Second-order Green's function theory of a Heisenberg paramagnet

The Heisenberg paramagnet in one, two, and three dimensions is analyzed by a second-order Green's function theory similar to that used by Knapp and ter Haar. This theory, which incorporates the exact values for the zero, first, and second moments of the relaxation function as boundary conditions, yields results satisfying the rotational symmetry of the paramagnetic region as well as the principle of detailed balance. We find that our predictions for equal time properties in the classical limit are identical with the RPA Green's function theory of Liu as well as the spherical model results of Lax. The quantum limit is analyzed, and our predictions for the 1/T series coefficients for both internal energy and susceptibility are compared with exact results.Supported by National Science Foundation.     

Dye-assisted chromatographic determination of aliphatic ketones and esters with brilliant green

Determinations of neutral nonchromophoric organic compounds by dye-assisted chromatography are extended to the determination of aliphatic ketones and esters by using reversed-phase conditions and a mobile phase containing Brilliant Green. Detection limits of 6–20 μg were obtained when a mobile phase containing 50% (v/v) methanol/water and 0.00010 M Brilliant Green was used with detection at 575 nm, and 0.5–2 μg with detection in the ultraviolet region. In the absence of dye the detection limits for several solutes were about four times higher than the corresponding values obtained with the dye. The dye was shown to form a dimer having a molar absorptivity two orders of magnitude smaller than that of the monomeric dye. Detection of non-chromophoric compounds is concluded to be due to the desorption of adsorbed dye by the analytes and the shift of the aggregation and hydration equilibria of the dye promoted by the organic solutes. The lowering of the capacity factors is interpreted in terms of the adsorption of dye by the column which reduces the hydrophobicity of the stationary phase.     

Adaptive estimates of linear functionals

Summary Given a collection of nested closed, convex symmetric sets and a linear functional, we find estimates which are within a logarithm term of being simultaneously asymptotically minimax. Moreover, these estimates can be constructed so that the loss of this logarithm term only occurs on a small subset of functions. These estimates are quasi-optimal since there do not exist estimators which do not lose a logarithm term on some part of the parameter spaces.This author was partially supported by an NSF Grant DMS-9123956This author was supported by an NSF Postdoctoral Research Fellowship     

1,3-dialkylimidazolium-based room-temperature ionic liquids as background electrolyte and coating material in aqueous capillary electrophoresis

The 1-ethyl-3-methylimidazolium (EMIM) cation was found to have constant mobility of 4.5 x 10(-4) cm2 V(-1) s(-1) over the pH range of 3 to 11. The electroosmotic flow of bare silica capillary was reversed by the covalently bonded room-temperature ionic liquid (RTIL) coating. With run buffer of 5 mM EMIM (pH 8.5), NH4+ in human urine was separated from the K+ matrix and was detected to be 0.37 +/- 0.012%. K+, Na+, Li+, Ca2+, Mg2+ and Ba2+ were baseline separated in RTIL-coated capillary with run buffer of 10 mM EMIMOH-acetic acid at pH 5, and the concentration of the above ions in a red wine were detected to be 907, 27.9, 0, 71.0, 83.4 and 31.1 microg/ml, respectively. The RTIL-coated capillary showed stable electroosmotic flow for at least 80 h in the run buffer.     

Electrophoresis of DNA in ionic liquid coated capillary

An ionic liquid (IL) coated capillary was prepared and investigated for DNA separation. The electroosmotic flow of the capillary was reversed between pH 4.5 and 9. Below 900 base pairs the larger DNA fragment suffered more retardation in the IL coated capillary due to the increasing charge density of the fragment with size. In the presence of 4% hydroxyethylcellulose, the phiX174 DNA-Hae III digest fragments were baseline separated in both IL- and polyacrylamide-coated capillary except for the fragments of 271 and 281 base pairs; while the analysis time was shorter in the IL-coated capillary. Our experiments indicated that the IL-coated capillary could work stably in the run buffer for at least 96 h with no notable deterioration in performance.     

Granular entropy: explicit calculations for planar assemblies

This paper proposes a new volume function for calculation of the entropy of planar granular assemblies. This function is extracted from the antisymmetric part of a new geometric tensor and is rigorously additive when summed over grains. It leads to the identification of a conveniently small phase space. The utility of the volume function is demonstrated on several case studies, for which we calculate explicitly the mean volume and the volume fluctuations.     

1-Arylquinolizidines

The reaction of arylmagnesium bromides with 1-ketoquinolizidine provided predominantly 1(e)-aryl-1(a)-hydroxyquinolizidines. Dehydration of the latter and subsequent hydrogenation yielded 1-arylquinolizidines.     

On the impossibility of Directed Moore Graphs

This note introduces the notion (d, k) Directed Moore Graphs (DMG in short), and investigates the question of their existence. A (d, k) DMG is a regular directed graph of degree d and diameter k containing the maximum number of nodes according to a certain definition. It is shown that unless d = 1 or k = 1 there are no (d, k) DMG's.     

SO(N) higgs problem with adjoint+vector representations and non-linear potentials

Using the recently devised geometrical method, we analyze the quartic Higgs potential for SO(N) adjoint+vector representations. The minimum energy solutions are found to correspond to maxi-maximal little groups, but not all such groups are used. However, in the complete orbit space (including invariants not employed in the Higgs potential) we find that their strata have somewhat equal geometrical status of being low dimensional singular subspaces, i.e., cusps, edge curves, two-dimensional surfaces, etc. We also consider simple scalar potentials which are nonlinear with respect to orbit parameters and show that the directional extremum often, though not always, remains monotonic in orbit parameters within the orbit space and consequently the absolute extremum is likely to occur on the most protrudent portions of the orbit space boundary. Thus we clarify the range of validity of the Michel-Radicati conjecture and the Gell-Mann-Slansky conjecture.