The pillar of best efficiency

Let us imagine having to design an elastic vertical pillar that must transmit an axial compressive load. We know the extents of the upper and of the lower cross-sections of the pillar and its longitudinal length, but the profile of the lateral surface is arbitrary. We want to find the shape of this lateral surface in order that the distibution of the normal stresses at the bottom is as uniform as possible. A partial answer to the problem is given in two-dimensional elastostatics.     

Sugli insiemi di grandezze meccaniche derivate

Riassunto Si dà innanzi tutto un cenno del procedimento mediante il quale un insieme di grandezze meccaniche dotate di misura positiva può essere derivato da altri insiemi dello stesso tipo, per mezzo di una funzione generatrice che dipende dalle misure delle grandezze. Si stabilisce quindi la condizione necessaria e sufficiente che deve essere soddisfatta dalla funzione generatrice affinchè essa dia luogo ad insiemi indipendenti dalla scelta delle unità per le grandezze da cui sono derivati. Le soluzioni di un'equazione funzionale forniscono l'espressione di tutte le funzioni generatrici che soddisfano la precedente condizione di invarianza, insieme ad una condizione necessaria riguardante la osservabilità delle grandezze derivate. La trattazione è infine estesa alle grandezze dotate di misura algebrica.

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Summary An outline is first given of the process which is followed to derive a set of mechanical quantities with positive measure from other sets of the same type, by means of a generating function depending upon the measures. The necessary and sufficient condition is then found which must be satisfied by the generating function, to give rise to sets independent from the units chosen for the quantities from which they are derived. The solutions of a functional equation give the expression of all the generating functions which satisfy the above invariance condition, together with a necessary condition concerning the observable character of the derived quantities. The theory is finally extended to quantities with algebraic measures.

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A Dario Graffi nel suo 70^o compleanno

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Entrata in Redazione il 28 giugno 1975.     

Carbon 13 NMR spectra of pyridylbenz-X-azoles

The ¹³C nmr spectra of a series of pyridylbenzimidazoles and benzoxazoles and of their quaternary salts have been determined. The mutual effects of the two heterocyclic systems and the effect of the quaternization have been discussed. The results evidence the existence of some interactions between benzimidazole and pyridine moieties.     

Metal complexes of 2-(2′-or 8′-quinolyl)benzimidazoles and benzothiazoles

Summary The copper(II), cobalt(II) and nickel(II) chloride and bromide complexes with the ligands 2-(2-quinolyl)-benzimidazole (qbi), 2-(4-methyl-2-quinolyl)benzimidazole (mqbi), 2-(4-methyl-8-quinolyl)benzothiazole (m'q'bt) have been prepared and characterized by analytical methods, magnetic measurements as well as by electronic absorption, e.s.r. and far i.r. spectra. Complexes of various stoichiometries have been isolated, namely MLX₂ (all cobalt complexes with exception of the bromide qbi complex; the chloride and bromide nickel m'q'bt and mq'bt complexes), ML₂X₂ (M=Co,L=qbi and X=Br; M=Ni, L=mqbi, X=Cl or Br, M=Ni, L=qbi, X=Cl) and ML₃X₂(M=Ni, L=qbi or mqbi, X=Br). The cobalt ion has a distorted tetrahedral N₂X₂ coordination in all the CoLX₂ complexes, whereas Co(qbi)₂Br₂ is six-coordinate. The following conclusions may be drawn for the nickel complexes: in those with the 11 metal-to-ligand molar ratio the metal ion is four-or five-coordinate; in those with the 12 and 13 ratios the metal ion is hexa-coordinate, being essentially bound to four nitrogen atoms with halogens, oxygens from water or methanol or nitrogen atoms (from the third ligand) occupying the axial positions.     

Stepwise electron-induced demolition of the Ni-I σ-bond in complexes with tetradentate tripodal ligands: A theoretical rationalization of structural and electrochemical results

The X-ray structural analysis of the compound [(pp₃)Nil]BPh₄ (complex d), pp₃ = P(CH₂CH₂PPh₂)₃, is presented. The complex cation has an almost regular trigonal bipyramidal geometry (TBP) with distances Ni-I and Ni-P_ax of 2.546(2) and 2.142(3) Å, respectively. This structure completes a series of strictly related nickel complexes, namely [(np₃)Nil]I, complex a; (np₃)Nil, complex b; (np₃)Ni, complex c; [(pp₃)NiHClO₄), complex e; [np₃ = N(CH₂CH₂PPh₂)₃] The complexes are redox derivatives [Ni(II), Ni(I), Ni(O)] that can be isolated via chemistry and/or electrochemistry. In the solid state complexes c and e have a trigonal pyramidal (TP) structure, whereas, electrochemical measurements suggest that in solution the TBP structure with a very elongated Ni-I bond can also have a finite lifetime. EHMO calculations offer a satisfying interpretation of the main structural trends in complexes a e, in particular, those relative to axial bond stretching, and clarify the different roles of phosphine vs. the amine axial donor. Moreover, the correlation is discussed between the electrode potentials and the nature of the Ni-I ^* MO that accepts or releases the electrons exceeding thed ⁸ configuration of Ni(II).     

2h-1p Cl calculations of ionization potentials of small molecules: Corrections to the koopmans theorem

2h-1p Cl calculations of ionization potentials have been performed on N₂, F₂, HNO, HOF, trans-N₂H₂, cis-N₂H₂, H₂NN, O₃, F₂O and C₂N₂, both with ground state and relaxed orbitals. Several inversions present at the KT level are recovered and a good qualitative agreement with experimental values and results of accurate calculations is achieved. Interaction with the 2h-1p configurations is found to be responsible for the major correlation effects.     

Synthesis and characterization of zinc oxide nanoparticles: application to textiles as UV-absorbers

We report the synthesis and characterization of nanosized zinc oxide particles and their application on cotton and wool fabrics for UV shielding. The nanoparticles were produced in different conditions of temperature (90 or 150 °C) and reacting medium (water or 1,2-ethanediol). A high temperature was necessary to obtain small monodispersed particles. Fourier transformed infrared spectroscopy (FTIR), transmission electron microscopy (TEM), and X-ray powder diffractometry (XRD) were used to characterize the nanoparticles composition, their shape, size and crystallinity. The specific surface area of the dry powders was also determined. ZnO nanoparticles were then applied to cotton and wool samples to impart sunscreen activity to the treated textiles. The effectiveness of the treatment was assessed through UV–Vis spectrophotometry and the calculation of the ultraviolet protection factor (UPF). Physical tests (tensile strength and elongation) were performed on the fabrics before and after the treatment with ZnO nanoparticles.