Assume a diploid species consisting of an infinite number of competing demes, each having N(e) reproducing members and in which mating is at random. Then consider a locus at which a pair of alleles A and A' are segregating, where A' is the "altruistic allele," which has selective disadvantage s' relative to A with respect to individual selection, but which is beneficial for a deme in competitio...

By means of analyzing the notion verbal products groups, we show that soficity, hyperlinearity, amenability, Haagerup property, Kazhdan's property (T) and exactness are preserved under taking $k$-nilpotent while being orderable is not preserved. We also study these properties for solvable Burnside groups. then if two discrete groups sofic, or have their restricted wreath product arising from ni...

Let φ be a w-continuous homomorphism from a dual Banach algebra to C. The notion of φ-Connes amenability is studied and some characterizations is given. A type of diagonal for dual Banach algebras is dened. It is proved that the existence of such a diagonal is equivalent to φ-Connes amenability. It is also shown that φ-Connes amenability is equivalent to so-called φ-splitting of a certain short...

Let A $\mathcal {A}$ be a countable ℵ0-homogeneous structure. The primary motivation of this work is to study different amenability properties (subgroups of) the automorphism group Aut ( ) $\operatorname{Aut}(\mathcal {A})$ ; secondary existence weakly generic automorphisms . Among others, we present sufficient conditions implying invariant probability measures on certain subsets and also that ...

The main purpose of this manuscript is to prove a common fixed point theorem for two weakly compatible maps satisfying the following integral type contraction in \(G\)-metric space:\[\int^{G(\mathcal{F}x,\mathcal{F}y,\mathcal{F}z)}_0\varphi (t)dt\le \alpha \int^{L(x,y,z)}_0\varphi (t)dt,\] all \(x,y, z\in X\), where\begin{align*}L(x,y,z)&=\max\{G(gx, gy, gz), G(gx, \mathcal{F}x, \mathcal{F}...

We investigate amenability and weak amenability of the l1-algebra of polynomial hypergroups. We derive conditions for (weak) amenability adapted to polynomial hypergroups and show that these conditions are often not satisfied. However, for the hypergroup induced by Chebyshev polynomials of the first kind we prove amenability.

We study homogenization of a boundary obstacle problem on $ C^{1,\alpha} domain $D$ for some elliptic equations with uniformly coefficient matrices $\gamma$. For any \epsilon\in\mathbb{R}_+$, $\partial D=\Gamma \cup \Sigma$, $\Gamma \cap \Sigma=\emptyset and S_{\epsilon}\subset \Sigma suitable assumptions,\ we prove that as $\epsilon$ tends to zero, the energy minimizer u^{\epsilon} \int_{D} |\...

In this paper we prove that every n-Jordan homomorphis varphi:mathcal {A} longrightarrowmathcal {B} from unital Banach algebras mathcal {A} into varphi -commutative Banach algebra mathcal {B} satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0, xin mathcal {A}, is an n-homomorphism. In this paper we prove that every n-Jordan homomorphism varphi:mathcal {A} longrightarrowmathcal...

In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $ngeq 1$ implies the weak amenability of A.