Physical Sciences and Mathematics Commons^™

Elementary Differential Equations With Boundary Value Problems, William F. Trench

William F. Trench

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some prepa- ration in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. …

Elementary Differential Equations, William F. Trench

William F. Trench

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. An …

Student Solutions Manual For Elementary Differential Equations And Elementary Differential Equations With Boundary Value Problems, William F. Trench

William F. Trench

No abstract provided.

Introduction To Real Analysis, William F. Trench

William F. Trench

This is a text for a two-term course in introductory real analysis for junior or senior math- ematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathe- matical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calcu- lus sequence …

Modeling The Progress And Retention Of International Students Using Markov Chains, Lucas Gagne

Lucas Gagne

Motivation For Achievement And Attitudes Toward Mathematics Instruction In A Required Calculus Course At The Norwegian University Of Science And Technology, Donna Sundre, Carol Barry, Vidar Gynnild, Erin Tangen Ostgard

Donna L. Sundre

This study from the Norwegian University of Science and Technology (NTNU) examines students’ learning goals and attitudes toward mathematics in a first-year calculus course in undergraduate engineering education. Achievement motivation research using the Achievement Goal Questionnaire (AGQ) is advanced from current literature with two additions: (1) a course specific context using introductory college calculus students, and (2) participation of Norwegian students. Pre- and posttest measures of attitudes indicate that students do change learning goals over time, unfortunately opposite to the instructors’ aspirations. A significant increase in “Mastery Avoidance” and “Work Avoidance” was accompanied with a drop in “Mastery Approach” and …

On The Data Of Images, Lori Ziegelmeier

Lori Beth Ziegelmeier

No abstract provided.

An Unnoticed Consequence Of Szego's Distribution Theorem, William F. Trench

William F. Trench

No abstract provided.

Making The Journey From A Traditional Model To An Online Model, Jenny Shrensker, Nazire Koc

Jenny Shrensker

A Bijective Proof Of A Factorization Formula For Specialized Macdonald Polynomials, Nicholas A. Loehr, Elizabeth Niese

Elizabeth Niese

Let μ and ν = (ν 1, . . . , ν k ) be partitions such that μ is obtained from ν by adding m parts of sizer. Descouens and Morita proved algebraically that the modified Macdonald polynomials H~μ(X;q,t) satisfy the identity H~μ=H~νH~(rm) when the parameter t is specialize to an mth root of unity. Descouens, Morita, and Numata proved this formula bijectively when r ≤ ν k and r∈{1,2}. This note gives a bijective proof of the formula for all r ≤ ν k .

New Combinatorial Formulations Of The Shuffle Conjecture, Nicholas A. Loehr, Elizabeth Niese

Elizabeth Niese

The shuffle conjecture (due to Haglund, Haiman, Loehr, Remmel, and Ulyanov) provides a combinatorial formula for the Frobenius series of the diagonal harmonics module DHn, which is the symmetric function∇(en). This formula is a sum over all labeled Dyck paths of terms built from combinatorial statistics called area, dinv, and IDes. We provide three new combinatorial formulations of the shuffle conjecture based on other statistics on labeled paths, parking functions, and related objects. Each such reformulation arises by introducing an appropriate new definition of the inverse descent set. Analogous results are proved for the higher-order shuffle conjecture involving ∇m(en). We …

A New Recursion For Three-Column Combinatorial Macdonald Polynomials, Elizabeth Niese

Elizabeth Niese

The Hilbert series of the Garsia–Haiman module Mμ can be described combinatorially as the generating function of certain fillings of the Ferrers diagram of μ where μ is an integer partition of n . Since there are n ! fillings that generate , it is desirable to find recursions to reduce the number of fillings that need to be considered when computing combinatorially. In this paper, we present a combinatorial recursion for the case where μ is an n by 3 rectangle. This allows us to reduce the number of fillings under consideration from (3n)! to (3n)!/(3!nn!).

Network Analysis Of World Trade Using The Baci-Cepii Dataset, Luca De Benedictis, Silvia Nenci, Gianluca Santoni, Lucia Tajoli, Claudio Vicarelli

Luca De Benedictis

In this paper we explore the BACI-CEPII database using Network Analysis. Starting from the visualization of the World Trade Network, we then define and describe the topology of the network, both in its binary version and in its weighted version, calculating and discussing some of the commonly used network’s statistics. We finally discuss some specific topic that can be studied using Network Analysis and International Trade data, both at the aggregated and sectoral level. The analysis is done using multiple software (Stata, R, and Pajek). The scripts to replicate part of the analysis are included in the appendix, and can …

Computing, Symbols And Math, Stephen M. Watt

Stephen M. Watt

No abstract provided.

Composite Dilation Wavelets With High Degrees, Tian-Xiao He

Tian-Xiao He

No abstract provided.

Asymptotic Expansions And Computation Of Generalized Stirling Numbers And Generalized Stirling Functions, Tian-Xiao He

Tian-Xiao He

Here presented is a unified approach to Stirling numbers and their generalizations as well as generalized Stirling functions by using generalized factorial functions, k-Gamma functions, and generalized divided difference. Previous well-known extensions of Stirling numbers due to Riordan, Carlitz, Howard, Charalambides-Koutras, Gould-Hopper, Hsu-Shiue, Tsylova Todorov, Ahuja-Enneking, and Stirling functions introduced by Butzer and Hauss, Butzer, Kilbas, and Trujilloet and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations and generating functions are discussed. Some asymptotic expansions for the generalized Stirling functions and generalized Stirling numbers are established. …

A Study Of Flipping Vs. Not Flipping In Applied Calculus, Lori Ziegelmeier

Lori Beth Ziegelmeier

No abstract provided.

English Translation (From Latin) Of "A Solution Of A Most Difficult Problem, In Which The Two Forms Aaxx + Bbyy Et Aayy + Bbxx Must Be Rendered Into Squares" By L. Euler, Christopher Goff

Christopher Goff

A Covariance Inequality With A Non-Monotone Function, Martin Egozcue

Martin Egozcue

No abstract provided.

The Pitman Inequality For Exchangeable Random Vectors, J. Behboodian, Naveen Bansal, Gholamhossein Hamedani, Hans Volkmer

Naveen Bansal

In this short article the following inequality called the “Pitman inequality” is proved for the exchangeable random vector (X₁,X₂,…,X_n)(X1,X2,…,Xn) without the assumption of continuity and symmetry for each component X_iXi:

P(|1n∑i=1nXi|≤|∑i=1nαiXi|)≥12 ,

where allαi≥0 are special weights with∑i=1nαi=1.

Empirical Bayes And Hierarchical Bayes Estimation Of Skew Normal Populations, Naveen K. Bansal, Mehdi Maadooliat, Xiaowei Wang

Naveen Bansal

We develop empirical and hierarchical Bayesian methodologies for the skew normal populations through the EM algorithm and the Gibbs sampler. A general concept of skewness to the normal distribution is considered throughout. Motivations are given for considering the skew normal population in applications, and an example is presented to demonstrate why the skew normal distribution is more applicable than the normal distribution for certain applications.

Randomized Detection Of Extraneous Factors, Manfred Minimair

Manfred Minimair

A projection operator of a system of parametric polynomials is a polynomial in the coefficients of the system that vanishes if the system has a common root. The projection operator is a multiple of the resultant of the system, and the factors of the projection operator that are not contained in the resultant are called extraneous factors. The main contribution of this work is to provide a randomized algorithm to check whether a factor is extraneous, which is an important task in applications. A lower bound for the success probability is determined which can be set arbitrarily close to one. …

Spontaneous Oscillations In Simple Fluid Networks, Nathaniel Karst, Brian Storey, John Geddes

Brian Storey

Nonlinear phenomena including multiple equilibria and spontaneous oscillations are common in fluid networks containing either multiple phases or constituents. In many systems, such behavior might be attributed to the complicated geometry of the network, the complex rheology of the constituent fluids, or, in the case of microvascular blood flow, biological control. In this paper we investigate two examples of a simple three-node fluid network containing two miscible Newtonian fluids of differing viscosities, the first modeling microvascular blood flow and the second modeling stratified laminar flow. We use a combination of analytic and numerical techniques to identify and track saddle-node and …

Spontaneous Oscillations In Simple Fluid Networks, Nathaniel Karst, Brian Storey, John Geddes

John B. Geddes

Nonlinear phenomena including multiple equilibria and spontaneous oscillations are common in fluid networks containing either multiple phases or constituents. In many systems, such behavior might be attributed to the complicated geometry of the network, the complex rheology of the constituent fluids, or, in the case of microvascular blood flow, biological control. In this paper we investigate two examples of a simple three-node fluid network containing two miscible Newtonian fluids of differing viscosities, the first modeling microvascular blood flow and the second modeling stratified laminar flow. We use a combination of analytic and numerical techniques to identify and track saddle-node and …

An Injection From Standard Fillings To Parking Functions, Elizabeth Niese

Elizabeth Niese

The Hilbert series of the Garsia-Haiman module can be written as a generating function of standard fillings of Ferrers diagrams. It is conjectured by Haglund and Loehr that the Hilbert series of the diagonal harmonics can be written as a generating function of parking functions. In this paper we present a weight-preserving injection from standard fillings to parking functions for certain cases.

Session A-1: Problem Solving Through Graph Theory, Noah Prince

Noah Prince

Graph theory is an area of mathematics often not encountered before college, and not always even there. Nonetheless, it is full of problems that novices can quickly understand and begin to figure out. Often, sixty seconds of introduction to such a problem can lead to literally an hour of discussion as students engage in finding solutions. In this presentation, I will offer some sample problems and discuss how to use them with students in middle or high school.

Total Acquisition In Graphs, Timothy D. Lesaulnier, Noah Prince, Paul S. Wenger, Douglas B. West, Pratik Worah

Noah Prince

Let G be a weighted graph in which each vertex initially has weight 1. A total acquisition move transfers all the weight from a vertex u to a neighboring vertex v, under the condition that before the move the weight on v is at least as large as the weight on u. The (total) acquisition number of G, written a_t(G), is the minimum size of the set of vertices with positive weight after a sequence of total acquisition moves. Among connected n-vertex graphs, a_t(G) is maximized by trees. …

Mathematical Reasoning: Writing And Proof, Version 2.0, Ted Sundstrom

Ted Sundstrom, Professor of Mathematics

English Translation (From Latin) Of “On A Notable Advancement Of Diophantine Analysis,” By L. Euler, Christopher Goff

Christopher Goff

English Translation (From Latin) Of “On Finding Three Or More Numbers, The Sum Of Which Is A Square, While The Sum Of The Squares Is A Fourth Power,” By L. Euler, Christopher Goff

Christopher Goff