Harer has shown that the mapping class group is a virtual duality groupmirroring the work of Borel-Serre on arithmetic groups in semisimple Q-groups. Just as the homology of the rational Tits building provides the dualizing module for any torsion-free arithmetic group, the homology of the curve complex is the dualizingmodule for any torsion-free, finite index subgroup of the mapping class group...

In this research we have implemented the Random Vortex Method to calculate velocity fields of fluids inside open cavities in both turbulent and laminar flows. the Random Vortex Method is a CFD method (in both turbulent and laminar fields) which needs the Schwarz-Christoffel transformation formula to map the physical geometry into the upper half plane. In some complex geometries like the flow in...

Introduction: Fundamental notions of mapping hypothesis and canonicity were scrutinized in Persian-speaking aphasics.  Methods: To this end, the performance of four age-, education-, and gender matched Persian-speaking Broca's patients and eight matched healthy controls in diverse complex structures were compared via the conduction of two tasks of syntactic comprehension and grammaticality jud...

We define a category Fat whose objects are isomorphism classes of bordered fat graphs and show that its geometric realization is a classifying space for the bordered mapping class groups. We then construct a CW structure on this geometric realization with one cell per isomorphism classes of bordered fat graphs. Its cellular cochain complex gives a bordered graph complex which computes the integ...