Bicyclic [b]-heteroannulated pyridazine derivatives. 4. Cyclization reactions of 4-aryltetrahydropyridazine-3,6-dione 3-hydrazones with some keto esters

Ethoxycarbonylalkylidene derivatives 2 and 6 of the title hydrazones were obtained in the reaction with ethyl pyruvate or ethyl aroylformate and ethyl acetoacetate, respectively, in methanol. Both compounds were mixtures of geometric isomers with high predominance of one of them. Nmr spectroscopy revealed an unexpected magnetic non-equivalence of the CH₂ protons in the ester ethyl group of the major isomer of 6 . On heating (?200°) in an inert medium or on refluxing in ethanolic sodium ethoxide 2 cyclized to the corresponding pyridazino[6,1-c]-triazines 4 , whereas 6 formed pyrazolylpyridazines 7 . The structure of the latter was unambigously established by X-ray analysis. Alkylation of 4a with benzyl bromide in the presence of tetrabutylammonium bromide occurred selectively on the pyridazine N atom.     

Specific interaction of desthiobiotin lipids and water-soluble biotin compounds with streptavidin

As shown for biotin lipids (Ref. 1), the formation of perfect 2-D crystalline streptavidin domains can also be observed in the plane of desthiobiotin lipid monolayers. The binding constant of streptavidin with desthiobiotin (K_a = 5·10¹³ mol⁻¹) is lower than that with biotin (K_a = 10¹⁵ mol⁻¹) (Ref. 2). By adding free biotin into the subphase a competitive replacement and a detaching of the streptavidin domains from the desthiobiotin lipid monolayer takes place. Streptavidin domains built at receptor lipid monolayers are still functional. As could be shown, there are two biotin binding sites at each protein molecule that are fully accessible to biotin (Ref. 1). This can be proven by the interaction with biotinylated ferritin and fluoresceinated biotin. Further coupling of an anti-FITC-antibody can proceed and a second protein layer can be formed. Using a bifunctional biotin linker a second crystalline streptavidin layer underneath the first one can be obtained.     

ON THE CONVERGENCE OF THE PARABOLIC APPROXIMATION OF A CONSERVATION LAW IN SEVERAL SPACE DIMENSIONS

1.IntrodnctionWegiveaproofofthestrongconvergenceinofthesolutionoftheparabolicapproximationtowardstheentropicsolutiontothescalarconservationlawwhereuo(RN),udenotessomeapproximationofuosuchthatandthefluxfsatisfiesTheconvergenceoftheapproximatesolutions...     

Jaffard-Ohm correspondence and Hochster duality

We study categorical aspects of the Jaffard–Ohm correspondencebetween abelian l-groups and Bézout domains and showthat this correspondence is close to a localization. For thispurpose, we establish a general extension theorem for valuationswith value group that is an abelian l-group. As an application,we prove Anderson's conjecture which refines the Jaffard–Ohmcorrespondence. We then extend the correspondence to sheaveson spectral spaces and show that the spectrum of a Bézoutdomain and the spectrum of its corresponding abelian l-groupprovide a concrete example for Hochster's duality of spectralspaces.     

The Absolute of a Topological Space and its Application to Abelian l-groups

We give a axiomatic treatment of the absolute in the category of all topological spaces and characterize it as a cover with respect to the full subcategory of extremally disconnected spaces. As an application, we obtain the strongly projectable hull of an abelian l-group as a unique lifting of the absolute of its spectrum. Dedicated to B. V. M.     

Verified bounds for singular values,in particular for the spectral norm of a matrix and its inverse

The singular value decomposition and spectral norm of a matrix are ubiquitous in numerical analysis. They are extensively used in proofs, but usually it is not necessary to compute them. However, there are some important applications in the realm of verified error bounds for the solution of ordinary and partial differential equations where reasonably tight error bounds for the spectral norm of a matrix are mandatory. We present various approaches to this together with some auxiliary useful estimates.