Shrinking cities have been touted as an opportunity to rethink unsustainable growth-centric policies, but what extent they abdicated from the pro-growth urban agenda? We explore one of most overtly growth-oriented ‘solutions’ shrinkage: housing construction. Our nationwide analysis Spanish illustrates widespread emergence shrinking following Great Recession and disconnect between population dyn...

We show that gradient shrinking, expanding or steady Ricci solitons have potentials leading to suitable reference probability measures on the manifold. For shrinking solitons, as well as expanding soltions with nonnegative Ricci curvature, these reference measures satisfy sharp logarithmic Sobolev inequalities with lower bounds characterized by the geometry of the manifold. The geometric invari...

the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we design a self-shrinking scheme which combines a feedback with carry shift register and the self-shrinking generator, based on A. Kanso PhD study. We calculated the period of the designed algorithm. The ke...