Relatively finite measure-preserving extensions and lifting multipliers by Rokhlin cocycles

We show that under some natural ergodicity assumptions, extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L^∞-eigenvalues. We make use of some analogs of basic results from the theory of finite-rank modules associated to an extension of measure-preserving systems in the setting of a non-singular base.     

The equilibrium states for semigroups of rational maps

We consider the dynamics of skew product maps associated with finitely generated semigroups of rational maps on the Riemann sphere. We show that under some conditions on the dynamics and the potential function ψ, there exists a unique equilibrium state for ψ and a unique exp(P(ψ) − ψ)-conformal measure, where P(ψ) denotes the topological pressure of ψ. The research of M. Urbański was supported in part by the NSF Grant DMS 0400481. H. Sumi thanks University of North Texas for kind hospitality, during his stay there.     

EPR evidence of antiferromagnetic ordering in single‐layer graphene

We report electron paramagnetic resonance (EPR) evidence of the antiferromagnetic ordering in pristine single‐layer graphene. Temperature dependences of the parameters of EPR spectra obtained for vacuum‐processed samples were studied within the temperature range of 4.2–300 K. Our experiment has confirmed recent theoretical predictions that in single‐layer graphene the carrier‐mediated exchange interaction leads to antiferromagnetic coupling. We note some quantitative discrepancies between the theory and experimental findings and discuss their origins. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Effects of Ring Strain on Cyclic Tetraaryl[5]cumulenes

Cyclic tetraaryl[5]cumulenes ( 1 a–f ) have been synthesized and studied as a function of increasing ring strain. The magnitude of ring strain is approximated by the extent of bending of the cumulenic core as assessed by a combination of X-ray crystallographic analysis and DFT calculations. Trends are observed in ¹³C NMR, UV-vis, and Raman spectra associated with ring strain, but the effects are small. In particular, the experimental HOMO-LUMO gap is not appreciably affected by bending of the [5]cumulene framework from ca. 174° (λ_max=504 nm) in 1 a to ca. 178° (λ_max=494 nm) in 1 f .     

On the Uniqueness of the Density for the Invariant Measure in an Infinite Hyperbolic Iterated Function System

Periodica Mathematica Hungarica - We consider a regular infinite hyperbolic iterated function satisfying a property which guarantees that the associated Frobenius-Perron operator ? is almost...     

Dynamics of the rear part of a long-rod penetrator’s core during firing

A problem of the dynamics of long-rod penetrators loaded with the gunpowder combustion products has been solved in closed form by using the wave method (d’Alambert). The analytic recurrence formulae have been derived to define the fields of longitudinal stress and particle velocity in the rod penetrator. The problem of estimating the axial stress field and particle velocity caused by the gunpowder combustion products for a subcalibre projectile penetrator has been solved by using the substitute dynamic theoretical model. The reason for using the substitute dynamic theoretical model is that the pressure on the rear part of the projectile is controlled by gas-dynamic processes and it is not possible to readily estimate the loading. The method of characteristics net gets very complicated.      

Circle Maps,Measured Laminations,and Free Group Actions on IR-trees

This paper explores the connection between homeomorphisms of the unit circle, codimension-1 measured laminations on closed surfaces, and free actions of surface groups on IR-trees.     

Optimal double control problem for a PDE model of goodwill dynamics

We propose a new optimal control model of product goodwill in a segmented market where the state variable behaviour is described by a partial differential equation of the Lotka–Sharp–McKendrick type. In order to maximize the sum of discounted profits over a finite time horizon, we control the marketing communication activities which influence the state equation and the boundary condition. Moreover, we introduce the mathematical representation of heterogeneous electronic word of mouth. Based on the semigroup approach, we prove the existence and uniqueness of optimal controls. Using a maximum principle, we describe a numerical algorithm to find the optimal solution. Finally, we examine several examples on the optimal goodwill model and discover two types of marketing strategies.