Random lattice field theory: General formulation

A new type of lattice field theory is formulated in which the sites are chosen randomly in space. An algorithm is given for linking nearby sites; these links form the edges of non-overlapping simplices which fill the entire volume. All physical quantities averaged over such a lattice can therefore be translationally and rotationally symmetric.     

Fluoro-ketones. V reaction of alkyl and aryllithium compunds with perfluoroalkylether esters

n-Butyllithium and a variety of aryllithium compounds have been shown to react with a perfluoroalkylether ester (R_fOR_fCO₂R) at ?78°C to produce perfluoroalkylether ketones. In the absence of competing reactions, which may be due to additional reactive groups on the ester, high yields of ketones can be prepared. Steric hindrance adjacent to the carbonyl group has an important effect on rates of reactions. Low reaction temperature ?78°C is an important factor when secondary esters are used. At higher reaction temperatures >;?30°C, the secondary esters produce decreased yields of ketone due to the instability of the intermediate lithium salt of the hemiketal which decomposes to an aryl ester and a perfluorinated olefin.     

The synthesis of proximal-benzolumazine,proxirnal-benzoxanthine,proximal-benzotheophylline and proximal-benzocaffeine

The synthesis of pyrazino[2,3-f]quinazolin-8,10-(7H,9H)dione(proximal-benzolumazine, 1 ), imidazo[4,5-f]-quinazolin-7,9-(6H,8H)-dione (proximal-benzoxanthine, 2 ), 6,8-dimethylimidazo[4,5-f]-quinazolin-7,9-(6H,8H) dione (proximal-benzotheophylline, 3 ), and 1,6,8-trimethylimidazo[4,5-f]quinazolin-7,9-(6H,8H)dione (proximal-benzocaffeine, 4 ) is reported by commencing with 2-amino-6-chlorobenzamide and proceeding via a variety of 5,6-disubstituted-2,4-(1H,3H)quinazolinediones. Methylation of 3 is shown to yield 3,6,8-trimethylimidazo[4,5-f]quinazolin-7,9-(6H,8H)dione ( 15 ) and 4 in a ratio of 4:1.     

Fluoro-ketones IV. Synthesis of phenylperfluoroalkyl ketones - mechanism of reaction between phenyllithium and fluoroesters

Although fluorine containing ketones (R_fC(O)R_f and R_fC(O)R, R_f = perfluoroalkyl) have been prepared from the reaction between organolithium reagents and perfluoroalkyl esters, the reaction has not found general applicability. Variable yields of ketones and co-production of secondary and tertiary alcohol by-products have in most instances been experienced. We have examined in more detail the factors e.g., temperature, mode of addition and perfluoroalkyl ester structure which influence ketone product and by-products formation. By controlling experimental conditions excellent yields of C₆H₅C(O)R_f compounds can be attained. A lithium salt of a hemiketal (II) has been isolated and shown to be the active intermediate in the production of the ketone. The stability of the salt and its potential reaction with the solvent dictates the type of reaction products. Low temperature favors stability of the lithium salt of the hemiketal whereby high yields of ketones are produced on hydrolysis.     

The synthesis of lin-benzoreumycin,lin-benzo-1-methylxanthine,and lin-benzo-1,9-dimethylxanthine

Commencing with 7-chloro-3-methylquinazoline-2,4(1H,3H)-dione ( 9a ), a five step synthesis of 7-methylpyrimido[5,4-g]-1,2,4-benzotriazine-6,8(7H,9H)-dione (lin-benzoreumycin, 6 ) has been accomplished. A synthesis of 1,7-dimethylpyrimido[5,4-g]-1,2,4-benzotriazine-6,8(1H,7H)-dione (lin-benzotoxoflavin, 5 ) employing an intermediate from the preparation of 6 (i.e., 7-chloro-3-methyl-6-nitroquinazoline-2,4(1H,3H)-dione, 9b ) was attempted but could not be accomplished beyond the dihydro precursor of 5 (i.e., 12 ). Compound 9b did lead to successful preparations of 7-methylimidazo[4,5-g]quinazoline-6,8(5H,7H)-dione (lin-benzo-1-methylxanthine, 7 ) and 3,7-dimethylimidazo[4,5-g]quinazoline-6,8(5H,7H)-dione (lin-benzo-1,9-dimethylxanthine, 8 ) by first reacting 9b with ammonia (for 7) or methylamine (for 8 ) followed by reductive cyclization in formic acid.     

Static and dynamic thermal quantities near the consolute point of the binary liquid mixture aniline-cyclohexane studied with a photopyroelectric technique and adiabatic scanning calorimetry

We studied the thermal conductivity, thermal effusivity, and specific heat capacity at constant pressure of the critical binary liquid mixture aniline-cyclohexane near the consolute point, using a photopyroelectric (PPE) technique and adiabatic scanning calorimetry (ASC). According to recent theoretical predictions based on renormalization group theory calculations, a substantial (but not diverging) enhancement in the thermal conductivity in the homogeneous phase near the critical temperature was expected for this binary system near the consolute point. However, within an experimental precision of 0.05%, we found no deviation from linear behavior in the range of 5 K above Tc down to Tc. The specific heat capacity calculated from the results for the thermal conductivity and effusivity is in good agreement with that measured by ASC. For the ASC results, the theoretical power law expression with the Ising critical exponent was fitted to the specific heat capacity both above and below the transition temperature. Good agreement with theory was found both for the amplitude ratio and the two-scale universality.     

Correction: On the Severi problem in arbitrary characteristic

In this paper, we show that Severi varieties parameterizing irreducible reduced planar curves of a given degree and geometric genus are either empty or irreducible in any characteristic. Following Severi’s original idea, this gives a new proof of the irreducibility of the moduli space of smooth projective curves of a given genus in positive characteristic. It is the first proof that involves no reduction to the characteristic zero case. As a further consequence, we generalize Zariski’s theorem to positive characteristic and show that a general reduced planar curve of a given geometric genus is nodal.

     

A Green's function method for surface acoustic waves in functionally graded materials

Acoustic wave propagation in anisotropic media with one-dimensional inhomogeneity is discussed. Using a Green's function approach, the wave equation with inhomogeneous variation of elastic property and mass density is transformed into an integral equation, which is then solved numerically. The method is applied to find the dispersion relation of surface acoustic waves for a medium with continuously or discontinuously varying elastic property and mass density profiles.     

Temperature dependence of the electrical conductivity of imidazolium ionic liquids

The electrical conductivities of 1-alkyl-3-methylimidazolium tetrafluoroborate ionic liquids and of 1-hexyl-3-methylimidazolium ionic liquids with different anions were determined in the temperature range between 123 and 393 K on the basis of dielectric measurements in the frequency range from 1 to 10(7) Hz. Most of the ionic liquids form a glass and the conductivity values obey the Vogel-Fulcher-Tammann equation. The glass transition temperatures are increasing with increasing length of the alkyl chain. The fragility is weakly dependent on the alkyl chain length but is highly sensitive to the structure of the anion.