Energy-level statistics of model quantum systems: Universality and scaling in a lattice-point problem

We investigate the statistics of the numberN(R, S) of lattice pointsnZ ², in an annular domain (R, w)=(R+w)A\RA, whereR, w>0. HereA is a fixed convex set with smooth boundary andw is chosen so that the area of (R, w) isS. The statistics comes fromR being taken as random (with a smooth density) in some interval [c ₁ T,c ₂,T],c ₂>c ₁>0. We find that in the limitT the variance and distribution of N=N(R; S)–S depend strongly on howS grows withT. There is a saturation regimeS/T, asT, in which the fluctuations in N coming from the two boundaries of are independent. Then there is a scaling regime,S/Tz, 0<z<, in which the distribution depends onz in an almost periodic way going to a Gaussian asz0. The variance in this limit approachesz for genericA, but can be larger for degenerate cases. The former behavior is what one would expect from the Poisson limit of a distribution for annuli of finite area.     

Separation and determination of alditols and sugars by high-pH anion-exchange chromatography with pulsed amperometric detection

Carbohydrates such as alditols (polyols or sugar alcohols), monosaccharides and disaccharides are separated as anions by anion-exchange chromatography with a sodium hydroxide eluent, MA1 CarboPac column and pulsed amperometric detection. We report a high-pH anion-exchange chromatographic-pulsed amperometric detection (HPAEC-PAD) method that determines all the polyols used as food additives in food products and the most commonly found mono- and disaccharides on a routine basis. The linearity, repeatability, internal reproducibility and accuracy are described. The applicability of the method has been demonstrated by the analysis of 46 relevant samples and by participation twice in the Food Analysis Performance Assessment Scheme (FAPAS) testing programme for food additives.     

Paradigms and Paradoxes: Thoughts on the Enthalpy of Formation of Guanidine and Its Monosubstituted Derivatives

Despite their seeming simplicity, substituted guanidines have not particularly caught the attention of the thermochemical community. The current paper compares the enthalpy of formation of solid substituted guanidines with correspondingly substituted benzenes, also as solids.     

Toward the development of a structurally novel class of chiral auxiliaries: diastereoselective aldol reactions of a (1R,2S)-ephedrine-based 3,4,5,6-tetrahydro-2H-1,3,4-oxadiazin-2-one

[reaction: see text] Asymmetric aldol addition reactions have been conducted with (1R,2S)-ephedrine-derived 3,4,5,6-tetrahydro-2H-1,3,4-oxadiazin-2-one (2). Diastereoselectivities range from 75:25 to 99:1 for the formation of the crude non-Evans syn adducts 8a-h. The facial selectivity of the enolate is directed by the stereogenic N(4)-methyl substituent. Aldol adduct 8a is readily cleaved by acid hydrolysis to afford (2S,3S)-3-hydroxy-2-methyl-3-phenylpropionic acid (9) in >95% ee.     

Synthesis of novel fused isoxazoles and isoxazolines by sequential Ugi/INOC reactions

We report the synthesis of novel fused isoxazoles and isoxazolines by employing an unprecedented Ugi/INOC synthetic sequence. The coupling of the Ugi multicomponent reaction with the intramolecular N-oxide cyclization provides access to unique heterocyclic ring systems in two steps from easily available starting materials in moderate to good overall yields.