The main goal of this survey is the description of the fruitful interaction between Ergodic Theory and Number Theory via the study of two beautiful results: the first one by Ben Green and Terence Tao (about long arithmetic progressions of primes) and the second one by Noam Elkies and Curtis McMullen (about the distribution of the sequence {√n}mod 1). More precisely, during the first part, we wi...

Understanding and Controlling Crosstalk between Parallel Molecular Wires Matthew G. Reuter,* Gemma C. Solomon, Thorsten Hansen, Tamar Seideman, and Mark A. Ratner Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113, United States Nano-Science Center and Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø Denmark Department of Ch...

We classify all locally finite joinings of a horospherical subgroup action on Γ\G when Γ is a Zariski dense geometrically finite subgroup of G = PSL2(R) or PSL2(C). This generalizes Ratner’s 1983 joining theorem for the case when Γ is a lattice in G. One of the main ingredients is equidistribution of non-closed horospherical orbits with respect to the Burger-Roblin measure which we prove in a g...

In the present paper, we study some approximation properties of the Szász type operators involving Charlier polynomials introduced by Varma and Taşdelen in 2012. First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then we obtain the error in the approximation of functions having derivatives of bounded variation.

Convergence rates and central limit theorems for kernel estimators of the stationary density of a linear process have been obtained under the assumption that the innovation density is smooth (Lipschitz). We show that smoothness is not required. For example, it suffices that the innovation density has bounded variation.

In this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and  coincidence point  theorems on partially ordered fuzzy metric spaces are proved. Also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.