Economics is the study of optimal use of scarce resources to promote social welfare. Of particular interest has been the role of prices in achieving a socially optimal allocation of resources through co-ordinating the actions of self-seeking individuals in a decentralized economy. Alternative notions of economic equilibrium and their efficiency properties are sketched. Finally, some of the basi...

Temporal

the concept of algebraic hyperstructures introduced by marty as a generalization of ordinary algebraic structures. in an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. the concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper rings and a generalizat...

We prove that certain topologically mixing two-dimensional shifts of finite type have a ‘fundamental’ 1-cocycle with the property that every continuous 1-cocycle on the shift space with values in a discrete group is continuously cohomologous to a homomorphic image of the fundamental cocycle. These fundamental cocycles are closely connected with representations of the shift space by Wang tilings...

In many biological systems, robustness is achieved by redundant wiring, and reflected by the presence of cycles in the graphs connecting the systems’ components. When analyzing such graphs, cyclically robust cycle bases of are of interest since they can be used to generate all cycles of a given 2-connected graph by iteratively adding basis cycles. It is known that strictly fundamental (or Kirch...