Maximum gradient embeddings and monotone clustering

Let (X,d _X ) be an n-point metric space. We show that there exists a distribution over non-contractive embeddings into trees f: X → T such that for every x ∈ X, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.     

First chemical on-line separation and detection of a subsecond α-decaying nuclide, 224Pa

Subsecond ²²⁴ Pa (T _1/2 = 0.85 s) was produced via the ²⁰⁹ Bi(¹⁸ O,3n)²²⁴ Pa reaction at the 88 inch cyclotron at the Lawrence Berkeley National Laboratory. After production it was transported via a gas-jet system to the centrifuge system SISAK 3. Following on-line extraction with trioctylamine/scintillation solutions from 1M lactic acid, ²²⁴ Pa was detected applying on-line -liquid scintillation counting. Unambiguous identification was achieved using time-correlated --decay chain analysis. This constitutes the first chemical on-line separation and detection of a subsecond -decaying nuclide, 0.85-s ²²⁴ Pa with the fast extraction system SISAK 3.     

An ab initio study of the in-plane harmonic force field and frequencies of cis- and trans-glyoxal

The in-plane harmonic force fields of trans- and cis-glyoxal are computed ab initio using a (7,3) basis set contracted to 〈5,3〉. With the trans conformer comparison with experiment is made for both force constants and the derived vibrational frequencies. No such comparison can be made in the case of the cis conformer because only a few assignments of experimental vibrational frequencies have been made, and the calculations thus serve to predict values for the in-plane fundamentals.     

Roles of vitamins B5, B8, B9, B12 and molybdenum cofactor at cellular and organismal levels

Many efforts have been made in recent decades to understand how coenzymes, including vitamins, are synthesised in organisms. In the present review, we describe the most recent findings about the biological roles of five coenzymes: folate (vitamin B9), pantothenate (vitamin B5), cobalamin (vitamin B12), biotin (vitamin B8) and molybdenum cofactor (Moco). In the first part, we will emphasise their biological functions, including the specific roles found in some organisms. In the second part we will present some nutritional aspects and potential strategies to enhance the cofactor contents in organisms of interest.     

Evaluation of decay times in coupled spaces: reliability analysis of Bayeisan decay time estimation

This paper discusses quantitative tools to evaluate the reliability of "decay time estimates" and inter-relationships between multiple decay times for estimates made within a Bayesian framework. Previous works [Xiang and Goggans, J. Acoust. Soc. Am. 110, 1415-1424 (2001); 113, 2685-2697 (2003)] have applied Bayesian framework to cope with the demanding tasks in estimating multiple decay times from Schroeder decay functions measured in acoustically coupled spaces. A parametric model of Schroeder decay function [Xiang, J. Acoust. Soc. Am. 98, 2112-2121 (1995)] has been used for the Bayesian model-based analysis. The relevance of this work is that architectural acousticians need to know how well determined are the estimated decay times calculated within Bayesian framework using Schroeder decay function data. This paper will first address the estimation of global variance of the residual errors between the Schroeder function data and its model. Moreover, this paper discusses how the "landscape" shape of the posterior probability density function over the decay parameter space influences the individual decay time estimates, their associated variances, and their inter-relationships. This paper uses experimental results from measured room impulse responses in real halls to describe a model-based sampling method for an efficient estimation of decay times, and their individual variances. These parameters along with decay times are relevant decay parameters for evaluation and understanding of acoustically coupled spaces.     

Sur l'intégration des systèmes différentiels extérieurs

Résumé L'étude des intégrales des systèmes différentiels extérieurs en involution a été commencée parE. Cartan [3]. Ses mémoires sur ce sujet s'occupent, il est vrai, seulement des systèmes de Pfaff, mais ils contiennent tout ce qui est essentiel pour le cas général. C'est àE. Kahler qu'on doit l'extension des résultats de Cartan aux systèmes de degré queconque. Depuis lors, d'autres auteurs se sont occupés du même probleme. En particulier, on doit d'importants résultats àSchouten et àVan der Kulk [12]. Tous ce auteurs étudié surtout les éléments plans intégraux réguliers et les variétés intégrales régulières. Or, il se trouve que, assez souvent, il est intéressant d'étudier aussi les variétés intégrales singulières. Pour prendre un exemple banal, si on considère un système d'équations du I^er ordre à une fonction inconnue dek variables indépendantes à M. Enrico Bompiani pour son Jubilé scientifique.     

Anionic graft polymerization of methyl acrylate to protein functional groups

Graft polymerization of methyl acrylate to functional groups in proteins was studied with model compounds and with whole gluten proteins. Polymerization was carried out in the presence of sodium hydride or sodium in dimethyl sulfoxide. Initiation proceeds by an anionic mechanism, and the rate-determining step is the production of the initially formed carbanion. The rate of disappearance of methyl acrylate was followed via gas chromatography. Amino acid analyses indicated that the functional groups of the amino acids, as well as the peptide bonds, were acting as the initiation sites in proteins. Reaction rates of the functional groups were determined on model compounds in the presence of sodium and sodium hydride. With both the model compounds and the proteins, polymerization was initially rapid and then leveled off, although rates depended on the concentration of activator and acrylate. Methoxyl group analyses of modified model compounds and proteins indicated that from 5 to 10 methyl acrylate residues were introduced per reactive site.     

An ab initio study of the influence of substituents and intramolecular hydrogen bonding on the carbonyl bond length and stretching force constant. I. Monosubstituted carbonyl compounds

The C?O bond length and f_C?O,C?O, the corresponding harmonic stretching force constant, are calculated ab initio using the 4-31G basis set (augmented by polarization functions on the sulfur and chlorine) with full geometry optimization for the monosubstituted carbonyl compounds RCHO, where R = H, CHO, CH?CH₂, CO₂H, CH?CHOH, OH, OC(?O)OH, OOH, S? H, Li, F, Cl, and NH₂. Straight-line relationships are found in plots of ln[f_C?O,C?O] vs. ln[r_C?O] for the series of compounds in which carbon atoms and oxygen atoms are bonded directly to the carbonyl carbon, in accordance with the empirical expression f = C′/rⁿ. The slopes and intercepts give n = 7.62 and 6.47, C′ = 62.6 and 48.6, for the lines with carbon and oxygen as the atom bonded directly to the carbonyl carbon, respectively. The point for formaldehyde lies very close to the C line, whereas the points for SH, Li, F, Cl, and NH₂ lie closer to the O line.     

The effect of including polarization functions on the geometrical parameters calculated for benzene,fluorobenzene and cyanobenzene

The geometrical parameters for benzene, fluorobenzene, and cyanobenzene have been calculated using the 6–31G*(5D) and 6–31G** basis sets, and, in addition, the 6–31 + G*(5D) basis set in the case of fluorobenzene. Compared to previous results obtained using the 6-31G basis set there are minor changes in the magnitude of the bond lengths and angles in the ring, but the relative values remain unaltered. The values for the ipso angles in fluorobenzene and cyanobenzene are again somewhat less than those reported from microwave and/or electron diffraction studies. The distortion of the ring is characterized as either an elongation or a flattening with respect to the F–C₁ ⃛C₄ and NC C₁C₄ axes, and the shape is characterized as either a broadening or a narrowing across the ring just below the F and Cn group, i.e., an increase or a decrease in the C₂ ⃛C₆ internuclear distance, relative of the C₃ ⃛C₅ distance.