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Ohne Zusammenfassung     

Searchability in merging and implicit data structures

We introduce the notion ofsearchability as a property of an in place merging algorithm. We show that a pair of sorted arrays can be merged in place in linear time, so that a search can be performed in logarithmic time at any point during the merging process. We apply this method to devise an implicit data structure which can support searches inO(log² n) time in the worst case, andO(logn) on the average, and insertions inO(logn) time, in the worst case.This research was partly supported by NSERC under grant A8237 and presented in preliminary form at the 10th International Colloquium on Automata, Languages and Programming.On leave from the University of Chile.     

Unconventional hydrogen bonding and π‐stacking in two substituted pyridine carboxamides

The crystal structures of two para‐substituted aryl derivatives of pyridine‐2‐carboxamide, namely N‐(4‐fluorophenyl)pyridine‐2‐carboxamide, C₁₂H₉FN₂O, (I), and N‐(4‐nitrophenyl)pyridine‐2‐carboxamide, C₁₂H₉N₃O₃, (II), have been studied. Compound (I) exhibits unconventional aryl–carbonyl C—H...O and pyridine–fluorine C—H...F hydrogen bonding in two dimensions and well defined π‐stacking involving pyridine rings in the third dimension. The conformation of (II) is more nearly planar than that of (I) and the intermolecular interactions comprise one‐dimensional aryl–carbonyl C—H...O hydrogen bonds leading to a stepped or staircase‐like progression of loosely π‐stacked molecules. The close‐packed layers of planar π‐stacked molecules are related by inversion symmetry. Two alternating interplanar separations of 3.439 (1) and 3.476 (1) Å are observed in the crystal lattice and are consistent with a repetitive packing sequence, ABA′B′AB…, for the π‐stacked inversion pairs of (II).     

Attenuation technique for measuring sediment displacement levels

A technique for obtaining accurate, high (spatial) resolution measurements of sediment redeposition levels is described. In certain regimes, the method may also be employed to provide measurements of sediment layer thickness as a function of time. The method uses a uniform light source placed beneath the layer, consisting of transparent particles, so that the intensity of light at a point on the surface of the layer can be related to the depth of particles at that point. A set of experiments, using the impact of a vortex ring with a glass ballotini particle layer as the resuspension mechanism, are described to test and illustrate the technique.

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Biomimetic mineralisation of polymeric scaffolds using a combined soaking approach: adaptation with various mineral salts

Biomimetic strategies which utilise hydrogels have been targeted due to favourable hydrogel characteristics such as the presentation of a large surface area for crystal nucleation within a structured yet responsive scaffold. Chitosan hydrogels were prepared and mineralised using a combined method which involves alternate soaking of the films with precursor solutions, followed by treatment with saturated mineral solution. This method has been shown to be effective for the synthesis of calcium carbonate-chitosan composite materials with tensile strength comparable to nacre. The ratio of organic to inorganic is readily controlled through the presoaking solution concentrations. The ubiquity of this method is shown here with respect to switching out both the anion (CaHPO(4)) and the cation (BaSO(4)). Cation doping is also readily achieved allowing formation of Mg-rich CaCO(3). Poly(acrylic acid) added to (Mg,Ca)CO(3)-chitosan systems induces the formation of two polymorphs (vaterite and calcite) which coexist within the composite material. The mineralised scaffolds were analysed by SEM and powder XRD. The successful mineralisation of chitosan templates with various inorganic compounds shows that this combined approach is widely applicable as a biomimetic approach.     

Interactions of halichondrin B and eribulin with tubulin

Compounds that modulate microtubule dynamics include highly effective anticancer drugs, leading to continuing efforts to identify new agents and improve the activity of established ones. Here, we demonstrate that [(3)H]-labeled halichondrin B (HB), a complex, sponge-derived natural product, is bound to and dissociated from tubulin rapidly at one binding site per αβ-heterodimer, with an apparent K(d) of 0.31 μM. We found no HB-induced aggregation of tubulin by high-performance liquid chromatography, even following column equilibration with HB. Binding of [(3)H]HB was competitively inhibited by a newly approved clinical agent, the truncated HB analogue eribulin (apparent K(i), 0.80 μM) and noncompetitively by dolastatin 10 and vincristine (apparent K(i)'s, 0.35 and 5.4 μM, respectively). Our earlier studies demonstrated that HB inhibits nucleotide exchange on β-tubulin, and this, together with the results presented here, indicated the HB site is located on β-tubulin. Using molecular dynamics simulations, we determined complementary conformations of HB and β-tubulin that delineated in atomic detail binding interactions of HB with only β-tubulin, with no involvement of the α-subunit in the binding interaction. Moreover, the HB model served as a template for an eribulin binding model that furthered our understanding of the properties of eribulin as a drug. Overall, these results established a mechanistic basis for the antimitotic activity of the halichondrin class of compounds.     

Probing the nature of the Co(III) ion in corrins: the structural and electronic properties of dicyano- and aquacyanocobyrinic acid heptamethyl ester and a stable yellow dicyano- and aquacyanocobyrinic acid heptamethyl ester

A stable yellow derivative of cobyrinic acid heptamethyl ester, (5R,6R)-Coα,Coβ-dicyano-5,6-dihydro-5-hydroxy-heptamethylcob(III)yrinate-c,6-lactone (DCSYCbs), was prepared from dicyanocobyrinic acid heptamethyl ester (DCCbs). The C5 carbon is oxidized and the c side chain cyclized to form a lactone at C6; the 13 atom, 14 π-e(-) delocalized system of corrins is interrupted, giving a triazamethine system with four conjugated double bonds between N22 and N24 and an isolated double bond between N21 and C4. Stable yellow aquacyanocobyrinic acid heptamethyl ester (ACSYCbs) was prepared by driving off HCN with N(2) in a methanol/acetic acid solution. The electronic spectra of DCCbs and DCSYCbs appear similar except that the bands in DCSYCbs are shifted to shorter wavelengths and the γ-band is much less intense. The experimental spectra were adequately modeled using TD-DFT at the PBE1PBE/6-311G(d,p) level of theory. DCSYCbs crystallizes in the space group P2(1)2(1)2(1) (R(1) = 6.08%) with Z = 4, including one methanol solvent molecule and one water molecule per cobester. The addition of a hydroxyl group at C5 causes loss of the double bond between C5 and C6 and elongation of the C5-C6 bond. From a combination of two-dimensional (1)H TOCSY and ROESY NMR spectra and (1)H/(13)C HSQC and HMBC data, the complete (1)H and (13)C NMR assignments of DCSYCbs were possible, except for two of the ester methyl groups and the (13)C resonances of the two axial cyanide ligands. The latter were assigned using relative chemical shifts calculated by GIAO-DFT methods. The (59)Co resonance of DCCbs was observed at 4074 ppm while that of DCSYCbs is shifted downfield to 4298 ppm. Comparison with available (59)Co data of analogous systems suggests that the more π-conjugated corrin of DCCbs interacts more strongly with the metal than the less extensively conjugated macrocycle of DCSYCbs. As the strength of the interaction between Co(III) and an equatorial macrocycle increases, ν(CN) of axially coordinated CN(-) shifts to lower frequency; in DCSYCbs and DCCbs ν(CN) occurs at 2138 and 2123 cm(-1), respectively. Hence the corrin ligand in DCCbs interacts more strongly with the metal than the stable yellow corrin ligand, with its diminished conjugation. The UV-vis spectral data and DFT-calculated MOs are consistent with greater overlap between the corrin and the metal orbitals in DCCbs relative to DCSYCbs, which gives the metal in the former a softer, more covalent character.     

A Differential Harnack Inequality for the Newell-Whitehead-Segel Equation

This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead-Segel equation on R^n.We then use our LYH-differential Harnack inequality to prove several properties about positive solutions to the equation,including deriving a classical Harnack inequality and characterizing standing solutions and traveling wave solutions.     

Efficient uses of the past

Existing data structures for maintaining sets do not remember the situation they represented at previous times. We propose a structure from which it is possible to efficiently reconstruct the state of the data it represented at any time. Applications of this data structure to several important problems in geometric computation are also given.