Robert Marshall, part I: Preserver of wilderness

Linear Preserver Problems

Linear preserver problems is an active research area in matrix and operator theory. These problems involve certain linear operators on spaces of matrices or operators. We give a general introduction to the subject in this article. In the first three sections, we discuss motivation, results, and problems. In the last three sections, we describe some techniques, outline a few proofs, and discuss ...

Algebraic and Arithmetic Lattices . Part I 1 Robert Milewski Warsaw University

The scheme LambdaCD deals with a non empty set A, a unary functor F yielding a set, a unary functor G yielding a set, and a unary predicate P, and states that: There exists a function f such that dom f = A and for every element x of A holds if P[x], then f(x) = F(x) and if not P[x], then f(x) = G(x) for all values of the parameters. The following propositions are true: (1) Let L be a non empty ...

Robert Frost and Darwin's theory of evolution: part 1.

Part] I I

Amyloid- : a (life) preserver for the brain

For nearly two decades, the amyloidhypothesis [22] has dominated the field of Alzheimer’s disease (AD) and during that time, massive efforts have focused on the role of amyloidin the pathogenesis of the disease. Given such focus, it is truly unfortunate that it is still unclear whether amyloidis either necessary or sufficient for the frank development of AD or whether amyloidcauses the associat...