Bell-type inequalities in horizontal sums of Boolean algebras

We give a necessary and sufficient condition for a Bell-type inequality to hold in a horizontal sum of finitely many finite Boolean algebras.     

Convexity theories III. Classification of certain real convexity theories

In this paper we classify all real convexity theories that contain the standard convexity theory _c. For this purpose we consider three subcases: finitary; infinitary and (_sc\_c)Ø; infinitary and _sc=_c. In each of these subcases one encounters a phenomenon resembling bifurcation.This research was supported by the Deutsche Forschungsgemeinschaft.     

Relative entropy maximization and directed diffusion equations

Motivated by the concept of maximum entropy methods in signal and image processing, we introduce and discuss a class of ‘directed diffusion equations’ with suitable boundary conditions. The paradigmatic ‘directed diffusion equation’ is The relative entropy $ Sb[f](t): = - \int_\Omega {f(t,x)} \;\ln \;(f(t,x)/b(x))dx $ is rapidly increasing along solution trajectories of (i). This suggests that solving (i) will yield efficient procedures for entropy maximization. We also discuss the asymptotic behavior of solutions of (i)—this is readily done because (i) has a large family of Ljapunov functionals.     

Synthesis and acid-base properties of (1H-benzimidazol-2-yl-methyl)phosphonate (Bimp2-). Evidence for intramolecular hydrogen-bond formation in aqueous solution between (N-1)H and the phosphonate group

The synthesis of (1H-benzimidazol-2-yl-methyl)phosphonic acid, H2(Bimp)+/-, is described: 2-chloromethylbenzimidazole was reacted with ethylchloroformate to give 1-carboethoxy-2-chloromethylbenzimidazole which was treated with trimethyl phosphite and after hydrolysis with aqueous HBr H2(Bimp)+/- was obtained. In H2(Bimp)+/- one proton is at the N-3 site and the other at the phosphonate group; both acidity constants were determined in aqueous solution by potentiometric pH titrations (25 degrees C; I = 0.1 M, NaNO3) and this furnished the pKa values of 5.37 +/- 0.02 and 7.41 +/- 0.02, respectively. The acidity constant for the release of the primary proton from the P(O)(OH)2 group of H3(Bimp)+ was estimated: pKa = 1.5 +/- 0.2. Moreover, Bimp2- can be further deprotonated at its neutral (N-1/N-3)H site to give the benzimidazolate residue, but this reaction occurs only in strongly alkaline solution (KOH); application of the H_ scale developed by G. Yagil (J. Phys. Chem., 1967, 71, 1034) together with UV spectrophotometric measurements gave pKa = 14.65 +/- 0.12. Comparisons with acidity constants taken from the literature show that this latter pKa value is far too large and this allows the conclusion that an intramolecular hydrogen bond is formed between the (N-1/N-3)H site and the phosphonate group of Bimp2-; the formation degree of this hydrogen-bonded isomer is estimated to be 98 +/- 2%. The general relevance of this and the other results are shortly discussed and the species distribution for the Bimp system in dependence on pH is provided.     

Formation of the First Trimeric Monoterpenoid Indole Alkaloids

Under O², the Aspidosperma alkaloid tabersonine ( 1 ) was converted by a crude enzyme preparation from leaves of mature plants of Catharanthus roseus G DON into the trimeric 3-hydroxy-14′-(3α″-tabersonyl)voafrine B ( 4 ) which was easily reduced by NaBH₄ to 14′-(3α″-tabersonyl)voafrine B ( = tertabersonine; 5 ). Compounds such as 4 and 5 are the first trimeric alkaloids in the series of monoterpenoid indole alkaloids.     

Analysis of an intermediate in a 1,3-dipolar cycloaddition of methylsulfonyl azide

MNDO-PM3 calculations, carried out on an experimentally determined structure of an intermediate in the cycloaddition of an electrophilic azide and a nucleophilic 1,3-dipolarophile, show that the semiempirical MO scheme models this structure closely. Transition structures for formation of the intermediate and ring closure of the latter are described.     

Models for the Active Center of Pterin-Containing Molybdenum Enzymes: Crystal structure of a molybdenum complex with sulfur and pterin ligands

The first crystal structure of a molybdenum complex 9 with a hydrogenated pterin and a sulfur ligand contributes to the discussion about the active center of molybdenum and tungsten enzymes containing a molybdopterin cofactor. Complex 9 was synthesized through a redox reaction of [Mo^VIO₂ (LN-S₂)] ( 8 ; LN-S₂ = pyridine-2, 6-bis(methanethiolato)) with 5, 6, 7, 8-tetrahydropterin ( 7 ). 2 HCl (H₄Ptr.2 HCl). The complex crystallizes, with a non-coordinating Cl-atom acting as a counterion, in the monoclinic space group C2/c (No. 15) with cell dimensions a = 22.900(5), b = 10.716(2), c = 17.551(4) Å, β = 120.36(3)°, and Z = 8. We interpret 9 as [Mo^IVO(LN-S₂)(H⁺-q-H₂Ptr)]Cl (q = quinonoid; H₂Ptr = dihydropterin), i.e., a Mo^IV monooxo center coordinated by a pyridine-2, 6-bis(methanethiolato) ligand and a protonated dihydropterin. The spectroscopic properties of this new complex are comparable to those of other crystalline molybdenum complexes of hydrogenated pterins without additional S-coordination. The slightly H₂O-soluble complex 9 reacts with the natural enzyme substrate DMSO very slowly, possibly due to the lack of easily dissociable ligands at the metal center.