A construction is given for the recovery of a disjoint union of strictly convex smooth planar obstacles from travelling-time information. The obstacles are required to be such that no Euclidean line meets more than two of them.
A special class of doubly stochastic (Markov) operators is constructed. These operators come from measure preserving transformations and inherit some of their properties, namely ergodicity and positivity of entropy, yet they may have no pointwise factors.
Daniel Spalink, Jocelyn Pender, Marcial Escudero
et al.
AbstractSystematically quantifying diversity across landscapes is necessary to understand how clade history and ecological heterogeneity contribute to the origin, distribution, and maintenance of biodiversity. Here, we chart the spatial structure of diversity among all species in the sedge family (Cyperaceae) throughout the USA and Canada. We first identify areas of remarkable species richness, phylogenetic diversity, and functional trait diversity, and highlight regions of conservation priority. We then test predictions about the spatial structure of this diversity based on the historical biogeography of the family. Incorporating a phylogeny, over 400 000 herbarium records, and a database of functional traits mined from online floras, we find that species richness and functional trait diversity peak in the Northeastern USA, while phylogenetic diversity peaks along the Gulf of Mexico. Floristic turnover among assemblages increases significantly with distance, but phylogenetic turnover is twice as rapid along latitudinal gradients as along longitudinal gradients. These patterns reflect the expected distribution of Cyperaceae, which originated in the tropics but radiated in temperate regions. We identify assemblages with an abundance of rare, range‐restricted lineages, and assemblages composed of species generally lacking from diverse regions. We argue that both of these metrics are useful for developing targeted conservation strategies. We use the data generated here to establish future research priorities, including the testing of a series of hypotheses regarding the distribution of chromosome numbers, photosynthetic pathways, and resource partitioning in sedges.
By using the Picard-Fuchs equation and the property of Chebyshev space to the discontinuous differential system, we obtain an upper bound of the number of limit cycles for the nongeneric quadratic reversible system when it is perturbed inside all discontinuous polynomials with degree $n$.
We consider projections of planar self-similar sets, and show that one can create nonempty interior in the projections by applying arbitrary small perturbations, if the self-similar set satisfies the open set condition and has Hausdorff dimension greater than 1.
Suppose $\{f_t\}$ is an analytic one-parameter family of rational maps defined over a non-Archimedean field $K$. We prove a finiteness theorem for the set of rescalings for $\{f_t\}$. This complements results of J. Kiwi.
The aim of this note is to provide a conceptually simple demonstration of the fact that repetitive model sets are characterized as the repetitive Meyer sets with an almost automorphic associated dynamical system.
In this paper, we define a new construction of completely scrambled 0-dimensional systems using the inverse limit of sequences of directed graph covers. These examples are transitive and are not locally equicontinuous.
We consider the billiard in the exterior of a piecewise smooth body in two-dimensional Euclidean space and show that the maximum number of directions of invisibility in such billiard is at most finite.
We prove that a flow on a compact surface is expansive if and only if the singularities are of saddle type and the union of their separatrices is dense. Moreover we show that such flows are obtained by surgery on the suspension of minimal interval exchange maps.
It is shown that on compact hyperbolic manifolds, certain stable configurations of points which mutually repel along all interconnecting geodesics become equidistributed as the number of points increases
Using a structure theorem from [FG2010] we prove a version of multiple recurrence for sets of positive measure in a general stationary dynamical system.
This paper shows that there exists a non-minimal sequence $\bar{x} \in ([0,1]^2)^{\mathbb{N}}$ such that for any continuous function $f:[0,1]^2 \to [0,1]$, the sequence obtained by mapping terms of $\bar{x}$ by $f$ is minimal.