On the construction of least favourable pairs of distributions

Summary Convex programming techniques were used by Witting and Krafft in [4] in order to reduce a testing problem for composite hypotheses to one for simple hypotheses. This is realized in terms of least favourable pairs of distributions, which represent the solution of the dual of a suitable program. Without further assumptions on the hypotheses, however, the results, derived that way (cf. Baumann [1], Österreicher [6] and Kusolitsch and Österreicher [5]), are of less practical impact. This is due to the fact that in this case the least favourable pairs depend on the level of the testing problem. Conditions avoiding this, were given by Huber and Strassen in [3]. These conditions make use of 2-alternating capacities in the sense of Choquet. The present paper offers a rather general principle of constructing the least favourable distribution in the case, when one of the two hypotheses is simple. This method works also for the local variation model and the Prohorov neighbourhood model in the case of monotone likelyhood ratio. For simple cases—subsuming the gross error model and the total variation model, for which the solution was given by Huber in [2]—a least favourable pair is obtained by using the mentioned technique of construction two times successively.     

Filtered backprojection for the reconstruction of a high-resolution (4,2)D CH3-NH NOESY spectrum on a 29 kDa protein

Projection-reconstruction (PR) NMR enables rapid collection of multidimensional NMR data. NOESY represents a particularly difficult challenge for currently existing reconstruction algorithms, as it requires the quantitative reconstruction of an unknown number of peaks, at full sensitivity. We have demonstrated the successful application of PR-NMR to NOESY by determining the 4D methyl/amide NOESY spectrum of a 29 kDa protein, human carbonic anhydrase II, from 2D projections, using filtered backprojection for reconstruction. Compared with a 3D control spectrum, all expected peaks were faithfully reconstructed, with correct volumes and with no artifacts. Filtered backprojection thus provides a way to obtain high-resolution 4D NOESY data in the time required for conventional 3D data collection.     

Molecular orbital theoretical prediction of the isomeric products formed from reactions of arene oxides and related metabolites of polycyclic aromatic hydrocarbons

MO theoretical calculations based on the perturbational method of Dewar provide good correlation between predicted and observed structures of products formed during: (1) isomerization of arene oxides to phenols; (2) hydration and nucleophilic addition to arene oxides; and (3) dehydration of arene dihydrodiols. The method is equally applicable to the arene oxides, dihydrodiols, etc. derived from carcinogenic and noncarcinogenic polycyclic hydrocarbons. Extension to the related enzymatic reactions occurring during metabolism of carcinogenic hydrocarbons and to the reactions of the biologically active arene diolepoxides and aryloxirenes suggests the potential utility of this approach in predicting (a) metabolite structure and (b) the structural requirements for carcinogenic and mutagenic activity.     

X=Y=ZH Systems as potential 1,3-dipoles. Part 58: Cycloaddition route to chiral conformationally constrained (R)-pro-(S)-pro peptidomimetics

Imines of (1S,9S)-t-butyl-9-amino-octahydro-6,10-dioxo-6H-pyridazino[1,2-a][1,2]diazepine-1-carboxylate undergo thermal (toluene, 110°C) or LiBr-DBU catalysed (MeCN, room temperature) regio- and stereo-specific cycloaddition to a range of chiral dipolarophiles giving enantiopure spiro-cycloadducts in excellent yield. The reactions proceed via intermediate NH azomethine ylides and litho azomethine ylides, respectively and results in the multiplication of chiral centres from 2 (one of which is lost in the process) to 5.     

Selective LC Determination of Cabergoline in the Bulk Drug and in Tablets: In Vitro Dissolution Studies

Cabergoline (CAB) is an ergot alkaloid derivative with dopamine agonist activity. A novel, simple, and rapid stability-indicating high-performance liquid chromatographic (HPLC) method for assay of CAB in tablets has been developed and validated. Chromatography was performed on a 4.6 mm i.d. × 250 mm, 5 μm particle, cyano column with acetonitrile–10 mM phosphoric acid, 35:65 (v/v), containing 0.04% triethylamine, as mobile phase, at a flow rate of 1.0 mL min^?1, and UV detection at 280 nm. Response was a linear function of concentration in the range 0.1–4 μg mL^?1 (r ² = 0.9999). The recovery of the method was good (99.45%) and RSD values for intra-day and inter-day precision were 0.24–0.88% and 0.66–1.19%, respectively. The method can be used for quality-control assay of CAB in tablets, for stability studies, and for in vitro dissolution studies.     

A generalization of the Rouse-Zimm model

The idea of consistently averaging the hydrodynamic interaction and its various consequences for Hookean dumbbells are reviewed. For long chains this idea can be used to generalize the Rouse-Zimm model for polymer solutions. Unlike the usual Rouse-Zimm model, the new model for steady shear flow predicts a nonzero second normal stress coefficient and shear rate dependent material functions. In the limit of long chains, the viscosity and the normal stress coefficients are universal functions of the reduced shear rate.This paper was presented at the Frühjahrstagung des Fachausschusses Polymerphysik der Deutschen Physikalischen Gesellschaft at Kaiserslautern (West Germany), March 12–14, 1986.     

Oxaziridinium salts as hydrophobic epoxidation reagents: remarkable hydrophobically-directed selectivity in olefin epoxidation

Selective epoxidation of cinnamates versus crotonate was used to detect hydrophobic binding of the cinnamates in the transition states with hydrophobic oxidizing agents in water solution. With peracids as oxidants, no such effect was seen, in accord with the calculated geometries of epoxidation in which the hydrophobic groups of substrate and oxidant could not stack. However, with oxaziridinium salts carrying fused benzene rings there was significantly high selectivity for the cinnamates in water solution, which could be suppressed with added 2-propanol. The hydrophobically induced selectivity changes were even larger, in free energy terms, than those reported previously for the atom-transfer reactions in hydride reductions. Furthermore, the oxaziridinium ions could be generated with oxone from catalytic amounts of the corresponding iminium salts. These substrate selectivities should also carry over to positional selectivities in polyenes.     

Facile synthesis of 2-bromo-3-fluorobenzonitrile: an application and study of the halodeboronation of aryl boronic acids

A scaleable synthesis of 2-bromo-3-fluorobenzonitrile via the NaOMe-catalyzed bromodeboronation of 2-cyano-6-fluorophenylboronic acid was developed. The generality of this transformation was demonstrated through the halodeboronation of a series of aryl boronic acids. Both aryl bromides and aryl chlorides were formed in good to excellent yields when the corresponding aryl boronic acid was treated with 1,3-dihalo-5,5-dimethylhydantoin and 5 mol % NaOMe.     

Microfluidic routing of aqueous and organic flows at high pressures: fabrication and characterization of integrated polymer microvalve elements

This paper presents the first systematic engineering study of the impact of chemical formulation and surface functionalization on the performace of free-standing microfluidic polymer elements used for high-pressure fluid control in glass microsystems. System design, chemical wet-etch processes, and laser-induced polymerization techniques are described, and parametric studies illustrate the effects of polymer formulation, glass surface modification, and geometric constraints on system performance parameters. In particular, this study shows that highly crosslinked and fluorinated polymers can overcome deficiencies in previously-reported microvalve architectures, particularly limited solvent compatibility. Substrate surface modification is shown effective in reducing the friction of the polymer-glass interface and thereby facilitating valve actuation. A microchip one-way valve constructed using this architecture shows a 2 x 10(8) ratio of forward and backward flow rates at 7 MPa. This valve architecture is integrated on chip with minimal dead volumes (70 pl), and should be applicable to systems (including chromatography and chemical synthesis devices) requiring high pressures and solvents of varying polarity.     

Rhodium-catalyzed 1,4-addition of terminal alkynes to vinyl ketones

The metal complex Rh(acac)(CO)₂ in the presence of an eqimolar amount of tris(o-methoxyphenyl)phosphine provides a useful catalyst system for the 1,4-addition of alkynes to unsubstituted vinyl ketones. Best yields are obtained when the transformation is performed in benzene at reflux with an excess of vinyl ketone. Both aryl and alkyl substituted alkynes participate in the reaction. Primary alcohols and alkyl chlorides are well tolerated under these reaction conditions. The reaction also proceeds in aqueous solvent mixtures, unlike most organometallic addition reactions.