The notions of purity and equational compactness of universal algebras have been studied by Banaschewski and Nelson. Also, Banaschewski deals with these notions in the special case of G-sets for a group G. In this paper we study these and related concepts in the category PRO of projection algebras, that is in N∞-sets, for the monoid N∞ with the binary operation m.n = min{m, n}. We show that eve...

A subgroup Q of a group G is commensurated if the commensurator of Q in G is the entire group G. Our main result is that a finitely generated group G containing an infinite, finitely generated, commensurated subgroup H, of infinite index in G is 1-ended and semistable at ∞. If additionally, Q and G are finitely presented and either Q is 1-ended or the pair (G,Q) has 1 filtered end, then G is si...

Here we analysed the role played by breeding systems and pollinators in the evolution of heterostyly by testing whether evolution towards heterostyly is associated with style polymorphism and changes in pollinator proficiency or breeding system variation (Darwinian hypothesis). We studied pollinators, pollen-transfer efficiency, and incompatibility systems in all seven species of Narcissus sect...

We prove the equivalence of the two important facts about finite metric spaces and universal Urysohn metric spaces U, namely theorem A and theorem B below: Theorem A (Approximation): The group of isometry ISO(U) contains everywhere dense locally finite subgroup; Theorem G(Globalization): For each finite metric space F there exists another finite metric space F̄ and isometric imbedding j of F to ...

Let Mg,n and Hg,n, for 2g − 2 + n > 0, be, respectively, the moduli stack of n-pointed, genus g smooth curves and its closed substack consisting of hyperelliptic curves. Their topological fundamental groups can be identified, respectively, with Γg,n and Hg,n, the so called Teichmüller modular group and hyperelliptic modular group. A choice of base point on Hg,n defines a monomorphism Hg,n →֒ Γg,...

Let (M, I, J,K, g) be a hyperkähler manifold, dimR M = 4n. We study positive, ∂-closed (2p, 0)-forms on (M, I). These forms are quaternionic analogues of the positive (p, p)-forms, well-known in complex geometry. We construct a monomorphism Vp,p : Λ I (M)−→ Λ n+p,n+p I (M), which maps ∂-closed (2p, 0)-forms to closed (n+p, n+p)-forms, and positive (2p, 0)forms to positive (n + p, n + p)-forms. ...

Intralocus sexual conflict (IaSC) is pervasive because males and females experience differences in selection but share much of the same genome. Traits with integrated genetic architecture should be reservoirs of sexually antagonistic genetic variation for fitness, but explorations of multivariate IaSC are scarce. Previously, we showed that upward artificial selection on male life span decreased...

Understanding the evolution of body size and sexual size dimorphism has been a longstanding goal in evolutionary biology. Previous work has shown that environmental stress can constrain male-biased sexual size dimorphism at the population level, but we know little about how this might translate to geographical patterns of body size and sexual size dimorphism at the species level. Environmental ...

Species traits have been hypothesized by one of us (Ponge, 2013) to evolve in a correlated manner as species colonize stable, undisturbed habitats, shifting from "ancestral" to "derived" strategies. We predicted that generalism, r-selection, sexual monomorphism, and migration/gregariousness are the ancestral states (collectively called strategy A) and evolved correlatively toward specialism, K-...