We prove some ergodic theorems for flat surfaces of finite area. The first result concerns such surfaces whose Teichmüller orbits are recurrent to a compact set of SL(2,R)/SL(S, α), where SL(S, α) is the Veech group of the surface. In this setting, this means that the translation flow on a flat surface can be renormalized through its Veech group. This result applies in particular to flat surfac...

The cell surface areas of 3T3 and SV40-3T3 cells both for suspended and for flat cells growing on the culture substrate have been determined in dependence on growth density. The surface areas of flat 3T3 and SV40-3T3 cells turn out to be independent of growth density over a wide range. For 3T3 cells the surface area of flat cells compares well with that determined by Collard and Temmink for sus...

‎we call a ring $r$ right generalized semiperfect if every simple right $r$-module is an epimorphic image of a flat right $r$-module with small kernel‎, ‎that is‎, ‎every simple right $r$-module has a flat $b$-cover‎. ‎we give some properties of such rings along with examples‎. ‎we introduce flat strong covers as flat covers which are also flat $b$-covers and give characterizations of $a$-perfe...

BACKGROUND The effect of reaming on bone volume and surface area of the glenoid is not precisely known. We hypothesize that (1) convex reamers create a larger surface area than flat reamers, (2) flat reamers cause less bone loss than convex reamers, and (3) the amount of bone loss increases with the amount of version correction. METHODS Reaming procedures with different types of reamers are p...