Polymorphic traits are central to many fundamental discoveries in evolution, yet why they are found in some species and not others remains poorly understood. We use the African genus Protea-within which more than 40% of species have co-occurring pink and white floral colour morphs-to ask whether convergent evolution and ecological similarity could explain the genus-wide pattern of polymorphism....

let $r$ be an associative ring with identity. an element $x in r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if there exist $g in g$, $n in mathbb{z}$ and $r in r$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). a ring $r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if every element of $r$ is $mathbb{z}g$-regular (resp. strongly $...

A. Borel proved that, if a finite group F acts effectively and continuously on a closed aspherical manifold M with centerless fundamental group π1(M), then a natural homomorphism ψ from F to the outer automorphism group Outπ1(M) of π1(M), called the associated abstract kernel, is a monomorphism. In this paper, we investigate to what extent Borel’s theorem holds for a compact Lie group G acting ...

During the last decades, structure of mod-2 cohomology Steenrod ring $\mathscr {A}$ became a major subject in Algebraic topology. One most direct attempt studying this by means modular representations general linear groups was surprising work [ Math. Z. 202 (1989), 493–523] William Singer, which introduced homomorphism, so-called algebraic transfer , mapping from coinvariants certain representa...

R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.

A relational structure is called reversible iff every bijective endomorphism of that an automorphism. We characterize property in the class disconnected binary structures, and one its subclasses—posets are disjoint union chains. Also, using concept a monotone function from structures preordered by monomorphism into well founded relation, we detect additional classes posets. further give equival...

We begin with some covering theory for complexes of groups. For example, we show that a covering of developable complexes of groups induces a monomorphism of fundamental groups, and an equivariant isometry of universal covers. As an application, we then investigate the asymptotics of the number of “overlattices” of a cocompact lattice Γ in Aut(K), where K is a locally finite polyhedral complex....