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.     

Unique description of chemical structures based on hierarchically ordered extended connectivities (HOC procedures). V. New topological indices,ordering of graphs,and recognition of graph similarity

The vertex numbering obtained by application of the HOC algorithm can be converted into two sequences of numbers: If each vertex starting with vertex 1 is only counted once, the sums of numberings of adjacent vertices form sequence S_i (i = 1?N), while the sums of S_i values form sequence M_i (i = 1?N). These two sequences can be used for (i) two new topological indices, ?? and ??, the latter being of extremely low degeneracy, and the former correlating with boiling points of alkanes; (ii) a criterion based on sequence S_i for ordering graphs which possess the same number N of vertices; and (iii) a quantitative measure, also based on sequence S_i, for appreciating the similarity or dissimilarity of pairs of graphs. Comparisons with other topological indices, ordering criteria, and similarity measures for graphs show that the newly devised procedures compare favorably with those known previously.     

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.     

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.     

Unique description of chemical structures based on hierarchically ordered extended connectivities (HOC procedures). III. Topological,chemical, and stereochemical coding of molecular structure

A topological code is devised on the basis of the unique topological representation of the molecule described in the preceding two parts of this series.¹ By adding to the topological code additional chemical information on atoms and/or bonds, as well as stereochemical information, a chemical and respectively stereochemical code (SHOC) are also constructed. The advantages of the new linear codes are that they are convention-free codes, preserving the symmetry of molecular graph, and easily implemented either manually or by means of computer programs. By concentrating all topological, chemical, and stereochemical information, our code (SHOC) is more compact and more general than the codes based on several separate lists.     

Partitioning of <Emphasis Type="Italic">π</Emphasis> -electrons in rings of polycyclic conjugated hydrocarbons: Part 6. Comparison with other methods for estimating the local aromaticity of rings in polycyclic benzenoids

By adopting the convention that shared double bonds in polycyclic conjugated hydrocarbons contribute with one -electron and unshared ones with two -electrons, a partition of -electrons in each ring (-electron content, EC) can be obtained by averaging over all Kekulé structures, which are assumed to have equal weights. This affords a simple measure of local aromaticity that is comparable with other such local aromaticity indices in polycyclic benzenoids.     

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.