Organotellurium Chemistry: Remarkably Facile Preparation of Benzo‐1,3‐tellurazoles

Benzo‐1,3‐tellurazoles carrying alkyl or aryl substituents in position 2 were prepared in a facile two‐step sequence, starting with readily available 2‐haloanilines. This approach relies on the preparation of bis(2‐aminophenyl) ditellurides by nucleophilic halide displacement from 2‐haloanilines with sodium telluride in N‐methylpyrrolidone. Subsequent reductive cyclization with carboxylic acid halides or carboxylic anhydrides furnished benzo‐1,3‐tellurazoles in good yields.     

Use of Griess reagent containing vanadium(III) for post-column derivatization and simultaneous determination of nitrite and nitrate in baby food

An ion chromatographic method with post-column derivatization and spectrophotometric detection is presented for the determination of nitrate and nitrite (NOx) in baby food. NOx residues found naturally or added as preservatives were extracted from baby foods and determined by using ion chromatography with post-column derivatization and spectrophotometric detection. Nitrate was reduced to nitrite online by post-column reduction using vanadium(lll) chloride and heat. Nitrite reacted with Griess reagent to produce a dye that was detected at 525 nm. The use of V(III) and heat to promote the reduction of nitrate to nitrite online is a novel feature of this detection system. The determination of incurred NOx residues in samples by using AOAC Method 993.03 yielded results comparable to those obtained by ion chromatography with spectrophotometric detection. The toxic and carcinogenic metal cadmium used in the AOAC Method to reduce the nitrate to nitrite was avoided. The proposed method provides simultaneous determination of nitrate and nitrite. Average recoveries of nitrate and nitrite residues ranged from 82 to 107% for fortification levels of 25-400 ppm.     

Total synthesis of natural and unnatural lamellarins with saturated and unsaturated D-rings

Twenty-eight natural and unnatural lamellarins with either a saturated or an unsaturated D-ring were synthesized according to our developed synthetic route. The key step involved the Michael addition/ring closure (Mi-RC) of the benzyldihydroisoquinoline and alpha-nitrocinnamate derivatives, which provided the 2-carboethoxypyrrole intermediates in moderate to good yields (up to 78% yield). Subsequent hydrogenolysis/lactonization furnished lamellarins with a saturated D-ring in excellent yields (up to 93% yield). DDQ oxidation of the saturated lamellarin acetates led directly to the corresponding unsaturated analogues in 54-95% yield. In addition, only two steps in our developed strategy require column chromatography.     

New Combinations of Convex Sets

The family of convex sets in a (finite dimensional) real vector space admits several unary and binary operations – dilatation, intersection, convex hull, vector sum – which preserve convexity. These generalize to convex functions, where there are in fact further operations of this kind. Some of the latter may be regarded as combinations of two such operations, acting on complementary subspaces. In this paper, a general theory of such mixed operations is introduced, and some of its consequences developed.     

Determination of lockbox collection points via simulated annealing

This research presents a heuristic to solve the lockbox location problem via a search-based technique known as simulated annealing. In the past, more traditional mathematical programming techniques have been used to address this problem, but with limited success due to its combinatorial nature. Because simulated annealing is a search-based technique, an optimal solution is not guaranteed, but past research has demonstrated that search-based heuristics can provide reasonable solutions without the difficulties associated with the more traditional formulations. In this paper, the simulated annealing methodology is used to solve a large lockbox location problem at several differing levels of cost. The results compare favourably to solutions obtained from a K-means clustering heuristic.     

Combining approaches for evaluating auditing populations: A simulation study

This research explores ways of combining four distinct bounds for the mean error in an auditing population. Two competing objectives for a bound are to be close to the true mean being estimated and to be reliable: not less than the true mean in more than 5% of estimations. The optimal combination should provide the best balance of these competing objectives. Estimating the mean error by a single approach is difficult because typically most accounts have no error and the distribution of the errors among those that do is discontinuous and highly skewed. This study reveals that the weights in the optimal combination are not constant but depend on the characteristic of the population being estimated. The optimally combined bound is only 7% smaller overall than the best of the constituents. However, while the best of the constituents fails in 50% of most challenging populations, the optimal combination never fails.     

Polyhedral 2-manifolds inE 3 with unusually large genus

An equivelar polyhedral 2-manifold in the class ?_p,q is one embedded inE ³ in which every face is a convexp-gon and every vertex isq-valent. In this paper, examples are constructed, to show that each of the classes ?_3,q (q≧7), ?_4,q (q≧5) and ?_p,4 (p≧5) contains infinitely many distinct combinatorial types. As particular examples, there are polyhedral 2-manifolds with 576 vertices and genus 577, and with 4096 faces and genus 4097. A modification of one construction shows that there is a constantk, such that for eachg≧2, there exists a closed polyhedral 2-manifold inE ³ of genusg with at mostkg/logg vertices.