In 1923 Schur considered the following problem. Let f ∈ Z[X] be a polynomial that induces a bijection on the residue fields Z/pZ for infinitely many primes p. His conjecture, that such polynomials are compositions of linear and Dickson polynomials, was proved by M. Fried in 1970. Here we investigate the analogous question for rational functions, and also we allow the base field to be any number...

Over the past decade there has been a growing public fascination with the complex connectedness of modern society. This connectedness is found in many incarnations: in the rapid growth of the Internet, in the ease with which global communication takes place, and in the ability of news and information as well as epidemics and financial crises to spread with surprising speed and intensity. These ...

the stability of a communication network composed of processing nodes and communication links is of prime importance to network designers. as the network begins losing links or nodes, eventually there is a loss in its effectiveness. thus, communication networks must be constructed to be as stable as possible, not only with respect to the initial disruption, but also with respect to the possible...

POLITICAL LEADERSHIP OF THE FIRST SECRETARIES IN PERIOD REAL SOCIALISM The subject of the analysis is issue political leadership leaders communist parties in countries Central and Eastern Europe. Formed functioning systems were characterized by an undemocratic centralized internal character. Although degree repressiveness system evolved changed (from condemnation crimes so-called distortion Sta...

For centuries scholars have tried to identify which features of legal systems are crucial to economic activity. Recently the legal origins school has posited that some legal systems contribute to different degrees of transaction costs and hence different levels of trade, investment, and innovation. The common law legal system is often singled out because it is believed to provide strong protect...