Contributed Papers
Org:
A. Bass Bagayogo (Université de SaintBoniface)
[
PDF]
 ABDUS SATTAR MIA, University of Saskatchewan
Conservation laws of the nonlinear twofluid model [PDF]

A nonlinear model has been derived by Camassa and Choi (1999) to approximate the twodimensional Euler equations of incompressible motion of two nonmixing fluids in a channel. We derive conservation laws for the twofluid model using the direct conservation law construction method. Eight different conservation laws are found, including the conservation of mass, horizontal momentum, and energy. The conserved quantities for the CamassaChoi model are compared with those for the full incompressible Euler system. A physical interpretation is given
for each of the conservation laws of the twofluid model.
 MARCO ANTONIO PÉREZ, Université du Québec à Montréal
Relative extensions and natural transformations from disk and sphere chain complexes [PDF]

In 2004, J. Gillespie constructed for every object $C$ in an Abelian category $\mathcal{C}$, and every chain complex $X$ over $\mathcal{C}$, a natural isomorphism ${\rm Ext}^1_{{\rm {\bf Ch}}(\mathcal{C})}(X, D^{m}(C)) \cong {\rm Ext}^1_{\mathcal{C}}(X_{m1}, C)$, where $D^{m}(C)$ is the $m$th disk complex centred at $C$. If in addition $X$ is exact, one also has ${\rm Ext}^1_{{\rm {\bf Ch}}(\mathcal{C})}(X, S^m(C)) \cong {\rm Ext}^1_{\mathcal{C}}(X_m / B_m(X), C)$, where $S^m(C)$ is the $m$th sphere complex centred at $C$. We extend Gillespie's results for precovering classes $\mathcal{F} \subseteq {\rm Ob}(\mathcal{C})$, to the more general context where ${\rm Ext}^1_{\mathcal{C}}(,)$ is replaced by the first right derived functor $\mathcal{F}\mbox{}{\rm Ext}^1_{\mathcal{C}}(,)$ of ${\rm Hom}_{\mathcal{C}}(,)$, computed by using left $\mathcal{F}$resolutions of the left variable.
 M. CAROL WILLIAMS, Texas Tech University
Strengthening the Mathematical Content Knowledge of InService Teachers [PDF]

We will describe the implementation and effectiveness of our new multidisciplinary graduate program for elementary teachers. With support from the US Department of Education and faculty from the the TTU Math Department, Physics Department, and College of Education, we have strengthened both the mathematical content knowledge of the participating teachers and their ability to correctly and clearly describe mathematical concepts to their students.