A Non-Parametric Approach to Model Evaluation

All existing tests and criteria for model evaluation are based on the sum of squared residuals. These measures do not evaluate the performance of a model in predicting turning points in the variable of interest. Here, three tests are proposed to evaluate models on the basis of their ability to predict turning points and to give an unbiased prediction of the relative order of magnitude of changes. Five models are evaluated using the proposed tests. Results indicate that the tests expose facets of models that R² and sum of squared residuals are unable to highlight. Hence, the tests are suggested to complement existing model evaluation techniques.     

A new and stereospecific synthesis of an inositol analogue: bis-homoinositol

The photooxygenation of trans-8-(acetyloxy)bicyclo[4.2.0]octa-2,4-dien-7-yl acetate afforded the bicyclic endoperoxide. Reduction of the endoperoxide with thiourea followed by acetylation gave the corresponding tetraacetate. The KMnO₄ oxidation of the tetraacetate followed by acetylation gave dihydroxytetraacetate Ammonolysis of tetraacetate afforded the bis-homoinositol, bicyclo[4.2.0]octane-2,3,4,5,7,8-hexol.     

Regio‐ and Stereocontrolled Synthesis of (2R*,3R*,4R*)‐3,4‐Dichloro‐1,2,3,4,5,8‐hexahydronaphthalen‐2‐yl Acetate via Tandem SN2′ Reactions

The hydroperoxy endoperoxide 3 , obtained by photooxygenation of isotetralin (= 1,4,5,8‐tetrahydronaphthalene; 1 ), was reduced with thiourea, and the resulting intermediate 4 was converted, after acetylation with acetyl chloride, to the interesting, double‐chlorinated acetate 5 in an unprecedented tandem reaction (Scheme 1). The structures and relative configurations of 3 and 5 were determined by NMR spectroscopy and by single‐crystal X‐ray‐diffraction analyses (Figs. 1 and 2, resp.). A mechanistic rationalization for the conversion of 4 to 5 is proposed (Scheme 2).     

Reaktionen mit cyclischen Oxalylverbindungen,XXIV. Zur Reaktion von 4-Benzoyl-5-phenyl-furan-2,3-dion mit Phenylhydrazonen bzw. Phenylhydrazin

4-Benzoyl-5-phenyl-furan-2,3-dione (1) reacts with various phenylhydrazones2 at 60–80°C to the pyrazole carboxylic acid3 a, which then can be decarboxylated to 4-benzoyl-1,5-diphenyl-pyrazole (5).1 and phenylhydrazine combine again yielding3 a as the main product and the isomeric pyridazinone6 as by-product. At higher temperatures (120–140°C) the reaction of1 with2 a leads to the formation of dibenzoyl acetic acid hydrazide derivatives8.The structures of all products were confirmed by IR, MS,¹⁵N- and¹³C-NMR spectroscopic measurements, in the case of the pyridazinone6 also by an X-ray study.6 crystallizes with one moleDMSO monoclinically in space group P 2₁/n (Nr. 14) with 4 molecules6 andDMSO per cell.The reaction pathways leading to the compounds3, 6 and8 are discussed.

     

Stereospecific synthesis of a new class of aminocyclitol with the conduramine D-2 configuration

A new aminocyclitol derived from bicyclo[4.2.0^1,6]octane was synthesized starting from cyclooctatetraene. Photooxygenation of trans-7,8-diacetoxy-bicyclo[4.2.0]octa-2,4-diene afforded a bicyclic endoperoxide. Reduction of the endoperoxide with thiourea followed by a palladium-catalyzed ionization/cyclization reaction gave an oxazolidinone derivative. Oxidation of the double bond in the oxazolidinone with KMnO₄ followed by acetylation gave the oxazolidinone-tetraacetate whose exact configuration was determined by X-ray diffraction analysis. Hydrolysis of the oxazolidinone ring and removal of the acetate groups furnished the desired aminocyclitol.     

Studies on the reactions of cyclic oxalyl compounds with hydrazines or hydrazones : Synthesis and reactions of 4‐benzoyl‐1‐(3‐nitrophenyl)‐5‐phenyl‐1H‐pyrazole‐3‐carboxylic acid

The 1H‐pyrazole‐3‐carboxylic acid 2 , obtained from the furan‐2,3‐dione 1 and N‐Benzylidene‐N'‐(3‐nitrophenyl) hydrazine, was converted via reactions of its acid chloride 3 with various alcohols or N‐nucleo‐philes into the corresponding ester or amide derivatives 4 or 5 , respectively. Nitrile 6 and anilino‐pyrazole acid 7 derivatives of 2 were also obtained by dehydration of 5a in a mixture of SOCl₂ with DMF and reduction of 2 with sodium polysulphide, respectively. While cyclocondensation reactions of 2 or 7 with phenyl hydrazine or hydrazine hydrate and 6 with only anhydrous hydrazine lead to derivatives of pyrazolo[3,4‐d]‐pyridazinone 8 and pyrazolo[3,4‐d]pyridazine amine 9 , respectivel. The reaction of 2 with 2‐hydrazinopyri‐dine provided hydrazono‐pyrazole acid derivative 10 , which was decarboxylated to give hydrazono‐pyra‐zole derivative 11 . Pyrazolo[4,3‐d]oxazinone 12 and 2‐quinolyl pyrazolo[3,4‐d]pyridazine 13 derivatives were also prepared by cyclocondensation reactions of 2 with hydroxylamine hydrochloride and 7 with acetaldehyde, respectively.     

New quasi-exactly solvable Hamiltonians in two dimensions

Quasi-exactly solvable Schrödinger operators have the remarkable property that a part of their spectrum can be computed by algebraic methods. Such operators lie in the enveloping algebra of a finite-dimensional Lie algebra of first order differential operators—the hidden symmetry algebra. In this paper we develop some general techniques for constructing quasi-exactly solvable operators. Our methods are applied to provide a wide variety of new explicit two-dimensional examples (on both flat and curved spaces) of quasi-exactly solvable Hamiltonians, corresponding to both semisimple and more general classes of Lie algebras.Supported in Part by DGICYT Grant PS 89-0011.Supported in Part by an NSERC Grant.Supported in Part by NSF Grant DMS 92-04192.     

Exterior Differential Systems and Cartan–Kähler Theory

We give an elementary introduction to exterior differential systems and the Cartan–Kähler theorem. No proofs are given, but the results are illustrated by means of examples.Mathematics Subject Classifications (2000) 58A15, 53B20.     

Two‐phase flow electrosynthesis: Comparing N‐octyl‐2‐pyrrolidone–aqueous and acetonitrile–aqueous three‐phase boundary reactions

A microfluidic double channel device is employed to study reactions at flowing liquid–liquid junctions in contact with a boron‐doped diamond (BDD) working electrode. The rectangular flow cell is calibrated for both single‐phase liquid flow and biphasic liquid–liquid flow for the case of (i) the immiscible N‐octyl‐2‐pyrrolidone (NOP)–aqueous electrolyte system and (ii) the immiscible acetonitrile–aqueous electrolyte system. The influence of flow speed and liquid viscosity on the position of the phase boundary and mass transport‐controlled limiting currents are examined. In contrast to the NOP–aqueous electrolyte case, the acetonitrile–aqueous electrolyte system is shown to behave close to ideal without ‘undercutting’ of the organic phase under the aqueous phase. The limiting current for three‐phase boundary reactions is only weakly dependent on flow rate but directly proportional to the concentration and the diffusion coefficient in the organic phase. Acetonitrile as a commonly employed synthetic solvent is shown here to allow effective three‐phase boundary processes to occur due to a lower viscosity enabling faster diffusion. N‐butylferrocene is shown to be oxidised at the acetonitrile–aqueous electrolyte interface about 12 times faster when compared with the same process at the NOP–aqueous electrolyte interface. Conditions suitable for clean two‐phase electrosynthetic processes without intentionally added supporting electrolyte in the organic phase are proposed. Copyright © 2008 John Wiley & Sons, Ltd.