Crystal structures of 1,1′-di(methylacetato)- and 1,1′-di(chloroethoxyethyl)-2,2′-biimidazole

1,1′-Di(methylacetato)-2,2′-biimidazole, C₁₂H₁₄N₄O₄, crystallizes from methanol in the space groupP2 ₁/c, wherea=9.535(2),b=13.385(2),c=5.1208(8) Å,V=652.2(2) ų, andZ=4.1,1′-Di(chloroethoxyethyl)-2,2′-biimidazole, C₁₄H₂₀Cl₂N₄O₂, crystallizes from cyclohexane in the space groupPbca, wherea=12.372(2),b=8.959(2),c=14.840(2) Å,V=1644.9(5) ų, andZ=8. The structures were refined toR=0.041 (1380 observed reflections) andR=0.043 (3243 observed reflections), respectively. Both molecules crystallize with coplanar rings and the substituents assume atrans configuration with a center of inversion between the bridging carbon atoms.     

The influence of aliphatic diols on the temperature of maximum density of water

The influence of various aliphatic diols on the temperature of maximum density (TMD) of water has been investigated. 1,2-Propanediol, 1,3-propanediol, 1,3-butanediol, 1,4-butanediol, 1,5-pentanediol, 1,6-hexanediol, and 2,5-hexanediol were found to yield positive structural contributions to the solute-induced shift in the TMD, i.e., they are structure makers. Contrariwise, data from the literature indicate that 1,2-ethanediol is a structure breaker. Relationships between the structure making/breaking tendencies of the solutes and the relative positions of the two hydroxyl groups are discussed.     

Long time behaviour of the solution to non-linear Kraichnan equations

We consider the solution of a nonlinear Kraichnan equation with a covariance kernel k and boundary condition H(t, t)=1. We study the long time behaviour of H as the time parameters t, s go to infinity, according to the asymptotic behaviour of k. This question appears in various subjects since it is related with the analysis of the asymptotic behaviour of the trace of non-commutative processes satisfying a linear differential equation, but also naturally shows up in the study of the so-called response function and aging properties of the dynamics of some disordered spin systems.