Deep Blue Collection: Mathematics, Department of http://hdl.handle.net/2027.42/61172 The Collection's search engine Search the Channel search http://deepblue.lib.umich.edu/simple-search On the Pythagorean hull of Q http://hdl.handle.net/2027.42/61250 Title: On the Pythagorean hull of Q<br/><br/>Authors: Pambuccian, Victor Sperner spaces and first-order logic http://hdl.handle.net/2027.42/61173 Title: Sperner spaces and first-order logic<br/><br/>Authors: Blass, Andreas; Pambuccian, Victor<br/><br/>Abstract: 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. Asymptotics of rare events in birth–death processes bypassing the exact solutions http://hdl.handle.net/2027.42/58127 Title: Asymptotics of rare events in birth–death processes bypassing the exact solutions<br/><br/>Authors: Doering, Charles R; Sargsyan, Khachik V; Sander, Leonard M; Vanden-Eijnden, Eric<br/><br/>Abstract: We investigate the near-continuum asymptotics of mean first passage times in some one-variable birth–death processes. The particular problem we address is how to extract mean first passage times in the near-continuum limit from their defining finite-difference equations alone. For the simple class of processes we consider here, exact closed-form solutions for the mean first passage time between any two states are available and the near-continuum expansion of these formulae defines the correct limiting behaviour and is used to check the results of asymptotic analysis of the difference equations. We find that in some cases the asymptotic approach does not lead unequivocally to the proper result. Self-similar solutions of semilinear wave equations with a focusing nonlinearity http://hdl.handle.net/2027.42/58120 Title: Self-similar solutions of semilinear wave equations with a focusing nonlinearity<br/><br/>Authors: Bizoń, Piotr; Maison, Dieter; Wasserman, Arthur<br/><br/>Abstract: We prove that in three space dimensions a nonlinear wave equation utt − Δu = up, with pges; 7 being an odd integer, has a countable family of regular spherically symmetric self-similar solutions.