Derived equivalences for Cohen–Macaulay Auslander algebras

Let $A$ and $B$ be Gorenstein Artin algebras of finite Cohen–Macaulay type. We prove that, if $A$ and $B$ are derived equivalent, then their Cohen–Macaulay Auslander algebras are also derived equivalent.     

Vertex-minors and the Erdős–Hajnal conjecture

We prove that for every graph $H$, there exists $\epsilon >0$ such that every $n$-vertex graph with no vertex-minors isomorphic to $H$ has a pair of disjoint sets $A$, $B$ of vertices such that $\left|A\right|,\left|B\right|\ge \epsilon n$ and $A$ is complete or anticomplete to $B$. We deduce this from recent work of Chudnovsky, Scott, Seymour, and Spirkl (2018). This proves the analog of the Erd?s–Hajnal conjecture for vertex-minors.     

The fixation probability and time for a doubly beneficial mutant

For a highly beneficial mutant $A$ entering a randomly reproducing population of constant size, we study the situation when a second beneficial mutant $B$ arises before $A$ has fixed. If the selection coefficient of $B$ is greater than the selection coefficient of $A$, and if $A$ and $B$ can recombine at some rate $\rho$, there is a chance that the double beneficial mutant $AB$ forms and eventually fixes. We give a convergence result for the fixation probability of $AB$ and its fixation time for large selection coefficients.     

Convergence to the equilibrium for the Pauli equation without detailed balance condition

Let $A?B$ be an extension of commutative rings with identity, X an analytic indeterminate over B, and $R\text{:}=A+XB[[X]]$, the subring of the formal power series ring $B[[X]]$, consisting of the series with constant terms in A. In this Note we study when the ring R is Noetherian. We prove that R is Noetherian if and only if A is Noetherian and B is a finitely generated A-module. To cite this article: S. Hizem, A. Benhissi, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Ideal amenability of module Lau Banach algebra

Given Banach algebras $A$ and $B$, where $A$ be a Banach $B$-bimodule. In this paper we study the ideal amenability, approximate ideal and cyclic ideal amenability of module Lau Banach algebra $A{\times }_{\alpha }B$.