Mathematics, Department of
http://hdl.handle.net/2027.42/61172
2017-01-22T05:55:23ZWell-posedness and self-similar asymptotics for a thin-film equation
http://hdl.handle.net/2027.42/117366
Well-posedness and self-similar asymptotics for a thin-film equation
Gnann, Manuel V.
We investigate compactly supported solutions for a thin-film equation with linear mobility in the regime of perfect wetting. This problem has already been addressed by Carrillo and Toscani, proving that the source-type self-similar profile is a global attractor of entropy solutions with compactly supported initial data. Here we study small perturbations of source-type self-similar solutions for the corresponding classical free boundary problem and set up a global existence and uniqueness theory within weighted L2-spaces under minimal assumptions. Furthermore, we derive asymptotics for the evolution of the solution, the free boundary, and the center of mass. As spatial translations are scaled out in our reference frame, the rate of convergence is higher than the one obtained by Carrillo and Toscani.
2015-07-30T00:00:00ZMathematical Knowledge for Teaching High School Geometry
http://hdl.handle.net/2027.42/91279
Mathematical Knowledge for Teaching High School Geometry
Herbst, Patricio; Kosko, Karl W.
This paper documents efforts to develop an instrument to measure mathematical knowledge for teaching high school geometry (MKT-G). We report on the process of developing and piloting questions that purported to measure various domains of MKT-G. Scores on the final set of items had no statistical relationship with total years of experience teaching, but all domain scores were found to have statistically significant correlations with years of experience teaching high school geometry. We use this result to propose ways of conceptualizing how instruction-specific considerations might matter in the design of MKT items.
2012-05-28T00:00:00ZOn the Pythagorean hull of Q
http://hdl.handle.net/2027.42/61250
On the Pythagorean hull of Q
Pambuccian, Victor
1990-01-01T00:00:00ZSperner spaces and first-order logic
http://hdl.handle.net/2027.42/61173
Sperner spaces and first-order logic
Blass, Andreas; Pambuccian, Victor
We study the class of Sperner spaces, a generalized version of affine spaces, as defined in the language of pointline incidence and line parallelity. We show that, although the class of Sperner spaces is a pseudo-elementary class, it is not elementary nor even ℒ[sub]∞ω-axiomatizable. We also axiomatize the first-order theory of this class.
2003-01-27T00:00:00Z