Open Access. Powered by Scholars. Published by Universities.®
- Publication
- Publication Type
Articles 1 - 10 of 10
Full-Text Articles in Entire DC Network
Mindfully Navigating The Wind And Water: Defining The Currents Of Metaphors That Interfere With Excellence In Mathematics Education, Rob Blom, Olivia Lu, Chunlei Lu
Mindfully Navigating The Wind And Water: Defining The Currents Of Metaphors That Interfere With Excellence In Mathematics Education, Rob Blom, Olivia Lu, Chunlei Lu
Journal of Humanistic Mathematics
We bring to the forefront of educational thought a specific attitude toward the COVID-19 crisis that harnesses the symbolism of wind and water to navigate the cultural storm interfering upon our mathematical and pedagogical craft. The purpose of our paper is to open up space for opportunities in mathematics education using integral mindfulness as the rudder to readjust our bearings. More specifically, through conceptual analyses and making explicit the currents of change, disorder, and technology, we can apply discernment to these metaphors that intersect our pedagogy to re-align efforts and attitudes toward an integrated (aperspectival) culture of mathematics education. Through …
Qualitative Analysis Of A Resource Management Model And Its Application To The Past And Future Of Endangered Whale Populations, Glenn Ledder
Qualitative Analysis Of A Resource Management Model And Its Application To The Past And Future Of Endangered Whale Populations, Glenn Ledder
CODEE Journal
Observed whale dynamics show drastic historical population declines, some of which have not been reversed in spite of restrictions on harvesting. This phenomenon is not explained by traditional predator prey models, but we can do better by using models that incorporate more sophisticated assumptions about consumer-resource interaction. To that end, we derive the Holling type 3 consumption rate model and use it in a one-variable differential equation obtained by treating the predator population in a predator-prey model as a parameter rather than a dynamic variable. The resulting model produces dynamics in which low and high consumption levels lead to single …
The Ocean And Climate Change: Stommel's Conceptual Model, James Walsh
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 mathematical …
Consensus Building By Committed Agents, William W. Hackborn, Tetiana Reznychenko, Yihang Zhang
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 …
Radial Solutions To Semipositone Dirichlet Problems, Ethan Sargent
Radial Solutions To Semipositone Dirichlet Problems, Ethan Sargent
HMC Senior Theses
We study a Dirichlet problem, investigating existence and uniqueness for semipositone and superlinear nonlinearities. We make use of Pohozaev identities, energy arguments, and bifurcation from a simple eigenvalue.
Resonant Solutions And Turning Points In An Elliptic Problem With Oscillatory Boundary Conditions, Alfonso Castro, Rosa Pardo
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.
Radial Solutions To A Dirichlet Problem Involving Critical Exponents When N=6, Alfonso Castro, Alexandra Kurepa
Radial Solutions To A Dirichlet Problem Involving Critical Exponents When N=6, Alfonso Castro, Alexandra Kurepa
All HMC Faculty Publications and Research
In this paper we show that, for each λ>0, the set of radially symmetric solutions to the boundary value problem
-Δu(x) = λu(x) + u(x)|u(x)|, x ε B := {x ε R6:|x|<1},
u(x) = 0, x ε ∂B
is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.
Radially Symmetric Solutions To A Dirichlet Problem Involving Critical Exponents, Alfonso Castro, Alexandra Kurepa
Radially Symmetric Solutions To A Dirichlet Problem Involving Critical Exponents, Alfonso Castro, Alexandra Kurepa
All HMC Faculty Publications and Research
In this paper we answer, for N = 3,4, the question raised in [1] on the number of radially symmetric solutions to the boundary value problem -Δu(x) = λu(x) + u(x)|u(x)|^{4/(N-2)}, x ε B: = x ε RN:{|x| < 1}, u(x)=0, x ε ∂B, where Δ is the Laplacean operator and λ>0. Indeed, we prove that if N = 3,4, then for any λ>0 this problem has only finitely many radial solutions. For N = 3,4,5 we show that, for each λ>0, the set of radially symmetric solutions is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.
A Bifurcation Theorem And Applications, Alfonso Castro, Jorge Cossio
A Bifurcation Theorem And Applications, Alfonso Castro, Jorge Cossio
All HMC Faculty Publications and Research
In this paper we give a sufficient condition on the nonlinear operator N for a point (λ, u) to be a local bifurcation point of equations of the form u + λL-1(N(u)) = 0, where L is a linear operator in a real Hilbert space, L has compact inverse, and λ ∈ R is a parameter. Our result does not depend on the variational structure of the equation or the multiplicity of the eigenvalue of the linear operator L. Applications are made to systems of differential equations and to the existence of periodic solutions of nonlinear second order …
Stability Of Steady Cross-Waves: Theory And Experiment, Seth Lichter, Andrew J. Bernoff
Stability Of Steady Cross-Waves: Theory And Experiment, Seth Lichter, Andrew J. Bernoff
All HMC Faculty Publications and Research
A bifurcation analysis is performed in the neighborhood of neutral stability for cross waves as a function of forcing, detuning, and viscous damping. A transition is seen from a subcritical to a supercritical bifurcation at a critical value of the detuning. The predicted hysteretic behavior is observed experimentally. A similarity scaling in the inviscid limit is also predicted. The experimentally observed bifurcation curves agree with this scaling.