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.     

Decomposition of anthranil. Single pulse shock-tube experiments, potential energy surfaces and multiwell transition-state calculations. The role of intersystem crossing

The thermal decomposition of anthranil diluted in argon was studied behind reflected shock waves in a 2 in. i.d. pressurized driver single-pulse shock tube over the temperature range 825-1000 K and overall densities of approximately 3 x 10(-5) mol/cm(3). Two major products: aniline and cyclopentadiene carbonitrile (accompanied by carbon monoxide) and four minor products resulting from the decomposition were found in the postshock samples. They were, in order of decreasing abundance, pyridine, CH(2)=CHCN, HCN and CHC-CN, and comprised only a few percents of the overall product distribution. Quantum chemical calculations were carried out to determine the sequence of the unimolecular reactions that lead to the formation of cyclopentadiene carbonitrile and of phenylnitrene/phenylimine that are the precursors of aniline. They form aniline by reactions with traces of water impurities. To produce cyclopentadiene carbonitrile, two main processes must take place: CO elimination and ring contraction from a six- to a five-membered ring. It was shown that this can occur via two parallel pathways where CO elimination takes place prior to or following ring contraction. Singlet potential energy surfaces for all the elementary reactions that lead to the formation of cyclopentadiene carbonitrile and phenylnitrene/phenylimine were obtained. Their rate constants were calculated on the basis of the results of the quantum chemical calculations using transition-state theory. A kinetic scheme containing these reactions was constructed and multiwell calculations were performed to evaluate the mole percent of the products as a function of temperature. A very serious disagreement between the experimental results and the results of calculations showed that the singlet PESs could not account for the observed experimental rates. No other singlet PESs that lead to the formation of these products could be found. In view of this observation, attempts to find pathways that lead to the formation of cyclopentadiene carbonitrile and phenylnitrene/phenylimine on triplet surfaces were made. Such surfaces were found, and singlet <--> triplet intersystem crossing probabilities and crossing rate constants were calculated as well as the rate constants of all the elementary steps on the triplet surfaces. A reaction scheme was constructed and multiwell calculations were performed, including also the pathways on the singlet surfaces, to evaluate the mole percent of the products as a function of temperature. The agreement between the experimental results and these calculations was quite satisfactory.     

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.     

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.     

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).     

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