Convergent Synthesis of 2H-Chromenes - a Formal [3+3] Cycloaddition by a One-pot, Three-Step Cascade

In cases in which the palladium-catalyzed coupling of a bromoquinone with a vinyl stannane affords a vinyl quinone that enolizes, the resulting ortho-quinone methide undergoes an oxa-6π electrocyclization. Enolization is promoted by the presence of a polar additive. The net conversion is a formal [3+3] cycloaddition that gives 2H-chromenes. Because the first two steps of the cascade are catalyzed, the overall conversion is an example of multicatalysis. Yields for the optimized, one-pot protocol are dramatically improved over the conventional stepwise process.     

On sums of degrees of the partial quotients in continued fraction expansions of Laurent series

For any formal Laurent series with coefficients cn lying in some given finite field, let x=[a₀(x);a₁(x),a₂(x),…] be its continued fraction expansion. It is known that, with respect to the Haar measure, almost surely, the sum of degrees of partial quotients grows linearly. In this note, we quantify the exceptional sets of points with faster growth orders than linear ones by their Hausdorff dimension, which covers an earlier result by J. Wu.     

Parametric Statistical Uncertainty Relations and Parametric Statistical Fundamental Equations

Multivariate parametric statistical uncertainty relations are proved to specify multivariate basic parametric statistical models. The relations are expressed by inequalities. They generally show that we cannot exactly determine simultaneously both a function of observation objects and a parametric statistical model in a compound parametric statistical system composed of observations and a model. As special cases of the relations, statistical fundamental equations are presented which are obtained as the conditions of attainment of the equality sign in the relations. Making use of the result, a generalized multivariate exponential family is derived as a family of minimum uncertainty distributions. In the final section, several multivariate distributions are derived as basic multivariate parametric statistical models.     

Lie Atoms and Their Deformations

A Lie atom is essentially a pair of Lie algebras and its deformation theory is that of a deformation with respect to the first algebra, endowed with a trivialization with respect to the second. Such deformations occur commonly in algebraic geometry, for instance as deformations of subvarieties of a fixed ambient variety. Here we study some basic notions related to Lie atoms, focussing especially on their deformation theory, in particular the universal deformation. We introduce Jacobi–Bernoulli cohomology, which yields the deformation ring, and show that, under suitable hypotheses, infinitesimal deformations are classified by certain Kodaira–Spencer data. Received: May 2006 Revision: January 2007 Accepted: March 2007     

Extra Theory Morphisms for Institutions: Logical Semantics for Multi-Paradigm Languages

We extend the ordinary concept of theory morphism in institutions to extra theory morphisms. Extra theory morphisms map theories belonging to different institutions across institution morphisms. We investigate the basic mathematical properties of extra theory morphisms supporting the semantics of logical multi-paradigm languages, especially structuring specifications (module systems) á la OBJ-Clear. They include model reducts, free constructions (liberality), co-limits, model amalgamation (exactness), and inclusion systems.We outline a general logical semantics for languages whose semantics satisfy certain logical principles by extending the institutional semantics developed within the Clear-OBJ tradition. Finally, in the Appendix, we briefly illustrate this with the concrete example of CafeOBJ.     

Racemic synthesis of an intermediate for the formal synthesis of madindoline A and B

On the basis of the application of the Darzens/ring-expansion process of cyclobutenedione developed previously by our group, a new strategy for the multisubstituted cyclopentene units of madindoline A and madindoline B has been reported in this paper. In light of the strategy, the synthesis of racemic Omura’s intermediate was finished in four steps and 34% overall yield, which furnished a new formal synthetic route to madindolines A and B.     

Dedekind–MacNeille Completion of n-ordered Sets

A completion of an n-ordered set is defined, by analogy with the case of posets (2-ordered sets), as a pair , where Q is a complete n-lattice and is an n-order embedding. The Basic Theorem of Polyadic Concept Analysis is exploited to construct a completion of an arbitrary n-ordered set. The completion reduces to the Dedekind–MacNeille completion in the dyadic case, the case of posets. A characterization theorem is provided, analogous to the well-known dyadic one, for the case of joined n-ordered sets. The condition of joinedness is trivial in the dyadic case and, therefore, this characterization theorem generalizes the uniqueness theorem for the Dedekind–MacNeille completion of an arbitrary poset.      

Complexing equilibria and redox potentials in the system Ag(II)/Ag(I)-1,10-phenanthroline in propylene carbonate

Predominance areas of various equilibria were identified and complex formation constants of Ag(I) with 1,10-phenanthroline were determined as well as the solubility product of the complex salt for Ag(phen)₂ClO₄ in propylene carbonate. The solubility product of AgNO₃ in propylene carbonate was estimated. The value of the formal potential of the system Ag(phen) ₂ ²⁺ /Ag(phen) ₂ ⁺ inPC was determined by chronovoltammetry. Differences in the stability of analogous complexes in water andPC are discussed.

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Die Gleichgewichtskonstante der Komplexierung und die Redoxpotentiale im System Ag(II)/Ag(I)-1,10-Phenantrolin in Propylencarbonat

Zusammenfassung Die Gebiete der Dominanz der einzelnen Gleichgewichte, die Bildungskonstanten ₁ und ₂ der Komplexe Ag(I) mit 1,10-Phenantrolin und der Wert des Löslichkeitsproduktes Ag(phen)₂ClO₄ in Propylencarbonat wurden bestimmt. Das Löslichkeitsprodukt von AgNO₃ in Propylencarbonat wurde abgeschätzt. Die Werte des formalen Potentials des Systems Ag(phen) ₂ ²⁺ /Ag(phen) ₂ ⁺ inPC wurden mit Hilfe cyclischer Voltametrie ermittelt. Es wurden weiterhin die Unterschiede in der Stabilität analoger Komplexe in Wasser und in Propylencarbonat diskutiert.