Reaction of O(1D) with N2O

O(¹D), produced from the photolysis of N₂O at 2139 Å, reacts with N₂O in accord with: We have used the method of chemical difference to obtain an accurate measure of k₂/k₃ = 0.59 ± 0.01. Furthermore, the quantum yield of production of O(³P), either on direct photolysis or on deactivation of O(¹D) by N₂O, is less than 0.02 and probably zero.     

Unimodality preservation in Markov chains

A subset of the stochastically monotone Markov chains has the property that the expectation of unimodal functions of the chain is itself unimodal in the initial state. The variation- diminishing property of TP₂ matrices is employed to characterize these Markov chains. Related properties are exhibited.     

Magnetic percolation in iron-platinum alloys

Conclusions We have shown that the transition at 30.5% Fe is a percolation transition with the formation of clusters being correctly described by the accepted model, and that the Mössbauer spectra of a 26.5 at% Fe alloy show evidence of a SDW. Such a SDW with wave vector parallel to a cube axis could provide a preferred direction in an otherwise cubic crystal.     

Comparison of SCC-DFTB and NDDO-based semiempirical molecular orbital methods for organic molecules

Extensive testing of the SCC-DFTB method has been performed, permitting direct comparison to data available for NDDO-based semiempirical methods. For 34 diverse isomerizations of neutral molecules containing the elements C, H, N, and O, the mean absolute errors (MAE) for the enthalpy changes are 2.7, 3.2, 5.0, 5.1, and 7.2 kcal/mol from PDDG/PM3, B3LYP/6-31G(d), PM3, SCC-DFTB, and AM1, respectively. A more comprehensive test was then performed by computing heats of formation for 622 neutral, closed-shell H, C, N, and O-containing molecules; the MAE of 5.8 kcal/mol for SCC-DFTB is intermediate between AM1 (6.8 kcal/mol) and PM3 (4.4 kcal/mol) and significantly higher than for PDDG/PM3 (3.2 kcal/mol). Similarly, SCC-DFTB is found to be less accurate for heats of formation of ions and radicals; however, it is more accurate for conformational energetics and intermolecular interaction energies, though none of the methods perform well for hydrogen bonds with strengths under ca. 7 kcal/mol. SCC-DFTB and the NDDO methods all reproduce MP2/cc-pVTZ molecular geometries with average errors for bond lengths, bond angles, and dihedral angles of only ca. 0.01 A, 1.5 degrees , and 3 degrees . Testing was also carried out for sulfur containing molecules; SCC-DFTB currently yields much less accurate heats of formation in this case than the NDDO-based methods due to the over-stabilization of molecules containing an SO bond.     

Coherence and wavefront characterization of Si‐111 monochromators using double‐grating interferometry

A study of the coherence and wavefront properties of a pseudo‐channel‐cut monochromator in comparison with a double‐crystal monochromator is presented. Using a double‐grating interferometer designed for the hard X‐ray regime, the complex coherence factor was measured and the wavefront distortions at the sample position were analyzed. A transverse coherence length was found in the vertical direction that was a factor of two larger for the channel‐cut monochromator owing to its higher mechanical stability. The wavefront distortions after different optical elements in the beam, such as monochromators and mirrors, were also quantified. This work is particularly relevant for coherent diffraction imaging experiments with synchrotron sources.     

A Gleason–Kahane–Żelazko theorem for the Dirichlet space

We show that every linear functional on the Dirichlet space that is non-zero on nowhere-vanishing functions is necessarily a multiple of a point evaluation. Continuity of the functional is not assumed. As an application, we obtain a characterization of weighted composition operators on the Dirichlet space as being exactly those linear maps that send nowhere-vanishing functions to nowhere-vanishing functions.We also investigate possible extensions to weighted Dirichlet spaces with superharmonic weights. As part of our investigation, we are led to determine which of these spaces contain functions that map the unit disk onto the whole complex plane.     

Existence of incomplete canonical Kirkman packing designs

For $u,v$ positive integers with $u\equiv v\equiv 4\left(mod6\right)$, let ICKPD$(u,v)$ denote a canonical Kirkman packing of order $u$ missing one of order $v$. In this paper, it is shown that the necessary condition for existence of an ICKPD$(u,v)$, namely $u\ge 3v+4$, is sufficient with a definite exception $(u,v)=(16,4)$, and except possibly when $v>76$, $v\equiv 4\left(mod12\right)$ and $u\in \{3v+4,3v+10\}$.     

Convergence in Wasserstein distance for self-stabilizing diffusion evolving in a double-well landscape

It is well-known (see Bolley et al. [3]) that there exists a contraction in Wasserstein distance between the solution to the granular media equation and its unique steady state, provided that the confining potential is strictly convex. Nevertheless, in the nonconvex case, just few is known. In particular, we do not have a unique steady state under easily checked assumptions if the diffusion coefficient is sufficiently small. Consequently, the method of Bolley, Gentil and Guillin can not be applied in this setting. However, here, we present a simple example (for the sake of the simplicity) of a double-well confining potential, and we show the convergence to 0 of the Wasserstein distance between the solution to the granular media equation and a related application (which characterizes the steady states) of this solution.     

Hydrolysis of Cutin by PET-Hydrolases

Functionalisation of synthetic polymers by using enzymes has been recently demonstrated. The major advantage of enzymes over chemical processes lies in their surface specific and endo-wise mode of action. Surface hydrophilisation of PET with lipases and cutinases leads to a dramatic increase of the surfacial acid and hydroxyl group content while conventional chemical treatment does not cause any change. However, this PET-hydrolysing activity by enzymes from distinct classes has not yet been correlated to activity on natural polyesters. Here, we show that lipases, cutinases and a PHA-depolymerase are all capable of hydrolysing PET, while only lipases and cutinases also hydrolysed cutin to various degrees. Lipases showed a higher specificity for terminal fatty acids while the cutinases preferred hydroxy fatty acids during cutin hydrolysis.