A fast algorithm for finding small solutions of <Emphasis Type=”Italic”>F(X,Y)=G(X,Y)</Emphasis> over number fields

Summary In the definition of semi-open sets and other kinds of generalized open sets, the role of the starting topology is given to a generalized topology. Some properties of the classes of sets so obtained is examined.     

GC–MS Studies of Thiophenes in the Supercritical Fluid CO2 and Solvent Extracts of Tagetes patula L.

The intact plant parts and genetically modified hairy root clone #TpA6 of Tagetes patula were extracted with supercritical fluid CO₂ extraction (SFE) and a conventional solvent extraction. SFE optimization included the variation of fluid CO₂ pressure, dynamic time, and the addition of methanol modifier co-solvent. The four characteristic thiophene metabolites, 5-(3-buten-1-ynyl)-2,2′-bithienyl (BBT), 2,2′:5′,2″-terthiophene (α-T), 5-(4-acetoxy-1-butynyl)-2,2′-bithienyl (BBTOAc), and 5-(3,4-diacetoxy-1-butynyl)-2,2′-bithienyl [BBT(OAc)₂], were analysed by GC–MS. The proposed SFE method allowed the selective extraction of thiophenes in 60 min dynamic time with supercritical CO₂ without modifier co-solvent, at 30 MPa and 40 °C. The SFE and the reference solvent extraction yielded similar results. The SFE of intact roots and flowers yielded 717 ± 31.3 and 480 ± 26.6 μg g^?1 α-T, respectively, while the leaves did not contain considerable amounts of thiophenes. Remarkable amounts of BBT, BBTOAc, and BBT(OAc)₂ were characteristic of the SFE of hairy root cultures.     

Comparison of the molecular structures of five benzene derivatives as determined independently by gas-phase electron diffraction in two different laboratories: a perspective

The merits and limitations of gas-phase electron diffraction as a technique for determining accurately the structures of small organic molecules are demonstrated by comparing the molecular structures of five benzene derivatives studied in two different laboratories. The existence of many possible representations of the structure of a molecule (r _a, r _g, r _α, r _α⁰, r _e, …), implying differences in the physical meaning of geometrical parameters, is discussed in some detail as it may cause difficulties in a comparison. Also illustrated are different ways of estimating and expressing uncertainties in the geometrical parameters from a gas-phase electron diffraction study.     

Study of gas generation in real L/ILW containers

To obtain reliable estimates of the quantities and rates of the gas production in L/ILW a series of measurements was carried in the last 7 years in Hungary. The typical gas production rates were 0.05–0.2 STP litre gas/day for CO₂ and CH₄ generation, and less for H₂. No explosive gas mixture was indicated in the L/ILW drums during the investigated storage period. Compositions of headspace gases in closed L/ILW vaults were in agreement with gas generation processes observed in L/ILW drums. The stable carbon isotope measurements show that the main source of the CO₂ gas is the degradation of organic matter and indicates microbial degradation processes as the main sources of CH₄. Typical tritium activity concentrations were <10 Bq/l gas in the drums and <1,000 Bq/l gas in the vaults. Typical ¹⁴C activity values of the headspace gases were <2.0 Bq/l gas in the drums and <1,000 Bq/l gas in the vaults.     

Reactions of 2-Deoxy-4, 5-O-Isopropylidene-D-Erythro- and D-Threo-Pent-1-Enose Derivatives

ABSTRACT

The reactivity of the title compounds has been studied toward different nucleophiles and electrophiles. Unlike other ketene dithioacetals, compounds 3-5 did not add nucleophiles to the double bond. Instead, in the presence of Lewis acids they underwent substitution reaction at position 3. If the nucleophile was not strong enough, formation of 6 and 7 were observed. With 2,3,4,6-tetra-O-acetyl-1-thio-β-D-glucopyranose (18), a 3:1 mixture of 11 and 12 was formed from 4. These observations may be interpreted in terms of easy formation of the allylic carbocation I which gives diastereomers with nucleophiles. However, this allylic ether-like behaviour was ruled out by the fact that compounds 9 and 10 did not undergo [2,3] sigmatropic rearrangement with lithium diisopropylamide. With N-bromosuccinimide compound 3 gave the 2-bromo derivative 8. Compounds 3 and 8 resisted common mercury salt assisted demercaptalization procedures.     

Effect of atmospheric pressure variations on the <Superscript>222</Superscript>Rn activity concentration in the air of a wine cellar

We have measured the variation of atmospheric pressure and of ²²²Rn activity concentration in the air of a wine cellar with an AlphaGAURD type ionization chamber radon monitor. We have found that the ²²²Rn activity concentration varies inversely with pressure. To explain this behavior we have done model calculations. We have compared the results of model calculations with the results of experimental measurements, and we have found that the model is capable to reproduce some part of the variation of ²²²Rn activity concentration.     

Linus Pauling’s quest for the structure of proteins

Linus Pauling, arguably the greatest chemist of the twentieth century, never publicly admitted that there was a race for the determination of the structure of the most important biopolymers. But according to his competitors there was a race, in fact, there were two, and Pauling won one and lost the other. He had a tremendous amount of ideas, many of them worthless, but a few were spectacular. Not only did he make seminal discoveries, he was also a master of announcing them in a most dramatic way. Eventually, Pauling shifted toward politics and controversial issues, but his science ensured him his place among the greats. Here, we follow Pauling’s route to the discovery of the alpha-helix; the defeat of the star-studded British team in the same quest; and a seemingly unrelated story about the fate of the theory of resonance that assured Pauling’s victory yet at the same time it was excommunicated in the Soviet Union.     

Book reviews

Unsigned book reviews are by the Book Review Editor.     

Semiovals contained in the union of three concurrent lines

Semiovals which are contained in the union of three concurrent lines are studied. The notion of a strong semioval is introduced, and a complete classification of these objects in PG(2,p) and PG(2,p²), p an odd prime, is given. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 491–501, 2007