Given a countable group $G$ splitting as free product $G=G_1\ast\dots\ast G_k\ast F_N$, we establish classification results for subgroups of the $Out(G,\mathcal{F})$ all outer automorphisms that preserve conjugacy classes each $G_i$. We show every finitely generated subgroup $H\subseteq Out(G,\mathcal{F})$ either contains relatively fully irreducible automorphism, or else it virtually preserves...

let $g$ be an $(n,m)$-graph. we say that $g$ has property $(ast)$if for every pair of its adjacent vertices $x$ and $y$, thereexists a vertex $z$, such that $z$ is not adjacentto either $x$ or $y$. if the graph $g$ has property $(ast)$, thenits complement $overline g$ is connected, has diameter 2, and itswiener index is equal to $binom{n}{2}+m$, i.e., the wiener indexis insensitive of any other...

Universal bi-Hamiltonian hierarchies of group-invariant (multicomponent) soliton equations are derived from non-stretching geometric curve flows γ(t, x) in Riemannian symmetric spaces M = G/H, including compact semisimple Lie groups M = K for G = K×K, H = diag G. The derivation of these soliton hierarchies utilizes a moving parallel frame and connection 1-form along the curve flows, related to ...

‎In this paper‎, ‎first we develop the duality concept for $g$-Bessel sequences‎ ‎and Bessel fusion sequences in Hilbert spaces‎. ‎We obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎We also expand every $g$-Bessel ‎sequence to a frame by summing some elements‎. ‎We define the restricted isometry property for ‎$g$-frames and generalize some resu...

The canonical evolution and symmetry generators are exhibited for a Klein-Gordon (K-G) system which has been partitioned by an accelerated coordinate frame into a pair of subsystems. This partitioning of the K-G system is conveyed to the canonical generators by the eigenfunction property of the Minkowski Bessel (M-B) modes. In terms of the M-B degrees of freedom, which are unitarily related to ...

Given certain compactly supported functions g ∈ L2(Rd) whose Zd-translates form a partition of unity, and real invertible d×d matrices B, C for which ||CT B|| is sufficiently small, we prove that the Gabor system {EBmTCng}m,n∈Zd forms a frame, with a (non-canonical) dual Gabor frame generated by an explicitly given finite linear combination of shifts of g. For functions g of the above type and ...

We study the following lesser-known low rank (LR) recovery problem: recover an $n \times q$ rank- notation="LaTeX">$r$ matrix, notation="LaTeX">${ \boldsymbol {X}}^{\ast}=[\boldsymbol {x}^{\ast}_{1}, {x}^{\ast}_{2}, \ldots, {x}^{\ast}...

An upper quasi-density on $\bf H$ (the integers or the non-negative integers) is a real-valued subadditive function $\mu^\ast$ defined whole power set of $\mathbf such that $\mu^\ast(X) \le \mu^\ast({\bf H}) = 1$ and $\mu^\ast(k \cdot X + h) \frac{1}{k}\, \mu^\ast(X)$ for all $X \subseteq \bf H$, $k \in {\bf N}^+$, $h N$, where := \{kx: x X\}$; an density non-decreasing with respect to inclusio...