Proper caterpillars are distinguished by their symmetric chromatic function

This paper deals with the so-called Stanley conjecture, which asks whether they are non-isomorphic trees with the same symmetric function generalization of the chromatic polynomial. By establishing a correspondence between caterpillars trees and integer compositions, we prove that caterpillars in a large class (we call trees in this class proper) have the same symmetric chromatic function generalization of the chromatic polynomial if and only if they are isomorphic

Almost periodic structures and the semiconjugacy problem

The description of almost periodic or quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80's. Frequently, the modelling of such structures leads to different types of dynamical systems which include, depending on the concept of quasiperiodicity being considered, skew products over quasiperiodic or almost-periodic base flows, mathematical quasicrystals or maps of the real line with almost-periodic displacement. An important problem in this context is to know whether the considered system is semiconjugate to a rigid translation. We solve this question in a general setting that includes all the above-mentioned examples and also allows to treat scalar differential equations that are almost-periodic both in space and time. To that end, we study a certain class of flows that preserve a one-dimensional foliation and show that a semiconjugacy to a minimal translation flow exists if and only if a boundedness condition, concerning the distance of orbits of the flow to those of the translation, holds

On the simplicity of homeomorphism groups of a tilable lamination

We show that the identity component of the group of homeomorphisms that preserve all leaves of a R^d-tilable lamination is simple. Moreover, in the one dimensional case, we show that this group is uniformly perfect. We obtain a similar result for a dense subgroup of homeomorphisms.Comment: 14

Return to Dollar, Generalized Distance Function and the Fisher Productivity Index

Exploring the duality between a return to dollar definition of profit and the generalized distance function we establish the relationship between the Laspeyres, Paasche and Fisher productivity indexes and their alternative Malmquist indexes counterparts. By proceeding this way, we propose a consistent decomposition of these productivity indexes into two mutually exclusive components. A technical component represented by the Malmquist index and an economical component which can be identified with the contribution that allocative criteria make to productivity change. With regard to the Fisher index, we indicate how researchers can further decompose the Malmquist technical component rendering explicit the sources of productivity change. We also show how the proposed model can be implemented by means of Data Envelopment Analysis techniques, and illustrate the empirical process with an example data set.Generalized Distance Function; Return to Dollar; Fisher and Malmquist Productivity Indexes

Forbidden island heights in stress-driven coherent Stranski-Krastanov growth

The observed height distribution of clusters obtained in strained epitaxy has been often interpreted in terms of electronic effects. We show that some aspects can be explained classically by the interplay of strain and edge energies. We find that soft materials can transform directly from monolayer into thicker islands by two-dimensional (2D) multilayer nucleation and growth. There is a critical thickness decreasing with the force constant. Thinner islands are thermodynamically forbidden, due to the insufficient stress relaxation upon clustering particularly under tensile stress. At sufficiently large misfits the barrier for 2D multilayer nucleation is significantly smaller than the barrier for subsequent single-layer nucleation. The effects are found to be quantitatively reasonable and offer a plausible explanation for the absence of thin islands and 2D growth of flattop islands usually attributed to quantum size effects.Comment: 4 pages, 4 figures. Accepted version. Includes quantitative estimations comparing with experiments plus minor change