Deformations of arithmetically Cohen-Macaulay subvarieties of pn

We show that every arithmetically Cohen-Macaulay two-codimensional subscheme ofP ⁿ can be deformed to a reduced union of two-codimensional linear subvarieties. This problem (classical for curves with the name of Zeuthen problem) was solved for curves by F.Gaeta.     

Computation of the Maslov index and the spectral flow via partial signatures

Given a smooth Lagrangian path, both in the finite and in the infinite dimensional (Fredholm) case, we introduce the notion of partial signatures at each isolated intersection of the path with the Maslov cycle. For real-analytic paths, we give a formula for the computation of the Maslov index using the partial signatures; a similar formula holds for the spectral flow of real-analytic paths of Fredholm self-adjoint operators on real separable Hilbert spaces. As applications of the theory, we obtain a semi-Riemannian version of the Morse index theorem for geodesics with possibly conjugate endpoints, and we prove a bifurcation result at conjugate points along semi-Riemannian geodesics. To cite this article: R. Giambò et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Multilayered Cu–Ti deposition on silicon substrates for chemiresistor applications

Abstract

On the perspective to develop CuO–TiO₂ MOS, multilayered Cu and Ti thin layers were alternatively deposited on silicon wafers using 25?keV Ar?+?ion beam sputtering and, subsequently, oxidized by thermal annealing in air at 400?°C for 24?h. The deposited films have variable ratios of the Cu and Ti % at. One of the main goal is to obtain such multilayers avoiding the presence of Cu–Ti–O compounds. The samples were characterized in terms of composition (by RBS and SIMS analyses) and morphology (by AFM and SEM investigations). In particular, SIMS maps allows to observe the spatial distribution and thickness of each phase of the Cu/Ti multilayers, and further to observe Cu diffusion and mixing with Ti, as well as phase separation of CuO and TiO₂ in the samples. The reasons of this effect represent an open issue that has to investigated, in order to improve the MOS fabrication.     

Shape recognition of alkylammonium ions by 1,3-bridged calix[5]arene crown-6 ethers: endo- vs exo-cavity complexation

A series of tri-O-substituted 1,3-bridged calix[5]arene crown-6 ethers bearing alkyl, arylalkyl, alkoxyalkyl, and alkoxycarbonylmethyl residues at the lower rim and either (t)()Bu or H substituents at the upper rim have been synthesized. (1)H NMR studies have shown that p-tert-butylcalix[5]crowns, irrespective of the size and nature of their lower rim pendant groups, adopt preorganized conelike conformations, whereas p-H-calix[5]crowns with bulky substituents preferentially exist in solution as partial cone conformers (C(1) symmetry). Calix[5]crown derivatives behave as mono- or ditopic receptors for isomeric butylammonium ions, forming endo-cavity (inside the calixarene cup) and/or exo-cavity (at the crown ether moiety) 1:1 complexes according to the shape of the guest. These two binding modes can be clearly distinguished and monitored by (1)H NMR titration experiments.     

New Cyclophanes as Initiator Cores for the Construction of Dendritic Receptors: Host-guest complexation in aqueous solutions and structures of solid-state inclusion compounds

Cyclophanes 3 and 4 were prepared as initiator cores for the construction of dendrophanes (dendritic cydophanes) 1 and 2 , respectively, which mimic recognition sites buried in globular proteins. The tetra-oxy[6.1.6.1]paracyclophane 3 was prepared by a short three-step route (Scheme 1) and possesses a cavity binding site shaped by two diphenylmethane units suitable for the inclusion of flat aromatic substrates such as benzene and naphthalene derivatives as was shown by ¹H-NMR binding titrations in basic D₂O phosphate buffer (Table 1). The larger cyclophane 4 , shaped by two wider naphthyl(phenyl)methane spacers, was prepared in a longer, ten-step synthesis (Scheme 2) which included as a key intermediate the tetrabromocyclophane 5 . ¹H-NMR Binding studies in basic borate buffer in D₂O/CD₃OD demonstrated that 4 is an efficient steroid receptor. In a series of steroids (Table 1), complexation strength decreased with increasing substrate polarity and increasing number of polar substituents; in addition, electrostatic repulsion between carboxylate residues of host and guest also affected the binding affinity strongly. The conformationally flexible tetrabromocyclophane 5 displayed a pronounced tendency to form solid-state inclusion compounds of defined stoichiometry, which were analyzed by X-ray crystallography (Fig. 2). 1,2-Dichloroethane formed a cavity inclusion complex 5a with 1:1 stoichiometry, while in the 1:3 inclusion compound 5b with benzene, one guest is fully buried in the macrocyclic cavity and two others are positioned in channels between the Cyclophanes in the crystal lattice. In the 1:2 inclusion compound 5c , two toluene molecules penetrate with their aromatic rings the macrocyclic cavity from opposite sides in an antiparallel fashion. On the other hand, p-xylene (= 1,4-dimethylbenzene) in the 1:1 compound 5d is sandwiched between the cyclophane molecules with its two Me groups penetrating the cavities of the two macrocycles. In the 1:2 inclusion compound 5e with tetralin (= 1,2,3,4-tetrahydronaphthalene), both host and guest are statically disordered. The shape of the macrocycle in 5a – e depends strongly on the nature of the guest (Fig. 4). Characteristic for these compounds is the pronounced tendency of 5 to undergo regular stacking and to form channels for guest inclusion; these channels can infinitely extend across the macrocyclic cavities (Fig. 6) or in the crystal lattice between neighboring cyclophane stacks (Fig. 5). Also, the crystal lattice of 5c displays a remarkable zig-zag pattern of short Br…?O contacts between neighboring macrocycles (Fig. 7).     

Dendrophanes: Water-soluble dendritic receptors as models for buried recognition sites in globular proteins

Water-soluble dendritic cyclophanes (dendrophanes) of first ( 1 , 4 ), second ( 2 5 ), and third generation ( 3 6 ) with poly(ether amide) branching and 12, 36, and 108 terminal carboxylate groups, respectively, were prepared by divergent synthesis, and their molecular recognition properties in aqueous solutions were investigated. Dendrophanes 1 – 3 incorporate as the initiator core a tetraoxa[6.1.6.1]paracyclophane 7 with a suitably sized cavity for inclusion complexation of benzene or naphthalene derivatives. The initiator core in 4 – 6 is the [6.1.6.1]cyclo-phane 8 shaped by two naphthyl(phenyl) methane units with a cavity suitable for steroid incorporation. The syntheses of 1 – 6 involved sequential peptide coupling to monomer 9 , followed by ester hydrolysis (Schemes 1 and 4), Purification by gel-permeation chromatography (GPC; Fig. 3) and full spectral characterization were accomplished at the stage of the intermediate poly(methyl carboxylates) 10 – 12 and 23 – 25 , respectively. The third-generation 108-ester 25 was also independently prepared by a semi-convergent synthetic strategy, starting from 4 (Scheme 5). All dendrophanes with terminal ester groups were obtained in pure form according to the ¹³C-NMR spectral criterion (Figs, 1 and 5). The MALDI-TOF mass spectra of the third-generation derivative 25 (mol. wt. 19328 D) displayed the molecular ion as base peak, accompanied by a series of ions [M – n(1041 ± 7)]⁺, tentatively assigned as characteristic fragment ions of the poly(ether amide) cascade. A similar fragmentation pattern was also observed in the spectra of other higher-generation poly(ether amide) dendrimers. Attempts to prepare monodisperse fourth-generation dendrophanes by divergent synthesis failed. ¹H-NMR and fluorescence binding titrations in basic aqueous buffer solutions showed that dendrophanes 1 – 3 complexed benzene and naphthalene derivatives, whereas 4 – 6 bound the steroid testosterone. Complexation occurred exclusively at the cavity-binding site of the central cyclophane core rather than in fluctuating voids in the dendritic branches, and the association strength was similar to that of the complexes formed by the initiator cores 7 and 8 , respectively (Tables 1 and 3). Fluorescence titrations with 6-(p-toluidino)naphthalene-2-sulfonate as fluorescent probe in aqueous buffer showed that the micropolarity at the cyclophane core in dendrophanes 1 - 3 becomes increasingly reduced with increasing size and density of the dendritic superstructure; the polarity at the core of the third-generation compound 3 is similar to that of EtOH (Table 2). Host-guest exchange kinetics were remarkably fast and, except for receptor 3 , the stabilities of all dendrophane complexes could be evaluated by ¹H-NMR titrations. The rapid complexation-decomplexation kinetics are explained by the specific attachment of the dendritic wedges to large, nanometer-sized cyclophane initiator cores, which generates apertures in the surrounding dendritic superstructure.     

Aldol condensations over reconstructed Mg-Al hydrotalcites: structure-activity relationships related to the rehydration method

Two different rehydration procedures in the liquid or gas phase have been applied to reconstruct mixed oxides derived from calcined hydrotalcite-like materials to be used as catalysts for aldol condensation reactions. The as-synthesized hydrotalcite, its decomposition product, as well as the reconstructed solids upon rehydration were characterized by XRD, N(2) adsorption, He pycnometry, FTIR, SEM, TEM, (27)Al MAS-NMR and CO(2)-TPD (TPD=temperature-programmed desorption). Compared to the Mg-Al mixed oxide rehydrated in the gas phase (HT-rg), that rehydrated in the liquid phase (HT-rl) exhibits a superior catalytic performance with respect to the aldol condensation of citral with ketones to yield pseudoionones and in the self-aldolization of acetone. The textural properties of HT-rl and HT-rg differ strongly and determine the catalytic behavior. A memory effect led to a higher degree of reconstruction of the lamellar structure when the mixed oxide was rehydrated in the gas phase rather than in the liquid phase, although liquid-phase rehydration under fast stirring produced a surface area that was 26 times greater. This contrasts to typical statements in the literature claiming a higher degree of reconstruction in the presence of large amounts of water in the medium. CO(2)-TPD shows that the number of OH(-) groups and their nature are very similar in HT-rg and HT-rl, and cannot explain the markedly different catalytic behavior. Accordingly, only a small fraction of the available basic sites in the rehydrated samples is active in liquid-phase aldol condensations. Our results support the model in which only basic sites near the edges of the hydrotalcite platelets are partaking in aldol reactions. Based on this, reconstructed materials with small crystallites (produced by exfoliation during mechanical stirring), that is, possessing a high external surface area, are beneficial in the reactions compared to larger crystals with a high degree of intraplatelet porosity.     

Enantiomeric resolution of anti-HIV agents on a cellulose derivative chiral stationary phase

Summary Anti-HIV enantiomeric 1H, 3H-thiazolo[3, 4-a] benzimidazoles have been stereospecifically analyzed by elution on a column of cellulose tris-(4-methyl-phenylbenzoate)ester adsorbed on macroporous silica (Chiralcel^R OJ).The enantiomeric resolution of the compounds examined is linked to a complex and competitive contribution of different factors.     

On the stereochemistry of photoaddition between α,β-unsaturated ketones and olefins—II

Some years ago an empirical rule, which allows the prediction of product stereochemistry in cis-photocycloaddition reactions of α,β-unsaturated ketones and olefins was tentatively proposed. Several additional examples, both selected from the literature and synthesized in our laboratory, seem to strengthen the validity of the rule.     

Compactifications,realcompletions and spectral structures

Summary We give an intrinsic (set theoretical) method to obtain all realcompletions of a Tychonoff space X. It is based on the concept of a spectral structure. Every realcompletion of the space can be obtained as a space of terminal clusters relative to an appropriate spectral structure on X. Various applications of this concept are then given. For example we may characterize those spectral structures which yield the realcompletions between X and X, or which yield spaces that are realcomplete (that is, realcompact), or compact or pseudocompact or Lindelöf. We also determine the class K of compactifications K of X for which X will be real closed in K for every K K.Here we continue the use of the word realcompletion (see [2]) in place of real-compactification. As many investigations have shown and as the present article reinforces, the former is more appropriate than the latter.