Folding transformations of the Painlevé equations

New symmetries of the Painlevé differential equations, called folding transformations, are determined. These transformations are not birational but algebraic transformations of degree 2, 3, or 4. These are associated with quotients of the spaces of initial conditions of each Painlevé equation. We make the complete list of such transformations up to birational symmetries. We also discuss correspondences of special solutions of Painlevé equations.Acknowledgement The authors wish to thank Prof. Yosuke Ohyama, Prof. Shun Shimomura, and Dr. Yoshikatsu Sasaki for valuable discussions.     

exo‐[N,N′‐Bis(3‐tert‐butyl­salicyl­idene)‐1,2‐di­phenyl‐(RS,SR)‐1,2‐ethane­diyl­diaminato]­oxovanadium(IV)

The title mononuclear oxovanadium(IV) complex, [VO(C₃₆H₃₈N₂O₂)], has a distorted square‐pyramidal coordination. The complex was shown to be the exo isomer.     

[N,N′‐Bis­(salicyl­idene)‐1,2‐di­phenyl‐(RS,SR)‐1,2‐ethane­di­amin­ato]­nickel(II)

In crystals of the title compound, [Ni(C₂₈H₂₂N₂O₂)], the coordination geometry around the Ni atom is square planar with a slight tetrahedral distortion. The five‐membered N,N′‐chelate ring adopts a distorted gauche conformation with the two phenyl groups in axial and equatorial orientations.     

Chiral recognition by cyclic oligosaccharides. Enantioselective complexation of binaphthyl derivatives with cyclodextrins

Abstract

Chiral recognition of binaphthyl derivatives, such as 1,1′-bi-2-naphthol (1), 1,1′-binaphthyl-2,2′-diyl hydrogen phosphate (2), and 2,2′-dihydroxy-1,1′-binaphthyl-3,3′-dicarboxylic acid (3), by cyclodextrins (CDxs) has been studied. The S enantiomers of 1 and 2 are bound to heptakis(2,3,6-tri-O-methyl)-β-CDx (TMe-β-CDx) as well as β-CDx more strongly than the R enantiomers. The molecular mechanics and molecular dynamics calculations for the 1:1 complex of 1 and β-CDx suggest that more effective van der Waals contacts and intermolecular hydrogen bonding stabilize the complex of S-1 compared with that of R-1. Meanwhile the R enantiomer of 3 is the preferable guest for β- and TMe-β-CDxs. Circular dichroism spectroscopy suggests that the complex of S-3 is more unstable than that of R-3 because the dihedral angle of the naphthalene planes of S-3 needs to be reduced for forming the inclusion complex. The enantiomers of the guest binaphthyls are completely separated by means of capillary zone electrophoresis (CZE) when TMe-β-CDx is used as a separating agent. The results of the CZE correspond well with those of the binding constants of the inclusion complexes.     

Electronic conductivity of pure ceria

The electronic conductivity of pure ceria with two different impurity levels is examined by dc polarization technique based on the Hebb-Wagner ion blocking method. The impurity level for the ceria with 99.999% purity (5N-CeO₂) is about 1/100 of that with 99.9% purity (3N-CeO₂) as confirmed by the fluorescence intensity of impurities obtained by Raman spectroscopy. The electronic conductivity for the 5N-CeO₂ was measured at T = 973 K to 1173 K, and the results are essentially the same as those for the 3N-CeO₂. The electronic conductivity increases with decreasing of P(O₂) following slope values of − 1/4 to − 1/6. The − 1/4 dependent region becomes narrower for the 5N-CeO₂ than that for the 3N-CeO₂. For both types of ceria, the P(O₂) independent region appears in the same region of higher than 10^− 2 and 10^− 3 MPa at T = 1073 K and 973 K, respectively. Activation energies for the 5N-CeO₂ were 2.2 eV, 2.6 eV and 1.9 eV in P(O₂) dependent regions of − 1/6, − 1/4 and 0, respectively.     

Preparation and thermodynamic stability of micron-sized, monodisperse composite polymer particles of disc-like shapes by seeded dispersion polymerization

Micron-sized, monodisperse composite polymer particles having "disc-like" and "polyhedral" shapes were prepared by seeded dispersion polymerization of 2-ethylhexylmethacrylate (EHMA) with 2.67-mum-sized polystyrene (PS) seed particles in methanol/water media in the presence of droplets of various saturated hydrocarbons and evaporation of the hydrocarbon after the polymerization. Such nonspherical shapes were based on the volume reduction due to the evaporation. The primary factors influencing the particle shape seemed to be the absorption rate of the hydrocarbon into the resulting PS/poly(EHMA)/hydrocarbon composite particles during the polymerization, which affected the viscosities and the volumes of the PS and poly(EHMA) phases. It was found that the morphological development during the polymerization was retarded at "hamburger-like" morphology, which is a precursor of the disc-like particle, although this morphology is a thermodynamically metastable state.     

Selective synthesis of β-alkylpyrroles

β-Alkylpyrroles are key structural motifs found in many natural products and biologically active compounds as well as functional organic materials. For this reason, synthetic chemists continue to be interested in construction of the framework of β-alkylpyrroles. Due to sufficient aromaticity and π-excessive nature of pyrroles, a straightforward approach to β-alkylpyrroles should be electrophilic aromatic substitution (S(E)Ar) toward the pyrrole ring. However, since a primary nucleophilic site of pyrroles is an α-position, some "trick" is required to direct incoming alkyl electrophiles toward a β-position. This Concept article focuses on presenting previous efforts that have been devoted to the synthesis of β-alkylpyrroles, mainly through the S(E)Ar route.