Graphical operations on projective spaces

Motivated by the work of Crapo and Rota [6] on the lifting of a projective complex, we introduce a class of invariant operations associated to integral-weighted graphs, which we call graphical operations. Such operations generalize the sixth harmonic of a quadranguler set on a projective line. We determine the expansion of the graphical operations in terms of multi-linear bracket polynomials in a Grassmann-Cayley algebra. Reducibility and compositions of such invariant operations are also investigated with a number of examples.Supported by Courant Instructorship, New York University.     

Microchemical Investigation of Archaeological Copper Based Artefacts Disclosing an Ancient Witness of the Transition from the Value of the Substance to the Value of the Appearance

In many Italian archaeological sites dated between the sixth and third centuries BC, unworked lumps of Cu-based materials are sometimes found, the so called Aes Rude, which according to archaeological considerations were appreciated as currency, as a medium of exchange and as a form of saving. The microchemical investigation of these ancient artefacts discloses their nature as apparently not usable for any functional applications or possible use. Indeed, Aes Rude resemble ordinary copper material, but microchemical results indicate that they are constituted by highly ferruginous leaded copper, making them useless for producing other metal objects by means of casting or hot and cold working. Notwithstanding this intrinsic negative feature, the production of these intractable Cu-based alloys was deliberately carried out to maximise the process yield in terms of produced metal from an impure and unselected metal ore by tailoring the smelting process parameters. With these considerations in mind, the microchemical investigation of these ancient iron–copper alloys gives evidence of the passage from the acceptance of an artefact value based on its true nature or potential use to the acceptance of the value based only on its appearance or form irrespective of its present or future use. This information could contribute to a better understanding of the evolution of human thought and economic and social interactions.     

An alternative for moduli stabilisation

The one-loop vacuum energy is explicitly computed for a class of perturbative string vacua where supersymmetry is spontaneously broken by a T-duality invariant asymmetric Scherk–Schwarz deformation. The low-lying spectrum is tachyon-free for any value of the compactification radii and thus no Hagedorn-like phase-transition takes place. Indeed, the induced effective potential is free of divergence, and has a global anti-de Sitter minimum where geometric moduli are naturally stabilised.     

Thermal reactions of tributyltin hydride with alpha-azido esters: unexpected intervention of tin triazene adducts under both nonradical and radical conditions

Thermal reaction of various alpha-azido esters with Bu(3)SnH in refluxing benzene results in smooth production of 3-(tributylstannyl)-1-triazene adducts affording cyclized 1,2,3-triazol-4-ones in preference to reduced amines and thence provides a new useful method for the preparation of these triazole derivatives. In the presence of AIBN the occurrence of triazene products still remains important or even exclusive and, consequently, generation of the expected stannylaminyl radicals is seriously limited. With 2-azidomalonates and alpha-azido-beta-keto esters stannyltriazenes can similarly occur in the absence of the radical initiator, but in the latter cases the ensuing triazenes undergo preferential cyclization onto the ketone moiety to give reactive hydroxytriazolines. Contrary to alpha-azido esters, in the presence of AIBN alpha-azido-beta-keto esters as well as azidomalonates give rise only to the usual stannylaminyl radicals. A possible explanation for the different behavior of the mono- and dicarbonyl azides in the presence of AIBN is put forward.     

Intramolecular cyclization of acyl radicals onto the azido group: a new radical approach to cyclized lactams

[reaction: see text] Aryl- and alkyl-derived azidoacyl radicals, generated from thiolesters by intramolecular homolytic substitution at the sulfur, can undergo five- and six-membered cyclization onto the azido moiety to give cyclized lactams.     

Traceless solid-phase synthesis of 2,4,6-chlorodiamino and triaminopyrimidines

An effective traceless solid-phase synthesis of chloro-diaminopyrimidines via an amino-de-chlorination reaction of polymer-bound 4-alkoxycarbonylamino-2,6-dichloropyrimidines has been developed. After release from the polymer the target molecules were obtained in good to excellent purity, although with modest regiocontrol. Further reaction of solid-supported N-alkoxycarbonyl-chloro-diaminopyrimidines with secondary amines afforded triaminopyrimidines in good purity under mild conditions, whereas less nucleophilic primary amines did not perform well under the conditions explored so far.     

Voltammetric Detection of Free Sulfhydryl Compounds in Food Flours

Cyclic voltammetry has been applied to the rapid measurement of free SH‐compounds in food flours samples. The protocol is based on the electrochemical adaptation of the Ellman's test, where the DTNB reacts with SH‐compounds present in food flour extracts, resulting in the equimolar production of the electroactive compound TNBA which, in turns, reacts with phenylendiamine. The reaction is found to provide an analytical signal from which to quantify indirectly free sulfhydryl compounds in flours extracts.