PRD) 98. 98.80.Es, 95.35.+d, 98.80.Hw, 04.20.Cv Averaging and evolving inhomogeneities are non-commuting operations. This implies the existence of deviations of an averaged model from the standard Friedmann-Lemaître cosmologies. We quantify these deviations, encoded in a backreaction parameter, in the framework of Newtonian cosmology. We employ the linear theory of gravitational instability in the Eulerian and Lagrangian approaches, as well as the spherically-and plane-symmetric solutions as standards of reference. We propose a model for the evolution of the average characteristics of a spatial domain for generic initial conditions that contains the spherical top-hat model and the planar collapse model as exact sub cases. A central result is that the backreaction term itself, calculated on sufficiently large domains, is small but, still, its presence can drive the cosmological parameters on the averaging domain far away from their global values of the standard model. We quantify the variations of these parameters in terms of the fluctuations in the initial data as derived from the power spectrum of initial cold dark matter density fluctuations. E.g. in a domain with a radius of 100Mpc today and initially one-σ fluctuations, the density parameters deviate from their homogeneous values by 15%; three-σ fluctuations lead to deviations larger than 100%. *

Oxoiron(IV) species have been found to act as the oxidants in the catalytic cycles of several mononuclear nonheme iron enzymes that activate dioxygen. To gain insight into the factors that govern the oxidative reactivity of such complexes, a series of five synthetic S = 1 [FeIV(O)(LN5)]2+ complexes has been characterized with respect to their spectroscopic and electrochemical properties as well as their relative abilities to carry out oxo transfer and hydrogen atom abstraction. The Fe=O units in these five complexes are supported by neutral pentadentate ligands having a combination of pyridine and tertiary amine donors but with different ligand frameworks. Characterization of the five complexes by X-ray absorption spectroscopy reveals Fe=O bonds of ca. 1.65 Å in length that give rise to the intense 1s→3d pre-edge features indicative of iron centers with substantial deviation from centrosymmetry. Resonance Raman studies show that the five complexes exhibit ν(Fe=O) modes at 825–841 cm−1. Spectropotentiometric experiments in acetonitrile with 0.1 M water reveal that the supporting pentadentate ligands modulate the E1/2(IV/III) redox potentials with values ranging from 0.83 to 1.23 V vs. Fc, providing the first electrochemical determination of the E1/2(IV/III) redox potentials for a series of oxoiron(IV) complexes. The 0.4-V difference in potential may arise from differences in the relative number of pyridine and tertiary amine donors on the LN5 ligand and in the orientations of the pyridine donors relative to the Fe=O bond that are enforced by the ligand architecture. The rates of oxo-atom transfer (OAT) to thioanisole correlate linearly with the increase in the redox potentials, reflecting the relative electrophilicities of the oxoiron(IV) units. However this linear relationship does not extend to the rates of hydrogen-atom transfer (HAT) from 1,3-cyclohexadiene (CHD), 9,10-dihydroanthracene (DHA), and benzyl alcohol, suggesting that the HAT reactions are not governed by thermodynamics alone. This study represents the first investigation to compare the electrochemical and oxidative properties of a series of S = 1 FeIV=O complexes with different ligand frameworks and sheds some light on the complexities of the reactivity of the oxoiron(IV) unit.

Nine of the most important estimators known for the two-point correlation function are compared using a predetermined, rigorous criterion. The indicators were extracted from over 500 subsamples of the Virgo Hubble volume simulation cluster catalog. The "real" correlation function was determined from the full survey in a 3000 h(-1) Mpc periodic cube. The estimators were ranked by the cumulative probability of returning a value within a certain tolerance of the real correlation function. This criterion takes into account bias and variance, and it is independent of the possibly non-Gaussian nature of the error statistics. As a result, for astrophysical applications, a clear recommendation has emerged: the Landy & Szalay estimator, in its original or grid version (Szapudi & Szalay), is preferred in comparison with the other indicators examined, with a performance almost indistinguishable from the Hamilton estimator.

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