Multicultural Art Education: Deconstructing Images of Social Reproduction

Exclusionary practices along with inaccurate and incomplete information have historically been used in the classroom by the dominant White culture as a means to disempower minority youth and widen the chasm between opposite ends of the power structure. Although reproducing the existing power structure may not be a conscious motive of art teachers in the 21st century, many of their actions replicate conditions necessary for domination by the Euro-White culture. Admirably, art educators have a history of being on the cutting edge of innovative ideas and inclusionary practices. The movement to include art from many cultures in art curriculums is an exemplary curricular milestone benefitting minority students. However, it is within the realm of multiculturalism that theory and practice slowly drift apart, often resulting in art teachers teaching students whose cultural heritages are very unlike their own. This can present an awkward position for art teachers who possess good intentions to include minority art but are deficient in the understanding, training or direction which would most benefit their students

Low Regularity Ray Tracing for Wave Equations with Gaussian beams

We prove observability estimates for oscillatory Cauchy data modulo a small kernel for $n$-dimensional wave equations with space and time dependent $C^2$ and $C^{1,1}$ coefficients using Gaussian beams. We assume the domains and observability regions are in $\mathbb{R}^n$, and the GCC applies. This work generalizes previous observability estimates to higher dimensions and time dependent coefficients. The construction for the Gaussian beamlets solving $C^{1,1}$ wave equations represents an improvement and simplification over Waters (2011).Comment: this version shortens and changes the previous construction and contains an extension to space time dependent coefficient

Unique Determination of Sound Speeds for Coupled Systems of Semi-linear Wave Equations

We consider coupled systems of semi-linear wave equations with different sound speeds on a finite time interval $[0,T]$ and a bounded Lipschitz domain $\Omega$ in $\mathbb{R}^3$, with boundary $\partial\Omega$. We show the coupled systems are well posed for variable coefficient sounds speeds and short times. Under the assumption of small initial data, we prove the source to solutions map on $[0,T]\times\partial\Omega$ associated with the nonlinear problem is sufficient to determine the source-to-solution map for the linear problem. We can then reconstruct the sound speeds in $\Omega$ for the coupled nonlinear wave equations under certain geometric assumptions. In the case of the full source to solution map in $\Omega\times[0,T]$ this reconstruction could also be accomplished under fewer geometric assumptions.Comment: minor update

Chebyshev Action on Finite Fields

Given a polynomial f and a finite field F one can construct a directed graph where the vertices are the values in the finite field, and emanating from each vertex is an edge joining the vertex to its image under f. When f is a Chebyshev polynomial of prime degree, the graphs display an unusual degree of symmetry. In this paper we provide a complete description of these graphs, and also provide some examples of how these graphs can be used to determine the decomposition of primes in certain field extensions