In a series of studies, we examined how mothers naturally stress words across multiple mentions in speech to their infants and how this marking influences infants' recognition of words in fluent speech. We first collected samples of mothers' infant-directed speech using a technique that induced multiple repetitions of target words. Acoustic analyses revealed that mothers systematically alternat...

M . Ratner's theorem on the rigidity of horocycle flows is extended to the rigidity of horospherical foliations on bundles over finite-volume locally-symmetric spaces of non-positive sectional curvature, and to other foliations of the same algebraic form.

Under explicit diophantine conditions on (α, β) ∈ R2, we prove that the local two-point correlations of the sequence given by the values (m − α)2 + (n−β)2, with (m,n) ∈ Z2, are those of a Poisson process. This partly confirms a conjecture of Berry and Tabor [2] on spectral statistics of quantized integrable systems, and also establishes a particular case of the quantitative version of the Oppen...

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 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.

This paper addresses a single item two-level supply chain inventory model considering deterioration during carrying of deteriorating from supplier’s warehouse to retailer’s as well in the warehouse. The assumes preservation technology prevent rate deterioration. An upper limit for investment has been set constraint model. maximizes profit per unit time, simultaneously calculated optimal order q...

A set Y ⊆ R that intersects every convex set of volume 1 is called a Danzer set. It is not known whether there are Danzer sets in R with growth rate O(T ). We prove that natural candidates, such as discrete sets that arise from substitutions and from cut-and-project constructions, are not Danzer sets. For cut and project sets our proof relies on the dynamics of homogeneous flows. We consider a ...

Direct quotations from business leaders can communicate to the wider public the latent state of their organization as well as the beliefs of the organization’s leaders. Candid quotes from business leaders can have dramatic effects upon the share price of their organization. For example, Gerald Ratner in 1991 stated that his company’s products were crap and consequently his company (Ratners) los...