Large Cross‐Free Sets in Steiner Triple Systems

A cross‐free set of size m in a Steiner triple system is three pairwise disjoint m‐element subsets such that no intersects all the three ‐s. We conjecture that for every admissible n there is an STS(n) with a cross‐free set of size which if true, is best possible. We prove this conjecture for the case , constructing an STS containing a cross‐free set of size 6k. We note that some of the 3‐bichromatic STSs, constructed by Colbourn, Dinitz, and Rosa, have cross‐free sets of size close to 6k (but cannot have size exactly 6k). The constructed STS shows that equality is possible for in the following result: in every 3‐coloring of the blocks of any Steiner triple system STS(n) there is a monochromatic connected component of size at least (we conjecture that equality holds for every admissible n). The analog problem can be asked for r‐colorings as well, if and is a prime power, we show that the answer is the same as in case of complete graphs: in every r‐coloring of the blocks of any STS(n), there is a monochromatic connected component with at least points, and this is sharp for infinitely many n.     

Gold(III) π-Allyl Complexes

Gold(III) π-complexes have been authenticated recently with alkenes, alkynes, and arenes. The key importance of Pd^II π-allyl complexes in organometallic chemistry (Tsuji–Trost reaction) prompted us to explore gold(III) π-allyl complexes, which have remained elusive so far. The (P,C)Au^III(allyl) and (methallyl) complexes 3 and 3′ were readily prepared and isolated as thermally and air-stable solids. Spectroscopic and crystallographic analyses combined with detailed DFT calculations support tight quasi-symmetric η³-coordination of the allyl moiety. The π-allyl gold(III) complexes are activated towards nucleophilic additions, as substantiated with β-diketo enolates.     

Convenient Method for the Reduction of the Double-Bond of Cyclic Vinylphosphine Oxides Using Borane

The electronpoor double-bond of cyclic vinylphosphine oxides (1, 3 and 4) is easily reduced by borane in a selective manner to give the corresponding saturated derivatives (2, 4 and 5, respectively) Under forcing conditions, change of the functionality may also take place.     

Notes on Semiarcs

The semiarcs are generalizations of semiovals. Estimates on the sizes of semiarcs, some characterization theorems of semiarcs with large collinear subsets, of semiarcs contained in the union of three concurrent lines and the complete classification of strong semiovals in PG(2, q), q odd, are given.     

Large Cliques in -Free Graphs

Dedicated to the memory of Paul Erdős A graph is called -free if it contains no cycle of length four as an induced subgraph. We prove that if a -free graph has n vertices and at least edges then it has a complete subgraph of vertices, where depends only on . We also give estimates on and show that a similar result does not hold for H-free graphs––unless H is an induced subgraph of . The best value of is determined for chordal graphs. Received October 25, 1999 RID="*" ID="*" Supported by OTKA grant T029074. RID="**" ID="**" Supported by TKI grant stochastics@TUB and by OTKA grant T026203.     

Biological UV dosimeters in quality control of tanning tubes

Although according to the International Radiological Protection Association-International Non-Ionizing Radiation Committee recommendation (1991) the use of sunbeds for cosmetic purposes is not recommended, tanning devices are used widely. Ten different types of commercially available sunbed tubes have been studied using a uracil biological UV dosimeter, and three of them were analyzed in detail. Dimerization effectiveness of the tubes was measured directly, whereas efficiency of erythema induction was calculated weighting the emission spectra by the Commission Internationale de l'Eclairage erythema action spectrum. The data obtained demonstrate that quality control of sunbed tubes has to include not only the determination of the UV doses administered but also the assessment of the health risk due to the UVB and UVA components of the lamp. A method of quality control using the uracil biological dosimeter was elaborated, and the estimation of the "acceptable" exposure time was checked/controlled on 15 volunteers by assessing individually the erythema induction threshold. A correct classification of the sunbed tubes is proposed by characterizing the erythema induction versus DNA-damaging effectiveness of tubes.     

Structure of aqueous solutions of tetraethylammonium chloride investigated by positron annihilation and ultrasonic methods

The structure of aqueous solutions of tetraethylammonium chloride was investigated using compressibility and density measurements and positron annihilation methods. The experimental results are different from those obtained earlier for systems where hydrophobic hydration dominates, although some evidences for formation of cage-like hydrates in liquid phase were observed. The results are interpreted, among others, in terms of competition among different hydrates of the tetraethylammonium cations, hydration of chloride anions, and formation of ionic pairs.