Subbundles of maximal degree of the normal bundle of algebraic space curves almost complete intersection of special type

Summary LetX⊂P ³ be an irreducible smooth curve which is not a complete intersection. The main result of this paper shows that whenX is an a.c.i. of special type, i.e. its homogeneous ideal is generated by three polynomial of the same degreem, and additionallym>2, the subbundles of maximal degree of the normal bundle ofX inP ³ correspond to the singular points of maximal multiplicity of a plane curve which is the image ofX by a map (the linear system of the surfaces of minimal degree throughX). In particular this normal bundle is stable. The initial case of this family of curves, i.e. form=3, has been studied by E. Ballico-Ph. Ellia with different methods.

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Riassunto SiaX⊂P ³ una curva irriducibile e liscia che non è una completa intersezione. Il risultato principale di questa Nota mostra che quandoX è una almost completa intersezione di tipo speciale, cioè il suo ideale omogeneo è generato minimamente da 3 polinomi dello stesso gradom, e, inoltre,m>2, i sottofibrati di grado massimo del fibrato normale diX inP ³ corrispondono ai punti singolari di molteplicità massima di una curva piana che è l’immagine diX tramite una mappa (il sistema lineare delle superficie di grado minimo passanti perX). In particolare questo fibrato normale è stabile. Il caso iniziale di questa famiglia di curve, i.e. perm=3, è stato studiato da E. Ballico-Ph. Ellia con differenti metodi.

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This research is supported by GNSAGA (Italy).

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The main results of this paper have been the object of a talk at the meeting on ?Curves in Projective Space? held at Rocca di Papa in june 1985.     

Topological indices for molecular fragments and new graph invariants

Whereas the internal fragment topological index (IFTI) is calculated in the normal manner as for any molecule, the external fragment topological index (EFTI) is calculated so as to reflect the interaction between the excised fragment F and the remainder of the molecule (G-F). For selected topological indices (TIs), a survey of EFTI values, formulas and examples is presented. Some requirements as to the fragment indices are formulated and examined. In the discussion of the results, it is shown that for some TIs regularities exist in the dependence of EFTI values upon the branching of fragment F, or upon the marginal versus central position of the fragment F in the graph G. New vortex invariants can be computed as EFTI values for one-atom fragments over all graph vertices; by iteration, it is in principle possible to devise an infinite number of now vertex invariants.     

Development of novel antioxidants: design,synthesis, and reactivity

We are attempting to develop novel synthetic antioxidants aimed at retarding the effects of free-radical induced cell damage. In this paper we discuss the design strategy and report the synthesis of seven novel antioxidants, including six catechols and a benzylic phenol. The bond dissociation enthalpy (BDE) for the most active (weakest) OH bond in each molecule was calculated by theoretical methods, as well as the BDE for the semiquinone radical. Reaction rates with the nitrogen-centered free radical DPPH(*) were measured in ethyl acetate. The log of k(DPPH) for bimolecular reaction correlated well with the primary BDE. The correlation between rate constants and calculated BDEs shows that the BDE is a good predictor of antioxidant activity with DPPH(*), suggesting that our design criteria are useful and that these compounds should undergo further testing in cell cultures and in animal models.     

Heterogeneous oxidation of pyrimidine and alkyl thioethers in ionic liquids over mesoporous Ti or Ti/Ge catalysts

Heterogeneous catalytic oxidation of a series of thioethers (2-thiomethylpyrimidine, 2-thiomethyl-4,6-dimethyl-pyrimidine, 2-thiobenzylpyrimidine, 2-thiobenzyl-4,6-dimethylpyrimidine, thioanisole, and n-heptyl methyl sulfide) was performed in ionic liquids by using MCM-41 and UVM-type mesoporous catalysts containing Ti, or Ti and Ge. A range of triflate, tetrafluoroborate, trifluoroacetate, lactate and bis(trifluoromethanesulfonyl)imide-based ionic liquids were used. The oxidations were carried out by using anhydrous hydrogen peroxide or the urea-hydrogen peroxide adduct and showed that ionic liquids are very effective solvents, achieving greater reactivity and selectivity than reactions performed in dioxane. The effects of halide and acid impurities on the reactions were also investigated. Recycling experiments on catalysts were carried out in order to evaluate Ti leaching and its effect on activity and selectivity.     

Gas-phase structures and mass spectra of binary pentafluorides

Most known non-radioactive pentafluorides have been examined by molecular-beam mass spectrometry and by the deflection of molecular beams in inhomogeneous electric fields. Extensive association of the vapors occurs for all but the lighter pentafluorides and the interhalogens. The interhalogen pentafluorides are strongly polar, consistent with the accepted C_4v symmetry. The transition-metal and Group V pentafluorides are all non-polar, except VF₅ and CrF₅ for which temperature-dependent polarity is observed. However, uncertainty exists as to whether these observations are applicable to monomeric pentafluorides in all cases. Mass-spectral cracking patterns are presented for all species.     

Janus-type isopropyl groups revealed by 1H-NMR spectra of alkylpyridines with lanthanide shift reagents (LSR)

Two Isomeric pyridines were designed and prepared : 2-isopropyl-4,5,6-trimethyl-(3) and 2-isopropyl-3,4,6-trimethyl-pyridine (7); the latter, with a buttressed isopropyl, leads to much lower induced shifts by Eu(dpm)₃ and Pr(dpm)₃ than the former, owing to the conformation in which the Janus-type iPr group how to the LSR a t-butyl-like face.     

Graph-theoretical analysis of the bonding topology in polyhedral organic cations

It is shown that in several cases where planar delocalisation in organic cations would result in the formation of an anti-aromatic system, polyhedral delocalisation is the form of bonding actually preferred. This explains, for instance, why organic cations in such cases adopt cage-like structures. A full graph-theoretical analysis, similar to one previously published¹² for polyhedral boranes, carboranes and metal clusters, indicates that the nido structure for (CH)₅⁺ may readily be accounted for. Moreover, in the case of the dication (CH)₆²⁺ the fact that its energy minimum also corresponds to a nido structure is explained. In fact, no closo- or arachno-type structures appear to be possible for organic cations. A number of structural predictions concerning these species are given in the conclusion.     

Gear effect—10 : Conformational aspects of the positive or negative buttressing effects of methyl groups: polymethylpyridines

The effect of the shape of a methyl group on reactivity, which cannot be accounted for by considering a methyl group as a spherical substituent with the appropriate van der Waals radius, was considered in kinetics of alkylalion of substituted pyridines and barriers to rotation and ground state conformations of an isopropyl group attached to a planar framework. The perturbation of a methyl group by an o-methyl group is accounted for by a unique conformational explanation which involves the polyhedral shape of the methyl group.     

A Comparative Loading and Release Study of Vancomycin from a Green Mesoporous Silica

Since its first use as a drug delivery system, mesoporous silica has proven to be a surprisingly efficient vehicle due to its porous structure. Unfortunately, most synthesis methods are based on using large amounts of surfactants, which are then removed by solvent extraction or heat treatment, leading to an undesired environmental impact because of the generated by-products. Hence, in the present study, we followed the synthesis of a silica material with a wormhole-like pore arrangement, using two FDA-approved substances as templates, namely Tween-20 and starch. As far as we know, it is the first study using the Tween-20/starch combo as a template for mesoporous silica synthesis. Furthermore, we investigated whether the obtained material using this novel synthesis had any potential in using it as a DDS. The material was further analyzed by XRD, TEM, FT-IR, N₂ adsorption/desorption, and DLS to investigate its physicochemical features. Vancomycin was selected as the active molecule based on the extensive research engaged towards improving its bioavailability for oral delivery. The drug was loaded onto the material by using three different approaches, assuming its full retention in the final system. Thermal analysis confirmed the successful loading of vancomycin by all means, and pore volume significantly decreased upon loading, especially in the case of the vacuum-assisted method. All methods showed a slower release rate compared to the same amount of the pure drug. Loadings by physical mixing and solvent evaporation released the whole amount of the drug in 140 min, and the material loaded by the vacuum-assisted method released only 68.2% over the same period of time, leading us to conclude that vancomycin was adsorbed deeper inside the pores. The kinetic release of the three systems followed the Higuchi model for the samples loaded by physical mixing and vacuum-assisted procedures, while the solvent evaporation loading method was in compliance with the first-order model.     

All-Polymer Piezo-Composites for Scalable Energy Harvesting and Sensing Devices

Silicone elastomer composites with piezoelectric properties, conferred by incorporated polyimide copolymers, with pressure sensors similar to human skin and kinetic energy harvester capabilities, were developed as thin film (<100 micron thick) layered architecture. They are based on polymer materials which can be produced in industrial amounts and are scalable for large areas (m²). The piezoelectric properties of the tested materials were determined using a dynamic mode of piezoelectric force microscopy. These composite materials bring together polydimethylsiloxane polymers with customized poly(siloxane-imide) copolymers (2–20 wt% relative to siloxanes), with siloxane segments inserted into the structure to ensure the compatibility of the components. The morphology of the materials as free-standing films was studied by SEM and AFM, revealing separated phases for higher polyimide concentration (10, 20 wt%). The composites show dielectric behavior with a low loss (<10⁻¹) and a relative permittivity superior (3–4) to pure siloxane within a 0.1–10⁶ Hz range. The composite in the form of a thin film can generate up to 750 mV under contact with a 30 g steel ball dropped from 10 cm high. This capability to convert a pressure signal into a direct current for the tested device has potential for applications in self-powered sensors and kinetic energy-harvesting applications. Furthermore, the materials preserve the known electromechanical properties of pure polysiloxane, with lateral strain actuation values of up to 6.2% at 28.9 V/μm.