We consider smooth actions of lattices in higher-rank semisimple Lie groups on manifolds. define two numbers $r(G)$ and $m(G)$ associated with the roots system algebra a group $G$. If dimension manifold is smaller than $r(G)$, then we show action preserves Borel probability measure. at most $m(G)$, there quasi-invariant measure such that measurably isomorphic to relatively measure-preserving ov...

Quantum trajectories are Markov processes that describe the time evolution of a quantum system undergoing continuous indirect measurement. Mathematically, they defined as solutions so-called Stochastic Schrödinger Equations, which nonlinear stochastic differential equations driven by Poisson and Wiener processes. This paper is devoted to study invariant measures trajectories. Particularly, we p...

We exhibit a change of variables that maintains the Mahler measure given polynomial. This method leads to construction highly non-trivial polynomials with and settles some conjectural numerical formulas due Boyd Brunault.

We extend the results of Walters on the uniqueness of invariant measures with maximal entropy on compact groups to an arbitrary locally compact group. We show that the maximal entropy is attained at the left Haar measure and the measure of maximal entropy is unique.

magnetotelluric (mt) method is an electromagnetic technique that uses the earth natural field to map the electrical resistivity changes in subsurface structures. because of the high penetration depth of the electromagnetic fields in this method (tens of meters to tens of kilometers), the mt data is used to investigate the shallow to deep subsurface geoelectrical structures and their dimensions....

let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .