On thep-ranks of net graphs

Let be ak-net of ordern with line-point incidence matrixN and letA be the adjacency matrix of its collinearity graph. In this paper we study thep-ranks (that is, the rank over ) of the matrixA+kl withp a prime dividingn. SinceA+kI=N ^T N thesep-ranks are closely related to thep-ranks ofN. Using results of Moorhouse on thep-ranks ofN, we can determiner _p (A+kI) if is a 3-net (latin square) or a desarguesian net of prime order. On the other hand we show how results for thep-ranks ofA+kI can be used to get results for thep-ranks ofN, especially in connection with the Moorhouse conjecture. Finally we generalize the result of Moorhouse on thep-rank ofN for desarguesian nets of orderp a bit to special subnets of the desarguesian affine plane of orderp ^e .The author is financially supported by the Cooperation Centre Tilburg and Eindhoven Universities.     

Pulsed laser photolysis and quantum chemical-statistical rate study of the reaction of the ethynyl radical with water vapor

The rate coefficient of the gas-phase reaction C(2)H + H(2)O-->products has been experimentally determined over the temperature range 500-825 K using a pulsed laser photolysis-chemiluminescence (PLP-CL) technique. Ethynyl radicals (C(2)H) were generated by pulsed 193 nm photolysis of C(2)H(2) in the presence of H(2)O vapor and buffer gas N(2) at 15 Torr. The relative concentration of C(2)H radicals was monitored as a function of time using a CH* chemiluminescence method. The rate constant determinations for C(2)H + H(2)O were k(1)(550 K) = (2.3 +/- 1.3) x 10(-13) cm(3) s(-1), k(1)(770 K) =(7.2 +/- 1.4) x 10(-13) cm(3) s(-1), and k(1)(825 K) = (7.7 +/- 1.5) x 10(-13) cm(3) s(-1). The error in the only other measurement of this rate constant is also discussed. We have also characterized the reaction theoretically using quantum chemical computations. The relevant portion of the potential energy surface of C(2)H(3)O in its doublet electronic ground state has been investigated using density functional theory B3LYP6-311 + + G(3df,2p) and molecular orbital computations at the unrestricted coupled-cluster level of theory that incorporates all single and double excitations plus perturbative corrections for the triple excitations, along with the 6-311 + + G(3df,2p) basis set [(U)CCSD(T)6-311 + + G(3df,2p)] and using UCCSD(T)6-31G(d,p) optimized geometries. Five isomers, six dissociation products, and sixteen transition structures were characterized. The results confirm that the hydrogen abstraction producing C(2)H(2)+OH is the most facile reaction channel. For this channel, refined computations using (U)CCSD(T)6-311 + + G(3df,2p)(U)CCSD(T)6-311 + + G(d,p) and complete-active-space second-order perturbation theory/complete-active-space self-consistent-field theory (CASPT2/CASSCF) [B. O. Roos, Adv. Chem. Phys. 69, 399 (1987)] using the contracted atomic natural orbitals basis set (ANO-L) [J. Almlof and P. R. Taylor, J. Chem. Phys.86, 4070 (1987)] were performed, yielding zero-point energy-corrected potential energy barriers of 17 kJ mol(-1) and 15 kJ mol(-1), respectively. Transition-state theory rate constant calculations, based on the UCCSD(T) and CASPT2/CASSCF computations that also include H-atom tunneling and a hindered internal rotation, are in perfect agreement with the experimental values. Considering both our experimental and theoretical determinations, the rate constant can best be expressed, in modified Arrhenius form as k(1)(T) = (2.2 +/- 0.1) x 10(-21)T(3.05) exp[-(376 +/- 100)T] cm(3) s(-1) for the range 300-2000 K. Thus, at temperatures above 1500 K, reaction of C(2)H with H(2)O is predicted to be one of the dominant C(2)H reactions in hydrocarbon combustion.     

DSC analysis of the anti-HIV agent loviride as a preformulation tool in the development of hot-melt extrudates

Thermal analysis was performed on the anti-HIV agent loviride in order to test its suitability to be processed using hot-melt extrusion. Temperature characteristic parameters of crystallization were determined to quantify the stability of amorphous loviride. The present study has shown that cooling and heating loviride at different rates influenced its thermal stability. At high cooling rates melted loviride did not crystallize during cooling, and formed a glass that recrystallized during reheating. Very low cooling rates resulted in significant decomposition of the drug. The glass transition temperature was found to increase as a function of increasing heating rates and the activation energy for the transition from the glassy to the super-cooled liquid state was relatively high, indicating good stability of the glass. This revised version was published online in July 2006 with corrections to the Cover Date.     

Theoretical and experimental study of the product branching in the reaction of acetic acid with OH radicals

The product distribution of the reaction of acetic acid, CH(3)COOH, with hydroxyl radicals, OH, was studied experimentally and theoretically. Mass-spectrometric measurements at 290 K and 2 Torr of He of the CO(2) yield versus the loss of acetic acid yielded a branching fraction of 64 +/- 14% for the abstraction of the acidic hydrogen as follows: CH(3)COOH + OH --> CH(3)COO + H(2)O --> CH(3) + CO(2) + H(2)O. A quantum chemical and theoretical kinetic analysis showed that the abstraction of the acidic hydrogen is enhanced relative to the abstraction of -CH(3) hydrogens because of the formation of a strong pre-reactive H-bonded complex, where the H-bonds are retained in the H-abstraction transition state. The potential energy surface of the reaction is explored in detail, and the reaction products of the individual channels are identified. The theoretical product branching is found to be critically dependent on the energetic and rovibrational differences between the H-abstraction transition states.     

Ab initio investigation of the Young's modulus of polyamide‐6

The Young's modulus of the α form of polyamide‐6 has been calculated using the supermolecule model. The crystalline polymer was represented by a single‐chain molecule, divided into a head, body, and tail part. The body of the model contains an even number of polyamide‐6 units (4–16 units) and is representative for a polyamide‐6 chain. The periodicity of the system was not explicitly taken into account, but in a few tests the effect of a linear constraint has been evaluated. An n‐butyl and n‐pentyl group have been used as head and tail, respectively. In a number of additional calculations the length of the head and tail has been varied. For all supermolecule models the equilibrium and elongated structures have been optimized using ab initio Hartree–Fock calculations with a 6‐31G** basis set. From the energy values of the optimized structure a Young's modulus of 334 GPa has been extrapolated for both the unconstrained and linearly constrained models. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003