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.     

Partitioning 2-edge-colored graphs by monochromatic paths and cycles

We present results on partitioning the vertices of 2-edge-colored graphs into monochromatic paths and cycles. We prove asymptotically the two-color case of a conjecture of Sárközy: the vertex set of every 2-edge-colored graph can be partitioned into at most 2α(G) monochromatic cycles, where α(G) denotes the independence number of G. Another direction, emerged recently from a conjecture of Schelp, is to consider colorings of graphs with given minimum degree. We prove that apart from o(|V (G)|) vertices, the vertex set of any 2-edge-colored graph G with minimum degree at least \(\tfrac{{(1 + \varepsilon )3|V(G)|}} {4}\) can be covered by the vertices of two vertex disjoint monochromatic cycles of distinct colors. Finally, under the assumption that \(\bar G\) does not contain a fixed bipartite graph H, we show that in every 2-edge-coloring of G, |V (G)| ? c(H) vertices can be covered by two vertex disjoint paths of different colors, where c(H) is a constant depending only on H. In particular, we prove that c(C ₄)=1, which is best possible.     

Large antipodal families

A family {A _i | i ∈ I} of sets in ℝ ^d is antipodal if for any distinct i, j ∈ I and any p ∈ A _i , q ∈ A _j , there is a linear functional ϕ:ℝ ^d → ℝ such that ϕ(p) ≠ ϕ(q) and ϕ(p) ≤ ϕ(r) ≤ ϕ(q) for all r ∈ ∪ _i∈I A _i . We study the existence of antipodal families of large finite or infinite sets in ℝ³. The research was supported by the Hungarian-South African Intergovernmental Scientific and Technological Cooperation Programme, NKTH Grant no. ZA-21/2006 and South African National Research Foundation Grant no. UID 61853, as well as Hungarian National Foundation for Scientific Research Grants no. NK 67867, no. T47102, and no. K72537.     

An improved method for assay of vitamin C in fish feed and tissues

Summary A method was devised to assay four forms of vitamin C: L-ascorbic acid (AA), dehydroascorbic acid (DHA), ascorbate-2-mono- and polyphosphate (AMP, APP), as well as ascorbate-2-monosulphate (AMS), in sample series of different fish tissues and feed. Direct and indirect detection were combined. Sample extractions were carried out with 0.2 mol L⁻¹ sodium acetate buffer (pH 4.8) and extracts were deproteinized after different chemical or enzymatic reactions, with perchloric acid. The DHA was reduced to AA with dithioerythritol (DTE). Ascorbate oxidase enzyme was used for the detection of background and an acidic phosphatase enzyme for the hydrolysis of different phosphate esters. Ascorbate-2-sulphate was detected directly with help of coinjection of the compound. Chromatographic analysis was carried out with a single column isocratic reverse phase method. The mobile phase was an aqueous buffer of 0.04 M sodium-acetate, 0.05 mM EDTA, 0.5 mM tetrabutylammonium dihydrogen phosphate (TBA) adjusted to pH 3.76 with 85% H₃PO₄ and with 24 mL methanol added to 1000 mL. C-18 columns were used with 0.6 mL min⁻¹ flow rate at 23°C. The vitamin C forms were detected by UV absorption at 250 nm. The determination limit was 1.0–5.0 μg g⁻¹ in AA equivalent. The standard deviations were between 1–6% and depended on the concentrations of vitamin C forms and tissues. Recoveries were between 90–96% in samples. Presented at: Balaton Symposium on High-Performance Separation Methods, Siófok, Hungary, September 3–5, 1997     

A new approach for development of rugged sample preparation of metabolites of albendazole in cow milk

Sample preparation is the critical step in analysis of residues in biological samples. The development of a ragged method is time-consuming, because a huge number of parameters must be checked. To reduce the number of experiments Taguchi's method was applied in the sample preparation of metabolites of albendazole. During the experiments 11 controllable and 7 noise factors were investigated. From the influence of controllable and noise factors on recovery and standard deviation, conditions for the sample preparation and recovery could be concluded with high accuracy and reliability.     

Intrinsically flame retardant epoxy resin - Fire performance and background - Part II

The flame retardant mechanism of a newly synthesized phosphorus-containing reactive amine, which can be used both as crosslinking agent in epoxy resins and as flame retardant, was investigated. The mode of action and degradation pathway were investigated by in situ analysis of the gases evolved during the degradation by thermogravimetric measurements coupled online with infrared (TG-EGA-FTIR) and mass spectroscopy (TG/DTA-EGA-MS) and by solid residue analysis by infrared (ATR) spectroscopic methods and X-ray photoelectron spectroscopy (XPS). It was observed that the main difference in the degradation of the reference and the flame retardant system is that the degradation of the latter begins at lower temperature mainly with the emission of degradation products of the phosphorus amine, which act as flame retardants in the gas phase slowing down the further degradation steps. At the high temperature degradation stage the solid phase effect of the phosphorus prevails: the formation of phosphorocarbonaceous intumescent char results in a mass residue of 23.4%. The ratio of phosphorus acting in gas phase and solid phase, respectively, was determined on the basis of thermogravimetric and XPS measurements.     

Toward a consistent treatment of polarization in model QM/MM calculations

The concept of model chemistries within hybrid QM/MM calculations has been addressed through analysis of the polarization energy determined by two distinct approaches based on (i) induced charges and (ii) induced dipoles. The quantum mechanical polarization energy for four configurations of the water dimer has been determined for a range of basis sets using Morokuma energy decomposition analysis. This benchmark value has been compared to the fully classical polarization energy determined using the induced dipole approach, and the molecular mechanics polarization energy calculated using induced charges within the MM region of hybrid QM/MM calculations. From the water dimer calculations, it is concluded that the induced charge approach is consistent with medium sized basis set calculations whereas the induced dipole approach is consistent with large basis set calculations. This result is highly relevant to the concept of QM/MM model chemistries.     

Catalytic transfer hydrogenation of 2-butanone over oxide catalysts

Catalytic transfer hydrogenation of 2-butanone with 2-propanol was studied in gas phase over a series of oxides of different acid-base properties. Although the basic oxides (MgO, La₂O₃) gave high initial conversions, these oxides underwent deactivation during the reaction. This deactivation could be partially prevented by a previous treatment with chloroform of the oxide. The amphoteric oxides (TiO₂, ZrO₂, Al₂O₃) were also active in this reaction. Increasing the acidic character of the catalyst (Nb₂O₅, WO₃) led to a pronounced dehydration of 2-propanol. The results obtained over a series of rare earth oxides (La₂O₃, Sm₂O₃, Gd₂O₃, Dy₂O₃, Er₂O₃) revealed that beside the role of basic and acid sites a correlation seems to exist between the number of unpaired electrons of the metal ion and the catalytic activity, indicating the role of one electron donor sites.     

The photochemical reaction cycle of retinal reconstituted bacteriorhodopsin

The function of three types of bacteriorhodopsins was compared: the wild-type, the bleached and retinal reconstituted and retinal deficient bacteriorhodopsin after retinal addition. The apparent pK(a) of the proton acceptor group for the bleached BR and retinal deficient BR shifted toward higher pH values compared to the wild-type BR. Fitting the photocycle model to the absorption kinetic signals for all three proteins showed the existence of the same intermediates, but the time-dependent concentration of the intermediates was different. Although measurements were made at pH 7, the absorption kinetics and photoelectric signals in both retinal reconstituted samples acted as wild-type bacteriorhodopsin at significantly higher pH. Below pH 3 the retinal deficient and reconstituted sample bleached. These results suggested that the added retinal was not able to rebind in the same position in the protein as in native bacteriorhodopsin. This points out that care should be taken, when bleached bacteriorhodopsin is reconstituted with different retinal analogs.