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.     

Phosphodiester cleavage of guanylyl-(3',3')-(2'-amino-2'-deoxyuridine): rate acceleration by the 2'-amino function

Hydrolytic reactions of the structural analogue of guanylyl-(3',3')-uridine, guanylyl-(3',3')-(2'-amino-2'-deoxyuridine), having one of the 2'-hydroxyl groups replaced with an amino function, have been followed by RP HPLC in the pH range 0-13 at 90 degrees C. The results are compared to those obtained earlier with guanylyl-(3',3')-uridine, guanylyl-(3',3')-(2',5'-di-O-methyluridine), and uridylyl-(3',5')-uridine. Under basic conditions (pH > 8), the hydroxide ion-catalyzed cleavage of the P-O3' bond (first-order in [OH(-)]) yields a mixture of 2'-amino-2'-deoxyuridine and guanosine 2',3'-cyclic phosphate which is hydrolyzed to guanosine 2'- and 3'-phosphates. Under these conditions, guanylyl-(3',3')-(2'-amino-2'-deoxyuridine) is 10 times less reactive than guanylyl-(3',3')-uridine. Under acidic and neutral conditions (pH 3-8), where the pH-rate profile for the cleavage consists of two pH-independent regions (from pH 3 to pH 4 and from 6 to 8), guanylyl-(3',3')-(2'-amino-2'-deoxyuridine) is considerably reactive. For example, in the latter pH range, guanylyl-(3',3')-(2'-amino-2'-deoxyuridine) is more than 2 orders of magnitude more labile than guanylyl-(3',3')-(2',5'-di-O-methyluridine), while in the former pH range the reactivity difference is 1 order of magnitude. Under very acidic conditions (pH < 3), the isomerization giving guanylyl-(2',3')-(2'-amino-2'-deoxyuridine) and depurination yielding guanine (both first-order in [H(+)]) compete with the cleavage. The Zn(2+)-promoted cleavage ([Zn(2+)] = 5 mmol L(-)(1)) is 15 times faster than the uncatalyzed reaction at pH 5.6. The mechanisms of the reactions of guanylyl-(3',3')-(2'-amino-2'-deoxyuridine) are discussed, particularly focusing on the possible stabilization of phosphorane intermediate and/or transition state via an intramolecular hydrogen bonding by the 2'-amino group.     

In situ quadrupole mass spectrometry study of atomic-layer deposition of ZrO2 using Cp2Zr(CH3)2 and water

Reactions during the atomic layer deposition (ALD) process of ZrO(2) from Cp(2)Zr(CH(3))(2) and deuterated water as precursors were studied with a quadrupole mass spectrometer (QMS) at 210-440 degrees C. The detected reaction byproducts were CpD (m/z = 67) and CH(3)D (m/z = 17). Almost all (90%) of the CH(3) ligands were released during the Cp(2)Zr(CH(3))(2) precursor pulse because of exchange reactions with the OD-terminated surface, and the rest, during the D(2)O pulse. About 40% of the CpD was released during the metal precursor pulse, and 60%, during the D(2)O pulse. ALD-type self-limiting growth was confirmed from 210 to 400 degrees C. However, below 300 degrees C the growth rate was low. Precursor decomposition affected the film growth mechanism at temperatures exceeding 400 degrees C.     

Formation and Structure of Hydrolytic Methylaluminoxane Activators

Methylaluminoxane (MAO) activators have sheet structures which form ion-pairs on reaction of neutral donors such as octamethyltrisiloxane (OMTS). The ion-pairs can be detected by electrospray ionization mass spectrometry (ESI-MS) in polar media. The growth of these reactive precursors during hydrolysis of Me₃Al can be monitored using ESI-MS. Density functional theory, combined with numerical simulation of growth, indicates that this process involves rapid formation of low MW oligomers, followed by assembly of these species into low MW sheets. These can grow through further addition of low MW oligomers or by fusion into larger sheets. The mechanism of these growth processes leads to the prediction that even-numbered sheets should be favored, and this surprising result is confirmed by ESI-MS monitoring experiments of both activator growth and MAO aging.     

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.     

A Note on the Finite-Dimensional Distributions of Dispersing Billiard Processes

In this short note we consider the finite-dimensional distributions of sets of states generated by dispersing billiards with a random initial condition. We establish a functional correlation bound on the distance between the finite-dimensional distributions and corresponding product distributions. We demonstrate the usefulness of the bound by showing that it implies several limit theorems. The purpose of this note is to provide a tool facilitating the study of more general functionals of the billiard process.     

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.     

Tilt: major factor in sterols' ordering capability in membranes

Using extensive atomistic simulations, we show that there is a single experimentally accessible parameter--the sterol tilt--that can be used to determine a sterol's capability to induce order, and thus to promote, e.g., formation of lipid rafts. The observations also facilitate designing new effective sterols.