We report the preparation of novel quasi-one-dimensional (quasi-1D) C60 nanostructures on rippled graphene. Through careful control of the subtle balance between the linear periodic potential of rippled graphene and the C60 surface mobility, we demonstrate that C60 molecules can be arranged into a quasi-1D C60 chain structure with widths of two to three molecules. At a higher annealing temperat...

We give a streamlined proof of the multiplicative ergodic theorem for quasi-compact operators on Banach spaces with

In investigating homotopy equivalences of smooth G-manifolds where G is a compact Lie group, Pétrie [3], [4], [5] makes use of proper G-maps of degree 1 from one G-module to another of the same complex dimension. The first nontrivial example of such a map, called a quasi-equivalence, was given by Pétrie [6] for two-dimensional S -modules. Necessary and sufficient conditions for the existence of...

A leaf of a compact foliated space has a well defined quasi-isometry type and it is a natural question to ask which quasi-isometry types of (intrinsic) metric spaces can appear as leaves of foliated spaces. There are two more or less related concepts of quasi-isometry. The first one is that used in Riemannian geometry, namely, two (Lipschitz) manifolds are quasi-isometric if there is a Lipschit...

In this note we study the higher direct image functors Rf∗(−) and the higher coinverse image functors Rf (−) which will play a role in our study of Serre duality. The main theorem is the proof that if F is quasi-coherent then so is Rf∗(F ), which we prove first for noetherian schemes and then more generally for quasi-compact quasi-separated schemes. Most proofs are from either Hartshorne’s book...

Let R be a quasi-order on a compact Hausdorff topological space X. We prove that if X is scattered, then R satisfies the Priestley separation axiom if and only if R is closed in the product space X × X. Furthermore, if X is not scattered, then we show that there is a quasi-order on X that is closed in X × X but does not satisfy the Priestley separation axiom. As a result, we obtain a new charac...

We study a concept of 1-local retract in quasi-metric spaces. In this article, we generalize further known results about 1-local retract subsets from metric setting to quasi-metric point of view. In particular we show that any commuting family of nonexpansive self-mappings in a nonempty T0-quasi-metric space (X, d) for which Aq(X) is compact and normal has a common fixed point and the common fi...

A quasi-measure is a non-subadditive measure defined on only open or closed subsets of a compact Hausdorf space. We investigate the nature of irreducible partitions as defined by Aarnes and use the results to construct quasi-measures when g(X) = 1. The cohomology ring is an important tool for this investigation.

We prove the Nagata compactification theorem for any separated map of finite type between quasi-compact and quasi-separated algebraic spaces, generalizing earlier results of Raoult. Along the way we also prove (and use) absolute noetherian approximation for such algebraic spaces, generalizing earlier results in the case of schemes. To the memory of Masayoshi Nagata

If a group acts by uniformly quasi-Möbius homeomorphisms on a compact Ahlfors n-regular space of topological dimension n such that the induced action on the space of distinct triples is cocompact, then the action is quasi-symmetrically conjugate to an action on the standard n-sphere by Möbius transformations.