An effective equidistribution with explicit constants for the isometry group of rational forms with signature (2, 1) is proved. As an application we get an effective discreteness of Markov spectrum.

We study the sublattices of the rank 2d Barnes-Wall lattices BW2d which occur as fixed points of involutions. They have ranks 2d−1 (for dirty involutions) or 2d−1 ± 2k−1 (for clean involutions), where k, the defect, is an integer at most d2 . We discuss the involutions on BW2d and determine the isometry groups of the fixed point sublattices for all involutions of defect 1. Transitivity results ...

Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy this property with optimal parameters are mainly obtained via probabilistic arguments. Given any matrix, deciding whether it satisfies the restricted isometry property i...

Given polar spaces (V, β) and (V, Q) where V is a vector space over a field K, β a reflexive sesquilinear form and Q a quadratic form, we have associated classical isometry groups. Given a subfield F of K and an F -linear function L : K → F we can define new spaces (V, Lβ) and (V, LQ) which are polar spaces over F . The construction so described gives an embedding of the isometry groups of (V, ...

In this paper, we first define an equivalence relation on the sequence space $\Sigma _{2}$. Then equip quotient set _{2}/_{\sim}$ with a metric $d_1$. We also determine isometry map between spaces $(\Sigma _{2}/_{\sim},d_1)$ and $([0,1],d_{eucl})$. Finally, investigate symmetry conditions respect to some points compare truncation errors for computations which is obtained by metrics $d_{eucl}$