Approximation of plurisubharmonic functions

We extend a result by Fornaæss and Wiegerinck [Ark. Mat. 1989;27:257–272] on plurisubharmonic Mergelyan type approximation to domains with boundaries locally given by graphs of continuous functions.     

Vibrational spectroscopy of triacetone triperoxide (TATP): anharmonic fundamentals, overtones and combination bands

The vibrational spectrum of triacetone triperoxide (TATP) is studied by the correlation-corrected vibrational self-consistent field (CC-VSCF) method which incorporates anharmonic effects. Fundamental, overtone, and combination band frequencies are obtained by using a potential based on the PM3 method and yielding the same harmonic frequencies as DFT/cc-pVDZ calculations. Fundamentals and overtones are also studied with anharmonic single-mode (without coupling) DFT/cc-pVDZ calculations. Average deviations from experiment are similar for all methods: 2.1-2.5%. Groups of degenerate vibrations form regions of numerous combination bands with low intensity: the 5600-5800 cm(-1) region contains ca. 70 overtones and combinations of CH stretches. Anharmonic interactions are analyzed.     

Dynamics of proton recombination with NO3- anion in water clusters

Recombination events of a proton with NO3- at (H2O)8 clusters are studied by molecular dynamics, using "on-the-fly" reliable ab initio MP2 potentials. The main findings are: (1) the lifetime of the ions is less than 1.2 picoseconds; (2) the recombination step invariably involves H3O+, not H5O2+; and (3) an essentially unique transition-state structure of H3O+/NO3- for recombination is found in all cases. Proton migration involves both H3O+ and H5O2+ species: Grotthuss and other mechanisms contribute.     

A small neutral molecule with two noble-gas atoms: HXeOXeH

A novel noble-gas compound, HXeOXeH, is identified using IR spectroscopy, and it seems to be the smallest known neutral molecule with two noble-gas atoms. HXeOXeH is prepared using, for example, UV photolysis of water in solid xenon and subsequent annealing at 40-45 K. The experimental observations are fully supported by extensive quantum chemical calculations. A large energy release of 8.3 eV is computationally predicted for the decomposition of HXeOXeH into the 2Xe + H2O global energy minimum. HXeOXeH may represent a first step toward the possible preparation of (Xe-O)n chains and it may be relevant to the terrestrial "missing xenon" problem.     

Determination of free and reversibly-bound sulfite in selected foods by high-performance liquid chromatography with fluorometric detection

A rapid and accurate method for measuring low part-per-million levels of free and reversibly-bound sulfites in selected foods by using high-performance liquid chromatography (HPLC) with fluorometric detection was developed. Sulfites were extracted with sodium tetrachloromercurate solution and determined by HPLC-fluorescence spectrometry. During the HPLC analysis, the sample extract was reacted with sodium hydroxide to liberate the reversibly-bound sulfite and subsequently separated from other interferences by a size exclusion column. The effluent was then reacted with o-phthalaldehydelammonium chloride reagent to form a fluorescing 1-sulfonatoisoindole derivative and analyzed by a fluorescence detector. The method has been applied to a variety of foods and food products, with no significant interference encountered in matrixes such as soy products, cabbage, broccoli, brassica, ginger, fungus, mushroom, mandarin peel, potato chips, and biscuits. It was shown to have a broad linear range of 0.01 to 0.4 mg/L as SO2. The spike recoveries of sodium sulfite, sodium metabisulfite, and formaldehyde-sodium bisulfite adduct at the 5 to 10 mg/kg level in the tested food matrix were within 80-120%, and the limit of detection was 5 mg/kg. Laboratory of Government Chemist Reference Material LGC7111 (potato powder) was used to assess the accuracy of the method. The expanded measurement uncertainty of the method at 95% confidence level was estimated to be 17%.     

Calculation of vibrational transition frequencies and intensities in water dimer: comparison of different vibrational approaches

We have calculated frequencies and intensities of fundamental and overtone vibrational transitions in water and water dimer with use of different vibrational methods. We have compared results obtained with correlation-corrected vibrational self-consistent-field theory and vibrational second-order perturbation theory both using normal modes and finally with a harmonically coupled anharmonic oscillator local mode model including OH-stretching and HOH-bending local modes. The coupled cluster with singles, doubles, and perturbative triples ab initio method with augmented correlation-consistent triple-zeta Dunning and atomic natural orbital basis sets has been used to obtain the necessary potential energy and dipole moment surfaces. We identify the strengths and weaknesses of these different vibrational approaches and compare our results to the available experimental results.     

On A Hypergraph Turán Problem Of Frankl

Let be the 2k-uniform hypergraph obtained by letting P₁, . . .,P_r be pairwise disjoint sets of size k and taking as edges all sets P_i∪P_j with i ≠ j. This can be thought of as the ‘k-expansion’ of the complete graph K_r: each vertex has been replaced with a set of size k. An example of a hypergraph with vertex set V that does not contain can be obtained by partitioning V = V1 ∪V₂ and taking as edges all sets of size 2k that intersect each of V₁ and V₂ in an odd number of elements. Let denote a hypergraph on n vertices obtained by this construction that has as many edges as possible. For n sufficiently large we prove a conjecture of Frankl, which states that any hypergraph on n vertices that contains no has at most as many edges as . Sidorenko has given an upper bound of for the Tur′an density of for any r, and a construction establishing a matching lower bound when r is of the form 2^p+1. In this paper we also show that when r=2^p+1, any -free hypergraph of density looks approximately like Sidorenko’s construction. On the other hand, when r is not of this form, we show that corresponding constructions do not exist and improve the upper bound on the Turán density of to , where c(r) is a constant depending only on r. The backbone of our arguments is a strategy of first proving approximate structure theorems, and then showing that any imperfections in the structure must lead to a suboptimal configuration. The tools for its realisation draw on extremal graph theory, linear algebra, the Kruskal–Katona theorem and properties of Krawtchouck polynomials. * Research supported in part by NSF grants DMS-0355497, DMS-0106589, and by an Alfred P. Sloan fellowship.     

Time-dependent strength of colloidal gels

Colloidal silica gels are shown to stiffen with time, as demonstrated by both dynamic light scattering and bulk rheological measurements. Their elastic moduli increase as a power law with time, independent of particle volume fraction; however, static light scattering indicates that there are no large-scale structural changes. We propose that increases in local elasticity arising from bonding between neighboring colloidal particles can account for the strengthening of the network, while preserving network structure.