On nonuniform dichotomy for stochastic skew-evolution semiflows in Hilbert spaces

In this paper we study a general concept of nonuniform exponential dichotomy in mean square for stochastic skew-evolution semiflows in Hilbert spaces. We obtain a variant for the stochastic case of some well-known results, of the deterministic case, due to R. Datko: Uniform asymptotic stability of evolutionary processes in a Banach space, SIAM J. Math. Anal., 3(1972), 428–445. Our approach is based on the extension of some techniques used in the deterministic case for the study of asymptotic behavior of skew-evolution semiflows in Banach spaces.     

The deformation of flat connections and affine manifolds

Geodesically complete affine manifolds are quotients of the Euclidean space through a properly discontinuous action of a subgroup of affine Euclidean transformations. An equivalent definition is that the tangent bundle of such a manifold admits a flat, symmetric and complete connection. If the completeness assumption is dropped, the manifold is not necessarily obtained as the quotient of the Euclidean space through a properly discontinuous group of affine transformations. In fact the universal cover may no longer be the Euclidean space. The main result of this paper states that if a flat connection of a bundle can be properly deformed into a metric connection then its Euler class vanishes. This is a partial result toward an old question of Chern.     

European ring exercise on water toxicity using different bioluminescence inhibition tests based on Vibrio fischeri, in support to the implementation of the water framework directive

An inter-laboratory comparison exercise was conducted under the European Union funded project entitled: Screening Methods for Water Data Information in Support of the Implementation of the Water Framework Directive (SWIFT-WFD) and coordinated by the Consejo Superior de Investigaciones Científicas (CSIC), in order to evaluate the reproducibility of different toxicity tests based on the bioluminescence inhibition of Vibrio fischeri, for the rapid water toxicity assessment.For the first time, this type of exercise has been organized in Europe, and using different tests based on the same principle. In this exercise, 10 laboratories from 8 countries (Austria, Cyprus, Germany, Greece, Italy, Portugal, Romania, and Spain) took place, and a total number of 360 samples were distributed.During the exercise, six series of six samples were analyzed along 5 months. Every batch of samples was composed by three real samples and three standard solutions. The real samples were: a raw influent and the effluent of a wastewater treatment plant (WWTP), and a sample from a first settlement of the WWTP spiked with a mixture of toxicant standards.A final number of 330 (91.7%) samples was analyzed, 3300 values in duplicate were collected, and the results for each sample were expressed as the 50% effective concentration (EC₅₀) values calculated through five points of dilution inhibition curves, after 5 and 15 min of incubation times.A statistical study was initiated using 660 results. The mean values, standard deviations (σ), variances (σ²), and upper and lower warning limits (UWL and LWL) were obtained, using the EC₅₀ values calculated with the result from the participating laboratories.The main objectives of this toxicity ring study were to evaluate the repeatability (r) and reproducibility (R) when different laboratories conduct the test, the influence of complex matrix samples, the variability between different tests based on the same principle, and to determine the rate at which participating laboratories successfully completed tests initiated.In this exercise, the 3.93% toxicity values were outliers according with the Z-score values and the Dixon test. The samples with the greater number of outliers were those with the smallest variability coefficient, corresponding to the greater and the smaller toxicity level.No relation was found through the cluster analysis, between the final results and the different commercial devices involved. Testing by multiple commercial devices did not appear to reduce the precision of the results, and the variability coefficient for the exercise was nearby to the average value for past editions carried out at national level, where the different participants used the same commercial device.Stability of samples was also followed during the exercise. While statistical significance differences were not found for the greater part of samples, for the sample from the WWTP influent, a significant decrease of the toxicity value was found along this study. Nevertheless, this was a type of sample with a high toxicity level during all the exercise.On the other hand, in order to obtain the chemical characterization of real samples, those were analyzed by chromatographic techniques, using different sequential solid phase extraction (SSPE) procedures, followed by liquid chromatography coupled with mass spectrometry (LC-MS), and gas chromatography-mass spectrometry (GC-MS). Good agreement was found between the chemical analysis results and the toxicity level of the samples.     

A Constrained Disorder Refinement: “Reinvestigation of “Single‐Crystal X‐ray Structure of 1,3‐Dimethylcyclobutadiene” by M. Shatruk and I. V. Alabugin”

Shatruk and Alabugin propose an alternative structural model for the observed electron density that we have attributed to the photochemical formation of 1,3‐dimethylcyclobutadiene in a protective solid crystalline matrix. The main criticism from Shatruk and Alabugin concerns the modeling of the disorder in the calixarene cavity and in particular the neglect of a residual electron density close to the O1 atom. We published (Chem. Eur. J. 2011 , 17, 10021) our opinion concerning this “ignored peak” in the Supporting Information of the paper. The current response to the Correspondence demonstrates that Shatruk and Alabugin have over‐modeled our data by assigning a small electron density peak, which is hardly more than the density corresponding to a hydrogen atom, to an under‐occupied oxygen site, using inappropriate refinement contraints.     

Detailed ab initio first-principles study of the magnetic anisotropy in a family of trigonal pyramidal iron(II) pyrrolide complexes

A theoretical, computational, and conceptual framework for the interpretation and prediction of the magnetic anisotropy of transition metal complexes with orbitally degenerate or orbitally nearly degenerate ground states is explored. The treatment is based on complete active space self-consistent field (CASSCF) wave functions in conjunction with N-electron valence perturbation theory (NEVPT2) and quasidegenerate perturbation theory (QDPT) for treatment of magnetic field- and spin-dependent relativistic effects. The methodology is applied to a series of Fe(II) complexes in ligand fields of almost trigonal pyramidal symmetry as provided by several variants of the tris-pyrrolylmethyl amine ligand (tpa). These systems have recently attracted much attention as mononuclear single-molecule magnet (SMM) complexes. This study aims to establish how the ligand field can be fine tuned in order to maximize the magnetic anisotropy barrier. In trigonal ligand fields high-spin Fe(II) complexes adopt an orbitally degenerate (5)E ground state with strong in-state spin-orbit coupling (SOC). We study the competing effects of SOC and the (5)E?ε multimode Jahn-Teller effect as a function of the peripheral substituents on the tpa ligand. These subtle distortions were found to have a significant effect on the magnetic anisotropy. Using a rigorous treatment of all spin multiplets arising from the triplet and quintet states in the d(6) configuration the parameters of the effective spin-Hamiltonian (SH) approach were predicted from first principles. Being based on a nonperturbative approach we investigate under which conditions the SH approach is valid and what terms need to be retained. It is demonstrated that already tiny geometric distortions observed in the crystal structures of four structurally and magnetically well-documented systems, reported recently, i.e., [Fe(tpa(R))](-) (R = tert-butyl, Tbu (1), mesityl, Mes (2), phenyl, Ph (3), and 2,6-difluorophenyl, Dfp (4), are enough to lead to five lowest and thermally accessible spin sublevels described sufficiently well by S = 2 SH provided that it is extended with one fourth order anisotropy term. Using this most elementary parametrization that is consistent with the actual physics, the reported magnetization data for the target systems were reinterpreted and found to be in good agreement with the ab initio results. The multiplet energies from the ab initio calculations have been fitted with remarkable consistency using a ligand field (angular overlap) model (ab initio ligand field, AILFT). This allows for determination of bonding parameters and quantitatively demonstrates the correlation between increasingly negative D values and changes in the σ-bond strength induced by the peripheral ligands. In fact, the sigma-bonding capacity (and hence the Lewis basicity) of the ligand decreases along the series 1 > 2 > 3 > 4.