A result on sets,with applications to vector optimization

In this paper there is stated a result on sets in ordered linear spaces which can be used to show that some properties of the sets are inherited by their convex hulls under suitable conditions. As applications one gives a characterization of weakly efficient points and a duality result for nonconvex vector optimization problems.     

Symmetric Hilbert spaces arising from species of structures

Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some lsquo;one particle space’ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of symmetrization by building on Joyal's notion of a combinatorial species. Any such species F gives rise to an endofunctor of the category of Hilbert spaces with contractions mapping a Hilbert space to a symmetric Hilbert space with the same symmetry as the species F. A general framework for annihilation and creation operators on these spaces is developed, and compared to the generalised Brownian motions of R. Speicher and M. Bożejko. As a corollary we find that the commutation relation with admits a realization on a symmetric Hilbert space whenever f has a power series with infinite radius of convergence and positive coefficients. Received: 7 April 2000; in final form: 28 November 2000 / Published online: 19 October 2001     

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.     

Neue stellungsisomere reineckesalzähnliche Verbindungen mit Toluidinen

Zusammenfassung Es wurden eine Reihe von Substitutionsreaktionen mit entwässertem K₃[Cr(NCS)₆] und aromatischen Aminen, ohne Verwendung von Lösungsmitteln, durchgeführt. Es wurde beobachtet, da die sehr schwachen Basen mit p_K-Werten 14–16, wie die isomeren Mono- und Dinitro-aniline, die Anthranil- und Sulfanilsäuren, für diese Substitutionsreaktionen ungeeignet sind. Die Alkyl-anilinderivate, wie daso-, m- undp-Toluidin (p_K=10–11) bilden dagegen leicht reineckesalzähnliche Verbindungen: Amin· H[Cr(Toluidin)₂(NCS)₄]. Die Zusammensetzung der neuen Komplexanionen wurde bei einer Reihe von doppelten Umsetzungsreaktionen mit den Chlorhydraten einiger heterocyclischen Aminen festgestellt.Für die Klärung einiger Strukturfragen wurden spektrophotometrische Untersuchungen im UV und IR durchgeführt und die thermische Stabilität bzw. der Mechanismus des Pyrolysenvorganges auf thermogravimetrischem Wege verfolgt.

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Substitution reactions of anhydrous K₃[Cr(NCS)₆] with aromatic amines without applying of solvents were studied.It was observed, that the very weak bases (pK-values 14–16, e.g. isomeric mono- and dinitro-anilines, the anthranilic and sulfanilic acids) are unsuitable for substitution reactions. The alkylaniline derivates e.g.o-, m- andp-toluidine (pK=10–11) form easily reineckesalt analogous compounds: Amin· ·H[Cr(toluidine)₂(NCS)₄]·The formula of the 3 new complex anions: [Cr(toluidine)₂ (NCS)₄]- was established by preparative methods, with a series of double decomposition reactions, using chlorohydrates of some heterocyclic amines for this purpose. From spectroscopical investigations (UV and IR) some structural problems are resolved and discussed.The thermal stability and the mechanism of pyrolysis of these salts was studied by thermogravimetric analysis.

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Mit 8 Abbildungen     

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.     

Thermal behaviour of the homopolynuclear glyoxylate complex combinations with Cu(II) and Cr(III)

Homopolynuclear complexes of Cu(II) respectively Cr(III) with the glyoxylate dianion, C₂H₂O₄ ^2-, have been studied in non-isothermal regime in air and nitrogen. The results of the non-isothermal analysis performed for the synthesised complexes, Cu(C₂H₂O₄)·0.5H₂O, respectively [Cr₂(OH)₂(C₂H₂O₄)₂(OH₂)₄]·2H₂O, correlated with the results of the IR and TG analysis of the compounds obtained by thermal treatment from the initial complexes and the results of the GLC and XR analysis have led to the establishment of the thermal decomposition mechanisms for the two studied complexes. The decomposition mechanisms confirm the stoichiometric and structural formulae proposed for the two synthesised homopolynuclear complexes. This revised version was published online in July 2006 with corrections to the Cover Date.     

Isolated subgroups of finite abelian groups

Czechoslovak Mathematical Journal - We say that a subgroup H is isolated in a group G if for every x ∈ G we have either x ∈ H or 〈x〉 ∩ H = 1. We describe the set of...     

Existence of rank 3 vector bundles with given chern classes on homogeneous rational 3-folds

One proves that any rank 3 topological vector bundle on a homogeneous rational 3-fold has an algebraic structure. The proof uses extensions of ideals by rank 2 vector bundles. The paper also contains a construction of rank 3 vector bundles on 3-folds using extensions of ideals by rank 2 reflexive sheaves.     

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.