Inclusion complexes of alcohols with α-cyclodextrin

Calorimetric studies of the inclusion complexes of straight and branched alcohols and of diols with alpha-cyclodextrin (-CD) have been carried out in water solvent. The data suggest that straight and branched chain alcohols enter the cavity of -CD alkyl end first. The hydroxyl group hydrogen bonds to the outer oxygen ring of the cyclodextrin. For branched chain alcohols the longer alkyl part of the molecule penetrates the -CD cavity up to the hydroxyl group. Diols form two hydrogen bonds to the outer oxygen ring of the cyclodextrin with some penetration into its interior.     

Existence and positivity of solutions of a fourth-order nonlinear PDE describing interface fluctuations

We study the partial differential equation which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case × R S¹. We establish existence, uniqueness, and regularity of solutions, locally in time, for positive initial data in H¹(S¹), and prove the existence of several families of Lyapunov functions for the evolution. From the latter we establish a sharp connection between existence globally in time and positivity preservation: if [0], T*) is a maximal half open interval of existence for a positive solution of the equation, with T* < ∞, then lim_tT* w(t,·) exists in C¹(S¹) but vanishes at some point. We show further that if T* > (1 + √3)/16π² √3 then T* = ∞ and lim_t∞ w(t,.) exists and is constant. We discuss also some explicit solutions and propose a generalization to higher dimensions. © 1994 John Wiley & Sons, Inc.     

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.     

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 and photolysis of doxyl derivatives of 5β-androstan-3-ones

In an unsuccessful attempt to effect remote functionalization at C9, 4,4-dimethyloxazolidine-N-oxyl (doxyl) derivatives at C3 of 5β-androstan-3,17-dione and 5β-androstan-17β-ol-3-one were prepared and photolyzed. The former doxyl yielded its C13 stereoisomer; the latter was converted very slowly to intractable material.