# Applied Mathematics Commons™

## All Articles in Applied Mathematics

4626 full-text articles. Page 1 of 146.

Calculus For Business And Economics, 2018 Fort Valley State University

#### Calculus For Business And Economics, Samuel Cartwright, Bhavana Burell, Patcharin Marion, Jianmin Zhu

##### Mathematics Grants Collections

This Grants Collection for Calculus for Business and Economics was created under a Round Six ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Initial Proposal
• Final Report

Algebraic Methods For The Construction Of Algebraic-Difference Equations With Desired Behavior, 2018 Aristotle University of Thessaloniki

#### Algebraic Methods For The Construction Of Algebraic-Difference Equations With Desired Behavior, Lazaros Moysis, Nicholas Karampetakis

##### Electronic Journal of Linear Algebra

For a given system of algebraic and difference equations, written as an Auto-Regressive (AR) representation $A(\sigma)\beta(k)=0$, where $\sigma$ denotes the shift forward operator and $A\left( \sigma \right)$ a regular polynomial matrix, the forward-backward behavior of this system can be constructed by using the finite and infinite elementary divisor structure of $A\left( \sigma \right)$. This work studies the inverse problem: Given a specific forward-backward behavior, find a family of regular or non-regular polynomial matrices $A\left( \sigma \right)$, such that the constructed system $A\left( \sigma \right) \beta \left( k\right) =0$ has exactly the ...

Inventing Around Edison’S Lamp Patent: The Role Of Patents In Stimulating Downstream Development And Competition, 2018 Bi-Level Technologies

#### Inventing Around Edison’S Lamp Patent: The Role Of Patents In Stimulating Downstream Development And Competition, Ron D. Katznelson, John Howells

##### Ron D. Katznelson

We provide the first detailed empirical study of inventing around patent claims.  The enforcement of Edison’s incandescent lamp patent in 1891-1894 stimulated a surge of patenting. Most of these later patents disclosed inventions around the Edison patent.  Some of these patents introduced important new technology in their own right and became prior art for new fields, indicating that invention around patents contributes to dynamic efficiency.  Contrary to widespread contemporary understanding, the Edison lamp patent did not suppress technological advance in electric lighting.  The market position of General Electric (“GE”), the Edison patent-owner, weakened through the period of this patent ...

Mathematical Arguments In Favor Of Risk In Andy Weir's The Martian, 2018 Midwestern State University

#### Mathematical Arguments In Favor Of Risk In Andy Weir's The Martian, Sarah C. Cobb, Jeff B. Hood

##### Journal of Humanistic Mathematics

In Andy Weir’s novel The Martian, the characters encounter high-stakes, life-or-death situations, in which they must make choices based on their assessment of risk and likely outcomes. They have different reactions to risky situations, based on their approaches to assessing risk and their perspectives on the stakes involved. In this paper, we examine the ways that characters in The Martian intuitively assess risk and compare them to mathematical analysis of the situations in the book.

Truancy In High School, 2018 Northeastern Illinois University

#### Truancy In High School, Itzel Ruiz, Jason Mink, Xochitl Aleman

##### SPACE: Student Perspectives About Civic Engagement

The main focus of this project is to analyze students’ poor attendance in order to understand the applicable factors as to why upperclassmen tend to miss more school than students in younger grades. We will be focusing on how students relationships with parents and teachers affect upperclassmen attendance. An anonymous ten question survey was given to five Junior and Senior Civics and U.S. History classes at Steinmetz College Prep high school. The questions were geared towards the students days absent during the school year, and their relationship with teachers and parents. Majority of the students surveyed missed more than ...

Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, 2018 Augsburg College

#### Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John M. Zobitz

##### Spora: A Journal of Biomathematics

We analyze a process-based temperature model for the length distribution and population over time of mayfly nymphs. Model parameters are estimated using a Markov Chain Monte Carlo parameter estimation method utilizing length distribution data at five different stream sites. Two different models (a standard exponential model and a modified Weibull model) of mayfly mortality are evaluated, where in both cases mayfly length growth is a function of stream temperature. Based on model-data comparisons to the modeled length distribution and the Bayesian Information Criterion, we found that approaches that length distribution data can reliably estimate 2–3 model parameters. Future model ...

Motion Planning For Educational Robots, 2018 Selected Works

#### Motion Planning For Educational Robots, Ronald I. Greenberg, Jeffery M. Karp

##### Ronald Greenberg

This paper considers various simple ways of navigating in a 2-dimensional territory with a two-wheeled robot of a type typical in educational robotics. We determine shortest paths under various modes of operation and compare.

An Interval Arithmetic Newton Method For Solving Systems Of Nonlinear Equations, 2018 Washington University in St. Louis

#### An Interval Arithmetic Newton Method For Solving Systems Of Nonlinear Equations, Ronald I. Greenberg, Eldon R. Hansen

##### Ronald Greenberg

We introduce an interval Newton method for bounding solutions of systems of nonlinear equations. It entails three sub-algorithms. The first is a Gauss-Seidel type step. The second is a real (non-interval) Newton iteration. The third solves the linearized equations by elimination. We explain why each sub-algorithm is desirable and how they fit together to provide solutions in as little as 1/3 to 1/4 the time required by a commonly used method due to Krawczyk.

2018 Harvey Mudd College

#### Iterative Matrix Factorization Method For Social Media Data Location Prediction, Natchanon Suaysom

##### HMC Senior Theses

Since some of the location of where the users posted their tweets collected by social media company have varied accuracy, and some are missing. We want to use those tweets with highest accuracy to help fill in the data of those tweets with incomplete information. To test our algorithm, we used the sets of social media data from a city, we separated them into training sets, where we know all the information, and the testing sets, where we intentionally pretend to not know the location. One prediction method that was used in (Dukler, Han and Wang, 2016) requires appending one-hot ...

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, 2018 Nanjing University of Science and Technology

#### Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

##### SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters tau_i, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of exp(-tau_i s). It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper- scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence between local strong ...

Nonlinear Coupled Effects In Nanomaterials, 2018 Wilfrid Laurier University

#### Nonlinear Coupled Effects In Nanomaterials, Sia Bhowmick

##### Theses and Dissertations (Comprehensive)

Materials at the nanoscale have different chemical, structural, and optoelectrical properties compared to their bulk counterparts. As a result, such materials, called nanomaterials, exhibit observable differences in certain physical phenomena. One such resulting phenomenon called the piezoelectric effect has played a crucial role in miniature self-powering electronic devices called nanogenerators which are fabricated by using nanostructures, such as nanowires, nanorods, and nanofilms. These devices are capable of harvesting electrical energy by inducing mechanical strain on the individual nanostructures. Electrical energy created in this manner does not have environmental limitations. In this thesis, important coupled effects, such as the nonlinear piezoelectric ...

Generalized Position-Velocity Variables And The Existence Of A Lagrange-Hamilton Formalism For Given N-Dimensional Newtonian Equations Of Motion, 2018 University of North Georgia

#### Generalized Position-Velocity Variables And The Existence Of A Lagrange-Hamilton Formalism For Given N-Dimensional Newtonian Equations Of Motion, Piotr W. Hebda Ph.D., Beata Hebda Dr.

##### Faculty Publications

Given a time-independent system of equations of motion that would not allow the existence of a Lagrangian, generalized position-velocity systems of variables are proposed. It is shown that some of these variable systems will allow the existence of a Lagrangian. It is shown that if a Lagrangian exist, then the Hamiltonian and Poisson Brackets associated with that Lagrangian also exist. A way of constructing an explicit generalized position-velocity system of variables, an explicit Lagrangian, and an associated explicit Hamiltonian and Poisson Brackets is shown for the case when general solutions of the original equations of motion are explicitly known.

The Use Of Item Response Theory In Survey Methodology: Application In Seat Belt Data, 2018 Old Dominion University

#### The Use Of Item Response Theory In Survey Methodology: Application In Seat Belt Data, Mark K. Ledbetter, Norou Diawara, Bryan E. Porter

##### Mathematics & Statistics Faculty Publications

Problem: Several approaches to analyze survey data have been proposed in the literature. One method that is not popular in survey research methodology is the use of item response theory (IRT). Since accurate methods to make prediction behaviors are based upon observed data, the design model must overcome computation challenges, but also consideration towards calibration and proficiency estimation. The IRT model deems to be offered those latter options. We review that model and apply it to an observational survey data. We then compare the findings with the more popular weighted logistic regression. Method: Apply IRT model to the observed data ...

Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, 2018 Augsburg University

#### Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John Zobitz

##### Faculty Authored Articles

We analyze a process-based temperature model for the length distribution and population over time of mayfly nymphs. Model parameters are estimated using a Markov Chain Monte Carlo parameter estimation method utilizing length distribution data at five different stream sites. Two different models (a standard exponential model and a modified Weibull model) of mayfly mortality are evaluated, where in both cases mayfly length growth is a function of stream temperature. Based on model-data comparisons to the modeled length distribution and the Bayesian Information Criterion, we found that approaches that length distribution data can reliably estimate 2–3 model parameters. Future model ...

Decoding Book Barcode Images, 2018 Claremont McKenna College

#### Decoding Book Barcode Images, Yizhou Tao

##### CMC Senior Theses

This thesis investigated a method of barcode reconstruction to address the recovery of a blurred and convoluted one-dimensional barcode. There are a lot of types of barcodes used today, such as Code 39, Code 93, Code 128, etc. Our algorithm applies to the universal barcode, EAN 13. We extend the methodologies proposed by Iwen et al. (2013) in the journal article "A Symbol-Based Algorithm for Decoding barcodes." The algorithm proposed in the paper requires a signal measured by a laser scanner as an input. The observed signal is modeled as a true signal corrupted by a Gaussian convolution, additional noises ...

Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, 2017 Wojciech Budzianowski Consulting Services

#### Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, Wojciech M. Budzianowski

##### Wojciech Budzianowski

No abstract provided.

Registration Form Resrb 2018, 2017 Wojciech Budzianowski Consulting Services

#### Registration Form Resrb 2018, Wojciech M. Budzianowski

##### Wojciech Budzianowski

No abstract provided.

Abstract Template Resrb 2018, 2017 Wojciech Budzianowski Consulting Services

#### Abstract Template Resrb 2018, Wojciech M. Budzianowski

##### Wojciech Budzianowski

No abstract provided.

From Convergence In Measure To Convergence Of Matrix-Sequences Through Concave Functions And Singular Values, 2017 Scuola Normale Superiore, Pisa, Italy

#### From Convergence In Measure To Convergence Of Matrix-Sequences Through Concave Functions And Singular Values, Giovanni Barbarino, Carlo Garoni

##### Electronic Journal of Linear Algebra

Sequences of matrices with increasing size naturally arise in several areas of science, such as, for example, the numerical discretization of differential and integral equations. An approximation theory for sequences of this kind has recently been developed, with the aim of providing tools for computing their asymptotic singular value and eigenvalue distributions. The cornerstone of this theory is the notion of approximating classes of sequences (a.c.s.), which is also fundamental to the theory of generalized locally Toeplitz (GLT) sequences, and hence to the spectral analysis of PDE discretization matrices. Drawing inspiration from measure theory, here it is introduced ...

The General $\Phi$-Hermitian Solution To Mixed Pairs Of Quaternion Matrix Sylvester Equations, 2017 Auburn University

#### The General $\Phi$-Hermitian Solution To Mixed Pairs Of Quaternion Matrix Sylvester Equations, Zhuo-Heng He, Jianzhen Liu, Tin-Yau Tam

##### Electronic Journal of Linear Algebra

Let $\mathbb{H}^{m\times n}$ be the space of $m\times n$ matrices over $\mathbb{H}$, where $\mathbb{H}$ is the real quaternion algebra. Let $A_{\phi}$ be the $n\times m$ matrix obtained by applying $\phi$ entrywise to the transposed matrix $A^{T}$, where $A\in\mathbb{H}^{m\times n}$ and $\phi$ is a nonstandard involution of $\mathbb{H}$. In this paper, some properties of the Moore-Penrose inverse of the quaternion matrix $A_{\phi}$ are given. Two systems of mixed pairs of quaternion matrix Sylvester equations \$A_{1}X-YB_{1}=C_{1},~A_{2}Z-YB_{2}=C_ ...