On the order of projective curves

Here we prove the existence of several componentsW of the Hilbert scheme of curves inP ⁿ such that the generalC W has Hartshorne-Rao module with order equal to its diameter.     

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).     

In silico rationalization of the structural and physicochemical requirements for photobiological activity in angelicine derivatives and their heteroanalogues

In PUVA (Psoralen plus UVA) chemotherapy 8-methoxypsoralen is the most widely used compound, although its efficacy is endowed with undesired side effects. In order to have an evident anti-proliferative activity with a reduced phototoxicity, many linear and angular derivatives have been synthesised. In this paper we describe a QSAR study in which, by means of the neural networks methodology, a useful model for predicting biological activity, expressed as ID₅₀ (the UVA dose that reduces to 50% the DNA synthesis in Ehrlich cells), has been derived. A decision tree that is able to discriminate between active and inactive compounds has been built based on recursive partitioning. The study shows the key structural features responsible for the activity and could be a helpful tool in the rational design of new, less toxic, photochemotherapeuthic agents.     

Reaction of sulfenes with heterocyclic N,N-disubstituted α-aminomethyleneketones. XII. Synthesis of [1]benzothiepino[4,5-e][1,2]oxathiin derivatives

The 1,4-cycloaddition of sulfene to N,N-disubstituted (E)-4-aminomethylene-3,4-dihydro[1]benzothiepin-5(2H)-ones I occurred only in the case of aliphatic N,N-disubstitution to give in good yield 4-dialkylamino-3,4,5,6-tetrahydro[1]benzothiepino[4,5-e][1,2]oxathiin 2,2-dioxides, which are derivatives of the new heterocyclic system [1]benzothiepino[4,5-e][1,2]oxathiin. Also the reaction of I with chlorosulfene occurred only in the case of aliphatic N,N-disubstitution to afford chiefly trans-4-dialkylamino-3-chloro-3,4,5,6-tetrahydro-[1]benzothiepino[4,5-e][1,2]oxathiin 2,2-dioxides III in satisfactory yield. Adducts III were dehydrochlorinated with DBN to 4-dialkylamino-5,6-dihydro[1]benzothiepino[4,5-e][1,2]oxathiin 2,2-dioxides in good yield.     

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).     

Reaction of sulfene with heterocyclic N,N-disubstituted α-aminomethyleneketones. VIII. Synthesis of furo[2,3-h]-1,2-benzoxathiin derivatives

Cycloaddition of sulfene to N,N-disubstituted (E)5-aminomethylene-6,7-dihydrobenzo[b]furan-4(5H)ones I gave, only in the case of aliphatic N-substitution and generally in satisfactory yields, N,N-disubstituted 4-amino-3,4,5,6-tetrahydrofuro[2,3-h]-1,2-benzoxathiin 2,2-dioxides II, which are derivatives of the new heterocyclic system furo[2,3-h]-1,2-benzoxathiin. The 4-dimethylamino and 4-piperidino cycloadducts IIa,e were dehydrogenated with DDQ to the corresponding 4-dialkylamino-3,4-dihydrofuro[2,3-h]-1,2-benzoxathiin 2,2-dioxides IIIa,e in low yield. Compounds IIIa,e were tested for photobiological activity and found to be inactive.     

Reaction of sulfene with heterocyclic N,N-disubstituted α-aminomethyleneketones. XI. Synthesis of 1,2-oxathiino[5,6-d]-1-benzoxepin derivatives

The 1,4-cycloaddition of sulfene to N,N-disubstituted (E)-4-aminomethylene-3,4-dihydro-1-benzoxepin-5(2H)-ones gave, generally in excellent yield, N,N-disubstituted 4-amino-3,4,5,6-tetrahydro-1,2-oxathiino-[5,6-d)-1-benzoxepin 2,2-dioxides, which are derivatives of the new heterocyclic system 1,2-oxathiino[5,6-d]-1-benzoxepin. This reaction did not occur only with the N,N-diphenylenaminone.