The reactions of diaminomaleonitrile with isocyanates and either aldehydes or ketones revisited.

A reinvestigation of the reactions of urea derivatives of diaminomaleonitrile 2 with aldehydes or ketones in the presence of triethylamine has established that the products of these reactions are not pyrimidino[5,4-d]pyrimidines 9 as previously reported, but 8-oxo-6-carboxamido-1,2-dihydropurines 12, which are oxidized rapidly in air to the corresponding 6-carboxamidopurines 13. Similarly, the reaction of Schiff base derivatives of DAMN 5 with isocyanates in the presence of triethylamine gives the substituted 2-oxoimidazoles 20 and not the pyrimidine derivatives 8 as previously claimed. The compounds 20 cyclize in solution and are easily oxidized to 8-oxopurine-6-carbonitriles 22, which give the same 8-oxopurine-6-carboxamides 13 upon further hydrolysis.     

Linear aminophenol polymers using the mannich reaction

Mannich reactions were used to prepare a series of low-molecular-weight linear polymers from substituted phenols, formaldehyde, and secondary diamines. The physical and spectroscopic properties of these new aminophenol polymers are described and compared with those of the bisphenolic diamines formed as an intermediate step in the polymerization process. The polymers were found to give coloured, water-soluble, metal complexes with copper and iron salts.     

Kripke submodels and universal sentences

We define two notions for intuitionistic predicate logic: that of a submodel of a Kripke model, and that of a universal sentence. We then prove a corresponding preservation theorem. If a Kripke model is viewed as a functor from a small category to the category of all classical models with (homo)morphisms between them, then we define a submodel of a Kripke model to be a restriction of the original Kripke model to a subcategory of its domain, where every node in the subcategory is mapped to a classical submodel of the corresponding classical model in the range of the original Kripke model. We call a sentence universal if it is built inductively from atoms (including ? and ⊥) using ∧, ∨, ?, and →, with the restriction that antecedents of → must be atomic. We prove that an intuitionistic theory is axiomatized by universal sentences if and only if it is preserved under Kripke submodels. We also prove the following analogue of a classical model‐consistency theorem: The universal fragment of a theory Γ is contained in the universal fragment of a theory Δ if and only if every rooted Kripke model of Δ is strongly equivalent to a submodel of a rooted Kripke model of Γ. Our notions of Kripke submodel and universal sentence are natural in the sense that in the presence of the rule of excluded middle, they collapse to the classical notions of submodel and universal sentence. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A practical general approximation criterion for methods of multipliers based on Bregman distances

 This paper demonstrates that for generalized methods of multipliers for convex programming based on Bregman distance kernels – including the classical quadratic method of multipliers – the minimization of the augmented Lagrangian can be truncated using a simple, generally implementable stopping criterion based only on the norms of the primal iterate and the gradient (or a subgradient) of the augmented Lagrangian at that iterate. Previous results in this and related areas have required conditions that are much harder to verify, such as ε-optimality with respect to the augmented Lagrangian, or strong conditions on the convex program to be solved. Here, only existence of a KKT pair is required, and the convergence properties of the exact form of the method are preserved. The key new element in the analysis is the use of a full conjugate duality framework, as opposed to mainly examining the action of the method on the standard dual function of the convex program. An existence result for the iterates, stronger than those possible for the exact form of the algorithm, is also included. Received: February 6, 2001 / Accepted: January 25, 2003 Published online: March 21, 2003 Mathematics Subject Classification (1991): 90C25, 90C46, 47H05     

Hyperfine interactions,including Bhf[FrFe], studied in the decay chain of225Ra by alpha and gamma anisotropy measurements

A low temperature nuclear orientation experiment has been performed on the 14.8d²²⁵Ra activity. Gamma anistotropy [²²¹Fr (4.8m) and²¹³Bi (45.6m)] and alpha anisotropy [²²⁵Ac (10.0d),²²¹Fr,²¹⁷At (32.3ms) and²⁰⁹Po (4.2μs)] measurements has been carried out and values for the hyperfine field of²²⁵Ac and²²¹Fr in iron and the magnetic moment of²¹³Bi are reported.     

New Families of Semi-Regular Relative Difference Sets

We give two constructions for semi-regular relative difference sets (RDSs) in groups whose order is not a prime power, where the order u of the forbidden subgroup is greater than 2. No such RDSs were previously known. We use examples from the first construction to produce semi-regular RDSs in groups whose order can contain more than two distinct prime factors. For u greater than 2 these are the first such RDSs, and for u=2 we obtain new examples.     

The Algebraic K-Theory of Operator Algebras

We the study the algebraic K-theory of C *-algebras, forgetting the topology. The main results include a proof that commutative C*-algebras are K-regular in all degrees (that is, all theirN ^T K _iand extensions of the Fischer-Prasolov Theorem comparing algebraic and topological K-theory with finite coefficients.