George Klosko attempts to solve a problem put forth by Rawls, namely how to create a persisting, just and stable liberal democracy in light of pluralism. He believes Rawls has failed at this task through the employment of political constructivism. Klosko claims that since Rawls does not utilize actual views within the existing public to form principles of justice, his method would fail to reach an overlapping consensus. As an alternative, Klosko proposes the method of convergence, which utilizes actual societal views to find overlapping concepts that inform the principles of justice. My argument is that Klosko misconstrues the method and aims of political constructivism. Klosko seems to incorrectly believe that stability is primary to establishing a liberal democracy, whereas it is secondary to the achievement of justice. Because of this error, Klosko’s method of convergence potentially has the consequence of creating a society which is stable but unjust.

We prove strong convergence of order 1/4 - E for arbitrarily small E > 0 of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler-Maruyama scheme and another numerical method, which is constructed by applying the Euler-Maruyama scheme to a transformation of the SDE we aim to solve.

<p>U tezi se istražuje uniformna konvergencija Galerkinovog postupka konačnih elemenata na mrežama različitog tipa za dvoparametarske singularno&nbsp;perturbovane probleme.</p><p>Uvedene su slojno-adaptivne mreže za probleme konvekcije-reakcije-difuzije: &nbsp;Bahvalovljeva, Duran-&Scaron;i&scaron;kinova i Duranova za jednodimenzionalni i&nbsp;Duran-&Scaron;i&scaron;kinova i Duranova mreža za dvodimenzionalni problem. Za pomenute&nbsp;probleme na svim ovim mrežama analizirane su gre&scaron;ke interpolacije,&nbsp;diskretizacije i gre&scaron;ka u energetskoj normi i dokazana je uniformna konvergencija&nbsp;Galerkinovog postupka konačnih elemenata. Sva teorijska tvrđenja su&nbsp;potvrđena numeričkim eksperimentima.<br />&nbsp;</p> / <p>The thesis explores the uniform convergence for Galerkin nite element<br />method on various meshes for two parameter singularly perturbed problems.<br />Layer-adapted meshes are introduced for convection-reaction-diusion<br />problems: Bakhvalov, Duran-Shishkin and Duran meshes for a one dimensional<br />and Duran-Shishkin and Duran meshes for a two dimensional problem.<br />We analyze the errors of interpolation, discretization and error in the energy<br />norm and prove the parameter uniform convergence for Galerkin nite element<br />method on mentioned meshes. Numerical experiments support theoretical<br />ndings.<br />&nbsp;</p>

Wir betrachten die lineare inverse Probleme mit gestörter rechter Seite und gestörtem Operator in Hilberträumen, die inkorrekt sind. Um die Auswirkung der Inkorrektheit zu verringen, müssen spezielle Lösungsmethode angewendet werden, hier nutzen wir die sogenannte Tikhonov Regularisierungsmethode. Die Regularisierungsparameter wählen wir aus das verallgemeinerte Defektprinzip. Eine typische numerische Methode zur Lösen der nichtlinearen äquivalenten Defektgleichung ist Newtonverfahren. Wir schreiben einen Algorithmus, die global und monoton konvergent für beliebige Startwerte garantiert. Um die Stabilität zu garantieren, benutzen wir die Glattheit der Lösung, dann erhalten wir eine sogenannte bedingte Stabilität. Wir demonstrieren die sogenannte Interpolationsmethode zur Herleitung von bedingten Stabilitätsabschätzungen bei inversen Problemen für partielle Differentialgleichungen.