Uniqueness and clustering properties of Gibbs states for classical and quantum unbounded spin systems

We consider quantum unbounded spin systems (lattice boson systems) in -dimensional lattice space Z. Under appropriate conditions on the interactions we prove that in a region of high temperatures the Gibbs state is unique, is translationally invariant, and has clustering properties. The main methods we use are the Wiener integral representation, the cluster expansions for zero boundary conditions and for general Gibbs state, and explicitly -dependent probability estimates. For one-dimensional systems we show the uniqueness of Gibbs states for any value of temperature by using the method of perturbed states. We also consider classical unbounded spin systems. We derive necessary estimates so that all of the results for the quantum systems hold for the classical systems by straightforward applications of the methods used in the quantum case.     

Asymptotic expansions in the integral and local limit theorems in banach spaces with applications to ω-statistics

LetB be a real separable Banach space and letX,X ₁,X ₂,...∈B denote a sequence of independent identically distributed random variables taking values inB. DenoteS _n =n ^?1/2(X ₁+...X _n ). Let π:B→R be a polynomial. We consider (truncated) Edgeworth expansions and other asymptotic expansions for the distribution function of the r.v. π(S _n ) with uniform and nonuniform bounds for the remainder terms. Expansions for the density of π(S _n ) and its higher order derivatives are derived as well. As an application of the general results we get expansions in the integral and local limit theorems for ω-statistics $$\omega _n^p (q)\mathop { = n^{{p \mathord{\left/ {\vphantom {p 2}} \right. \kern-\nulldelimiterspace} 2}} }\limits^\Delta \smallint _{(0,1)} \{ F_n (x) - x\} ^p q(x)dx$$ and investigate smoothness properties of their distribution functions. Herep≥2 is an even number,q: [0, 1]→[0, ∞] is a measurable weight function, andF _n denotes the empirical distribution function. Roughly speaking, we show that in order to get an asymptotic expansion with remainder termO(n ^?α), α<p/2, for the distribution function of the ω-statistic, it is sufficient thatq is nontrivial, i.e., mes{t∈(0, 1):q(t)≠0}>0. Expansions of arbitrary length are available provided the weight functionq is absolutely continuous and positive on an nonempty subinterval of (0, 1). Similar results hold for the density of the distribution function and its derivatives providedq satisfies certain very mild smoothness condition and is bounded away from zero. The last condition is essential since the distribution function of the ω-statistic has no density whenq is vanishing on an nonempty subinterval of (0, 1).     

Mononuclear nonheme ferric-peroxo complex in aldehyde deformylation

A mononuclear nonheme ferric-peroxo complex bearing a macrocyclic tetradentate N4 ligand, [(TMC)Fe(III)-O2]+, was prepared and used in mechanistic studies of aldehyde deformylation; a catalytic aldehyde deformylation by a nonheme iron(II) complex, [Fe(II)(TMC)]2+, and molecular oxygen is reported as well.     

H-NMR studies of duplex DNA decamer containing a uracil cyclobutane dimer: implications regarding the high UV mutagenecity of CC photolesions

To determine the origin of the UV-specific CC to TT tandem mutation at the CC site, we made a duplex DNA decamer containing a uracil cis-syn cyclobutane dimer (CBD) as the deaminated model of a cytosine dimer. Two-dimensional 1H-NMR spectroscopy studies were performed on this sequence where two adenines (Ade) were opposite to the uracil dimer. Two imino protons of the uracil dimer were found to retain Watson-Crick hydrogen bonding with the opposite Ade, although the 5'-U(NH) of the dimer site showed unusual upfield shift like that of the 5'-T(NH) of the TT dimer, which seemed to be associated with deshielding by the flanking base rather than with reduced hydrogen bonding. (McAteer et al. 1998, J. Mol. Biol. 282:1013-1032). Hydrogen bondings at the dimer site were also supported by detecting typical strong nuclear Overhauser effects (NOE) between two imino protons and the opposite Ade H2 or NH2. But sequential NOE interactions of base protons with sugar protons were absent at the two flanking nucleotides of the 5' side of the uracil dimer and at the intradimer site, contrasting with its thymine analog where sequential NOE was absent only at the A4-T5 step. In addition, NOE cross peak for U5(NH) <--> A4(H2) was detected, although the NOE interactions of U6(NH) with A7(H2) and A17(H2) were not observed in contrast to the thymine dimer duplex. This different local structural alteration may be affected by the induced right-hand twisted puckering mode of cis-syn cyclobutane ring of the uracil dimer in the B-DNA duplex, even though the isolated uracil dimer had left-hand twisted puckering rigidly. In parallel, these observations may be correlated with observed differences in mutagenic properties between cis-syn UU dimer and cis-syn TT dimer.     

Optimization,validation and comparison of various extraction techniques for the trace determination of polycyclic aromatic hydrocarbons in sewage sludges by liquid chromatography coupled to diode-array and fluorescence detection

There is a need for a better characterization of sludges from wastewater treatment plants which are destined to be spread on agricultural lands. Inorganic pollutants are regularly controlled but organic pollutants have received few attention up to now. On this paper, we have been interested on the analysis of the 16 polycyclic aromatic hydrocarbons (PAHs) listed in the US Environmental Protection Agency (US EPA) priority list and more particularly of the six PAHs listed in the European community list (fluoranthene, benzo[b and k]fluoranthene, benzo[a]pyrene, benzo[ghi]perylene, indeno[1,2,3-cd]pyrene). The analysis step consists on liquid chromatography with both fluorescence and UV detections as described in the EPA Method 8310. As for the extraction step, several techniques such as supercritical fluid extraction, pressurized liquid extraction, focused microwave extraction in open vessels, Soxhlet and ultrasonic extractions are compared after optimization of the experimental conditions (solvent nature and quantity, temperature, pressure, duration, ... ) and validation with certified sludges. When optimized, these five extraction techniques are as much efficient with similar relative standard deviation. Whatever the extraction techniques used, the whole analysis protocol permits to quantify PAHs in the range of 0.09 to 0.9 mg/kg of dried sludges.     

Construction of a 2,6-difunctionalized 2-methyl-2H-1-benzopyran library by using a solid-phase synthesis protocol

[reaction: see text] A library containing 1200 analogues of 2,6-difunctionalized 2-methyl-2H-1-benzopyran was constructed by using a solid-phase synthesis protocol. Polymer-bound 6-amido-, 6-sulfonamido-, and 6-uredo-functionalized 2-hydroxymethyl-2-methylbenzopyrans 10 were prepared as part of a first-generation diversification step by employing reactions of respective acid halides, sulfonyl chlorides, and isocyanates with the amine precursor 7. Transformations of the resin-bound intermediates 10 by reactions with alkyl and acid halides were then used to produce a diverse series of 2,6-difunctionalized 2-methyl-2H-1-benzopyran analogues 12 and 14.     

Stereoselective synthesis of (+)-SCH 351448: a unique ligand system for sodium, calcium, and other cations

(+)-SCH 351448 (Na+ salt A) was synthesized employing ring-closing olefin metathesis reaction of an open diene diester intermediate for construction of the 28-membered macrodiolide structure. The open diene diester was prepared from the monomeric hydroxy carboxylic acid and two different olefin fragments. The monomeric hydroxy acid was synthesized via Julia-Julia coupling reaction of intermediates derived from the same olefinic fragments. Oxane units in these fragments were prepared by radical cyclization reactions of beta-alkoxyacrylates. Analogous SCH 351448 salts incorporating other mono- and divalent cations may be prepared. Under acidic conditions, SCH 351448 (Na+ salt A) was the most stable complex, but SCH 351448 (Ca2+ salt) and (Na+ salt B) appear to be physiologically important species.