相关论文: On the maximal spectral type of nilsystems

We proved that for the countably infinite number of one-parameterized one dimensional dynamical systems, they preserve the Lebesgue measure and they are ergodic for the measure (infinite ergodicity). Considered systems connect the parameter…

For a torsion free Kleinian group $\Gamma$ without parabolics, we consider the decomposition of the limit set $L(\Gamma)$ into conical and ending limit sets and compare the Patterson-Sullivan measure with the harmonic measure on $L(\Gamma)$…

Two method for computation of the spectra of certain infinite graphs are suggested. The first one can be viewed as a reversed Gram--Schmidt orthogonalization procedure. It relies heavily on the spectral theory of Jacobi matrices. The second…

Let $(X,\Gamma)$ be a topological system, where $\Gamma$ is a nilpotent group generated by $T_1,\ldots, T_d$ such that for each $T\in \Gamma$, $T\neq e_\Gamma$, $(X,T)$ is weakly mixing and minimal. For $d,k\in \mathbb{N}$, let $p_{i,j}(n),…

Let $\alpha>0$ and $0<\gamma<1$. Define $g_{\alpha,\gamma}\colon \mathbb{N}\to\mathbb{N}_0$ by $g_{\alpha,\gamma}(n)=\lfloor n\alpha +\gamma\rfloor$, where $\lfloor x \rfloor$ is the largest integer less than or equal to $x$. The set…

Let $L/K$ be a cyclic extension of degree $n = 2m$. It is known that the space $\text{Alt}_K(L)$ of alternating $K$-bilinear forms (skew-forms) on $L$ decomposes into a direct sum of $K$-subspaces $A^{\sigma^i}$ indexed by the elements of…

Let $G$ be a compact Lie group, $N\geq 1$ and $L>0$. The random geometric graph on $G$ is the random graph $\Gamma(N,L)$ whose vertices are $N$ random points $g_1,\ldots,g_N$ chosen under the Haar measure of $G$, and whose edges are the…

Let $G$ be a group and $S$ a unital epsilon-strongly $G$-graded algebra. We construct spectral sequences converging to the Hochschild (co)homology of $S$. Each spectral sequence is expressed in terms of the partial group (co)homology of $G$…

Mkrtchyan and Steffen [J. Graph Theory, 70 (4), 473--482, 2012] showed that every class II simple graph can be decomposed into a maximum $\Delta$-edge-colorable subgraph and a matching. They further conjectured that every graph $G$ with…

Spheres can be written as homogeneous spaces $G/H$ for compact Lie groups in a small number of ways. In each case, the decomposition of $L^2(G/H)$ into irreducible representations of $G$ contains interesting information. We recall these…

We prove ergodicity for random dynamics satisfying some expansion and irreducibility conditions. As a particular application, we show that if $R_1,R_2\in \mathrm{SO}(d+1)$, $d\ge 2$, generate a dense subgroup, then the random dynamics of…

We perform an exhaustive classification of G_2 invariant extrema of the most general gauged N=8 supergravity in four dimensions. They comprise four branches of Anti-de Sitter solutions labelled by a single parameter. Interestingly, while…

We study the structure of arbitrary split Leibniz superalgebras. We show that any of such superalgebras ${\frak L}$ is of the form ${\frak L} = {\mathcal U} + \sum_jI_j$ with ${\mathcal U}$ a subspace of an abelian (graded) subalgebra $H$…

Let $(M,\tau,\sigma,\Gamma)$ be a (finite) von Neumann dynamical system and let $N$ be a $\Gamma$-invariant unital von Neumann subalgebra of $M$. If $V\subset L^2(M)$ is a right $N$-submodule whose projection $p_V$ has finite trace in $<…

We show that if a list of nonzero complex numbers $\sigma=(\lambda_1,\lambda_2,\ldots,\lambda_k)$ is the nonzero spectrum of a diagonalizable nonnegative matrix, then $\sigma$ is the nonzero spectrum of a diagonalizable nonnegative matrix…

The co-maximal subgroup graph $\Gamma(G)$ of a group $G$ is a graph whose vertices are non-trivial proper subgroups of $G$ and two vertices $H$ and $K$ are adjacent if $HK=G$. In this paper, we continue the study of $\Gamma(G)$, especially…

Given a non-degenerate Peano continuum $X$, a dimension function $D:2^X_*\to[0,\infty]$ defined on the family $2^X_*$ of compact subsets of $X$, and a subset $\Gamma\subset[0,\infty)$, we recognize the topological structure of the system…

We present a systematic weak-coupling renormalization group (RG) technique for studying a collection of $N$ coupled one-dimensional interacting electron systems, focusing on the example of N-leg Hubbard ladders. For $N=2,3$, we recover…

The cross topology $\gamma$ on a product of topological spaces $X$ and $Y$ is the collection of all sets $G\subseteq X\times Y$ such that the intersection of $G$ with every vertical line and every horizontal line is an open subset of either…

We give a geometric classification of complex $n$-dimensional $2$-step nilpotent (all, commutative and anticommutative) algebras. Namely, has been found the number of irreducible components and their dimensions. As a corollary, we have a…