Lines on Fermat surfaces

We prove that the Néron-Severi groups of several complex Fermat surfaces are generated by lines. Specifically, we obtain these new results for all degrees up to 100 that are relatively prime to 6. The proof uses reduction modulo a supersingular prime. The techniques are developed in detail. They can be applied to other surfaces and varieties as well.     

Extremal solutions for stochastic equations indexed by negative integers and taking values in compact groups

Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied to characterize several properties of the set of all solutions in terms of the law of the driving noise.     

Anion- and cation-exchange studies of Zr,Hf, and Th using ion-exchange resin and fiber in H2SO4 media for chemical characterization of sulfate complex of Rf

Journal of Radioanalytical and Nuclear Chemistry - To investigate sulfate complex formation of Rf, we performed batch-wise ion-exchange experiments of its homologues Zr and Hf and its pseudo...     

Studies on the syntheses of heteroeyelie compounds. Part DVII. A synthesis of (±)-N-norgalanthamine

(±)-N-Norgalanthamine (la) and (±)-N-norlycoramine (Ib) was synthesized through the phenolie oxidation of N-(4-hydroxyphenethyl)-2-bromo-5-hydroxy-4-methoxybenzamide (lIb).     

Studies of the polymerization of diallyl compounds. XXVII. Copolymerization of diallyl tartrate with several vinyl monomers

The radical copolymerization of diallyl tartrate (DATa) (M₁) with diallyl succinate (DASu), diallyl phthalate (DAP), allyl benzoate (ABz), vinyl acetate (VAc), or styrene (St) was investigated in order to disclose in more detail the characteristic hydroxyl group's effect observed in the homopolymerization of DATa. In the copolymerization with DASu or DAP as a typical diallyldicarboxylate, the dependence of the rate of copolymerization on monomer composition was different for different copolymerization systems and unusual values larger than unity for the product of monomer reactivity ratios, r₁r₂, were obtained. In the copolymerization with ABz or VAc (M₂), the r₁ and r₂ values were estimated to be 1.50 and 0.64 for the DATa/ABz system and 0.76 and 2.34 for the DATa/VAc system, respectively; the product r₁r₂ for the latter copolymerization system was found again to be larger than unity. In the copolymerization with St, the largest effect due to DATa monomer of high polarity was observed. Solvent effects were tentatively examined to improve the copolymerizability of DATa. These results are discussed in terms of hydrogen-bonding ability of DATa.     

Cubic phases of binary systems of 4′-n-tetradecyloxy-3′-nitrobiphenyl-4-carboxylic acid (ANBC-14)-n-alkane

The phase behaviour of the binary systems 4′- ⁿ -tetradecyloxy-3′-nitrobiphenyl-4-carboxylic acid (ANBC-14)- ⁿ -alkane ( ⁿ -tetradecane or ⁿ -hexadecane) was investigated by differential scanning calorimetry, polarizing optical microscopy, and X-ray diffraction. The phase behaviour was a function of temperature ( ^T ) and the effective carbon number of the system ( ^n*), where ^n* involves carbon atoms both from the alkoxy group of ANBC-14 and from the ⁿ -alkane added. ANBC-14 shows no cubic phase, but the addition of ⁿ -alkane induced cubic phases when ^n*≧c. 15. An interesting point is that the type of cubic phase is ^Ia 3 ^d for 15^≦n*≦17, while an ^Im 3 ^m type is formed for 18^≦n*≦20. Furthermore, for ^n* = 22, two types of cubic phase, one with ^Im 3 ^m symmetry in the low temperature region and the other with ^Ia 3 ^d in the high temperature region, were observed both on heating and cooling. The phase diagram with respect to ^T and ^n* is very similar to that of pure one-component ANBC- ⁿ , which is a function of ^T and the number of carbon atoms in the alkoxy group ⁿ .