Nondense orbits of nonquasiunipotent flows and applications to Diophantine approximation Dmitry Y. Kleinbock Yale University 1996 Let G be a Lie group and Γ a lattice in G. Consider a partially hyperbolic (nonquasiunipotent) flow on the homogeneous space G/Γ. We prove that for certain classes of subsets Z of G/Γ, the set of points with orbits staying away from Z, even though it may have measure...

Abstract. Denote by ‖ · ‖ the euclidean norm in R. We prove that the local pair correlation density of the sequence ‖m− α‖k, m ∈ Z, is that of a Poisson process, under diophantine conditions on the fixed vector α ∈ R: in dimension two, vectors α of any diophantine type are admissible; in higher dimensions (k > 2), Poisson statistics are only observed for diophantine vectors of type κ < (k − 1)/...

The Continuous Skolem Problem asks whether a real-valued function satisfying a linear differential equation has a zero in a given interval of real numbers. This is a fundamental reachability problem for continuous linear dynamical systems, such as linear hybrid automata and continuoustime Markov chains. Decidability of the problem is currently open—indeed decidability is open even for the sub-p...

Linear algebraic techniques based on minimization of thermodynamic functional and/or other constraints are illustrated for mass balance of chemical reactions that do not exhibit stoichiometrically unique solutions in the linear algebraic vector space. The techniques demonstrate elegant casting of chemical equations in terms of generalized linear Diophantine matrices and generalized elimination ...

In this chapter we propose a Key exchange protocol based on random solution of linear Diophantine equation in n variables, where the considered satisfies condition for existence infinitely many solutions. Also crypt analysis is analysed.

The Continuous Skolem Problem asks whether a real-valued function satisfying a linear differential equation has a zero in a given interval of real numbers. This is a fundamental reachability problem for continuous linear dynamical systems, such as linear hybrid automata and continuoustime Markov chains. Decidability of the problem is currently open; indeed decidability is open even for the sub-...