Eigenvalue estimates for Schrödinger operators on metric trees

We consider Schrödinger operators on radial metric trees and prove Lieb–Thirring and Cwikel–Lieb–Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show that the bounds are valid in the endpoint case and reflect the correct order in the weak or strong coupling limit.     

Chemical triple-mutant boxes for quantifying cooperativity in intermolecular interactions

Chemical double-mutant cycles have been used to quantify intermolecular functional-group interactions in H-bonded zipper complexes in chloroform. If the same interaction is measured in zippers of different overall stability, the double-mutant cycles can be combined to produce a triple-mutant box. This construct quantifies cooperativity between the functional group interaction of interest and the other interactions that are used to change the overall stability of the complexes. The sum of two edge-to-face aromatic interactions (-2.9 +/- 0.5 kJ mol-1) is shown to be insensitive to changes of up to 13.7 +/- 0.2 kJ mol-1 in the overall stability of the complex. In principle, enthalpic cooperative effects caused by entropy-enthalpy compensation could perturb the measurement of intermolecular interactions when using the double-mutant cycle approach, but these experiments show that, for this system, the magnitude of the effect lies within the error of the measurements.     

Mise en évidence d'une solution solide de type spinelle dans le diagramme de phase du systeme InS

Evidence is presented for normal-spinel domain of homogeneity between the compositions InS_1.50?ε and InS_1.35. Structural study of a single crystal of composition InS_1.44 indicates indium vacancies on the tetrahedral sites. The compound In₂S₃, regardless of conditions of formation, is a tetragonal superstructure of the spinel lattice (a₀) with $\text{a = a}{}_0\text{2}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and c = 3a₀. The spinel-type domain shows peritectic decomposition at 850°C for the composition InS_1.40.     

Hydrogen-bond topology and the ice VII/VIII and ice Ih/XI proton-ordering phase transitions

The existence of an ice Ih/XI proton-ordering transition to a low-temperature ferroelectric phase has sparked considerable debate in the literature. Electronic density functional theory calculations, extended using graph invariants, confirm that a transition to a low-temperature ferroelectric phase should occur. The predicted transition at 98 K is in qualitative agreement with the observed transition at 72 K, and the low-temperature phase is the ferroelectric phase determined in diffraction experiments. The theoretical methods used to predict the phase transition are validated by comparing their prediction to the well-characterized ice VII/VIII proton-ordering transition.     

Low-temperature thermal conductivity of superconductors with gap nodes

We report a detailed analytic and numerical study of electronic thermal conductivity in d-wave superconductors. We compare theory of the crossover at low temperatures from T dependence to T(3) dependence for increasing temperature with recent experiments on YBa(2)Cu(3)O(7) in zero magnetic field for T approximately [0.04 K,0.4 K] by Hill et al. [Phys. Rev. Lett. 92, 027001 (2004)]. Transport theory, including impurity scattering and inelastic scattering within strong-coupling superconductivity, can consistently fit the temperature dependence of the data in the lower half of the temperature regime. We discuss the conditions under which we expect power-law dependences over wide temperature intervals.     

Use of 19F NMR spectroscopy to screen chemical libraries for ligands that bind to proteins

Identification of compounds from chemical libraries that bind to macromolecules by use of NMR spectroscopy has gained increasing importance during recent years. A simple methodology based on (19)F NMR spectroscopy for the screening of ligands that bind to proteins, which also provides qualitative information about relative binding strengths and the presence of multiple binding sites, is presented here. A library of fluorinated compounds was assembled and investigated for binding to the two bacterial chaperones PapD and FimC, and also to human serum albumin (HSA). It was found that library members which are bound to a target protein could be identified directly from line broadening and/or induced chemical shifts in a single, one-dimensional (19)F NMR spectrum. The results obtained for binding to PapD using (19)F NMR spectroscopy agreed well with independent studies based on surface plasmon resonance, providing support for the versatility and accuracy of the technique. When the library was titrated to a solution of PapD chemical shift and linewidth changes were observed with increasing ligand concentration, which indicated the presence of several binding sites on PapD and enabled the assessment of relative binding strengths for the different ligands. Screening by (19)F NMR spectroscopy should thus be a valuable addition to existing NMR techniques for evaluation of chemical libraries in bioorganic and medicinal chemistry.     

Higher Hopf formulae for homology via Galois Theory

We use Janelidze's Categorical Galois Theory to extend Brown and Ellis's higher Hopf formulae for homology of groups to arbitrary semi-abelian monadic categories. Given such a category A and a chosen Birkhoff subcategory B of A, thus we describe the Barr-Beck derived functors of the reflector of A onto B in terms of centralization of higher extensions. In case A is the category Gp of all groups and B is the category Ab of all abelian groups, this yields a new proof for Brown and Ellis's formulae. We also give explicit formulae in the cases of groups vs. k-nilpotent groups, groups vs. k-solvable groups and precrossed modules vs. crossed modules.     

A type 2 Ferrier rearrangement-based synthesis of d-myo-inositol 1,4,5-trisphosphate

The synthesis of d-myo-inositol 1,4,5-trisphosphate (InsP₃) from methyl α-d-glucopyranose, via a type 2 Ferrier rearrangement is reported. A key intermediate in this synthesis possesses orthogonal protecting groups at the 1-, 4- and 5-position, making it a versatile starting point for the synthesis of unnatural InsP₃ derivatives. Biological evaluation of the synthetic InsP₃ demonstrates that this compound evokes selective Ca²⁺ release via activation of InsP₃ receptors.     

On an algorithm considered by Stieltjes

This paper studies an iterative algorithm of the type of Gauss's algorithm mentioned by Stieltjes in his correspondence with Hermite (lettre 323) and later investigated by Myrberg. In particular, what appears to be a false statement by Stieltjes is corrected. The same algorithm, apparently being unaware of his predecessors, has also been considered by Lehmer.