Structural verification of a tetrahydrotetrazole compound

Tetrahydrotetrazoles are five‐membered‐ring heterocycles containing four contiguous saturated nitrogen atoms. Very few examples of such compounds have been reported in the literature. Our previous attempt at the synthesis of a member of this class of compound suggested that the N—N bonds may be more labile than expected. This finding raised the question as to whether the structures of any of the previously reported tetrahydrotetrazoles had been properly assigned. We have reproduced the synthesis of a reported tetrahydrotetrazole, namely 1,2‐di‐tert‐butyl 3‐phenyl‐1H,2H,3H,10bH‐[1,2,3,4]tetrazolo[5,1‐a]isoquinoline‐1,2‐dicarboxylate, C₂₅H₃₀N₄O₄, and have now confidently confirmed its structure via X‐ray crystallography. However, while sufficiently stable in the crystal phase, we discovered that it remains very labile in solution (having a half‐life of only 15 min at 20 °C in CDCl₃). A tentative reaction pathway for its dissociation based on ¹H NMR spectral evidence is provided.     

Synthesis of β -Cyperone via Fungal Hydroxylation of thujone-derived tricyclic cyclopropanes

Synthesis of optically active sesquiterpenes with a eudesmane C-skeleton from the chiral starting material thujone involves transformation of a tricyclic intermediate (1R,2R,4S)-1,7-dimethyl-4-(1-methylethyl)tricyclo[4.4.0.0^2,4]dec-6-en-8-one ( 2 ) into the bicyclic compound β -cyperone ( 5 ). Hydroxylation of 2 at C(5) or C(11) permits subsequent opening of the cyclopropane ring and rearrangement to β -cyperone. In this publication, studies involving hydroxylation of 2 by fungal cultures are presented. The resultant products are useful intermediates in efficient synthesis of eudesmane sesquiterpenes. Of five fungi tested, Rhizopus oryzae ATCC 11145 proved most versatile. It hydroxylates at the exocyclic C(11) position in high yield (70%) and, to a lesser extent, at C(5) (5%). Enzymatic activity appears at the end of growth phase and at least 2.2 g of 2 per liter can be metabolized without significant loss of product yield. A second fungus, Cunninghamella echinulata ATCC 9244, proved most useful for hydroxylation of derivatives of 2 for the preparation of derivatives of β -cyperone, although product yields were low (2–20%), some derivatives were nonreactive, and hydroxylation at C(9) occurred. The relationship between precursor structure and enzyme affinity is discussed.     

An unstructured mesh finite volume method for modelling saltwater intrusion into coastal aquifers

In this paper, a two-dimensional finite volume unstructured mesh method (FVUM) based on a triangular background interpolation mesh is developed for analysing the evolution of the saltwater intrusion into single and multiple coastal aquifer systems. The model formulation consists of a ground-water flow equation and a salt transport equation. These coupled and non-linear partial differential equations are transformed by FVUM into a system of differential/algebraic equations, which is solved using backward differentiation formulas of order one through five. Simulation results are compared with previously published solutions where good agreement is observed.     

Products of mixed covering arrays of strength two

A covering array CA(N;t,k, v is an N × k array such that every N × t subarray contains all t‐tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t‐sets of component interactions. The particular case when t = 2 (pairwise coverage) has been extensively studied, both to develop combinatorial constructions and to provide effective algorithmic search techniques. In this paper, a simple “cut‐and‐paste” construction is extended to covering arrays in which different columns (factors) admit different numbers of symbols (values); in the process an improved recursive construction for covering arrays with t = 2 is derived. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 124–138, 2006     

The Third-Order Singular-Perturbation Expansion of the Planar Cold-Fluid Magnetron Equations

The singular-perturbation expansion of the plasma cold-fluid equations for crossed fields in a planar geometry is presented. The general expansion is carried out to third order. Various instabilities that occur in the first, second, and third orders are discussed.     

Microwave-accelerated Claisen rearrangements of allyl tetronates and tetramates

[3,3]-Sigmatropic rearrangements of allyl tetronates and allyl tetramates to give 3-allyltetronic or -tetramic acids, respectively, proceed within 20-60 min under microwave irradiation (300 W, 130-190 °C). Consecutive (homo)sigmatropic [1,5] H-shifts such as oxa-ene reactions are promoted less effectively, which allows the isolation of Claisen intermediates of sigmatropic domino sequences, in contrast to conventional heating.