in this paper, two-dimensional heat transfer in a semi-infinite wall with fins of rectangular profile has been investigated. the conduction equations of the wall and fins are solved simultaneously by a numerical method. the principal parameters of the problem are the fin spacing, length, and fin-to-wall conductivity ratio. in this investigation, the effect of these parameters on two-dimensional...

We show that products of sufficiently thick Cantor sets generate trees in the plane with constant distance between adjacent vertices. Moreover, we prove set choices for this has non-empty interior. allow our to be countably infinite, which further distinguishes work from previous results on patterns fractal sets. This builds authors’ graphs and over sufficient Newhouse thickness.

It is shown that there exists a finitely generated infinite simple group of infinite commutator width and infinite square width in which every conjugation-invariant norm is stably bounded, and in particular stable commutator length vanishes. Moreover, a recursive presentation of such a group with decidable word and conjugacy problems is constructed.