Bases, determining sets, metric dimension, . . . The notion of a base, and various combinatorial variants on it, have been rediscovered many times in different parts of combinatorics, especially graph theory: base size has been called fixing number, determining number, rigidity index, etc. Robert Bailey and I have written a survey paper attempting to describe all these and related concepts and ...

We present a special constraint structure that possesses both reducable and chain structure. Using our constraint structure, we show that the number of required gauge fixing conditions is just equal to the number of chains and the remaining requirements follow from consistency conditions. Electrodynamics and Yang-Mills theories are discussed as examples. e-mail address: [email protected] e-m...

The gauge-fixing parameter ξ dependence of two-point gauge variant correlation functions is studied for QED and QCD. We show that, in three Euclidean dimensions, or for four-dimensional thermal gauge theories, the usual procedure of getting a general covariant gauge-fixing term by averaging over a class of covariant gauge-fixing conditions leads to a nontrivial gauge-fixing parameter dependence...

The factors and processes driving cyanobacterial blooms in eutrophic freshwater ecosystems have been extensively studied in the past decade. A growing number of these studies concern the direct or indirect interactions between cyanobacteria and heterotrophic bacteria. The presence of bacteria that are directly attached or immediately adjacent to cyanobacterial cells suggests that intense nutrie...