The synthesis of 2-amino-4(3H)-quinazolinones and related heterocycles via a mild electrocyclization of aryl guanidines

A new method for the preparation of 2-amino-4(3H)-quinazolinones and similar fused heterocycles is described. Simply warming a mixture of an aryl guanidine and carbonyl diimidazole in acetonitrile results in formation of a putative N-amidinoisocyanate intermediate which undergoes a 6π-electron electrocyclic reaction with the aryl ring to generate the quinazolinone ring system. The mild conditions are compatible with a variety of functional groups, and the reaction is shown to be successful on multigram scale.     

A Multi‐Component Sensor System for Detection of Amphiphilic Compounds

Many biologically important compounds are amphiphilic in character. Glycolipids, for example, represent a biologically important class of amphiphiles. Receptors and sensors for such compounds must also be amphiphilic making them a challenge to prepare. Here, a cucurbit[8]uril (CB[8])‐based sensor system has been prepared and tested for detection of amphiphilic compounds. This multi‐component system consists: a CB[8], which acts as a hydrophobic lipid receptor, a hydrophilic pyridinium‐based carbohydrate receptor, and a fluorescent indicator. The system self‐assembles in aqueous solution. The pyridinium quenches the fluorescence of the indicator giving a strong turn‐on response when it is displaced by the analyte. The sensor system was characterized by NMR, X‐ray crystallography, and fluorescence titrations.     

Thermal Studies on Some Substituted Aminobenzoic Acids

The thermal behaviour of various substituted aminobenzoic acids(3-aminobenzoic acid (3-ABA), 4-aminobenzoic acid (4-ABA), 3-aminosalicylic acid(3-ASA), 4-aminosalicylic acid (4-ASA), and 5-aminosalicylic acid (5-ASA), as well as the‘parent’ benzoic acid (BA) and salicylic acid (SA) as reference substances, and possible decomposition products: 2-aminophenol (2-AP), 3-aminophenol (3-AP) and 4-aminophenol(4-AP) in the solid state has been examined. The various sets of isomers studied showed considerable and interesting differences. Most sublimed well before melting, generally with an increasing rate of mass loss beyond their very different melting points. The differences in behaviour of 4-ASA and 5-ASA were the most remarkable, with 5-ASA being far more stable and apparently not decarboxylating readily, while 4-ASA sublimed at temperatures below the melting point, becoming less stable and decarboxylating in the liquid form. This revised version was published online in July 2006 with corrections to the Cover Date.     

Linkage isomerism in 5-exo thiocyanate and isothiocyanate substituted tricarbonyl(η-cyclohexa-1,3-diene)iron and tricarbonyl(η-cyclohepta-1,3-diene)iron

Nucleophilic addition to the tricarbonyl(η-cyclohexadienyl)iron cation and the tricarbonyl(η-cycloheptadienyl)iron cation by the thiocyanate ion forms initially the 5-exo-isothiocyanate (NCS) isomers, C₆H₇NCSFe(CO)₃ and C₇H₉NCSFe(CO)₃, both of which isomerise to the corresponding 5-exo thiocyanate isomers C₆H₇SCNFe(CO)₃ and C₇H₉SCNFe(CO)₃ on exposure to air.     

On actions of Drinfel'd doubles on finite dimensional algebras

Let q be an nth root of unity for $n>2$ and let $T_n(q)$ be the Taft (Hopf) algebra of dimension $n^2$. In 2001, Susan Montgomery and Hans-Jürgen Schneider classified all non-trivial $T_n(q)$-module algebra structures on an n-dimensional associative algebra A. They further showed that each such module structure extends uniquely to make A a module algebra over the Drinfel'd double of $T_n(q)$. We explore what it is about the Taft algebras that leads to this uniqueness, by examining actions of (the Drinfel'd double of) Hopf algebras H “close” to the Taft algebras on finite-dimensional algebras analogous to A above. Such Hopf algebras H include the Sweedler (Hopf) algebra of dimension 4, bosonizations of quantum linear spaces, and the Frobenius–Lusztig kernel $u_q({\mathfrak{sl}}_2)$.     

Level sets of the Takagi function: Hausdorff dimension

The Takagi function τ(x) is a continuous non-differentiable function on the unit interval defined by Takagi in 1903. This paper studies level sets L(y) = {x : τ(x) = y} of the Takagi function and bounds their Minkowski dimensions and Hausdorff dimensions above by 0.668. There exist level sets with Minkowski dimension 1/2. The method of proof involves a multiscale analysis that relies upon the self-similarity of τ(x) up to affine shifts.     

A sufficiency class for global (in time) solutions to the 3D Navier-Stokes equations

Let Ω be an open domain of class C² contained in R³, let L²(Ω)³ be the Hilbert space of square integrable functions on Ω and let H[Ω]?H be the completion of the set, , with respect to the inner product of L²(Ω)³. A well-known unsolved problem is that of the construction of a sufficient class of functions in H which will allow global, in time, strong solutions to the three-dimensional Navier-Stokes equations. These equations describe the time evolution of the fluid velocity and pressure of an incompressible viscous homogeneous Newtonian fluid in terms of a given initial velocity and given external body forces. In this paper, we use the analytic nature of the Stokes semigroup to construct an equivalent norm for H, which provides strong bounds on the nonlinear term. This allows us to prove that, under appropriate conditions, there exists a number u₊, depending only on the domain, the viscosity, the body forces and the eigenvalues of the Stokes operator, such that, for all functions in a dense set D contained in the closed ball B(Ω)?B of radius in H, the Navier-Stokes equations have unique, strong, solutions in C¹((0,∞),H).