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Pbw Bases And Marginally Large Tableaux In Types B And C, Jackson A. Criswell, Ben Salisbury, Peter Tingley 2019 Central Michigan University

Pbw Bases And Marginally Large Tableaux In Types B And C, Jackson A. Criswell, Ben Salisbury, Peter Tingley

Mathematics and Statistics: Faculty Publications and Other Works

We explicitly describe the isomorphism between two combinatorial realizations of Kashiwara’s infinity crystal in types B and C. The first realization is in terms of marginally large tableaux and the other is in terms of Kostant partitions coming from PBW bases. We also discuss a stack notation for Kostant partitions which simplifies that realization.


Create Pretty Documents With Latex!, Evan Brummet, Patrick Davis, Micah Fogel 2019 Illinois Mathematics and Science Academy

Create Pretty Documents With Latex!, Evan Brummet, Patrick Davis, Micah Fogel

Faculty Publications & Research

LaTeX is a typesetting system for the educator who wants to create documents with beautifully typeset mathematics. It is free, available for all major platforms, and cross-platform compatible.

In this workshop, we will introduce participants to LaTeX, and then demonstrate how to typeset a variety of documents (e.g., tests or presentations). We are happy to tailor the demonstration to answer any specific questions raised by participants.

Please bring your laptop to get hands-on experience.

This web page contains links to the handouts and the sample files: staff.imsa.edu/~fogel/latex


Measurement (Book Review), Calvin Jongsma 2019 Dordt College

Measurement (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Measurement by Paul Lockhart. Cambridge, MA: Harvard University Press, 2012. 407 pp. ISBN: 9780674057555.


A Mathematician's Lament: How School Cheats Us Out Of Our Most Fascinating And Imaginative Art Form (Book Review), Calvin Jongsma 2019 Dordt College

A Mathematician's Lament: How School Cheats Us Out Of Our Most Fascinating And Imaginative Art Form (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form by Paul Lockhart. New York: Bellevue Literary Press, 2009. 144 pp. ISBN: 9781934137178.


Neuroevolutional Methods For Decision Support Under Uncertainty, Nina Komleva, Olga Khlopkova, Matthew He 2019 Plekhanov Russian University of Economics - Moscow

Neuroevolutional Methods For Decision Support Under Uncertainty, Nina Komleva, Olga Khlopkova, Matthew He

Mathematics Faculty Articles

The article presents a comparative analysis of the fundamental neuroevolutional methods, which are widely applied for the intellectualization of the decision making support systems under uncertainty. Based on this analysis the new neuroevolutionary method is introduced. It is intended to modify both the topology and the parameters of the neural network, and not to impose additional constraints on the individual. The results of the experimental evaluation of the performance of the methods based on the series of benchmark tasks of adaptive control, classification and restoration of damaged data are carried out. As criteria of the methods evaluation the number of ...


The Role Of Sister Cities’ Staff Exchanges In Developing “Learning Cities”: Exploring Necessary And Sufficient Conditions In Social Capital Development Utilizing Proportional Odds Modeling, Patrick H. Buckley, Akio Takahashi, Amy D. Anderson 2019 Western Washington University

The Role Of Sister Cities’ Staff Exchanges In Developing “Learning Cities”: Exploring Necessary And Sufficient Conditions In Social Capital Development Utilizing Proportional Odds Modeling, Patrick H. Buckley, Akio Takahashi, Amy D. Anderson

Amy D. Anderson

In the last half century former international adversaries have become cooperators through networking and knowledge sharing for decision making aimed at improving quality of life and sustainability; nowhere has this been more striking then at the urban level where such activity is seen as a key component in building “learning cities” through the development of social capital. Although mega-cities have been leaders in such efforts, mid-sized cities with lesser resource endowments have striven to follow by focusing on more frugal sister city type exchanges. The underlying thesis of our research is that great value can be derived from city-to-city exchanges ...


Modeling Cross-Border Regions, Place-Making, And Resource Management: A Delphi Analysis, Amy D. Anderson, Patrick H. Buckley, John Belec 2019 Western Washington University

Modeling Cross-Border Regions, Place-Making, And Resource Management: A Delphi Analysis, Amy D. Anderson, Patrick H. Buckley, John Belec

Amy D. Anderson

Along international borders, spillover of resource management issues is a growing challenge. Development of cross-border regions (CBRs) is seen as an emerging means of addressing these issues. A set of theoretical models, geo-economic mobilization and a resource-focused territorial program of place-making have been proposed as a lens for understanding why such change could occur. From this theory, we identify three C’s as critical initial or necessary conditions to start the process: common territorial identity, convergence of knowledge and values, willingness for cooperation. We then utilize results of a Delphi study in the Fraser Lowland, a sub-district of the American-Canadian ...


Sustainable Energy Governance In South Tyrol (Italy): A Probabilistic Bipartite Network Model, Jessica Belest, Laura Secco, Elena Pisani, Alberto Caimo 2019 EURAC Research, Italy

Sustainable Energy Governance In South Tyrol (Italy): A Probabilistic Bipartite Network Model, Jessica Belest, Laura Secco, Elena Pisani, Alberto Caimo

Articles

At the national scale, almost all of the European countries have already achieved energy transition targets, while at the regional and local scales, there is still some potential to further push sustainable energy transitions. Regions and localities have the support of political, social, and economic actors who make decisions for meeting existing social, environmental and economic needs recognising local specificities.

These actors compose the sustainable energy governance that is fundamental to effectively plan and manage energy resources. In collaborative relationships, these actors share, save, and protect several kinds of resources, thereby making energy transitions deeper and more effective.

This research ...


Almost Oscillatory Three Dimensional Dynamic Systems, Elvan Akin, Zuzana Dosla, Bonita Lawrence 2019 Missouri University of Science and Technology

Almost Oscillatory Three Dimensional Dynamic Systems, Elvan Akin, Zuzana Dosla, Bonita Lawrence

Bonita Lawrence

In this article, we investigate oscillation and asymptotic properties for 3D systems of dynamic equations. We show the role of nonlinearities and we apply our results to the adjoint dynamic systems.


Brauer's Theorem And Nonnegative Matrices With Prescribed Diagonal Entries, Ricardo L. Soto, Ana I. Julio, Macarena A. Collao 2019 Universidad Católica del Norte

Brauer's Theorem And Nonnegative Matrices With Prescribed Diagonal Entries, Ricardo L. Soto, Ana I. Julio, Macarena A. Collao

Electronic Journal of Linear Algebra

The problem of the existence and construction of nonnegative matrices with prescribed eigenvalues and diagonal entries is an important inverse problem, interesting by itself, but also necessary to apply a perturbation result, which has played an important role in the study of certain nonnegative inverse spectral problems. A number of partial results about the problem have been published by several authors, mainly by H. \v{S}migoc. In this paper, the relevance of a Brauer's result, and its implication for the nonnegative inverse eigenvalue problem with prescribed diagonal entries is emphasized. As a consequence, given a list of complex ...


Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li 2019 Georgian Court University

Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li

Electronic Journal of Linear Algebra

Let $\Omega_n$ denote the convex polytope of all $n\times n$ doubly stochastic matrices, and $\omega_{n}$ denote the convex polytope of all $n\times n$ doubly substochastic matrices. For a matrix $A\in\omega_n$, define the sub-defect of $A$ to be the smallest integer $k$ such that there exists an $(n+k)\times(n+k)$ doubly stochastic matrix containing $A$ as a submatrix. Let $\omega_{n,k}$ denote the subset of $\omega_n$ which contains all doubly substochastic matrices with sub-defect $k$. For $\pi$ a permutation of symmetric group of degree $n$, the sequence of elements $a_{1\pi(1 ...


Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene 2019 Frostburg State University

Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene

CODEE Journal

The environmental phenomenon of climate change is of critical importance to today's science and global communities. Differential equations give a powerful lens onto this phenomenon, and so we should commit to discussing the mathematics of this environmental issue in differential equations courses. Doing so highlights the power of linking differential equations to environmental and social justice causes, and also brings important science to the forefront in the mathematics classroom. In this paper, we provide an extended problem, appropriate for a first course in differential equations, that uses bifurcation analysis to study climate change. Specifically, through studying hysteresis, this problem ...


The Ocean And Climate Change: Stommel's Conceptual Model, James Walsh 2019 Oberlin College

The Ocean And Climate Change: Stommel's Conceptual Model, James Walsh

CODEE Journal

The ocean plays a major role in our climate system and in climate change. In this article we present a conceptual model of the Atlantic Meridional Overturning Circulation (AMOC), an important component of the ocean's global energy transport circulation that has, in recent times, been weakening anomalously. Introduced by Henry Stommel, the model results in a two-dimensional system of first order ODEs, which we explore via Mathematica. The model exhibits two stable regimes, one having an orientation aligned with today's AMOC, and the other corresponding to a reversal of the AMOC. This material is appropriate for a junior-level ...


Modeling The Spread And Prevention Of Malaria In Central America, Michael Huber 2019 Muhlenberg College

Modeling The Spread And Prevention Of Malaria In Central America, Michael Huber

CODEE Journal

In 2016, the World Health Organization (WHO) estimated that there were 216 million cases of Malaria reported in 91 countries around the world. The Central American country of Honduras has a high risk of malaria exposure, especially to United States soldiers deployed in the region. This article will discuss various aspects of the disease, its spread and its treatment and the development of models of some of these aspects with differential equations. Exercises are developed which involve, respectively, exponential growth, logistics growth, systems of first-order equations and Laplace transforms. Notes for instructors are included.


An Epidemiological Math Model Approach To A Political System With Three Parties, Selenne Bañuelos, Ty Danet, Cynthia Flores, Angel Ramos 2019 California State University, Channel Islands

An Epidemiological Math Model Approach To A Political System With Three Parties, Selenne Bañuelos, Ty Danet, Cynthia Flores, Angel Ramos

CODEE Journal

The United States has proven to be and remains a dual political party system. Each party is associated to its own ideologies, yet work by Baldassarri and Goldberg in Neither Ideologues Nor Agnostics show that many Americans have positions on economic and social issues that don't fall into one of the two mainstream party platforms. Our interest lies in studying how recruitment from one party into another impacts an election. In particular, there was a growing third party presence in the 2000 and 2016 elections. Motivated by previous work, an epidemiological approach is taken to treat the spread of ...


A Note On Equity Within Differential Equations Education By Visualization, Younes KarimiFardinpour 2019 Islamic Azad University, Ahar Branch

A Note On Equity Within Differential Equations Education By Visualization, Younes Karimifardinpour

CODEE Journal

The growing importance of education equity is partly based on the premise that an individual's level of education directly correlates to future quality of life. Educational equity for differential equations (DEs) is related to achievement, fairness, and opportunity. Therefore, a pedagogy that practices DE educational equity gives a strong foundation of social justice. However, linguistic barriers pose a challenge to equity education in DEs. For example, I found myself teaching DEs either in classrooms with a low proficiency in the language of instruction or in multilingual classrooms. I grappled with a way to create an equity educational environment that ...


Linking Differential Equations To Social Justice And Environmental Concerns, 2019 Claremont Colleges

Linking Differential Equations To Social Justice And Environmental Concerns

CODEE Journal

Special issue of the CODEE Journal in honor of its founder, Professor Robert Borrelli.


Kremer's Model Relating Population Growth To Changes In Income And Technology, Dan Flath 2019 University of Arizona

Kremer's Model Relating Population Growth To Changes In Income And Technology, Dan Flath

CODEE Journal

For thousands of years the population of Earth increased slowly, while per capita income remained essentially constant, at subsistence level. At the beginning of the industrial revolution around 1800, population began to increase very rapidly and income started to climb. Then in the second half of the twentieth century as a demographic transition began, the birth and death rates, as well as the world population growth rate, began to decline. The reasons for these transitions are hotly debated with no expert consensus yet emerging. It's the problem of economic growth. In this document we investigate a mathematical model of ...


Consensus Building By Committed Agents, William W. Hackborn, Tetiana Reznychenko, Yihang Zhang 2019 University of Alberta

Consensus Building By Committed Agents, William W. Hackborn, Tetiana Reznychenko, Yihang Zhang

CODEE Journal

One of the most striking features of our time is the polarization, nationally and globally, in politics and religion. How can a society achieve anything, let alone justice, when there are fundamental disagreements about what problems a society needs to address, about priorities among those problems, and no consensus on what constitutes justice itself? This paper explores a model for building social consensus in an ideologically divided community. Our model has three states: two of these represent ideological extremes while the third state designates a moderate position that blends aspects of the two extremes. Each individual in the community is ...


A Model Of The Transmission Of Cholera In A Population With Contaminated Water, Therese Shelton, Emma Kathryn Groves, Sherry Adrian 2019 Southwestern University

A Model Of The Transmission Of Cholera In A Population With Contaminated Water, Therese Shelton, Emma Kathryn Groves, Sherry Adrian

CODEE Journal

Cholera is an infectious disease that is a major concern in countries with inadequate access to clean water and proper sanitation. According to the World Health Organization (WHO), "cholera is a disease of inequity--an ancient illness that today sickens and kills only the poorest and most vulnerable people\dots The map of cholera is essentially the same as a map of poverty." We implement a published model (Fung, "Cholera Transmission Dynamic Models for Public Health Practitioners," Emerging Themes in Epidemiology, 2014) of a SIR model that includes a bacterial reservoir. Bacterial concentration in the water is modeled by the Monod ...


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