Synthesis and combinatorial approach of the reactivity of 6- and 7-arylthieno[3,2-d][1,3]oxazine-2,4-diones

This paper describes a general procedure for the synthesis of new substituted thiaisatoic anhydrides or 6- or 7-aryl-1H-thiéno[3,2-d][1,3]oxazine-2,4-diones 3a-j and 4a-f. They were synthesized in large scale under microwave heating conditions with high yields. The reactivity vs nucleophilic reagents of these compounds was studied and permitted to develop a simple combinatorial procedure to synthesize a library of new thiophene ureidoacids 7a-j and 8a-j.     

Solid-phase synthesis of 2-substituted 4-amino-7-oxo-5,6,7,8-tetrahydropyrido[2,3-d]pyrimidines: An example of cyclization-assisted cleavage

An efficient solid-phase synthesis of 2-substituted 4-aminopyrido[2,3-d]pyrimidines 12 by cyclization-assisted cleavage from resin is reported. The procedure starts by solid supporting an ,-unsaturated acid 8 to the Wang resin 13 by using DCC and 4-DMAP in THF. The resulting ,-unsaturated ester 14 is converted to the Michael adduct by treatment with malononitrile in NaOMe/THF. Such Michael addition constitutes the first example of a Michael reaction with malononitrile in solid-phase. Finally, the Michael adducts 15 are treated with an amidine system in MeOH to yield the corresponding pyridopyrimidines 12. Compounds 12 present three diversity centers R1, R2 and G. Having validated the chemistry on solid support, a 40-membered combinatorial library was obtained using this protocol.     

A reagent-based strategy for the design of large combinatorial libraries: A preliminary experimental validation

Combinatorial library design can be carried out at either the reagent or the product level. Various reports in the literature have come to conflicting conclusions in favor of one over the other. In this paper a reagent-based screening library design strategy is presented. The method relies on analysis of scaffolds and building blocks separately to define the overall diversity in a compound file. The primary diversity selection by properties relevant for molecular recognition and by redundancy is followed by the application of filters for molecular properties known to be relevant for drug-likeness. Filter properties are rapidly estimated at the product level using a fragmental estimation approach. Initial experimental data suggest that high diversity in vast screening libraries can be achieved by carefully applied reagent level analysis. A potential role of diverse screening libraries in chemical genomics (pharmacological knockouts) is also discussed.     

Exploring solid-phase approaches for the preparation of new β-lactams from amino acids

Two solid-phase approaches, involving the base-assisted intramolecular alkylation of N-chloroacetyl-Phe derivatives anchored to appropriate solid supports, were investigated for the preparation of novel beta-lactams. When a BAL-type strategy was used, the resin-bound azetidinones were easily formed, as established by MAS-NMR, but final compounds could not be removed from the resin, unless a suitable two linkers system was used. In the second approach, in which the Phe residue is anchored to a Wang-type resin through the carboxylate group, the corresponding 1,4,4-trisubstituted 2-azetidinone was obtained in moderate to good yield and high purity.     

On a Conjecture of R.P. Stanley; Part I—Monomial Ideals

In 1982 Richard P. Stanley conjectured that any finitely generated ⁿ -graded module M over a finitely generated ⁿ -graded K-algebra R can be decomposed in a direct sum M = _{i = 1} ^t _i S _i of finitely many free modules _i S _i which have to satisfy some additional conditions. Besides homogeneity conditions the most important restriction is that the S _i have to be subalgebras of R of dimension at least depth M.We will study this conjecture for the special case that R is a polynomial ring and M an ideal of R, where we encounter a strong connection to generalized involutive bases. We will derive a criterion which allows us to extract an upper bound on depth M from particular involutive bases. As a corollary we obtain that any monomial ideal M which possesses an involutive basis of this type satisfies Stanley's Conjecture and in this case the involutive decomposition defined by the basis is also a Stanley decomposition of M. Moreover, we will show that the criterion applies, for instance, to any monomial ideal of depth at most 2, to any monomial ideal in at most 3 variables, and to any monomial ideal which is generic with respect to one variable. The theory of involutive bases provides us with the algorithmic part for the computation of Stanley decompositions in these situations.     

Continuous two-scale equations and dyadic wavelets

The objective of this paper is to investigate the solvability of a continuous two-scale (or refinement) equation and to characterize the solutions of the equation. In addition, the notion of continuous multiresolution analysis (or approximation), CMRA, generated by such a solution is introduced. Here, the notion of continuity follows from a standard engineering terminology, meaning that continuous-time instead of discretetime considerations are studied. This solution, also called a scalling function of the CMRA, gives rise to some dyadic wavelet, a notion introduced by Mallat and Zhong, for multilevel signal decompositions. This research was supported by NSF Grant DMS-92-06928, ARO Contract DAAL 03-90-G0091, and Texas Coordinating Board of Higher Education Grant ATP 999903-054.     

A hybrid Tabu-ascent algorithm for the linear Bilevel Programming Problem

The linear Bilevel Programming Problem (BLP) is an instance of a linear hierarchical decision process where the lower level constraint set is dependent on decisions taken at the upper level. In this paper we propose to solve this NP-hard problem using an adaptive search method related to the Tabu Search metaheuristic. Numerical results on large scale linear BLPs are presented.     

Finite Energy Solutions of Maxwell''s Equations and Constructive Hodge Decompositions on Nonsmooth Riemannian Manifolds

We consider two basic potential theoretic problems in Riemannian manifolds: Hodge decompositions and Maxwell's equations. Here we are concerned with smoothness and integrability assumptions. In the context of L^p forms in Lipschitz domains, we show that both are well posed provided that 2−<p<2+, for some >0, depending on the domain. Our approach is constructive (in the sense that we produce integral representation formulas for the solutions) and emphasizes the intimate connections between the two problems at hand. Applications to other related PDEs, such as boundary problems for the Hodge Dirac operator, are also presented.