We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of finitely many coordinates). The relations we consider are defined by cocycles taking values in groups, including some nonabelian ones. This generalizes (half ...

We review previous solutions of problem nr. 10769 posed by Christian Blatter A 1988 paper by C. D. Godsil and J. Zaks [1] states the following result, which is the solution of problem nr. 10769: “Let G be the graph with the points of the unit sphere in three dimensions as its vertices, and two vertices adjacent if and only if they are orthogonal as unit vectors (i.e., their spherical distance i...

As his students in geography, archaeology, geology, and Latin American, African, and Middle Eastern Studies attest, you could learn more in one day in the field with Karl Butzer than you could in a semester-long course with any other professor. Karl’s fieldwork and active teaching endedMay 4, 2016. Future generations of students will learn fromKarl bymeans of his 15 books and monographs, and mo...

*Alfred Wegener Institute for Polar and Marine Research, Telegrafenberg A43, D-14473 Potsdam, Germany {State Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences, Xiangshan Nanxincun 20, 100093 Beijing, China {Department of Plant Ecology and Natural Conservation, Institute of Biochemistry and Biology, University of Potsdam, Maulbeerallee 2, D-1...

To every infinite lower Hessenberg matrix D is associated a linear operator on l2. In this paper we prove the similarity of the operator D − ∆, where ∆ belongs to a certain class of compact operators, to the operator D−∆′, where ∆′ is of rank one. We first consider the case when ∆ is lower triangular and has finite rank; then we extend this to ∆ of infinite rank assuming that D is bounded. In S...

The Springer variety is the set of flags stabilized by a nilpotent operator. In 1976, T.A. Springer observed that this variety’s cohomology ring carries a symmetric group action, and he offered a deep geometric construction of this action. Sixteen years later, Garsia and Procesi made Springer’s work more transparent and accessible by presenting the cohomology ring as a graded quotient of a poly...