Large families of mutually embeddable vertex‐transitive graphs

For each infinite cardinal κ, we give examples of 2^κ many non‐isomorphic vertex‐transitive graphs of order κ that are pairwise isomorphic to induced subgraphs of each other. We consider examples of graphs with these properties that are also universal, in the sense that they embed all graphs with smaller orders as induced subgraphs. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 99–106, 2003     

Continuum many universal Horn classes of graphs of bounded chromatic number

Received February 28, 1997; accepted in final form July 19, 1998.     

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

Studies on the 4-benzoylpyridine-3-carboxamide entity as a fragment model of the Isoniazid-NAD adduct

An ortho-metallation-electrophilic substitution sequence was employed as a key step to build the 4-benzoylpyridine framework. It was found that 4-benzoylpyridine-3-carboxamide and an N-pyridyl alkylated derivative both exist in a unique cyclized hemiamidal structure, not in the usually expected keto-amide open form. These structures represent fragment models of the Isoniazid-NAD adducts involved in the mechanism of action of the antituberculous drug Isoniazid.     

Chiral HPLC Separation of Rosiglitazone and its Main Metabolites and Studies on Their Racemization

Rosiglitazone (RSG) is marketed as a racemic mixture although the antidiabetic activity is essentially related to the (S)-enantiomer. The chiral center has an adjacent carbonyl group; therefore, the (R)-enantiomer could be transformed to the (S)-enantiomer or vice versa by keto-enolic tautomerism. The literature indicates that this racemization is slow enough to allow the evaluation of the properties of the isolated enantiomers. However, there is no information about the enantioselective kinetic disposition and metabolism of RSG. Additionally, there are no studies on the racemization of its metabolites. Considering these facts, a chiral HPLC method was developed and used for the first time to study the racemization of RSG and its main metabolites. Different conditions, including those used to evaluate the in vitro enantioselective metabolism, were employed. The simultaneous chiral separation of RSG and metabolites was achieved on a Chiralcel OJ-H column by employing methanol/ethanol (90:10, v/v) as mobile phase. The racemization studies showed that the half-life of RSG decreased more than 30 times when the temperature increased from 4 to 37 °C. It was also observed that the half-life of RSG changed from approximately 20 h at pH 3.5 to approximately 2 h at pH 7.4. The same profile was observed for its metabolites. Organic solvents and UV light did not present influence on the racemization process. In addition, a Complete Factorial Design was conducted to evaluate the influence of some parameters that can be changed during an in vitro metabolism study. The results obtained showed that the racemization occurs under in vitro metabolism conditions.

     

Bioactive Compounds from Pale Ale Beer Powder Attenuate Experimental Colitis in BALB/c Mice

Phenolic compounds (PCs) present in foods are associated with a decreased risk of developing inflammatory diseases. The aim of this study was to extract and characterize PCs from craft beer powder and evaluate their potential benefits in an experimental model of inflammatory bowel disease (IBD). PCs were extracted and quantified from pure beer samples. BALB/c mice received either the beer phenolic extract (BPE) or beer powder fortified with phenolic extract (BPFPE) of PCs daily for 20 days by gavage. Colon samples were collected for histopathological and immunohistochemical analyses. Dextran sodium sulfate (DSS)-induced mice lost more weight, had reduced colon length, and developed more inflammatory changes compared with DSS-induced mice treated with either BPE or BPFPE. In addition, in DSS-induced mice, the densities of CD4- and CD11b-positive cells, apoptotic rates, and activation of NF-κB and p-ERK1/2 MAPK intracellular signaling pathways were higher in those treated with BPE and BPFPE than in those not treated. Pretreatment with the phenolic extract and BPFPE remarkably attenuated DSS-induced colitis. The protective effect of PCs supports further investigation and development of therapies for human IBD.     

A general reduction scheme for the time-dependent Born–Oppenheimer approximation

We construct a general reduction scheme for the study of the quantum propagator of molecular Schrödinger operators with smooth potentials. This reduction is made up to infinitely (resp. exponentially) small error terms with respect to the inverse square root of the mass of the nuclei, depending on the C^∞ (resp. analytic) smoothness of the interactions. Then we apply this result to the case when an electronic level is isolated from the rest of the spectrum of the electronic Hamiltonian. To cite this article: A. Martinez, V. Sordoni, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 185–188.     

Capillary electrophoresis and hollow fiber liquid-phase microextraction for the enantioselective determination of albendazole sulfoxide after biotransformation of albendazole by an endophytic fungus

Hollow fiber liquid-phase microextraction and CE were applied for the determination of albendazole sulfoxide (ASOX) enantiomers in liquid culture medium after a fungal biotransformation study. The analytes were extracted from 1 mL of liquid culture medium spiked with the internal standard (rac-hydroxychloroquine) and buffered with 0.50 mol/L phosphate buffer, pH 10. The analytes were extracted into 1-octanol impregnated in the pores of the hollow fiber, and into an acid acceptor solution inside the polypropylene hollow fiber. The electrophoretic separations were carried out in 0.05 mol/L tris(hydroxymethyl)aminomethane buffer, pH 9.3, containing 3.0% w/v sulfated-β-CD (S-β-CD) with a constant voltage of +15 kV and detection at 220 nm. The method was linear over the concentration range of 250-5000 ng/mL for each ASOX enantiomer. Within-day and between-day assay precision and accuracy for the analytes were studied at three concentration levels and the values of RSD% and relative error % were lower than 15%. The developed method was applied for the determination of ASOX after a biotransformation study employing the endophytic fungus Penicillium crustosum (VR4). This study showed that the endophytic fungus was able to metabolize the albendazole to ASOX enantioselectively. In addition, it was demonstrated that hollow fiber liquid-phase microextraction coupled to CE can be an excellent and environmentally friendly technique for the analysis of samples obtained in biotransformation studies.     

Infinite Random Geometric Graphs

We introduce a new class of countably infinite random geometric graphs, whose vertices V are points in a metric space, and vertices are adjacent independently with probability p ? (0, 1){p \in (0, 1)} if the metric distance between the vertices is below a given threshold. For certain choices of V as a countable dense set in \mathbbRⁿ{\mathbb{R}^n} equipped with the metric derived from the L _∞-norm, it is shown that with probability 1 such infinite random geometric graphs have a unique isomorphism type. The isomorphism type, which we call GR _n , is characterized by a geometric analogue of the existentially closed adjacency property, and we give a deterministic construction of GR _n . In contrast, we show that infinite random geometric graphs in \mathbbR²{\mathbb{R}^{2}} with the Euclidean metric are not necessarily isomorphic.