Games of Chains and Cutsets in the Boolean Lattice

B. Bajnok and S. Shahriari proved that in 2^[n], the Boolean lattice of order n, the width (the maximum size of an antichain) of a non-trivial cutset (a collection of subsets that meets every maximal chain and does not contain or [n]) is at least n-1. We prove that, for n5, in the Boolean lattice of order n, given -1 disjoint long chains, we can enlarge the collection to a cutset of width n-1. However, there exists a collection of long chains that cannot be so extended.     

Some thermodynamic properties of benzocaine

The vaporization enthalpy of benzocaine, ethyl 4-aminobenzoate, has been evaluated using correlation gas chromatography at 298.15 K. The temperature dependence of retention time has also been used to evaluate the vapor pressure of the sub-cooled liquid from 298.15 K to the fusion temperature, 365.2 K, by correlation with the vapor pressures of the compounds used as standards. The vaporization enthalpy calculated from the vapor pressures of benzocaine at the melting point was combined with the experimental fusion enthalpy to evaluate the sublimation enthalpy at the fusion temperature. Application of the Clausius–Clapeyron equation together with the vapor pressure common to both phases permitted calculation of the vapor pressure of the solid at 298.15 K. Similar calculations were performed for two of the standards that were solids for comparisons with experimental data. Vaporization and sublimation enthalpies of (91.8 ± 4.2) and (112.9 ± 4.3) kJ mol^?1 are calculated for benzocaine at 298.15 K as are vapor pressures of 0.0083 and 0.0018 Pa for the sub-cooled liquid and crystalline material, respectively.     

INACTIVATION OF GRAM-NEGATIVE BACTERIA BY PHOTOSENSITIZED PORPHYRINS

Photosensitization of Escherichia coli and Pseudomonas aeruginosa cells by deuteroporphyrin (DP) is shown to be possible in the presence of the polycationic agent polymyxin nonapeptide (PMNP). Previous studies established complete resistance of Gram-negative bacteria to the photodynamic effects of porphyrins. The present results show that combined treatment of E. coli or P. aeruginosa cultures with DP and PMNP inhibit cell growth and viability. No antibacterial activity of PMNP alone could be demonstrated and cell viability remained unchanged. Spectroscopically, PMNP was found to bind DP, a mechanism which probably assists its penetration into the cell's membranes. Insertion of DP into the cells was monitored by the characteristic fluorescence band of bound DP at 622 nm. Binding times were 5-40 min and the extent of binding increased with decreasing the pH from 8.5 to 6.5. DP binding constants, as well as the concentrations of PMNP which were required for maximal effect on the various Gram-negative bacteria, were determined fluorometrically. By the treatment of DP, PMNP and light the growth of E. coli and P. aeruginosa cultures was stopped and the viability of the culture was dramatically reduced. Within 60 min of treatment the survival fraction of E. coli culture was 9 x 10(-6) and that of P. aeruginosa was 5.2 x 10(-4). Electron microscopy depicted ultrastructural alterations in the Gram-negative cells treated by DP and PMNP. The completion of cell division was inhibited and the chromosomal domain was altered markedly.