Weights of links and plaquettes in a random lattice

In a random lattice, links and plaquettes have varying sizes and orientations. Therefore, they should enter the action function with different weights. A particularly attractive choice of these weights is presented; its consequences for $\text{spin}\text{-0,}\text{1}\text{2}\text{and}\text{1}$ fields on such a lattice are discussed.     

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.     

Maximal functions associated with Fourier multipliers of Mikhlin-Hörmander type

We show that maximal operators formed by dilations of Mikhlin- Hörmander multipliers are typically not bounded on L^p(^d). We also give rather weak conditions in terms of the decay of such multipliers under which L^p boundedness of the maximal operators holds.Christ, Grafakos and Seeger were supported in part by NSF grants. Honzík was supported by 201/03/0931 Grant Agency of the Czech Republic     

Flavor symmetry breaking and scaling for improved staggered actions in quenched QCD

We present a study of the flavor symmetry breaking in the pion spectrum for the p4-improved fermion action. Three different variants of the p4 action – p4fat3, p4fat7, and p4fat7tad – are compared to the Asqtad and naive staggered actions. To study the pattern of symmetry breaking, we measure all 15 pion masses in the four-flavor staggered theory. The measurements are done on a quenched gauge background, generated using a one-loop improved Symanzik action with β=10/g²=7.40, 7.75, and 8.00, corresponding to lattice spacings of approximately a= 0.31 fm, 0.21 fm, and 0.14 fm. PACS 11.15.Ha; 11.30.Rd; 12.38.Aw; 12.38.-t; 12.38.Gc     

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.     

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.