On the Rees algebra of certain codimension two perfect ideals

 Suppose ? is a set of arbitrary number of smooth points in ℙ² its defining ideal. In this paper, we study the Rees algebras of the ideals generated by I _t , t ≥α. When the points of ? are general, we give a set of defining equations for the Rees algebra . When the points of ? are arbitrary, we show that for all t≫ 0, the Rees algebra is Cohen-Macaulay and its defining ideal is generated by quadratics. A cohomological characterization for arithmetic Cohen-Macaulayness of subvarieties of a product space is also given. Received 4 April 2001     

Local mean field models of uniform to nonuniform density fluid-crystal transitions

We investigate the existence of nontranslation invariant (periodic) density profiles, for systems interacting via translation invariant long-range potentials, as minimizers of local mean field free energy functionals. The existence of a second-order transition from a uniform to a nonuniform density at a specified temperature is proven for a class of model systems.     

Immunological and biochemical evidence that blepharismin is not a prosthetic group

A polyclonal, multispecific antiserum was raised against a whole 3[(3-cholamidopropyl)-dimethylammonio]-1-propanesulfonate-extract of nonirradiated Blepharisma japonicum cells. It was used to reveal the composition of solutions that were hypothesized to contain the photoreceptor of the ciliate. A Bio-Gel A 1.5 m fine column chromatography of the extract allowed recovery of a single elution peak isolated by recording the 580 nm light absorbance. Fused-rocket immunoelectrophoresis of this material revealed a large number of > 300 kDa coeluted proteins. Blepharismin-rich material with a molecular mass of approximately 50 kDa, consisting of at least nine proteins was obtained when the same extract underwent preparative isoelectric focusing before column chromatography separation. Purification of the pigment obtained from light-exposed cells gave blepharismin-rich material with a molecular weight of approximately 200 kDa. Comparison of the materials obtained under the same conditions, either from the dark-kept or light-irradiated cells, by means of pore-gradient electrophoresis confirmed that proteins present in the two preparations were different. It revealed only a very small amount, if any, of proteins in the chromatography fractions with the highest absorbance at 600 nm. Results are discussed on the basis of the hypothesis that a specific blepharismin-binding protein does not exist in the protozoan.     

Calculation of Franck-Condon factors including anharmonicity: simulation of the C2H4+X2B3u<--C2H4X1A(g) band in the photoelectron spectrum of ethylene

Our new simple method for calculating accurate Franck-Condon factors including nondiagonal (i.e., mode-mode) anharmonic coupling is used to simulate the C2H4+X2B3u<--C2H4X1A(g) band in the photoelectron spectrum. An improved vibrational basis set truncation algorithm, which permits very efficient computations, is employed. Because the torsional mode is highly anharmonic it is separated from the other modes and treated exactly. All other modes are treated through the second-order perturbation theory. The perturbation-theory corrections are significant and lead to a good agreement with experiment, although the separability assumption for torsion causes the C2D4 results to be not as good as those for C2H4. A variational formulation to overcome this circumstance, and deal with large anharmonicities in general, is suggested.     

Complex formation of isocytosine tautomers with PdII and PtII

Isocytosine (ICH) exists in solution as two major tautomers, the keto form with N1 carrying a proton (1a) and the keto form with N3 being protonated (1b). In water, 1a and 1b exist in equilibrium with almost equal amounts of both forms present. Reactions with a series of Pd(II) and Pt(II) am(m)ine species such as (dien)Pd(II), (dien)Pt(II), and trans-(NH(3))(2)Pt(II) reveal, however, a distinct preference of these metals for the N3 site, as determined by (1)H NMR spectroscopy. Individual species have been identified by the pD dependence of the ICH resonances. pK(a) values (calculated for H(2)O) for deprotonation of the individual tautomers complexes are 6.5 and 6.4 for the N3 linkage isomers of dienPd(II) and dienPt(II), respectively, as well as 6.2 and 6.0 for the N1 linkage isomers. The dimetalated species [(dienM)(2)(IC-N1,N3)](3+) (M = Pd(II) or Pt(II)) are insensitive over a wide range of pD. The crystal structure analysis of [(dien)Pd(ICH-N3)](NO(3))(2) is reported. Ab initio calculations have been performed for tautomer compounds of composition [(NH(3))(3)Pt(ICH)](2+), cis- and trans-[(NH(3))(2)PtCl(ICH)](+), as well as trans-[(NH(3))(2)Pt(ICH)(2)](2+). Without exception, N3 linkage isomers are more stable, in agreement with experimental findings. As to the reasons for this binding preference, an NBO (natural bond orbital) analysis for [(NH(3))(3)Pt(ICH-N3)](2+)strongly suggests that intramolecular hydrogen bonding between trans-positioned NH(3) ligands and the two exocyclic groups of the ICH is of prime importance. The calculations furthermore show a marked pyramidalization of the NH(2) group of ICH in the complex once the heterocyclic ligand forms a dihedral angle <90 degrees with the Pt coordination plane.     

Electrochemical oxidation of aliphatic amines and their attachment to carbon and metal surfaces

The electrochemical oxidation of aliphatic amines (primary, secondary, and tertiary) has been investigated by cyclic voltammetry and preparative electrolysis. The oxidation mechanisms have been established, and the lifetimes of the radical cations have been measured for secondary and tertiary amines. These results have been put in parallel with the attachment of amines to glassy carbon, Au, and Pt electrodes by cyclic voltammetry, X-ray photoelectron spectroscopy (XPS), and infrared reflection-absorption spectroscopy (IRRAS). It is then possible to show that it is not the radical cation but the radical obtained after the deprotonation which reacts with the electrode surface. XPS results also point to the existence of a covalent bond between Au or Pt and the organic moiety.     

Synthesis of 4H-3,1-benzoxazines, quinazolin-2-ones, and quinoline-4-ones by palladium-catalyzed oxidative carbonylation of 2-ethynylaniline derivatives

An effective and straightforward approach to the synthesis of 4H-3,1-benzoxazines 3 and 4, quinazolin-2-ones 5, and quinoline-4-one derivatives 6 and 7 is provided by palladium-catalyzed cyclization-alkoxycarbonylation of variously substituted 2-(trimethylsilanyl)ethynylaniline amide or urea derivatives 2. Reactions are carried out in 7:1 MeCN/MeOH at 65 or 75 degrees C in the presence of catalytic amounts of 10% Pd/C in conjunction with Bu(4)NI and KF and under 2.4 MPa of a 3:1 mixture of CO and air. Anti and syn 6-exo-dig cyclization modes account for the formation of the two stereoisomers. Isomerization of the vinylpalladium intermediate may occur as well. Formation of a double carbonylation product 7r and of a gem-dimethoxycarbonylation product 6s, whose structures have been determined by X-ray diffraction analysis, is justified through an unusual type of rearrangement.     

DABCO-directed self-assembly of bisporphyrins (DABCO=1,4-diazabicyclo[2.2.2]octane)

Three isomeric zinc bisporphyrins have been prepared by covalently linking together two aminoporphyrins with an isophthalic acid derivative. The porphyrins differ in the substitution pattern on the meso phenyl groups, that is, ortho, meta, or para. Titrations carried out by UV-visible and 1H NMR spectroscopy have been used to map out the stabilities and the stoichiometries of the complexes formed with 1,4-diazabicyclo[2.2.2]octane (DABCO) in chloroform. The ortho- and meta-substituted bisporphyrins form 1:1 intramolecular sandwich complexes. The para-substituted bisporphyrin cannot adopt the cofacial conformation required for this type of complex and forms a higher order 2:2 intermolecular assembly, which is stable over a wide range of DABCO concentrations.