Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus

The functional Ito formula, in the form df() = f( + d ) –f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() – f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25.     

Synthesis of rhenium chelated MAG3 functionalized rosette nanotubes

Rosette nanotubes (RNTs) are discrete nanostructures self-assembled from a guanine–cytosine hybrid motif (G∧C) under aqueous conditions. These materials have substantial design flexibility and a range of applications, which are partly attributed to their diverse surface functionalization. Given the potential for interesting properties resulting from a metal-RNT construct, here we describe an oxorhenium-functionalized RNT. More specifically, we present the synthesis of a twin G∧C motif expressing the mercaptoacetyl triglycine (MAG₃) ligand. We then examine the chelation reaction of the MAG₃ with ReOCl₃(PPh₃)₂ and self-assemble the resulting ReO-MAG₃-G∧C conjugate into RNTs under DMSO and aqueous conditions.     

A regioselective approach to trisubstituted 2 (or 6)-arylaminopyrimidine-5-carbaldehydes and their application in the synthesis of structurally and electronically unique GlambdaC base precursors

An efficient regioselective synthesis of trisubstituted 2(or 6)-arylaminopyrimidine-5-carbaldehydes has been developed via an S(N)Ar reaction of 2,4,6-trichloropyrimidine-5-carbaldehyde with aniline, methylamine, and alkoxide nucleophiles using a combination of phase-transfer catalysis and more traditional SNAr reaction conditions. We demonstrate that in a few synthetic steps, highly functionalized fused-bicyclic pyrimidine substrates can be accessed from the trisubstituted 2-arylaminopyrimidine-5-carbaldehydes. Furthermore, these fused-bicyclic compounds are readily derivatized using the Suzuki cross-coupling reaction to generate electronically and structurally unique GlambdaC base precursors.     

Synthesis of a tetracyclic G∧C scaffold for the assembly of rosette nanotubes with 1.7 nm inner diameter

The synthesis of a tetracyclic self-complementary molecule 4 for self-assembly into rosette nanotubes is presented. This new heterocycle has a core structure containing two pyrido[2,3-d]pyrimidine molecules fused together and features the Watson-Crick hydrogen bond donor-acceptor arrays of both guanine (G) and cytosine (C). Current methods to synthesize pyrido[2,3-d]pyrimidines require harsh conditions and long reaction times and result usually in low product yields. This is particularly problematic for the direct incorporation of functional groups that cannot withstand these conditions. Here, we present an efficient approach to access the multifunctional pyrido[2,3-d]pyrimidine intermediate 2 under relatively mild conditions using three regioselective S(N)Ar reactions at C2, C4, and C7 on the trichloro compound 1. The electron-withdrawing group and amino functionalities on 2 are then used as a handle to install the third and fourth rings of 4 using a Friedla?nder-type condensation followed by mixed urea synthesis and cyclization.     

Supramolecular Synthesis of Solid‐State Tapes Through Molecular Facial Self‐Recognition

Four heterocyclic compounds are presented which exhibit specific self‐recognition of identical Donor–Acceptor (D–A) H‐bonding arrays, resulting in solid‐state tapes with the same, but anti‐parallel functional‐group distribution on opposite sides. A detailed X‐ray‐crystallographic analysis of these supramolecular structures is described.