On packing 3‐vertex paths in a graph

Let G be a connected graph and let eb(G) and λ(G) denote the number of end‐blocks and the maximum number of disjoint 3‐vertex paths Λ in G. We prove the following theorems on claw‐free graphs: (t1) if G is claw‐free and eb(G) ≤ 2 (and in particular, G is 2‐connected) then λ(G) = ⌊| V(G)|/3⌋; (t2) if G is claw‐free and eb(G) ≥ 2 then λ(G) ≥ ⌊(| V(G) | − eb(G) + 2)/3 ⌋; and (t3) if G is claw‐free and Δ^*‐free then λ(G) = ⌊| V(G) |/3⌋ (here Δ^* is a graph obtained from a triangle Δ by attaching to each vertex a new dangling edge). We also give the following sufficient condition for a graph to have a Λ‐factor: Let n and p be integers, 1 ≤ p ≤ n − 2, G a 2‐connected graph, and |V(G)| = 3n. Suppose that G − S has a Λ‐factor for every S ⊆ V(G) such that |S| = 3p and both V(G) − S and S induce connected subgraphs in G. Then G has a Λ‐factor. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 175–197, 2001     

Novel Asymmetric and Stereospecific Aziridination of Alkenes with a Chiral Nitridomanganese Complex

The addition of pyridine N -oxide is necessary to obtain high enantioselectivities in the asymmetric aziridination of styrene derivatives through transfer of a nitrogen atom from chiral, toluenesulfonic anhydride activated nitridomanganese complex 1 [Eq. (a)]. Remarkably, high stereospecificity was observed in all the aziridinations of trans- and cis-1,2-disubstituted alkenes. R¹=H, Me, nPr, iPr; R²=H, Me; Ts=p-toluenesulfonyl.     

Synthesis and polymerization of N‐(4‐tetrahydropyranyl‐oxyphenyl)maleimide

N‐(4‐Tetrahydropyranyl‐oxy‐phenyl)maleimide (THPMI) was prepared and polymerized by radical or anionic initiators. THPMI could be polymerized by 2,2′‐azobis(isobutyronitrile) (AIBN) and potassium tert‐butoxide. Radical polymers (poly(THPMI)r) were obtained in 15–50% yields for AIBN in THF at 65°C after 2–5 h. The yield of anionic polymers (poly(THPMI)a) obtained from potassium tert‐butoxide in THF at 0°C after 20 h was 91%. The molecular weights of poly(THPMI)r and poly(THPMI)a were M_n = 2750–3300 (M_w/M_n = 1.2–3.3) and M_n = 11300 (M_w/M_n = 6.0), respectively. The difference in molecular weights of the polymers was due to the differences in the termination mechanism of polymerization and the solubility of these polymers in THF. The thermal decomposition temperatures were 205 and 365°C. The first decomposition step was based on elimination of the tetrahydropyranyl group from the poly(THPMI). Positive image patterns were obtained by chemical amplification of positive photoresist composed of poly(THPMI) and 4‐morpholinophenyl diazonium trifluoromethanesulfonate used as an acid generator. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 341–347, 1999     

Pentamethylcyclopentadienylrhodium(III) and -iridium(III) Complexes Showing P,O Coordination: Unprecedented Insertion of tcne and tcnq into a C−H Bond

Strongly electron withdrawing cyanoolefins tetracyanoethylene (tcne) and 7,7,8,8-tetracyano-p-quinodimethane (tcnq) react with [(η⁵-C₅Me₅)MCl(MDMPP-P,O)] (M=Rh, Ir; MDMPP-P,O=PPh₂(2-O-6-MeO-C₆H₃), a P,O chelating phosphane) by insertion into the C−H bond adjacent to the M−O σ bond. The crystal structure of the iridium complex formed upon insertion of tcne is shown.     

Sound propagation in soundproofing casement windows

Casement windows consisted of two wooden frames that can be opened and closed at various angles are widely used in developing countries with tropical climates. However, an annual increase in a number of motorcycles and automobiles and traffic noise level these countries have rendered these windows to be useless. In this paper, we present a model for manufacturing windows which are suitable for the developing tropical countries. These windows are capable of ventilating, regulating sunlight, protecting against coldness, and reducing traffic noise and fumes from motor vehicles. The ventilation and soundproofing unit hold an importance place in the design of the windows and are calculated using the wave equation and observations of higher-order mode waves. In order to maximize the soundproofing ability, the selection of size and placement of input and output openings in such a way that would minimize the effects of higher-order mode waves are considered in details.     

A new approach for standard preparation in microbeam analysis: Development and validation

Microbeam analysis is used in biomedical and environmental sciences to determine the presence and concentration of trace elements. However, quantitative analyses of biological samples are challenging because the chemical and physical compositions of existing standards differ from those typically encountered in biological samples. We developed a thin standard using polyvinyl alcohol and assessed its quality by microbeam scanning particle induced X-ray emission (micro-PIXE) analysis. The relationship between metal concentration and X-ray intensity was linear for certain standards up to 500 μg·g⁻¹. Using this new thin standard, micro-PIXE analysis of Zn content in samples of human hair agreed well with analysis performed by inductively-coupled plasma mass spectrometry, validating the use of these new thin standards for quantitative mapping with microbeam analysis.