We prove that the pure global dimension of a polynomial ring over an integral domain k in a finite or countable number n⩾2 of commuting (non-commuting, resp.) variables is t + 1, provided <img height="18" border="0" style="vertical-align:bottom" width="52" alt="" title="" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-0022404982900408-si1.gif">. As an application, we determine the pure global dimension of wild algebras Original Uggs Uk
of quiver type, also (in case k is an algebraically closed field) of the wild local and wild commutative algebras of finite k-dimension.
The strategy of bold play in the game of red and black leads to a number of interesting mathematical Cheap Kids Uggs Online properties: the player's fortune follows a deterministic map, before the transition that ends the game; the bold strategy can be “re-scaled” to produce new strategies with the same win probability; the win probability is a continuous function of the initial fortune, and in the fair case, equals the initial fortune. We consider several Markov chains in more general settings and study the extent to which the properties are preserved. In particular, we study two “k-player” models.