Aldo Cossu’s Work in Finite Geometry

A survey of the contributions of Aldo Cossu in finite geometry is given. Dedicated to the memory of Professor Aldo Cossu     

On Intersection Problem for Perfect Binary Codes

The main result is that to any even integer q in the interval 0 ≤ q ≤ 2^{n+1-2log(n+1)}, there are two perfect codes C₁ and C₂ of length n = 2^m − 1, m ≥ 4, such that |C₁ ∩ C₂| = q.     

One-pot sequences of reactions with sol-gel entrapped opposing reagents: an enzyme and metal-complex catalysts

We extend our sol-gel methodology of one-pot sequences of reactions with opposing reagents to an enzyme/metal-complex pair. Sol-gel entrapped lipase and sol-gel entrapped RhCl[P(C(6)H(5))(3)](3) or Rh(2)Co(2)(CO)(12) were used for one-pot esterification and C-C double bond hydrogenation reactions, leading to saturated esters in good yields. When only the enzyme is entrapped, the homogeneous catalysts quench its activity and poison it. Thus, when 10-undecenoic acid and 1-pentanol were subjected in one pot to the entrapped lipase and to homogeneously dissolved RhCl[P(C(6)H(5))(3)](3) under hydrogen pressure, only 7% of the saturated 1-pentyl undecanoate was obtained. The yield jumped 6.5-fold when both the enzyme and the catalyst were immobilized separately in silica sol-gel matrixes. Similar one-pot esterifications and hydrogenations by sol-gel entrapped lipase and heterogenized rhodium complexes were carried out successfully with the saturated nonoic, undecanoic, and lauric acids together with several saturated and unsaturated alcohols. The use of (S)-(-)-2-methylbutanol afforded an optically pure ester. The heterogenized lipase is capable of inducing asymmetry during esterification with a prochiral alcohol. Both the entrapped lipase and the immobilized rhodium catalysts can be recovered simply by filtration and recycled in further runs without loss of catalytic activity.     

A class of completek-caps inPG(3,q) forq an odd prime

The main problem on caps, posed originally by Segre in the fifties, is to determine the values of k for which there exists a complete k-cap. Very few results on this problem are known. The cardinality of the largest cap(s) and the smallest complete cap(s) are crucial. In this paper it is shown that there exist complete k-caps in PG(3, q), q an odd prime 5 or q = 9, such that k = (q² + q + 6)/3 or k = (q² + 2q + 6)/3. These complete caps are smaller than those currently known for q odd.In memoriam Giuseppe Tallini     

Decomposition of triacetone triperoxide is an entropic explosion

Both X-ray crystallography and electronic structure calculations using the cc-pVDZ basis set at the DFT B3LYP level were employed to study the explosive properties of triacetone triperoxide (TATP) and diacetone diperoxide (DADP). The thermal decomposition pathway of TATP was investigated by a series of calculations that identified transition states, intermediates, and the final products. Counterintuitively, these calculations predict that the explosion of TATP is not a thermochemically highly favored event. It rather involves entropy burst, which is the result of formation of one ozone and three acetone molecules from every molecule of TATP in the solid state.     

Atomistic-scale simulations of the initial chemical events in the thermal initiation of triacetonetriperoxide

To study the initial chemical events related to the detonation of triacetonetriperoxide (TATP), we have performed a series of molecular dynamics (MD) simulations. In these simulations we used the ReaxFF reactive force field, which we have extended to reproduce the quantum mechanics (QM)-derived relative energies of the reactants, products, intermediates, and transition states related to the TATP unimolecular decomposition. We find excellent agreement between the QM-predicted reaction products and those observed from 100 independent ReaxFF unimolecular MD cookoff simulations. Furthermore, the primary reaction products and average initiation temperature observed in these 100 independent unimolecular cookoff simulations match closely with those observed from a TATP condensed-phase cookoff simulation, indicating that unimolecular decomposition dominates the thermal initiation of the TATP condensed phase. Our simulations demonstrate that thermal initiation of condensed-phase TATP is entropy-driven (rather than enthalpy-driven), since the initial reaction (which mainly leads to the formation of acetone, O(2), and several unstable C(3)H(6)O(2) isomers) is almost energy-neutral. The O(2) generated in the initiation steps is subsequently utilized in exothermic secondary reactions, leading finally to formation of water and a wide range of small hydrocarbons, acids, aldehydes, ketones, ethers, and alcohols.     

Complete Caps in with Both N and q Odd

In this work, an inductive method to construct complete caps in affine spaces is provided. Using this tool, for odd and q odd, complete caps smaller than all already known ones are obtained.     

Sull'esistenza di certe configurazioni geometriche collegate ai piani proiettivi di ordine 10

In this paper it is shown that there is no abstract oval of order 10. Also it is shown that there is no partial geometrypg (6,9,4), which in turn would imply the nonexistence of Steiner systemS(3,12,112).