Nonaqueous diazotization of 4-amino-3-arylisothiazole-5-carboxylate esters

4-Amino-3-arylisothiazole-5-carboxylate esters are converted to the corresponding desamino, chloro, bromo, and iodo esters by processes involving nonaqueous diazotization. These related procedures open up the possibility for the conversion of readily available heterocyclic ortho-amino esters and nitriles to related heterocyclic derivatives, which are not easily obtained by alternate routes.     

Codimension-one minimal projections onto Haar subspaces

Let H_n be an n-dimensional Haar subspace of and let H_n−1 be a Haar subspace of H_n of dimension n−1. In this note we show (Theorem 6) that if the norm of a minimal projection from H_n onto H_n−1 is greater than 1, then this projection is an interpolating projection. This is a surprising result in comparison with Cheney and Morris (J. Reine Angew. Math. 270 (1974) 61 (see also (Lecture Notes in Mathematics, Vol. 1449, Springer, Berlin, Heilderberg, New York, 1990, Corollary III.2.12, p. 104) which shows that there is no interpolating minimal projection from C[a,b] onto the space of polynomials of degree n, (n2). Moreover, this minimal projection is unique (Theorem 9). In particular, Theorem 6 holds for polynomial spaces, generalizing a result of Prophet [(J. Approx. Theory 85 (1996) 27), Theorem 2.1].     

The number of linear extensions of bipartite graphs

The number of linear extensions among the orientations of a bipartite graph is maximum just if the orientation itself is bipartite, the natural one.     

Determination of dipole moment in the ground and excited state by experimental and theoretical methods of N-nonyl acridine orange

The absorption and fluorescence spectra of N-nonyl acridine orange are determined at room temperature (298 K) in cyclohexane, benzene, carbon tetrachloride, chloroform, chlorobenzene and dichloromethane. The ground state of dipole moment was obtained by impedance measurements using Guggenheim-Debeye's method. The experimental excited state dipole moment of N-nonyl acridine orange was determined using Bakhshiev's and Kawski-Chamma-Viallet's formulae and solvent polarity parameter proposed by Reichardt. These experimental results were completed with theoretical results using quantum chemical methods. The experimental (muexp=10.76 D) and theoretical (mucal=9.9 D) dipole moments in the ground and excited state (muexp*=14.56 D) were compared.     

Acid-base reactions of 1,3,4-thiadiazolines and thiocarbonyl ylides; 1,3,4-thiadiazoline-2-spiro-2′-adamantane

The surprising formation of C₂₂H₃₂N₂S₂ from the title compound 1 at 45°C involves the interaction of the basic adamantanethione S-methylide ($\text{2}$) with its acidic precursor $\text{1}$, in the course of which the anion $\text{6}$ undergoes electrocyclic ring opening; the acid and base functions offer the clue to a prolific chemistry of the thiadiazoline $\text{1}$ and the thiocarbonyl ylide $\text{2}$.     

Secondary deuterium kinetic isotope effects in irreversible additions of allyl reagents to benzaldehyde

The competitive kinetics of additions of allyl to benzaldehyde-h and -d from allyltributyl tin, from diisopropyltartrylallyl boronate, and from allyl bromide and zinc dust in aqueous tetrahydrofuran have inverse secondary deuterium kinetic isotope effects, SDKIEs. These inverse SDKIEs are in contrast to the normal SDKIEs that were obtained with allyl lithium and allyl Grignard, suggesting rate-determining single-electron transfer in these cases. By various MO calculations the transition state for addition of allyl boronate occurs with substantial B-O bond formation and little C-C bond formation. The magnitudes of the SDKIEs with the other two allylating reagents, when compared with reasonable equilibrium isotope effects for the addition, suggest transition states with substantial C-C bond formation.     

ContinuousK-theory

We study arithmetical properties of homotopy groups of thel-adic completion of Quillen'sK-theory space of number field, with a view on the Dwyer-Friedlander comparison map into étaleK-theory. The relation of these groups toK-theory is a complete analogy to the relation of continuous étale cohomology to étale cohomology. We identify the torsion subgroup of the resulting term with the subgroup of divisible elements inK _2n (F). We prove that this term is sent isomorphically into étaleK-theory, giving some further evidence for the Lichtenbaum-Quillen conjectures.     

V. Thioanalogues of sparteine lactams. (+)-2-Thiono-17-oxosparteine and (+)-2,17-dithionosparteine

The X-ray and spectroscopic results clearly indicate that the (+)-2-thiono-17-oxosparteine (1) and (+)-2,17-ditihionosparteine (2) are conformationally rigid. In order to analyze deviations of lactam/thiolactam groups from planarity induced by ring constraints, the Dunitz-Winkler approach has been used. The lactam and thiolactam groups are close to planarity, only the lactam group in one of the two independent molecules of 1 is markedly non-planar. The bond angles in the thiolactam and lactam groups are highly diverse. Rings A and C adopt a distorted sofa conformation in both compounds. The distortions in the molecules of 2 as compared with those in the related monothiolactams correspond to the unusual chemical shifts of H5(eq), H5(ax) and H11, as well as to the extremely low J_5ax-6 and extremely large J_5eq-6 coupling constants. Also chemical shifts show a similar regularity being extremely high and low for C2 and C17, respectively.