We start up the study of stability general graph pairs. This notion is a generalization concept graphs. say that pair graphs $(\Gamma,\Sigma)$ stable if $Aut(\Gamma\times\Sigma) \cong Aut(\Gamma)\times Aut(\Sigma)$ and unstable otherwise, where $\Gamma\times\Sigma$ direct product $\Gamma$ $\Sigma$. An said to be nontrivially $\Sigma$ are connected coprime graphs, at least one them non-bipartite...

Following a similar result of Uspenskij on the unitary group of a separable Hilbert space we show that with respect to the lower (or Roelcke) uniform structure the Polish group G = Aut(μ), of automorphisms of an atomless standard Borel probability space (X,μ), is precompact. We identify the corresponding compactification as the space of Markov operators on L2(μ) and deduce that the algebra of r...

This document intends to present AUT speaker recognition system submitted to SITW (Speakers in the Wild) speaker recognition challenge. This challenge aims to provide real world data across a wide range of acoustic and environmental conditions in the context of automatic speaker recognition so as to facilitate the development of new algorithms. The presented system is based on the state-of-the-...

Let $\mathcal{F}$ denote a singular holomorphic foliation on $\mathbb{P}^2$ having finite automorphism group $\mbox{aut}(\mathcal{F})$. Fixed the degree of $\mathcal{F}$, we determine maximal value that $|\mbox{aut}(\mathcal{F})|$ can take and explicitly exhibit all foliations attaining this value. Furthermore, classify with large but group.

Let k be a field and A a finite dimensional (associative with 1) k-algebra. By modA we denote the category of finite dimensional left A-modules. In many important situations we may suppose that A is presented as a quiver with relations (Q, I) (e.g. if k is algebraically closed, then A is Morita equivalent to kQ/I). We recall that if A is presented by (Q, I), then Q is a finite quiver and I is a...

We give an explicit description of smoothly bounded Reinhardt domains with noncompact automorphism groups. In particular, this description confirms a special case of a conjecture of Greene/Krantz. 0. Introduction Let D be a bounded domain in C, n ≥ 2. Denote by Aut(D) the group of holomorphic automorphisms of D. The group Aut(D) with the topology of uniform convergence on compact subsets of D i...

Let $G$ be a finite non-abelian $p$-group and $L(G)$ denotes the absolute center of $G$. Also, let $Aut^{L}(G)$ and $Aut_c(G)$ denote the group of all absolute central and the class preserving automorphisms of $G$, respectively. In this paper, we give a necessary and sufficient condition for $G$ such that $Aut_c(G)=Aut^{L}(G)$. We also characterize all finite non-abelian $p$-groups of order $p^...

Let X be a rational nonsingular compact connected real algebraic surface. Denote by Aut(X) the group of real algebraic automorphisms of X. We show that the group Aut(X) acts n-transitively on X, for all natural integers n. As an application we give a new and simpler proof of the fact that two rational nonsingular compact connected real algebraic surfaces are isomorphic if and only if they are h...

Let X be a connected locally finite graph with vertex-transitive automorphism group. If X has polynomial growth then the set of all bounded automorphisms of finite order is a locally finite, periodic normal subgroup of AUT(X) and the action of AUT(X) on V(X) is imprimitive if X is not finite. If X has infinitely many ends, the group of bounded automorphisms itself is locally finite and periodic.