The solution structures and dynamics and the solid-state structures of substituted cyclopentadienyltitanium(IV) trifluorides

Organotitanium fluorides (C5Me4R)TiF3 (R = H, Me, Et) sublimate with formation of crystalline dimers. From solution, we obtained crystals of dimers and tetramers. The tetramer [{(C5Me5)TiF3}4] irreversibly dissociates in the solid state to dimers (DeltaH = 8.33 kcal mol(-1)). The variable-temperature (1)H and (19)F NMR spectroscopy measurements of the toluene-d(8) solution of [{(C5Me5)TiF3}2] revealed at 202 K one monomeric, two dimeric (with C2h and Cs symmetry), two tetrameric (with D2 and C2v symmetry), and two trimeric (both C2 symmetry) molecules. With the increase in temperature and dilution of the solution, the composition of the solution shifts to the smaller molecules. The thermodynamic and activation parameters for the reversible dissociation of dimers to monomers in the solution are DeltaH = 9.2 kcal mol(-1), DeltaS = 24.2 cal mol(-1) K(-1), DeltaH(double dagger) = 12.2 kcal mol(-1), DeltaS(double dagger) = 9.7 cal mol(-1) K(-1). The dissociation path with a weakly double-bridged transition-state dimer was proposed. The thermodynamic parameters for the reversible dissociation of the C2v tetramer to the dimers in solution are DeltaH = 7.9 kcal mol(-1) and DeltaS = 26.8 cal mol(-1) K(-1). From both tetramers, the D2 molecule is 0.34(5) kcal mol(-1) lower in enthalpy and 6.5(5) cal mol(-1) K(-1) lower in entropy than the C2v molecule. The structures of both trimers were proposed. The low-temperature 19F NMR spectra of the CDCl3 solution of [{(C5Me5)TiF3}2] are consistent with equilibria of a monomer, two dimers (with C2h and Cs symmetry), and a trimer. The vapor pressure osmometric molecular mass determination of CDCl3 solution of [{(C5Me5)TiF3}2] at 302 K is consistent with the equilibrium of the dimer and the monomer.     

Metric spaces in synthetic topology

We investigate the relationship between the synthetic approach to topology, in which every set is equipped with an intrinsic topology, and constructive theory of metric spaces. We relate the synthetic notion of compactness of Cantor space to Brouwer’s Fan Principle. We show that the intrinsic and metric topologies of complete separable metric spaces coincide if they do so for Baire space. In Russian Constructivism the match between synthetic and metric topology breaks down, as even a very simple complete totally bounded space fails to be compact, and its topology is strictly finer than the metric topology. In contrast, in Brouwer’s intuitionism synthetic and metric notions of topology and compactness agree.     

Shotgun lipidomics on a LTQ Orbitrap mass spectrometer by successive switching between acquisition polarity modes

Top-down shotgun lipidomics relies on direct infusion of total lipid extracts into a high-resolution tandem mass spectrometer and implies that individual lipids are recognized by their accurately determined m/z. Lipid ionization efficiency and detection specificity strongly depend on the acquisition polarity, and therefore it is beneficial to analyze lipid mixtures in both positive and negative modes. Hybrid LTQ Orbitrap mass spectrometers are widely applied in top-down lipidomics; however, rapid polarity switching was previously unfeasible because of the severe and immediate degradation of mass accuracy. Here, we report on a method to rapidly acquire high-resolution spectra in both polarity modes with sub-ppm mass accuracy and demonstrate that it not only simplifies and accelerates shotgun lipidomics analyses but also improves the lipidome coverage because more lipid classes and more individual species within each class are recognized. In this way, shotgun analysis of total lipid extracts of human blood plasma enabled to quantify 222 species from 15 major lipid classes within 7?min acquisition cycle.     

Photoinduced decarboxylation of 9‐oxo‐6,9‐dihydro[1,2,5]selenadiazolo[3,4‐f]quinoline‐8‐carboxylic acid

Photoinduced reactions of 9‐oxo‐6,9‐dihydro[1,2,5]selenadiazolo[3,4‐f]quinoline‐8‐carboxylic acid (SeQCA) were investigated in alkaline media (aqueous NaOH solutions) by electron paramagnetic resonance (EPR) spectroscopy, following the in situ formation of paramagnetic species. According to UV–Vis and nuclear magnetic resonance investigations, protonation (pH ≈ 11) and deprotonation (pH ≈ 13) of the imino hydrogen of the 4‐pyridone moiety has to be considered, reflected also in the different EPR spectra observed upon irradiation. Photoinduced generation of radicals was found only for carboxylate substituted SeQCA; other studied selenadiazoloquinolone derivatives, together with those substituted at the C(8) position (R = H, COOCH₂CH₃, COOCH₃, COCH₃ or CN), did not generate paramagnetic species during exposure. Consequently, photodecarboxylation was suggested as the decisive step, accompanied by the decomposition of the selenadiazole ring, resulting in the formation of ortho‐hydroxylate anions. EPR parameters elucidated from experimental EPR spectra obtained at pH ≈ 11 and pH ≈ 13 indicate the formation of oxygen‐centered radicals at the decarboxylated 4‐pyridone ring. EPR spin trapping experiments with nitromethane confirmed a very effective photoinduced electron transfer from all the selenadiazoloquinolones investigated. Copyright © 2011 John Wiley & Sons, Ltd.     

Transition fronts in inhomogeneous Fisher–KPP reaction–diffusion equations

We use a new method in the study of Fisher–KPP reaction–diffusion equations to prove existence of transition fronts for inhomogeneous KPP-type non-linearities in one spatial dimension. We also obtain new estimates on entire solutions of some KPP reaction–diffusion equations in several spatial dimensions. Our method is based on the construction of sub- and super-solutions to the non-linear PDE from solutions of its linearization at zero.     

On divergence-free drifts

We investigate the validity and failure of Liouville theorems and Harnack inequalities for parabolic and elliptic operators with low regularity coefficients. We are particularly interested in operators of the form ${?}_t?\mathrm{\Delta }+b?\mathrm{?}$ resp. $?\mathrm{\Delta }+b?\mathrm{?}$ with a divergence-free drift b. We prove the Liouville theorem and Harnack inequality when $b\in L_{\infty }({\mathit{BMO}}^{?1})$ resp. $b\in {\mathit{BMO}}^{?1}$ and provide a counterexample demonstrating sharpness of our conditions on the drift. Our results generalize to divergence-form operators with an elliptic symmetric part and a BMO skew-symmetric part. We also prove the existence of a modulus of continuity for solutions to the elliptic problem in two dimensions, depending on the non-scale-invariant norm $6b{6}_{L_1}$. In three dimensions, on the other hand, bounded solutions with $L_1$ drifts may be discontinuous.     

On linearizations of the quadratic two-parameter eigenvalue problem

We present several transformations that can be used to solve the quadratic two-parameter eigenvalue problem (QMEP), by formulating an associated linear multiparameter eigenvalue problem. Two of these transformations are generalizations of the well-known linearization of the quadratic eigenvalue problem and linearize the QMEP as a singular two-parameter eigenvalue problem. The third replaces all nonlinear terms by new variables and adds new equations for their relations. The QMEP is thus transformed into a nonsingular five-parameter eigenvalue problem. The advantage of these transformations is that they enable one to solve the QMEP using existing numerical methods for multiparameter eigenvalue problems. We also consider several special cases of the QMEP, where some matrix coefficients are zero     

Shotgun lipidomics on a LTQ Orbitrap mass spectrometer by successive switching between acquisition polarity modes

Top–down shotgun lipidomics relies on direct infusion of total lipid extracts into a high‐resolution tandem mass spectrometer and implies that individual lipids are recognized by their accurately determined m/z. Lipid ionization efficiency and detection specificity strongly depend on the acquisition polarity, and therefore it is beneficial to analyze lipid mixtures in both positive and negative modes. Hybrid LTQ Orbitrap mass spectrometers are widely applied in top–down lipidomics; however, rapid polarity switching was previously unfeasible because of the severe and immediate degradation of mass accuracy. Here, we report on a method to rapidly acquire high‐resolution spectra in both polarity modes with sub‐ppm mass accuracy and demonstrate that it not only simplifies and accelerates shotgun lipidomics analyses but also improves the lipidome coverage because more lipid classes and more individual species within each class are recognized. In this way, shotgun analysis of total lipid extracts of human blood plasma enabled to quantify 222 species from 15 major lipid classes within 7 min acquisition cycle. Copyright © 2012 John Wiley & Sons, Ltd.     

Neutron self-shielding in irradiation channels of small reactors is isotropic

In order to predict the self-shielding effect in neutron activation of non-spherical samples in reactor neutron spectra, it is important to know whether the neutron field is sufficiently anisotropic to cause significant variations between horizontal and vertical sample orientation or with orientation relative to the direction towards the reactor core. Metal wires with significant neutron self-shielding were irradiated in several channels of the SLOWPOKE reactor at Ecole Polytechnique Montreal and the TRIGA reactor at the Jožef Stefan Institute. In all cases, the amount of thermal or epithermal self-shielding was found to be identical, within the experimental uncertainty, regardless of the orientation of the wire, indicating that the neutron field is essentially isotropic. Models used to predict neutron self-shielding need to be adjusted accordingly. In our Monte Carlo model, the tube-shaped neutron source was moved back into the moderator and reflecting materials near the sample location were included, which produced an isotropic neutron field at the sample location.     

Phosphorylation of imidazo[2,1‐b]thiazoles with phosphorus(III) halides in the presence of bases

The reaction of phosphorus(III) halides with 6‐substituted imidazo[2,1‐b]thiazoles in the presence of bases proceeds regioselectively and affords 5‐phosphinoimidazo[2,1‐b]thiazoles, useful synthons for the preparation of various P(III) and P(V) derivatives. 5‐Phosphinoimidazo[2,1‐b]thiazoles are selectively alkylated at the phosphorus or heterocyclic nitrogen atom, depending on the alkylating agent. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:648–655, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20166