On the minimum size of complete arcs and minimal saturating sets in projective planes

The minimum size of a complete arc in the planes PG(2, 31) and PG(2, 32) and of a 1-saturating set in PG(2, 17) and PG(2, 19) is determined. Also, the minimal 1-saturating sets in PG(2, 9) and PG(2, 11) are classified. In addition, the minimal 1-saturating sets of the smallest size in PG(2, q) are classified for 16 ≤ q ≤ 23. These results have been found using a computer-based exhaustive search that exploits projective equivalence properties.     

Decomposition and isomerization of 1,2-benzisoxazole: single-pulse shock-tube experiments, quantum chemical and transition-state theory calculations

Isomerization and decomposition of 1,2-benzisoxazole were studied behind reflected shock waves in a pressurized driver, single-pulse shock tube. It isomerizes to o-hydroxybenzonitrile, and no fragmentation is observed up to a temperature where the isomerization is almost complete (approximately 1040 K at 2 ms reaction time). The isomerization experiments in this investigation covered the temperature range 900-1040 K. The lack of fragmentation is in complete contrast to the thermal behavior of isoxazole, where no isomerization was observed and the main decomposition products over the same temperature range were carbon monoxide and acetonitrile. In a series of experiments covering the temperature range 1190-1350 K, a plethora of fragmentation products appear in the post shock samples of 1,2-benzisoxazole. The product distribution is exactly the same regardless of whether the starting material is 1,2-benzisoxazole or o-hydroxybenzonitrile, indicating that over this temperature range the 1,2-benzisoxazole has completely isomerized to o-hydroxybenzonitrile prior to fragmentation. Two potential energy surfaces that lead to the isomerization were evaluated by quantum chemical calculations. One surface with one intermediate and two transition states has a high barrier and does not contribute to the process. The second surface is more complex. It has three intermediates and four transition states, but it has a lower overall barrier and yields the isomerization product o-hydroxybenzonitrile at a much higher rate. The unimolecular isomerization rate constants kinfinity at a number of temperatures in the range of 900-1040 K were calculated from the potential energy surface using transition-state theory and then expressed in an Arrhenius form. The value obtained is kfirst=4.15x10(14) exp(-51.7x10(3)/RT) s-1, where R is expressed in units of cal/(K mol). The calculated value is somewhat higher than the one obtained from the experimental results. When it is expressed in terms of energy difference it corresponds of ca. 2 kcal/mol.     

The B-ovals of order q ⩽ 8

The object of this paper is to classify all the Buekenhout ovals of order q ? 8. The close relationship between Buekenhout ovals of even order q = 2t ? 2 and partial geometries pg(t, 2t ? 3, t ? 2) is pointed out.     

One-Pot Reactions with Sol-Gel Entrapped Catalysts, Acids and Bases

Silica sol-gel entrapped acids, bases and organometallic catalysts are used successfully in one-pot reactions without interfering with each other. Both physically and covalently entrapped acids and bases were employed in these processes, including polystyrene sulfonic acid, 1-propane sulfonic acid, molybdosilicic acid (SiO₂-MoO₃), poly[(vinylbenzyltrimethyl)ammonium] hydroxide and 1,5,7-triazabicyclo[4.4.0]decene. The entrapped metal-based catalysts are Rh₂Co₂(CO)₁₂ and RuCl₂(PPh₃)₃. The one-pot reactions carried out with these heterogenized reagents and catalysts include formation of alkenes under acidic and basic conditions, C—C bond formation by condensation reactions with an -carbon to a carbonyl, hydroformylation and hydrogenation.     

PVT properties of concentrated electrolytes. VI. The speed of sound and apparent molal compressibilities of NaCl,Na2SO4, MgCl2, and MgSO4 solutions from 0 to 100°C

The sound velocities of aqueous NaCl, Na₂SO₄, MgCl₂, and MgSO₄ solutions were measured from 25 to 95°C in 10^o intervals from dilute to saturated solutions. The results were combined with our earlier data and fitted to functions of molality and temperature to within ±0.4 m-sec^–1. The adiabatic compressibilities _S were calculated from sound speeds and used to calculate the adiabatic apparent molal compressibilities . Isothermal compressibilities and isothermal apparent molal compressibilities were calculated from _S using literature values for the expansibilities and heat capacities. The values of were extrapolated to infinite dilution using the Debye-Huckel limiting law to determine partial molal compressibilities. The apparent molal compressibilities were fitted to Pitzer's equations. The Pitzer parameters for the concentration dependence of were determined as a function of temperature. Correlations of and V at various temperatures were found for the electrolytes.     

The Classification of Some Perfect Codes

Perfect 1-error correcting codes C in Z ₂ ⁿ , where n=2 ^m–1, are considered. Let ; denote the linear span of the words of C and let the rank of C be the dimension of the vector space . It is shown that if the rank of C is n–m+2 then C is equivalent to a code given by a construction of Phelps. These codes are, in case of rank n–m+2, described by a Hamming code H and a set of MDS-codes D _h , h H, over an alphabet with four symbols. The case of rank n–m+1 is much simpler: Any such code is a Vasil'ev code.     

PVT properties of concentrated aqueous electrolytes. III. Volume changes for mixing the major sea salts at I=1.0 and 3.0 at 25°C

The densities of mixtures of the six possible combinatons of the major sea salts (NaCl, Na₂SO₄, MgSO₄, and MgCl₂) were determined at constant ionic strengths of I=1.0 and I=3.0 at 25°C. The results are used to determine the volume changes for mixing (V _m ) the major sea salts. The values of V _m were fit to equations of the form V _m where y _i is the molal ionic strength fraction of solute i, and ₀ and ₁ are parameters related to the interaction of like-charged ions. The cross-square rule was found to hold at both ionic strengths. Density estimates were made without and with the addition of volume of mixing terms to Young's Rule and compared to the experimental values. The densities calculated with the addition of volume of mixing terms gave better estimates, demonstrating that the densities of concentrated brines can be more accurately estimated using V _m terms. The equations of Reilly and Wood which include the cross-square rule were used to estimate the densities of the cross mixtures (NaCl–MgSO₄ and MgCl₂–Na₂SO₄). The estimated densities agree with the measured values to within ±30 ppm at I=1.0 and ±125 ppm at I=3.0.     

Thermal isomerization and cyclization of 1-naphthylacetylene: Experimental results, quantum chemical and transition state theory calculations

The isomerization of 1-naphthylacetylene diluted in argon was studied behind reflected shock waves in a 2 in i.d. single pulse shock tube over the temperature range 1000-1250 K and overall densities of ∼3 × 10⁻⁵ mol/cm³. The only reaction product found in the post shock mixtures was acenaphthylene. The first order rate constant of the isomerization was found to be k = 2.08 × 10¹² exp(−54.2 × 10³/RT) s⁻¹, where R is expressed in units of cal/K mol. Potential energy surfaces of the cyclization reaction 1-naphthylacetylene → acenaphthylene and the isomerization 1-naphthylacetylene → 2-naphthylacetylene were calculated using the Becke three-parameter hybrid method with Lee-Yang-Parr correlation functional approximation (B3LYP). Structure, energy and frequency calculations were carried out with the Dunning correlation consistent polarized double ζ (cc-pVDZ) basis set. The rate constant (k_∞) for the 1-naphthylacetylene → acenaphthylene cyclization was calculated using transition state theory, the value obtained is k_∞ = 3.52 × 10¹² exp(−55.9 × 10³/RT) s⁻¹, where R is expressed in units of cal/K mol. The agreement between the experiment and the calculations is very good. RRKM calculations were done to transfer k_∞ to the pressure of the single pulse shock tube experiments. In view of high temperature and the large molecule involved the deviation from k_∞ is very small. The isomerization 1-naphthylacetylene → 2-naphthylacetylene proceeds via the formation of an unstable intermediate 1,2-naphthalenocyclobutene and has a high barrier of ∼83.5 kcal/mol. In view of this high barrier, the isomerization cannot compete with the cyclization that proceeds with a barrier of ∼56 kcal/mol.