and approximately five million barrels of oil spilled through by mid-July 2010. In this report, we analyze fish and bird data to assess the impact of the oil spill on the Gulf wildlife. Our findings based on the available fish data for 2005, 2006, and 2010 are not very helpful to make a judgement on the negative impact of the oil spill on fish species. On the other hand, the bird …

Modeling Spatial Uncertainties In Geospatial Data Fusion And Mining, Boris Kovalerchuk, Leonid Perlovsky, Michael Kovalerchuk

All Faculty Scholarship for the College of the Sciences

Geospatial data analysis relies on Spatial Data Fusion and Mining (SDFM), which heavily depend on topology and geometry of spatial objects. Capturing and representing geometric characteristics such as orientation, shape, proximity, similarity, and their measurement are of the highest interest in SDFM. Representation of uncertain and dynamically changing topological structure of spatial objects including social and communication networks, roads and waterways under the influence of noise, obstacles, temporary loss of communication, and other factors. is another challenge. Spatial distribution of the dynamic network is a complex and dynamic mixture of its topology and geometry. Historically, separation of topology and geometry …

The Effects Of Goal Setting In A Developmental Algebra Course, Richard Leo Hunt

Masters Theses & Specialist Projects

The purpose of this study was to study the effects of goal setting on students in a developmental algebra course. This study examined the effects on test scores for students that were prescribed a test score goal, students that created their own test score goal, and then compared to a control group. Three classes of developmental algebra were chosen with a total of 25 participants with reported results. Results showed that students with a goal on a test did not score significantly better than students without a goal, but did score significantly better on a test after the goal than …

Translation Representations And Scattering By Two Intervals, Palle Jorgensen, Steen Pedersen, Feng Tian

Mathematics and Statistics Faculty Publications

Studying unitary one-parameter groups in Hilbert space (U(t), H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L²-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U(t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator and scattering matrix. We illustrate our results in the Lax-Phillips model where (U(t), H) represents an acoustic wave equation …

Challenging Disciplinary Boundaries In The First Year: A New Introductory Integrated Science Course For Stem Majors, Lisa Gentile, Lester Caudill, Mirela Fetea, April L. Hill, Kathy Hoke, Barry Lawson, Ovidiu Z. Lipan, Michael Kerckhove, Carol A. Parish, Krista J. Stenger, Doug Szajda

Biology Faculty Publications

To help undergraduates make connections among disciplines so they are able to approach, evaluate, and contribute to the solutions of important global problems, our campus has been focused on interdisciplinary research and education opportunities across the science, technology, engineering, and mathematics (STEM) disciplines. This paper describes the mobilization, planning, and implementation of a first-year interdisciplinary course for STEM majors that integrates key concepts found in traditional first-semester biology, chemistry, computer science, mathematics, and physics courses. This team-taught course, Integrated Quantitative Science (IQS), is half of a first-year student’s schedule in both semesters and is composed of a double lecture and …

How Ipads Can Be Used In The Math Classroom To Improve Student Learning, Katie Ann Garrity Smieja

Mathematics Graduate Theses

This study explores how iPads can be used to enhance student learning in the math classroom. The author reviews current literature to determine how iPads are being used to facilitate communication, formative assessment, and promising practices in math education such as discovery learning and use of spreadsheets, graphing calculators, and manipulatives. Additionally, challenges and drawbacks to using iPads in the classroom are examined. Research supports the use of iPads to provide students access to digital content including online discussion boards and practice activities with instant feedback. iPads can also be used as student response systems to engage students in instruction …

Enumeration Of Independent Sets In Graphs, James Alexander

Theses, Dissertations and Culminating Projects

An independent set is one of the most natural structures in a graph to focus on, from both a pure and applied perspective. In the realm of graph theory, and any concept it can represent, an independent set is the mathematical way of capturing a set of objects, none of which are related to each other. As graph theory grows, many questions about independent sets are being asked and answered, many of which are concerned with the enumeration of independent sets in graphs. We provide a detailed introduction to general graph theory for those who are not familiar with the …

Tower Families Of Ribbon Graphs, Jordan Keller

Honors Capstones

No abstract provided.

Construction And Analysis Of Magic Squares Of Squares Over Certain Finite Fields, Stewart Hengeveld

Theses, Dissertations and Culminating Projects

This thesis presents results of the research on the study of Magic Squares of Squares over certain finite fields. The research is motivated by an open question, which is still not answered: "Does there exist a 3 x 3 magic square with all nine entries being distinct perfect squares of integers?" Instead of directly trying to answer this challenging question, this research attempts to answer a parallel question: "Does there exist a 3 x 3 magic square with all nine entries being distinct perfect squares modulo a prime number p?" Equivalently, the question can be restated as, "Does there exist …

The Persistence Of Infectious Diseases In Metapopulations, Jonathan Calvin Hayes

Theses, Dissertations and Culminating Projects

Mathematical models provide a great deal of information about the dynamics of disease spread. In this paper, we use stochastic simulation to investigate spontaneous disease extinction and réintroduction in a SIR model. We begin by investigating path to extinction and time to extinction in single population models, and then expand to a multipopulation model linked with linear migration. We have found that in a single population model, it is more effective to use random pulse vaccinations less per year at a higher removal rate. We have expanded this result by developing a vaccination strategy giving one large, well timed pulse …

The Number Of Ways To Write N As A Sum Of ` Regular Figurate Numbers, Seth Jacob Rothschild

Renée Crown University Honors Thesis Projects - All

See Document for Abstract