Controlling the α/γ-Reactivity of Vinylogous Ketone Enolates in Organocatalytic Enantioselective Michael Reactions

The first regio-, diastereo-, and enantioselective direct Michael reaction of β,γ-unsaturated ketones with nitroolefins is enabled by Brønsted base/hydrogen-bonding bifunctional catalysis. A squaramide-substituted tertiary amine catalyzes the reaction of a broad range of β,γ-unsaturated ketones to proceed at the α-site exclusively, giving rise to adducts with two consecutive tertiary carbon stereocenters in diastereomeric ratios of up to >20:1 and enantioselectivities generally in the 90–98 % ee range.     

Stokes waves with constant vorticity: I. Numerical computation

Periodic traveling waves are numerically computed in a constant vorticity flow subject to the force of gravity. The Stokes wave problem is formulated via a conformal mapping as a nonlinear pseudodifferential equation, involving a periodic Hilbert transform for a strip, and solved by the Newton‐GMRES method. For strong positive vorticity, in the finite or infinite depth, overhanging profiles are found as the amplitude increases and tend to a touching wave, whose surface contacts itself at the trough line, enclosing an air bubble; numerical solutions become unphysical as the amplitude increases further and make a gap in the wave speed versus amplitude plane; another touching wave takes over and physical solutions follow along the fold in the wave speed versus amplitude plane until they ultimately tend to an extreme wave, which exhibits a corner at the crest. Touching waves connected to zero amplitude are found to approach the limiting Crapper wave as the strength of positive vorticity increases unboundedly, while touching waves connected to the extreme waves approach the rigid body rotation of a fluid disk.     

(E)-3-Halo-2-styryl-4H-chromen-4-ones: synthesis and transformation to novel pyrazoles

New methods for the synthesis of (E)-3-halo-2-styryl-4H-chromen-4-ones were established. The reaction of these compounds with hydrazine hydrate afforded new and unexpected 3(5)-aryl-5(3)-[2-(2-hydroxyphenyl)-2-hydrazonoethyl]-1H-pyrazoles, which upon acid hydrolysis gave 3(5)-aryl-5(3)-[2-(2-hydroxyphenyl)-2-oxoethyl]-1H-pyrazoles. The reaction mechanisms for these transformations, involving 1,6- followed by 1,4-conjugate additions, are discussed and the structures of all new compounds were established by NMR studies.     

Interaction of heparin and tetraarginine in capillary electrophoresis: Implication for analytical applications

Interactions between heparin and tetraarginine in an acidic background electrolyte were investigated in capillary electrophoresis. The results showed that tetraarginine and heparin form a stable complex that migrates toward the anode immediately after coming into contact. When a zone of tetraarginine at a mg/mL concentration level passes through a zone of heparin at a μg/mL concentration level, tetraarginine is gradually removed by the formation of the complex that migrates in the opposite direction, thereby decreasing the tetraarginine peak area. The variation of the tetraarginine peak area as a function of the unfractionated heparin concentration was linear within the range 2–20 μg/mL, which enables us to detect and determine heparin concentrations undetectable with a UV detector. The same behavior was confirmed for low molecular weight heparin.     

Dimethylmalonoyl peroxide – the neglected lowest homologue: simple synthesis and high reactivity

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3,4-Epoxyperfluorooxolane in the synthesis of new fluorine-containing furo[3,4-b]quinoxaline derivatives

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Point classification of second order ODEs and its application to Painlevé equations

The first part of this work is a review of the point classification of second order ODEs done by Ruslan Sharipov. His works were published in 1997-1998 in the Electronic Archive at LANL. The second part is an application of this classification to Painlevé equations. In particular, it allows us to solve the equivalence problem for Painlevé equations in an algorithmic form.