Mathematics Commons^™

On The Generalized Linear And Non-Linear Dfc In Non-Linear Dynamics, Dmitriy Dmitrishin, Anna Khamitova, Alexander M. Stokolos

Mathematical Sciences: Faculty Publications

The article is devoted to investigation of robust stability of the generalized linear control of the discrete autonomous dynamical systems. Sharp necessary conditions on the size of the set of multipliers that guaranty robust stabilization of the equilibrium of the system are provided. Surprisingly enough it turns out that the generalized linear delayed feedback control has same limitation as the classical Pyragas DFC. This generalized Ushio 1996 DFC limitation statement. Note that in scalar case a generalized non-linear control can robustly stabilize an equilibrium for any admissible range of multipliers. In the current article similar result is obtained in the …

Introduction To Functions And Generality Of Logic. Reflections On Frege's And Dedekind's Logicisms, Hourya Benis Sinaceur, Marco Panza, Gabriel Sandu

MPP Published Research

This book examines three connected aspects of Frege’s logicism: the differences between Dedekind’s and Frege’s interpretation of the term ‘logic’ and related terms and reflects on Frege’s notion of function, comparing its understanding and the role it played in Frege’s and Lagrange’s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege’s, Ramsey’s and Russell’s view on the subject. Composed of three chapters, this book sheds light on important aspects of Dedekind’s and Frege’s logicisms. The first chapter explains how, although he shares Frege’s aim at substituting logical standards of rigor to intuitive …

Reproducing Kernel Hilbert Space Vs. Frame Estimates, Palle E. T. Jorgensen, Myung-Sin Song

SIUE Faculty Research, Scholarship, and Creative Activity

We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn Hinto a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω . We then identify conditions on these functions which automatically give H the structure of a reproducing kernel Hilbert space of functions on Ω. We further give an explicit formula for the kernel, and for the corresponding isometric isomorphism. Applications are given to Hilbert spaces associated to families of Gaussian processes.

Review Of Developing Quantitative Literacy Skills In History And The Social Sciences: A Web-Based Common Core Approach By Kathleen W. Craver, Victor J. Ricchezza, H L. Vacher

Numeracy

Kathleen W. Craver. Developing Quantitative Literacy Skills in History and Social Sciences: A Web-Based Common Core Standards Approach (Lantham MD: Rowman & Littlefield Publishing Group, Inc., 2014). 191 pp.
ISBN 978-1-4758-1050-9 (cloth); ISBN …-1051-6 (pbk); ISBN…-1052-3 (electronic).

This book could be a breakthrough for teachers in the trenches who are interested in or need to know about quantitative literacy (QL). It is a resource providing 85 topical pieces, averaging 1.5 pages, in which a featured Web site is presented, described, and accompanied by 2-4 critical-thinking questions purposefully drawing on data from the Web site. The featured Web sites range from …

Mathematics And Humor: John Allen Paulos And The Numeracy Crusade, Paul H. Grawe

Numeracy

John Allen Paulos at minimum gave the Numeracy movement a name through his book Innumeracy: Mathematical Illiteracy and Its Consequences. What may not be so obvious was Paulos’ strong interest in the relationship between mathematics and mathematicians on the one hand and humor and stand-up-comedian joke structures on the other. Innumeracy itself could be seen as a typically mathematical Gotcha joke on American culture generally. In this perspective, a Minnesotan acculturated to Minnesota-Nice Humor of Self-Immolation Proclivities (SImP) looks at the more raw-boned, take-no-prisoners humor style Paulos outlined in Mathematics and Humor and implemented in Innumeracy.

Despite the …

The Math You Need, When You Need It (Tmyn): Leveling The Playing Field, Jennifer M. Wenner, Eric M. D. Baer

Numeracy

The Math You Need, When You Need It (TMYN) is a set of online tutorials designed to help students develop and review mathematical skills that are applied in undergraduate geoscience courses. We present results of a three-year study of more than 4000 students in 106 geoscience courses at a variety of post-secondary schools who were assigned TMYN tutorials as supplemental mathematics instruction. Changes in student scores from pre- to post-test suggest that the support provided by programs such as TMYN can begin to reduce the gap between mathematically well-prepared and underprepared students; in essence, TMYN levels the quantitative playing field …

Why Linear (And Piecewise Linear) Models Often Successfully Describe Complex Non-Linear Economic And Financial Phenomena: A Fuzzy-Based Explanation, Hung T. Nguyen, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Economic and financial phenomena are highly complex and non-linear. However, surprisingly, in many cases, these phenomena are accurately described by linear models -- or, sometimes, by piecewise linear ones. In this paper, we show that fuzzy techniques can explain the unexpected efficiency of linear and piecewise linear models: namely, we show that a natural fuzzy-based precisiation of imprecise ("fuzzy") expert knowledge often leads to linear and piecewise linear models.

We also discuss which expert-motivated nonlinear models should be used to get a more accurate description of economic and financial phenomena.

New Lower Bounds For The Topological Complexity Of Aspherical Spaces, Mark Grant, Gregory Lupton, John Oprea

Mathematics and Statistics Faculty Publications

We show that the topological complexity of an aspherical space X is bounded below by the cohomological dimension of the direct product A×BA×B, whenever A and B are subgroups of π1(X)π1(X) whose conjugates intersect trivially. For instance, this assumption is satisfied whenever A and B are complementary subgroups of π1(X)π1(X). This gives computable lower bounds for the topological complexity of many groups of interest (including semidirect products, pure braid groups, certain link groups, and Higman's acyclic four-generator group), which in some cases improve upon the standard lower bounds in terms of zero-divisors cup-length. Our results illustrate an intimate relationship between …

Why Political Scientists Are Wrong 15% Of The Time, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

An experimental study has shown that among situations when political scientists claimed that a political outcome was impossible, this outcome actually occurred in 15% of the cases. In this paper, we provide a possible explanation for this empirical fact.

Al-Sijistani's And Maimonides's Double Negation Theology Explained By Constructive Logic, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Famous medieval philosophers Al-Sijistani and Maimonides argued that the use of double negation helps us to better understand issues related to theology. To a modern reader, however, their arguments are somewhat obscure and unclear. We show that these arguments can be drastically clarified if we take into account the 20 century use of double negation in constructive logic.

Course Proposal For A Mathematical Modeling Course In A High School Curriculum, Thomas P. Marlowe

Masters Essays

In the winter of 2015, I will be piloting a course on mathematical modeling at Hawken School, an independent high school in Gates Mills, OH. As I develop all elements of this course, such as lesson plans, assessments, and rubrics, I will be mindful of factors such as the newly adopted Common Core mathematics standards, the variety of student backgrounds in such a course, and how various mathematical societies and organizations such as SIAM, MAA, and COMAP can help in implementing it. However, there is one basic question driving my interest in and design of this course: “when am I …

Expectation Numbers Of Cyclic Groups, Miriam Mahannah El-Farrah

Masters Theses & Specialist Projects

When choosing k random elements from a group the kth expectation number is the expected size of the subgroup generated by those specific elements. The main purpose of this thesis is to study the asymptotic properties for the first and second expectation numbers of large cyclic groups. The first chapter introduces the kth expectation number. This formula allows us to determine the expected size of any group. Explicit examples and computations of the first and second expectation number are given in the second chapter. Here we show example of both cyclic and dihedral groups. In chapter three we discuss arithmetic …

Mexico City Normal Weight Children Exposed To High Concentrations Of Ambient Pm2.5 Show High Blood Leptin And Endothelin-1, Vitamin D Deficiency, And Food Reward Hormone Dysregulation Versus Low Pollution Controls. Relevance For Obesity And Alzheimer Disease, Partha S. Mukherjee

Mathematics Faculty Publications and Presentations

Millions of Mexico, US and across the world children are overweight and obese. Exposure to fossil-fuel combustion sources increases the risk for obesity and diabetes, while long-term exposure to fine particulate matter (PM _2.5) and ozone (O₃) above US EPA standards is associated with increased risk of Alzheimer’s disease (AD). Mexico City Metropolitan Area children are chronically exposed to PM_2.5 and O₃ concentrations above the standards and exhibit systemic, brain and intrathecal inflammation, cognitive deficits, and Alzheimer disease neuropathology. We investigated adipokines, food reward hormones, endothelial dysfunction, vitamin D and apolipoprotein E (APOE) relationships in …

Paratodo X: Una Introducción A La Lógica Formal, P.D. Magnus

Philosophy Faculty Books

A translation of the logic textbook forall x (v 1.30) into Spanish. Translation by José Ángel Gascón.

Toric Partial Orders, Mike Develin, Matthew Macauley, Victor Reiner

Publications

We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite posets under the equivalence relation generated by converting minimal elements into maximal elements, or sources into sinks. We derive toric analogues for several features of ordinary partial orders, such as chains, antichains, transitivity, Hasse diagrams, linear extensions, and total orders.

How Do U.S. And Chinese Biology Students Compare In Explaining Energy Consumption Issues?, Hui Jin, Hayat Hokayem, Sasha Wang, Xin Wei

Mathematics Faculty Publications and Presentations

This qualitative study investigates how biology majors explain energy consumption issues. In particular, we focus on two energy consumption activities that account for about two-thirds of global carbon dioxide emissions in 2011: burning fossil fuels for transportation and using electricity. We conducted in-depth clinical interviews with twenty U.S. students and twenty Chinese students. We compared these two groups of students in terms of two aspects of explanation: 1) naming scientific terms in the explanation, and 2) explaining an energy consumption issue. Regarding naming, we examined the frequency of naming different terms of scientific concepts and principles in students’ explanations. Regarding …

Gazelle Companies: What Is So Special About The 20% Threshold?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In business analysis, a special emphasis is placed on "gazelles", companies that grow by at least 20% per year for several years (usually four). While this 20% threshold is somewhat supported by empirical research, from the theoretical viewpoint, it is not clear what is so special about this value. In this paper, we provide a possible explanation for this empirical fact.

Mittag-Leffler Therorem, Elizabeth O. Agyeman

Masters Essays

No abstract provided.

Missing Photos, Suffering Withdrawal, Or Finding Freedom? How Experiences Of Social Media Non-Use Influence The Likelihood Of Reversion, Eric P.S. Baumer, Shion Guha, Emily Quan, David Mimno, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

This article examines social media reversion, when a user intentionally ceases using a social media site but then later resumes use of the site. We analyze a convenience sample of survey data from people who volunteered to stay off Facebook for 99 days but, in some cases, returned before that time. We conduct three separate analyses to triangulate on the phenomenon of reversion: simple quantitative predictors of reversion, factor analysis of adjectives used by respondents to describe their experiences of not using Facebook, and statistical topic analysis of free-text responses. Significant factors predicting either increased or decreased likelihood of reversion …

Characterizations Of Levy Distribution Via Sub-Independence Of The Random Variables And Truncated Moments, Gholamhossein G. Hamedani, M. Ahsanullah, Seyed Morteza Najibi

Mathematics, Statistics and Computer Science Faculty Research and Publications

The concept of sub-independence is based on the convolution of the distributions of the random variables. It is much weaker than that of independence, but is shown to be sufficient to yield the conclusions of important theorems and results in probability and statistics. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. Following Ahsanullah and Nevzorov (2014), we present certain characterizations of Levy distribution based on: (i) the sub-independence of the random variables; (ii) a simple relationship between two truncated moments; (iii) conditional expectation of certain function of the random variable. In …

2015 (Summer), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2015 Summer Colloquium.

Gottlieb Groups Of Function Spaces, Gregory Lupton, Samuel Bruce Smith

Mathematics and Statistics Faculty Publications

We analyze the Gottlieb groups of function spaces. Our results lead to explicit decompositions of the Gottlieb groups of many function spaces map(X,Y)---including the (iterated) free loop space of Y---directly in terms of the Gottlieb groups of Y. More generally, we give explicit decompositions of the generalized Gottlieb groups of map(X,Y) directly in terms of generalized Gottlieb groups of Y. Particular cases of our results relate to the torus homotopy groups of Fox. We draw some consequences for the classification of T-spaces and G-spaces. For X, Y finite and Y simply connected, we give a formula for the ranks of …

Prognostic Role Of Cardiac Power Index In Ambulatory Patients With Advanced Heart Failure, Justin L. Grodin, Wilfried Mullens, Matthias Dupont, Yuping Wu, David O. Taylor, Randall C. Starling, W.H. Wilson Tang

Mathematics and Statistics Faculty Publications

BACKGROUND: Cardiac pump function is often quantified by left ventricular ejection fraction by various imaging modalities. As the heart is commonly conceptualized as a hydraulic pump, cardiac power describes the hydraulic function of the heart. We aim to describe the prognostic value of resting cardiac power index (CPI) in ambulatory patients with advanced heart failure. METHODS AND RESULTS: We calculated CPI in 495 sequential ambulatory patients with advanced heart failure who underwent invasive haemodynamic assessment with longitudinal follow-up of adverse outcomes (all-cause mortality, cardiac transplantation, or ventricular assist device placement). The median CPI was 0.44 W/m(2) (interquartile range 0.37, 0.52). …

Local And Nonlocal Models In Thin-Plate And Bridge Dynamics, Jeremy Trageser

Department of Mathematics: Dissertations, Theses, and Student Research

This thesis explores several models in continuum mechanics from both local and nonlocal perspectives. The first portion settles a conjecture proposed by Filippo Gazzola and his collaborators on the finite-time blow-up for a class of fourth-order differential equations modeling suspension bridges. Under suitable assumptions on the nonlinearity and the initial data, a finite-time blowup is demonstrated as a result of rapid oscillations with geometrically growing amplitudes. The second section introduces a nonlocal peridynamic (integral) generalization of the biharmonic operator. Its action converges to that of the classical biharmonic as the radius of nonlocal interactions---the ``horizon"---tends to zero. For the corresponding …

Infinity In The High School Mathematics Classroom, Alyssa Hoslar

Masters Essays

No abstract provided.

Who Came Up With This? Mathematics History In The Classroom, Katie S. Schneck

Masters Essays

No abstract provided.

Approximate Analysis Solution Of Burgers-Kdv Equation, Hani Aldirawi

Theses and Dissertations - UTB/UTPA

In this thesis, we study the Two-Dimensional Burgers-Kortewege-de Vries(2D-BKdV) equation by analyzing the equivalent Abel equation, which indicates that under some particular conditions, the 2D-BKdV equation has a unique bounded traveling wave solution. By using the theorem of contractive mapping, a traveling wave solution to the 2D-BKdV equation is expressed explicitly.

The Facility Location Problem, Meghan E. Csoke

All Student Theses and Dissertations

The purpose of this study was to analyze the location of an emergency facility location within a town based on given information from the village and to use the results to determine the optimal location for an emergency facility. A model of the problem was developed using a spreadsheet and computer program to record and analyze the optimal response time based on different locations of emergency facilities. Assumptions were made to create situations easily computed through spreadsheet and computer programs. Once calculated, information was used to create a framework of demand density across a gridded map. Once the computer program …

High Impact Strategies And The Effect It Has On Students’ Mathematics Attitudes, Lauren A. Ryba

All Student Theses and Dissertations

This study was designed to determine if innovative strategies such as the use of technology and Supplemental Instruction (SI) could have an impact on students in an introductory statistics course. The study describes the use of a reliable instrument to measure students’ attitudes and beliefs about mathematics. Martha Tapia developed the Attitudes Toward Mathematics Inventory (ATMI) instrument in 1996 and later Lim and Chapman further refined a short form in 2012. The purpose of the ATMI was to measure mathematics attitudes in four ways: (1) enjoyment of mathematics, (2) motivation to do mathematics, (3) self confidence in mathematics, and (4) …

A Study On Hispanic College Students' Mathematics Anxiety, Study Habits, And Academic Performances On Mathematics, Luis M. Fernandez

Theses and Dissertations - UTB/UTPA

Mathematics anxiety has been described as a feeling of apprehension, fear, tension, and discomfort when confronted with mathematics. Mathematics anxiety has also been shown to interfere with mathematics performance; therefore, for our research we investigated what portions of individuals seem to suffer higher levels of mathematics anxiety and to what extent they are affected by it. We also investigated the study habits of the students and how these affect their mathematics anxiety levels and overall mathematics performance. Our data was obtained from Hispanic undergraduate students (n=405) who took Elementary Algebra (Math 1300), Intermediate Algebra (Math 1334), College Algebra (Math 1340) …