Harnack's inequality for a nonlinear eigenvalue problem on metric spaces

We prove Harnack's inequality for first eigenfunctions of the p-Laplacian in metric measure spaces. The proof is based on the famous Moser iteration method, which has the advantage that it only requires a weak (1,p)-Poincaré inequality. As a by-product we obtain the continuity and the fact that first eigenfunctions do not change signs in bounded domains.     

A computational and experimental study of the structures and Raman and 77Se NMR spectra of SeX3+ and SeX2 (X = Cl, Br, I): FT-Raman spectrum of (SeI3)[AsF6

The ability of MP2, B3PW91 and PBE0 methods to produce reliable predictions in structural and spectroscopic properties of small selenium-halogen molecules and cations has been demonstrated by using 6-311G(d) and cc-pVTZ basis sets. Optimized structures and vibrational frequencies agree closely with the experimental information, where available. Raman intensities are also well reproduced at all levels of theory. Calculated GIAO isotropic shielding tensors yield a reasonable linear correlation with the experimental chemical shift data at each level of theory. The largest deviations between calculated and experimental chemical shifts are found for selenium-iodine species. The agreement between observed and calculated chemical shifts for selenium-iodine species can be improved by inclusion of relativistic effects using the ZORA method. The best results are achieved by adding spin-orbit correction terms from ZORA calculations to nonrelativistic GIAO isotropic shielding tensors. The calculated isotropic shielding tensors can be utilized in the spectroscopic assignment of the 77Se chemical shifts of novel selenium-halogen molecules and cations. The experimental FT-Raman spectra of (SeI3)[AsF6] in the solid state and in SO2(l) solution are also reported.     

Solid-phase synthesis of 1,2,3-triazoles via 1,3-dipolar cycloaddition

The solid-phase synthesis of 1,2,3-triazoles via 1,3-dipolar cycloaddition of polymer-bound azides to various alkynes is reported. Polymer-bound azides were synthesized from polymer-bound halides and sodium azide and reacted with alkynes to produce polymer-bound 1,2,3-triazoles. Cleavage of the triazoles was performed with trifluoroacetic acid. A traceless synthesis of 1,2,3-triazoles was developed using 2-methoxy-substituted resin (polymer-bound 4-hydroxy-2-methoxybenzyl alcohol). In addition, a synthesis of 4-hydroxybenzyl-substituted 1,2,3-triazoles from the bromo-Wang resin (4-(bromomethyl)phenoxymethyl polystyrene) was achieved.     

Screening the Thermodynamics of Trimethylaluminum‐Hydrolysis Products and Their Co‐Catalytic Performance in Olefin‐Polymerization Catalysis

Herein, we introduce an approach for the computational screening of stoichiometric reactions between trimethylaluminum (TMA) and water. The thermodynamic products of these reactions are methylaluminoxanes (MAOs) with different compositions, which have the general formula (AlOMe)_n(AlMe₃)_m, in which n describes the degree of oligomerization and m is the number of associated TMA molecules. These reaction products were thoroughly explored up to n=4, thus demonstrating the thermodynamically preferable association of up to four AlMe₃ molecules, that is, TMA molecules in their monomeric form. The relative Lewis acidities of the Al sites in these MAOs were systematically explored and we found that the associated TMA molecules were a key ingredient for co‐catalytic activity in olefin‐polymerization catalysis. This conclusion was supported by computational studies on catalyst activation, which revealed an exergonic insertion of ethene into the metallocene/MAO complex.     

Influence of pyrene-labeling on fluid lipid membranes

We elucidate the influence of pyrene-labeled phospholipids on the structural properties of a fluid dipalmitoylphosphatidylcholine lipid membrane. To this end, we employ extensive atomic-scale molecular dynamics simulations with varying concentrations of pyrene-linked lipids. We find pyrene labeling to perturb the membrane structure significantly in the vicinity of the probe, the correlation length in the bilayer plane being about 1.0-1.5 nm. The local perturbations lead to enhanced ordering and packing of lipid acyl chains located in the vicinity of the probe. Surprisingly, this holds true not only for lipids that reside in the same leaflet as the pyrene-labeled probe but also for lipids in the opposite monolayer. The latter is due to substantial interdigitation of the pyrene moiety into the opposite leaflet, suggesting that occasional excimer formation may take place for probes in different leaflets. As a related issue, we also discuss the location and conformational orientation of the pyrene moieties. In particular, the orientational distribution of pyrene turns out to be more broad and diverse than the distribution of the corresponding acyl tails of nonlabeled lipids.     

Mass Spectrometric Characterization of Methylaluminoxane‐Activated Metallocene Complexes

Electrospray‐ionization mass spectrometric studies of poly(methylaluminoxane) (MAO) in the presence of [Cp₂ZrMe₂], [Cp₂ZrMe(Cl)], and [Cp₂ZrCl₂] in fluorobenzene (PhF) solution are reported. The results demonstrate that alkylation and ionization are separate events that occur at competitive rates in a polar solvent. Furthermore, there are significant differences in ion‐pair speciation that result from the use of metallocene dichloride complexes in comparison to alkylated precursors at otherwise identical Al/Zr ratios. Finally, the counter anions that form are dependent on the choice of precursor and Al/Zr ratio; halogenated aluminoxane anions [(MeAlO)_x(Me₃Al)_y?z(Me₂AlCl)_zMe]^? (z=1, 2, 3…?) are observed using metal chloride complexes and under some conditions may predominate over their non‐halogenated precursors [(MeAlO)_x(Me₃Al)_yMe]^?. Specifically, this halogenation process appears selective for the anions that form in comparison to the neutral components of MAO. Only at very high Al/Zr ratios is the same “native” anion distribution observed when using [Cp₂ZrCl₂] when compared with [Cp₂ZrMe₂]. Together, the results suggest that the need for a large excess of MAO when using metallocene dichloride complexes is a reflection of competitive alkylation vs. ionization, the persistence of unreactive, homodinuclear ion pairs in the case of [Cp₂ZrCl₂], as well as a change in ion pairing resulting from modification of the anions formed at lower Al/Zr ratios. Models for neutral precursors and anions are examined computationally.     

Cathodic protection of ships in brackish water

The operation of ice-going vessels depends on the condition of the hull surface. Corrosion increases the roughness of ship hull, which increases drag and fuel consumption. The hull surface smoothness is maintained by using coatings and cathodic protection. The cold brackish water is different from ocean water as it has lower salt content, lower conductivity, and higher concentration of dissolved oxygen. These factors mean that the design of the cathodic protection system for ship hulls requires different design values, such as protection current density and protected length, than those given in cathodic protection standards. In this paper, we have estimated the protection current density with polarization curves and the protected length by using Wagner number and dimension and conductivity scaling. In brackish water the protection current density was two times that in ocean water. The protected length in brackish water varied between 10 and 15% of that in ocean water. In poorly conducting brackish water, the current capacity of a cathodic protection system is used mostly for overcoming the solution resistance, not for delivering protection current.     

Aqueous Self‐Assembly and Cation Selectivity of Cobaltabisdicarbollide Dianionic Dumbbells

The anion [3,3′‐Co(C₂B₉H₁₁)₂]^? ([COSAN]^?) produces aggregates in water. These aggregates are interpreted to be the result of C?H???H?B interactions. It is possible to generate aggregates even after the incorporation of additional functional groups into the [COSAN]^? units. The approach is to join two [COSAN]^? anions by a linker that can adapt itself to act as a crown ether. The linker has been chosen to have six oxygen atoms, which is the ideal number for K⁺ selectivity in crown ethers. The linker binds the alkaline metal ions with different affinities; thus showing a distinct degree of selectivity. The highest affinity is shown towards K⁺ from a mixture containing Li⁺, Na⁺, K⁺, Rb⁺ and Cs⁺; this can be indicative of pseudo‐crown ether performance of the dumbbell. One interesting possibility is that the [COSAN]^? anions at the two ends of the linker can act as a hook‐and‐loop fastener to close the ring. This facet is intriguing and deserves further consideration for possible applications. The distinct affinity towards alkaline metal ions is corroborated by solubility studies and isothermal calorimetry thermograms. Furthermore, cryoTEM micrographs, along with light scattering results, reveal the existence of small self‐assemblies and compact nanostructures ranging from spheres to single‐/multi‐layer vesicles in aqueous solutions. The studies reported herein show that these dumbbells can have different appearances, either as molecules or aggregates, in water or lipophilic phases; this offers a distinct model as drug carriers.     

Theoretical studies of aluminoxane chains, rings, cages, and nanostructures

Alumina nanostructures and three families of aluminoxanes, linear, cyclic, and cagelike structures, have structures that resemble their isovalent electronic hydrocarbon analogues. Specific examples of each family are the counterparts of fullerene, allene, benzene, and cubane, respectively. The aluminoxanes and alumina nanostructures are related to each other; the latter can be regarded as a hydrogen- or alkyl-free form of aluminoxane. By exploiting this relationship, the relative stabilities of the three families of aluminoxanes, alumina nanostructures, and alumina crystal lattices have been estimated. According to ab initio calculations, aluminoxane cages, which take the form of a truncated octahedron and related polyhedra, are favored. The stability of the preferred cage, T-symmetric Al28O28H28, is practically equal to that of the alpha-alumina crystal lattice.     

Imidotungsten(VI) complexes with chelating amino and imino phenolates

The reaction of WOCl(4) with 2,4-di-tert-butyl-6-((isopropylamino)methyl)phenol followed by the reaction with phenyl isocyanate leads to the formation of imidotungsten(VI) complex [W(NPh)Cl(3)(OC(6)H(3)(CH(2)NH-i-Pr)-2-t-Bu(2)-4,6)] 4 with a chelating aminophenolate ligand. When the same procedure was applied using aminophenols with bulkier substituents in the amino group, the final product was an unexpected Schiff-base complex [W(NPh)Cl(3)(OC(6)H(3)(CH=NPh)-2-t-Bu(2)-4,6)] 5, where the ligand is derived from 2,4-di-tert-butyl-6-((phenylimino)methyl)phenol. Complex 5 is also formed in the thermal degradation of 4. On the whole, 5 appears to be formed by a disproportionation of intermediate compounds, which are analogous to complex 4. The solid-state structures of 4 and 5 have been determined by X-ray crystallography whereas the solution structures were studied by (1)H and (13)C NMR.