1H, 13C, 15N NMR coordination shifts in Fe(II), Ru(II) and Os(II) cationic complexes with 2,2':6',2″-terpyridine

(1)H, (13)C and (15)N NMR studies of iron(II), ruthenium(II) and osmium(II) bis-chelated cationic complexes with 2,2':6',2″-terpyridine ([M(terpy)(2) ](2+) ; M = Fe, Ru, Os) were performed. Significant shielding of nitrogen-adjacent H(6) and deshielding of H(3'), H(4') protons were observed, both effects being mostly expressed for Fe(II) compounds. The metal-bonded nitrogens were shielded, this effect being much larger for the outer N(1), N(1″) than the inner N(1') atoms, and enhanced in the Fe(II) → Ru(II) → Os(II) series.     

Determination of the N-methyl stereochemistry in tropane and granatane derivatives in solution: a computational and NMR spectroscopic study

Tropane (8-methyl-8-azabicyclo[3.2.1]octane) and granatane (9-methyl-9-azabicyclo[3.3.1]nonane) derivatives undergo fast N-methyl inversion. The distribution of axial and equatorial N-methyl invertomers of protonated and free amine forms in aqueous and methanol solutions was studied by room and low temperature NMR spectroscopy on tropinone, tropine, granatan-3-one (pseudopelletierine or pseudopelletrierin) and α-granatan-3-ol. Theoretical (DFT) distributions in both gas phase and solutions are also reported. Applicability of the computational model for the studied system was verified by comparison with invertomer distributions inferred from inverse-gated ¹³C NMR experiments. Among the tested functionals, the BH&HLYP/cc-pVDZ method yields the best agreement with experiment. Moreover, accounting for orbital relaxation upon immersion in the solution was found to be of importance in order to properly reproduce observed distributions.     

Synthesis of Functionalized Materials Using Aryloxo-Organometallic Compounds toward Spinel-like MM'(2)O(4) (M = Ba(2+), Sr(2+); M' = In(3+), Al(3+)) Double Oxides

The predesigned single-source precursors [Ba{(μ-ddbfo)(2)InMe(2)}(2)] (1), [Me(2)In(μ-ddbfo)](2) (2), [Sr{(μ-ddbfo)(2)AlMe(2)}(2)] (4), and [Me(2)Al(μ-ddbfo)](2) (5) (ddbfoH = 2,3-dihydro-2,2-dimethylbenzofuran-7-ol) for spinel-like double oxides and group 13 oxide materials were prepared via the direct reaction of the homoleptic aryloxide [M(ddbfoH)(4)](ddbfo)(2)·ddbfoH (M = Ba(2+), Sr(2+) (3)) and InMe(3) or AlMe(3) in toluene. In all of the reactions, there was an organometallic-driven abstraction of the OH protons from the 7-benzofuranols in the Ba(2+) and Sr(2+) cation sphere. All compounds were characterized by elemental analysis, (1)H NMR, and FT-IR spectroscopy. In addition, the molecular structures of 1, 2, and 3 were determined by single-crystal X-ray diffraction. The oxide products derived from the compounds mentioned above were studied using elemental analysis, Raman spectroscopy, X-ray powder diffraction, and scanning and transmission electron microscopy equipped with an energy-dispersive spectrometer. Moreover, their specific surface area and mesopore size distribution were evaluated using nitrogen porosimetry. Preliminary investigations of the Eu-doped SrAl(2)O(4) and In(2)O(3) phosphors revealed that the oxides obtained could be considered as matrices for lanthanide ions.     

Infrared spectra and ultraviolet-tunable laser induced photochemistry of matrix-isolated phenol and phenol-d5

Monomers of phenol and its ring-perdeuterated isotopologue phenol-d(5) were isolated in argon matrices at 15 K. The infrared (IR) spectra of these species were recorded and analyzed. In situ photochemical transformations of phenol and phenol-d(5) were induced by tunable UV laser light. The photoproducts have been characterized by IR spectroscopy supported by theoretical calculations of the infrared spectra. The primary product photogenerated from phenol was shown to be the phenoxyl radical. The analysis of the progress of the observed phototransformations led to identification of 2,5-cyclohexadienone as one of the secondary photoproducts. Spectral indications of other secondary products, such as the Dewar isomer and the open-ring ketene, were also detected. Identification of the photoproducts provided a guide for the interpretation of the mechanisms of the observed photoreactions.     

Using heavy atom rare gas matrix to control the reactivity of 4-methoxybenzaldehyde: a comparison with benzaldehyde

Different patterns of photochemical behavior were observed for 4-methoxybenzaldehyde (p-anisaldehyde) isolated in xenon and in argon matrices. Monomers of the compound isolated in solid Xe decarbonylate upon middle ultraviolet irradiation, yielding methoxybenzene (anisole), and CO. On the other hand, p-anisaldehyde isolated in an Ar matrix and subjected to identical irradiation, predominantly isomerizes to the closed-ring isomeric ketene (4-methoxycyclohexa-2,4-dien-1-ylidene) methanone. Experimental detection of a closed-ring ketene photoproduct, generated from an aromatic aldehyde, constitutes a rare observation. The difference between the patterns of photochemical transformations of p-anisaldehyde isolated in argon and xenon environments can be attributed to the external heavy-atom effect, where xenon enhances the rate of intersystem crossing from the singlet to the triplet manifold in which decarbonylation (via p-methoxybenzoyl radical) takes place. The parent compound, benzaldehyde, decarbonylates (to benzene + CO) when subjected to middle ultraviolet irradiation in both argon and xenon matrices. This demonstrates the role of the methoxy p-anisaldehyde substituent in activation of the reaction channel leading to the formation of the ketene photoproduct.     

Magnetically induced anisotropy of electric permittivity in the PDMS ferromagnetic gel

A polymer ferromagnetic gel is an assembly of ferromagnetic nanoparticles embedded in a gel. The finely distributed magnetic particles of iron oxide (Fe₃O₄) were suspended, due to adhesive forces, in the flexible matrix (poly(dimethyl siloxane) PDMS). The mean diameter of the suspended nanoparticles, equal to 8.9 nm, was determined by means of a vibrating sample magnetometer. The dispersion of the electric permittivity, studied in the frequency range of 400 Hz-5 MHz, revealed the maxima at approximately 92 kHz and 2.5 MHz. The application of the homogenous magnetic field, ranging from 0 mT to 500 mT induced the anisotropy of the electric permittivity for the mutual parallel orientation of the magnetic field, electric field and the axis of the sample. For the magnetic induction B = 500 mT the highest decrease in the electric permittivity and the shift of the maximum from 2.5 toward 2.9 MHz were found.     

Real closures of models of weak arithmetic

D’Aquino et al. (J Symb Log 75(1):1–11, 2010) have recently shown that every real-closed field with an integer part satisfying the arithmetic theory IΣ₄ is recursively saturated, and that this theorem fails if IΣ₄ is replaced by IΔ₀. We prove that the theorem holds if IΣ₄ is replaced by weak subtheories of Buss’ bounded arithmetic: PV or ${\Sigma^b_1-IND^{|x|_k}}$ . It also holds for IΔ₀ (and even its subtheory IE ₂) under a rather mild assumption on cofinality. On the other hand, it fails for the extension of IOpen by an axiom expressing the Bézout property, even under the same assumption on cofinality.     

A locking-free hp DPG method for linear elasticity with symmetric stresses

We present two new methods for linear elasticity that simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size $h$ and polynomial degree $p$ . This is achieved within the recently developed discontinuous Petrov–Galerkin (DPG) framework. In this framework, both the stress and the displacement approximations are discontinuous across element interfaces. We study locking-free convergence properties and the interrelationships between the two DPG methods.     

Lp solutions of reflected BSDEs under monotonicity condition

We prove existence and uniqueness of ${\mathbb{L}}^p$ solutions, $p\in [1,2]$, of reflected backward stochastic differential equations with $p$-integrable data and generators satisfying the monotonicity condition. We also show that the solution may be approximated by the penalization method. Our results are new even in the classical case $p=2$.     

On the twin paradox in static spacetimes: I. Schwarzschild metric

Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider the twin paradox in static spacetimes. According to a well known theorem in Lorentzian geometry the longest timelike worldline between two given points is the unique geodesic line without points conjugate to the initial point on the segment joining the two points. We calculate the proper times for static twins, for twins moving on a circular orbit (if it is a geodesic) around a centre of symmetry and for twins travelling on outgoing and ingoing radial timelike geodesics. We show that the twins on the radial geodesic worldlines are always the oldest ones and we explicitly find the the conjugate points (if they exist) outside the relevant segments. As it is of its own mathematical interest, we find general Jacobi vector fields on the geodesic lines under consideration. In the first part of the work we investigate Schwarzschild geometry.