Abstract We prove that certain families of homogenous affine iterated function systems in $\mathbb {R}^{d}$ have the property open set condition and existence exact overlaps both occur densely space translation parameters. These examples demonstrate theorems Falconer Jordan–Pollicott–Simon on almost sure dimensions self-affine sets measures, exceptional parameters can be a dense set. The proof ...

We consider drawings of graphs that contain dense subgraphs. We introduce intersection-link representations for such graphs, in which each vertex u is represented by a geometric object R(u) and each edge (u, v) is represented by the intersection between R(u) and R(v), if it belongs to a dense subgraph, or by a curve connecting the boundaries ofR(u) andR(v), otherwise. We study a notion of plana...

Ultra-reliability and low latency communication has long been an important but challenging task in the fifth sixth generation wireless systems. Scheduling as many users possible to serve on limited time-frequency resource is one of a crucial topic, subjecting maximum allowable transmission power minimum rate requirement each user. We address it by proposing mixed integer programming model, with...

Given S1, a starting set of points in the plane, not all on a line, we define a sequence of planar point sets {Si}∞i=1 as follows. With Si already determined, let Li be the set of all the lines determined by pairs of points from Si , and let Si+1 be the set of all the intersection points of lines in Li . We show that with the exception of some very particular starting configurations, the limiti...