Weighted composition operators and locally convex algebras

The Gleason-Kahane-Zelazko theorem characterizes the continuous homomorphism of an associative, locally multiplicatively convex, sequentially complete algebra A into the field ? among all linear forms on A. This characterization will be applied along two different directions. In the case in which A is a commutative Banach algebra, the theorem yields the representation of some classes of continuous linear maps A : A→ A as weighted composition operators, or as composition operators when A is a continuous algebra endomorphism. The theorem will then be applied to explore the behaviour of continuous linear forms on quasi-regular elements, when A is either the algebra of all Hilbert-Schmidt operators or a Hilbert algebra.     

A possible helical model for sodium glycocholate micellar aggregates

Sodium glycocholate crystallizes in the tetragonal space group14 witha =b = 27.793(4),c = 7.937(1) Å andZ = 8. Refinement based on 2290 observed reflections led to a conventionalR = 0.10. The bile salt molecules are arranged in a helix with 2₁ symmetry stabilized mainly by polar interactions. Four helices are held together by hydrogen bonds involving water molecules, giving rise to hydrophilic channels, with a small cross section, which can include water molecules. The packing of these tetramers form hydrophobic channels containing some disordered acetone and water molecules. The helices will be checked as a model for the micellar aggregates of this important conjugated bile salt, following the same strategy successfully applied to sodium deoxycholate. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82107 (20 pages).     

Curves of maximum genus in range A and stick-figures

In this paper we show the existence of smooth connected space curves not contained in a surface of degree less than , with genus maximal with respect to the degree, in half of the so-called range A. The main tool is a technique of deformation of stick-figures due to G. Fløystad.

     

High-level ab initio calculations for the four low-lying families of minima of (H2O)20. II. Spectroscopic signatures of the dodecahedron, fused cubes, face-sharing pentagonal prisms, and edge-sharing pentagonal prisms hydrogen bonding networks

We report the first harmonic vibrational spectra for each of the lowest lying isomers within the four major families of minima of (H2O)20, namely, the dodecahedron, fused cubes, face-sharing pentagonal prisms, and edge-sharing pentagonal prisms. These were obtained at the second-order Moller-Plesset perturbation level of theory (MP2) with the augmented correlation consistent basis set of double zeta quality (aug-cc-pVDZ) at the corresponding minimum energy geometries. The computed infrared (IR) spectra are the first ones obtained from first principles for these clusters. They were found to contain spectral features, which can be directly mapped onto the distinctive spectroscopic signatures of their constituent tetramer, pentamer, and octamer fragments. The dodecahedron spectra show the richest structure in the OH stretching region and are associated with the most redshifted OH vibrations with respect to the monomer. The lowest lying edge-sharing pentagonal prism isomer displays intense IR active vibrations that are redshifted by approximately 600 cm(-1) with respect to the water monomer. Furthermore the most redshifted, IR-active OH stretching vibrations for all four networks correspond to hydrogen bonded OH groups, which exhibit the following two common characteristics: (i) they belong to fragments which have a "free" OH stretch and (ii) they act as donors to a neighboring water molecule along a "dimerlike" (strong) hydrogen bond. The zero-point energy corrected MP2/CBS (complete basis set) limit binding energies D(0) for the four isomers are -163.1 kcal/mol (edge-sharing pentagonal prism), -160.1 kcal/mol (face-sharing pentagonal prism), -157.5 kcal/mol (fused cubes), and -148.1 kcal/mol (dodecahedron).     

Crystal structures of bile salts: Sodium taurocholate

Crystals of sodium taurocholate (NaC₂₆H₄₄NO₇S · 2.5 H₂O) belonging to the triclinic space groupP1 have unit cell parametersa = 12.731 (2),b = 16.104 (2),c = 7.628 (1) A, =83.40 (1), = 101.20 (1), = 105.35 (1)°, and two molecules in the asymmetric unit. The refinement, carried out on 4424 observed reflections, gaveR = 0.059 andR _w = 0.066. The packing is characterized by bilayers, formed by antiparallel monolayers and with nonpolar outermost surfaces, held together by van der Waals interactions. Inside the bilayers there are channels, lined with polar groups, and filled by sodium ions and water molecules. A structural unit has been identified that could provide a reasonable model for the micellar aggregates of this bile salt. Supplementary Data relevant to this article have been deposited with the British Library under the reference number SUP 82125 (38 pages).     

Synthesis of 7- and 10-spermine conjugates of paclitaxel and 10-deacetyl-paclitaxel as potential prodrugs

Efficient syntheses of two taxol analogs bearing the linear polyamine spermine at 7- and 10-positions of paclitaxel and 10-deacetyl-paclitaxel have been developed. These polyamine-taxol-conjugates were isolated as water soluble difluoride salts. The aim of the present work was to introduce a chemical modification into taxol skeleton in order to increase drug selectivity toward tumor cells. The cytotoxic activity of these conjugates was evaluated in MCF7 and MCF7-R cell lines. The observed low cytotoxicity suggests that these conjugates could act as potential prodrugs.     

Oxygen evolution on aged IrO x /Ti electrodes in alkaline solutions

O₂ evolution from 1 mol dm⁻¹ NaOH aqueous solution was studied on IrO _x /Ti electrodes already used for more than 3 years (aged). IrO _x was prepared by thermal decomposition of the chloride in the temperature range from 330 to 500 °C. Half of the electrodes were stored in air between experiments, the other half in water. The state of the electrode surface was monitored by recording voltammetric curves in a potential region prior to O₂ evolution before and after each group of experiments. O₂ evolution was studied by measuring quasistationary current–potential curves. Tafel slopes were derived using two different approaches. The reaction order with respect to OH⁻ was also determined and found to be fractional. Results show that the reaction mechanism does not depend on either the calcination temperature or the storage conditions. However, stability appears to be higher for electrodes calcined at higher temperatures and stored in air. Dedicated to Professor Algirdas Vaškelis on the occasion of his 70th birthday.     

Reactivity of the ReOX3(PPh3)2 complexes (X = Cl or Br) with Schiff bases

Summary The reactions of ReOX₃(PPh₃)₂ (X = CI or Br) withN-methylsalicylideneimine (Me-saIH),N-phenylsalicylideneimine (Ph-saIH),N,N-ethylenebis(salicyli(leneimine) [(SaIH)₂en] and 8-hvdroxyquinoline (Oxinell) are here reported. They give rise to the ReOX₂(Me-sal)PPh₂. ReOX-(Me-sal)₂, ReOX₂(Ph-sal)PPh₃, ReOX(Ph-sal),, Re₂O₂X₄-(Sal₂en)(PPh₃)₂, ReOX₂(Oxine)PPh, and ReOX(Oxine)₂ complexes.     

Crystal structure of the 2:1 inclusion compound between deoxycholic acid and quadricyclane

The 2:1 inclusion compound formed between deoxycholic acid (C₂₄H₄₀O₄,M _r=392.58) and quadricyclane (C₇H₈,M _r=92.14) crystallizes in space groupP2₁2₁2₁ witha=27.150(7),b=13.359(3),c=14.161(4) Å,Z=4. The structure was refined toR=0.08₆ andR _w=0.08₈ for 2079 observed reflections withI>2.5(I). The crystal packing is very similar to that found in the norbornadiene-deoxycholic acid inclusion compound and is characterized by an assembly of antiparallel pleated bilayers, formed by molecules of deoxycholic acid held together through hydrogen bonds. Quadricyclane occupies approximately the same position of norbornadiene and its atoms give rise to good van der Waals interactions with some methyl groups of deoxycholic acid. Supplementary Data relating to the article are deposited with the British Library as Supplementary Publication No. SUP 82006 (14) pages. To obtain copies, see page ii of this issue.     

Dynamic behaviour and X-ray analysis of chiral η-allylpalladium complexes. II

The DANTE technique and NOESY two-dimensional method have been employed to observe the isomerization of the chiral cationic complex [Pd(η³-CH₂CMeCH₂(P-P′)]⁺ (1a), where P-P′ = the chiral chelating ligand (S)(N-diphenylphosphino)(2-diphenylphosphinoxymethyl)pyrrolidine. The rate constant was found to be 0.5 s⁻¹ in CHCl₃ at 295 K and 1.50 s⁻¹ in the presence of added free ligand. In the latter case the epimerization proceeds by a π-σ-π mechanism via the intermediacy of a primary η¹-allylpalladium complex. Although the intermediate was not detected, the NMR findings reveal that it has the allylic terminus η¹-bonded to palladium. The structure of 1a in its PF₆⁻ salt has been determined. The compound crystallizes in the orthorhombic space group P2₁2₁2₁ with a 10.029(4) b 19.203(8) c 36.115(6) Å, Z = 8, R = 0.0572 and R_w = 0.0712 for 3716 observed reflections with I > 3σ(I).