Division points on curves

Summary A curve contained in a product of multiplicative groups passing through the origin, and containing infinitely many torsion points is a subgroup. The analogous statement on abelian varieties is discussed and reduced to an analogue of the irreducibility of the cyclotomic equation. In memory of Guido Castelnuovo in the recurrence of the first centenary of his birth.     

Non-Autonomous Evolution Equations on Nonsmooth Domair

The solution of a stationary boundary value problem on a domain with conical points has singularities near these points. Here we first consider existence results in appropriate weighted Sobolev spaces in order to incorporate the singularities. We secondly use these results to prove existence, uniqueness and regularity of solutions of non-autonomous second order evolution equations on such domains.     

Elliptic Interface Problems in Axisymmetric Domains. Part I: Singular Functions of Non - Tensorial Type

We study the regularity of solutions of interface problems for the Poisson equation in axisynunetric domains. The Fourier decomposition of the 3D-problem into a sequence of 2D-variational equations end uniform (with respect to the sequence parameter) a prior; estimates of their solutions are derived. Some non-tensorial singular functions describing the behaviour of the solution near interface edges are given and the smoothness of the stress intensity distribution as well as the tangential regularity are characterized in tenns of Sobolev spaces. In a forthcoming part II of this paper, the results will be applied to error estimates of the so-called Fourier-finite-element method for solving approximately elliptic interface problems in 3D.     

1H NMR utilization of through-space effects. II—conformation of dienic ketones

The configurational and conformational assignments of the carbonyl group in the Z- and E-1-(3-substituted-5,5-dimethyl-2-cyclohexen-1-ylidene)-2-butanones are carried out using only the through-space effects of the carbonyl group. It is demonstrated that, regardless of the Z- or E-configuration or the nature of the substituent in position 3, the conformation of the carbonyl group is always s-cis.     

A simple and efficient preparation of deoxynucleoside phosphoramidites in situ

A highly selective activation of bis-(pyrrolidino) methoxyphosphine by 4,5-dichloroimidazole has been developed and successfully used in the preparation of deoxynucleoside phosphoramidites.     

Direct copolymerization of sulfonated poly(phthalazinone arylene ether)s for proton‐exchange‐membrane materials

Sulfonated poly(phthalazinone ether ketone) (SPPEK) copolymers and sulfonated poly(phthalazinone ether sulfone) (SPPES) copolymers containing pendant sodium sulfonate groups were prepared by direct copolymerization. The reaction of disodium 3,3′‐disulfonate‐4,4′‐difluorobenzophenone (SDFB‐Na), 4,4′‐difluorobenzophenone (DFB), and 4‐(4‐hydroxyphenyl)‐1(2H)‐phthalazinone (DHPZ) at 170 °C in N‐methyl‐2‐pyrrolidione containing anhydrous potassium carbonate gave SPPEKs. SPPESs were similarly obtained with 3,3′‐disulfonate‐4,4′‐difluorophenyl sulfone, 4‐fluorophenyl sulfone (DFS), and DHPZ as monomers. The sulfonic acid groups, being on deactivated positions of the polymer backbone, were expected to be hydrolytically more stable than postsulfonated polymers. Fourier transform infrared and ¹H NMR were used to characterize the structures and degrees of sulfonation of the sulfonated polymers. Membrane films of SPPEKs with SDFB‐Na/DFB molar feed ratios of up to 60/40 and SPPESs with sulfonated 4‐fluorophenyl sulfone/DFS molar feed ratios of up to 50/50 were cast from N,N‐dimethylacetamide polymer solutions. Membrane films in acid form were then obtained by the treatment of the sodium‐form membrane films in 2 N sulfuric acid at room temperature. An increase in the number of sulfonate groups in the copolymers resulted in an increased glass‐transition temperature and enhanced membrane hydrophilicity. The sodium‐form copolymers were thermally more stable than their acid forms. The proton conductivities of the acid‐form copolymers with sulfonated monomer/unsulfonated monomer molar feed ratios of 0.5 and 0.6 were higher than 10^?2 S/cm and increased with temperature; they were less temperature‐dependent than those of the postsulfonated products. SPPESH‐50 showed higher conductivity than the corresponding postsulfonated poly(phthalazinone ether sulfone). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2731–2742, 2003     

Cordierite gels from TEOS and aluminum and magnesium nitrates under basic conditions

Synthesis of cordierite gels was performed using Si(OC₂H₅)₄ and aluminum and magnesium nitrates as starting materials under basic conditions. Further heat treatment yields the successive crystallisation of μ and α-cordierites and of some amounts of spinel as a secondary phase as revealed by X-ray diffraction. The poor final densification (84% of the theoretical value) of samples obtained from the as-prepared powders has been improved by ball-milling to values up to 95–98% of the theoretical value, the spinel proportion being simultaneously decreased.