A finiteness theorem for maximal independent sets

Denote bymi(G) the number of maximal independent sets ofG. This paper studies the setS(k) of all graphsG withmi(G) = k and without isolated vertices (exceptG K ₁) or duplicated vertices. We determineS(1), S(2), andS(3) and prove that |V(G)| 2 ^k–1 +k – 2 for anyG inS(k) andk 2; consequently,S(k) is finite for anyk. Supported in part by the National Science Council under grant NSC 83-0208-M009-050     

Natural products of the medicinal fungus Ganoderma lucidum: occurrence,biological activities,and pharmacological functions

Ganoderma lucidum, a fungus used in traditional Chinese medicine, produces polysaccharides and oxygenated triterpenoids with a very broad spectrum of biological activities and pharmacological functions. Among the Ganoderma triterpenoids, many pairs of C-3 alpha/beta stereoisomers and C-3/C-15 positional isomers have been identified. Biosynthetic study has indicated that the C-3alpha series of oxygenated triterpenoids is derived from the C-3beta series via an oxidation-reduction pathway. The interaction of Ganoderma triterpenoids with human platelets in the induction of aggregation and inhibition of agonist-induced aggregation and signal transduction has been elucidated. Reduction of cellular mevalonate content to a stage in which cholesterol synthesis is strongly inhibited and cell growth is marginally arrested sensitizes hepatoma cells to the oxygenated triterpenoids. A combination treatment of lovastatin and Ganoderma triterpenoids in animal studies has exhibited a potential anticancer effect.     

Syntheses of Novel Isopenam and Isocephem Antibiotics. Preparation of a retinamido derivative of a highly strained β-lactam as potent anticancer agent

Syntheses of the cis-configurated isopenam 9 (Scheme 1), isocephem 14 (Scheme 2), and isocephem 19 (Scheme 3) are described. The key step in the preparation of 14 and 19 involved a Pummerer-type rearrangement of the corresponding sulfoxides 12 and 18 . These β-lactams were found to possess biological activity against several pathogenic microorganisms in vitro. The electronic activation of the lactam moiety of 19 remarkably enhanced its biological activity. A retinoic moiety was attached to 19 via an amino linker. The resultant retinamido-β-lactam 21 showed significant cytostatic activity in tracheal organ cultures obtained from vitamin-A-deficient hamsters.     

Benzolignanoid and Polyphenols from Origanum Vulgare

A new dihydrobenzodioxane derivative, origalignanol ( 10 ), together with nine polyphenolic compounds, salvianolic acid A ( 1 ), salvianolic acid C ( 2 ), lithospermic acid ( 3 ), apigenin 7‐O‐β‐D‐glucuronide ( 4 ), apigenin 7‐O‐β‐D‐(6″‐methyl)glucuronide ( 5 ), luteolin, ( 6 ), luteolin 7‐O‐β‐D‐glucopyranoside ( 7 ), luteolin 7‐O‐β‐D‐glucuronide ( 8 ), and luteolin 7‐O‐β‐D‐xylopyranoside ( 9 ), were isolated from the aqueous ethanolic extract of the aerial parts of Origanum vulgare for the first time. The structure of new compound 10 was determined on the basis of spectroscopic methods. Compound 5 is probably an artifact formed during the isolation. Compounds 1, 2 and 3 showed strong DPPH radical scavenging activity with an EC₅₀ of 7.2 ± 0.4, 9.6 ± 0.9, and 9.5 ± 0.7 μM, respectively, and protected rat hepatocytes from CCl₄‐damage at 100 μM.     

A Convenient Synthesis of 3, 4′-Bipyridine

3, 4′-Bipyridine was synthesized from 6-methoxy-3, 4′-bipyridine or 6-benzyloxy-3, 4′-bipyridine via 6-chloro-3, 4′-bipyridine. The chloro derivative was catalytically dechlorinated into the corresponding 3, 4′ -bipyridine.     

Polyol-modified layered double hydroxides with attenuated basicity for a truly reversible capture of CO2

Dendrimers bearing hydroxyl groups supported by layered double hydroxides (CO₃–LDH) with Mg/Al ratio ranging from 1:1 to 5:1 showed improved properties for the reversible capture of carbon dioxide (CO₂). The adsorption capacity of the starting LDH was due to the intrinsic base-like behavior, and was found to depend on the Mg/Al ratio. When contacted with polyol dendrimers in aqueous media, no intercalation took place. This was explained in terms of low exfoliation grade of LDH and hydrophobic character of the dendrimer molecules. The latter rather adsorb on the external surface of the LDH stacks for low dendrimer loadings, or aggregate into organic clusters for higher contents. Analyses through thermal programmed desorption of CO₂ revealed that dendrimer incorporation advantageously attenuates the basicity strength of the starting LDH support, by lowering the desorption temperature. The OH groups of the organic moiety were found to display an amphoteric character, and act as the main adsorption sites. The weak interactions with CO₂ facilitate easier release of the major part of adsorbed CO₂ at temperature not exceeding 80–100 °C. On polyol organo-LDHs, the reversible CO₂ retention was discussed herein in terms of acid–base interactions. This concept allows envisaging the capture of diverse pollutants and other greenhouse gases by modifying the chemical groups on the dendritic moiety.     

Structural and mechanical properties of multi-element (TiVCrZrHf)N coatings by reactive magnetron sputtering

In this study, (TiVCrZrHf)N multi-component coatings with quinary metallic elements were deposited by reactive magnetron sputtering system. The composition, structure, and mechanical properties of the coatings deposited at different N₂ flow rates were investigated. The (TiVCrZrHf)N coatings deposited at N₂ flow rates of 0, 1, and 2 SCCM showed an amorphous structure, whereas those deposited at N₂ flow rates of 4 and 6 SCCM showed a simple face-centered cubic solid solution structure. A saturated nitride coating was obtained for N₂ flow of 4 SCCM and higher. By increasing N₂ flow to 4 SCCM, the hardness and modulus reached a maximum value of 23.8 ± 0.8 and 267.3 ± 4.0 GPa, respectively.     

Improved detection of reactive metabolites with a bromine‐containing glutathione analog using mass defect and isotope pattern matching

Drug bioactivation leading to the formation of reactive species capable of covalent binding to proteins represents an important cause of drug‐induced toxicity. Reactive metabolite detection using in vitro microsomal incubations is a crucial step in assessing potential toxicity of pharmaceutical compounds. The most common method for screening the formation of these unstable, electrophilic species is by trapping them with glutathione (GSH) followed by liquid chromatography/mass spectrometry (LC/MS) analysis. The present work describes the use of a brominated analog of glutathione, N‐(2‐bromocarbobenzyloxy)‐GSH (GSH‐Br), for the in vitro screening of reactive metabolites by LC/MS. This novel trapping agent was tested with four drug compounds known to form reactive metabolites, acetaminophen, fipexide, trimethoprim and clozapine. In vitro rat microsomal incubations were performed with GSH and GSH‐Br for each drug with subsequent analysis by liquid chromatography/high‐resolution mass spectrometry on an electrospray time‐of‐flight (ESI‐TOF) instrument. A generic LC/MS method was used for data acquisition, followed by drug‐specific processing of accurate mass data based on mass defect filtering and isotope pattern matching. GSH and GSH‐Br incubations were compared to control samples using differential analysis (Mass Profiler) software to identify adducts formed via the formation of reactive metabolites. In all four cases, GSH‐Br yielded improved results, with a decreased false positive rate, increased sensitivity and new adducts being identified in contrast to GSH alone. The combination of using this novel trapping agent with powerful processing routines for filtering accurate mass data and differential analysis represents a very reliable method for the identification of reactive metabolites formed in microsomal incubations. Copyright © 2010 John Wiley & Sons, Ltd.