The spectrum of equitable, 4‐chromatic Steiner quadruple systems

A Steiner quadruple system of order v (briefly an SQS(v)) is a pair (X, ) with |X| = v and a set of quadruples taken from X such that every triple in X is in a unique quadruple in . Hanani [Canad J Math 12 (1960), 145–157] showed that an SQS(v) exists if and only if v is {admissible}, that is, v = 0,1 or v ≡ 2,4 (mod 6). Each SQS(v) has a chromatic number when considered as a 4‐uniform hypergraph. Here we show that a 4‐chromatic SQS(v) exists for all admissible v ≥ 20, and that no 4‐chromatic SQS(v) exists for v < 20. Each system we construct admits a proper 4‐coloring that is equitable, that is, any two color classes differ in size by at most one. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 369–392, 2007     

Mechanism of the catalyzed by cysteine electroreduction of the insoluble in water cobalt(II) salt as a component of carbon paste electrode

The mechanism of the Co(II) catalytic electroreduction of water insoluble CoR₂ salt in the presence of cysteine was developed. CoR₂ = cobalt(II) cyclohexylbutyrate is the component of a carbon paste electrode. Electrode surface consecutive reactions are: (a) fast (equilibrium) reaction of the complex formation, (b) rate-determining reversible reaction of the promoting process of CoR(Ac⁺) complex formation, (c) rate-determining irreversible reaction of the electroactive complex formation with ligand-induced adsorption, and (d) fast irreversible reaction of the electroreduction. Reactions (a,b) connected with CoR₂ dissolution and reactions (c,d) connected with CoR₂ electroreduction are catalyzed by . Regeneration of (reactions “b,d”) and accumulation of atomic Co(0) (reaction “d”) take place. Experimental data [Sugawara et al., Bioelectrochem Bioenergetics 26:469, 1991]: i _a vs E (i _a is anodic peak, E is cathodic accumulation potential), i _a vs , and i _a vs pH have been quantitatively explained.     

S-alkylation of thiacalixarenes: a long-neglected possibility in the calixarene family

Despite the high nucleophilicity of sulfur atoms, thiacalixarenes have been alkylated only on oxygen atoms thus far. Using strong alkylating agents (triflates, trialkyloxonium salts), the substitution of the sulfur bridges has been successfully accomplished. The corresponding sulfonium salts of thiacalix[4]arene are formed regio- and stereoselectively as a completely new type of substitution pattern in thiacalixarene chemistry. These compounds possess interesting conformational behavior and could be used as unusual alkylating agents with uncommon selectivity.     

Mullite-derivative Bi2Mn(x)Al(7-x)O14 (x~1): structure determination by powder X-ray diffraction from a multi-phase sample

As a supplementary method to single crystal X-ray diffraction (XRD), nowadays crystal structure determination by powder XRD has become popular, especially for those areas with difficulties getting high quality single crystals. Here we observed an intermediate phase Bi(2)Mn(x)Al(7-x)O(14) (x~1) during the decomposition of mullite-Bi(2)Mn(x)Al(4-x)O(9+δ) (solid solution of Bi(2)Mn(4)O(10)-Bi(2)Al(4)O(9)). As a metastable phase, it started to decompose while forming, thus no single-phase sample can be obtained. We successfully determined its structure by powder XRD from a multi-phase sample. A modified Le Bail fitting using the atomic structure information of known impurities showed a more reliable intensity extraction from a multi-phase powder XRD than that without using atomic structures for the known impurities. The charge-flipping algorithm and Monte-Carlo based simulated annealing technique were then applied to obtain the full structural model. In principle, this strategy is applicable to more complex problems, and not limited to the oxide materials. Bi(2)Mn(x)Al(7-x)O(14) possesses a mullite-related structure. There are one tetrahedral and two octahedral sites for Mn and Al, where disordering with substantial site preferences is observed. Specifically, M1O(6) and M3O(6) octahedra share edges along the c-direction with the periodicity of 1 : 2. These octahedral chains are further connected into a 3D structure through M2O(4) dimmers and Bi.     

Identification of potential sources of thymoquinone and related compounds in Asteraceae, Cupressaceae, Lamiaceae, and Ranunculaceae families

In this study, forty-seven plant species belonging to seven families were analysed by GC and GC-MS for the contents of pharmacologically effective quinones: dithymoquinone (DTQ), thymohydroquinone (THQ), and thymoquinone (TQ). The results showed that detectable amounts (??1 mg kg^?1) of at least one of these compounds have been found in three species of both Monarda (M. didyma, M. media, and M. menthifolia) and Thymus (T. pulegioides, T. serpyllum, and T. vulgaris) genera, two Satureja (S. hortensis and S. montana) species, and in single representatives of Eupatorium (E. cannabinum), Juniperus (J. communis), and Nigella (N. sativa) genera. The maximum contents of THQ and TQ were found in M. media aerial parts and M. didyma inflorescences (2674 and 3564 mg kg^?1 of dried weight, respectively) in amounts significantly exceeding their maximum contents in N. sativa seeds (THQ = 530 mg kg^?1 and TQ = 1881 mg kg^?1), which are generally considered as the main natural source of both of these compounds. As a conclusion, M. didyma (bergamot) and M. media (purple bergamot) can be recommended as new prospective natural sources of THQ and TQ for pharmaceutical or food industries.