The strong Lefschetz property of the coinvariant ring of the Coxeter group of type H4

We prove that the coinvariant ring of the irreducible Coxeter group of type H₄ has the strong Lefschetz property.     

Ruthenium-catalyzed reaction of alpha,beta-unsaturated imines with carbon monoxide and alkenes leading to beta,gamma-unsaturated gamma-butyrolactams: involvement of direct carbonylation at olefinic C[bond]H Bonds as a key step

The reaction of alpha,beta-unsaturated imines with CO and alkenes in the presence of Ru(3)(CO)(12) as a catalyst results in a three-component coupling reaction that gives alpha,alpha-disubstituted beta,gamma-unsaturated gamma-butyrolactams. The reaction proceeds via a two-step sequence involving the initial formation of ketone derivatives by catalytic carbonylation at the beta-olefinic C-H bonds of alpha,beta-unsaturated imines, followed by the (uncatalyzed) intramolecular nucleophilic attack of the imine nitrogen on the ketonic carbon to generate a tetrahedral intermediate, which then undergoes a 1,2-ethyl migration. The reaction of a cyclic unsaturated imine, derived from the reaction of (1R)-(-)-myrtenal with tert-butylamine, gives a beta-aminocyclopentene derivative, which is formed by an aldol-type condensation of the initially formed ketone, indicating the initial formation of ethyl ketone.     

Rigid-rod polymers with polysiloxane side chains. 2. Synthesis and characterization of aromatic polybenzobisoxazoles with polysiloxane side chains and composite formation with polysiloxane matrices

Aromatic polybenzobisoxazoles, having polydimethylsiloxane side chains (SCPBOs), were prepared using terephthaloyl chloride-terminated polydimethylsiloxane macromonomers and 3,3′-bis(trimethylsiloxy)-4,4′-bis(trimethylsilylamino)biphenyl for the purpose of dispersing rigid-rod molecules in silicone matrices for molecular reinforcement. The degree of polymerization of the side chain was varied from 7.8 to 45.4, and a small amount of (3-butenyloxy)terephthaloyl chloride was copolymerized to give the polymers a functionality that can be linked to the matrices. For all the SCPBOs, the WAXD pattern showed only diffuse reflections, suggesting limited structural regularity, although the polymers were optically anisotropic. No melting transition was observed below the side chain decomposition temperature, 350°C. A polydimethylsiloxane/polybenzobisoxazole composite elastomer was obtained first curing the polysiloxane matrix containing the prepolymer of the SCPBO, followed by in situ thermal ring closure of the prepolymer. Some reinforcement was observed, but the presence of plasticizing effect by the unbound SCPBO was suggested at the same time. © 1995 John Wiley & Sons, Inc.     

Fisher Information of Free-Electron Landau States

An electron in a constant magnetic field has energy levels, known as the Landau levels. One can obtain the corresponding radial wavefunction of free-electron Landau states in cylindrical polar coordinates. However, this system has not been explored so far in terms of an information-theoretical viewpoint. Here, we focus on Fisher information associated with these Landau states specified by the two quantum numbers. Fisher information provides a useful measure of the electronic structure in quantum systems, such as hydrogen-like atoms and under some potentials. By numerically evaluating the generalized Laguerre polynomials in the radial densities, we report that Fisher information increases linearly with the principal quantum number that specifies energy levels, but decreases monotonically with the azimuthal quantum number m. We also present relative Fisher information of the Landau states against the reference density with m=0, which is proportional to the principal quantum number. We compare it with the case when the lowest Landau level state is set as the reference.     

Synthesis and toxicity assay of ceramic nanophosphors for bioimaging with near-infrared excitation

Yttrium hydroxyl carbonate (Y(OH)CO₃) precursors were synthesized by the homogeneous co-precipitation method in the presence of polyacrylic acid (PAAc). Resultant precursor particle size is about 15–20 nm with narrow size distribution whereas the particle size is smaller than those acquired by the conventional homogeneous precipitation method. Effective decrease of Y(OH)CO₃ particle size was found to be higher for the presence of weak polyanionic ionomer such as PAAc than the presence of strong polyanionic ionomer such as sodium polystyrene sulfonate (PSS). It was observed that the morphology and size of the precursors are almost unchanged after the calcination process. Er³⁺ doped Y₂O₃ nanoparticles were synthesized by PAAc assisted homogeneous co-precipitation method showed bright green (550 nm) and red (660 nm) upconversion (UC) as well as near-infrared (NIR) fluorescence (1550 nm) under 980-nm excitation. UC and NIR fluorescence bioimaging and in-vitro cytotoxicity assay of Er³⁺ doped Y₂O₃ nanoparticles were successfully attempted with commercially available macrophages and B-cell hybridomas. Cellular uptake of nanoparticles is evidenced from bright field, UC and NIR fluorescence images of macrophages.     

Officinatrione: an unusual (17S)-17,18-seco-lupane skeleton,and four novel lupane-type triterpenoids from the roots of Taraxacum officinale

Novel 5 lupane-type of triterpenois, i.e., 3β-acetoxy-18α,19α-epoxylupan-21β-ol (1), 18α,19α-epoxy-21β-hydroxylupan-3-one (2), lup-18-ene-3,21-dione (3), lupa-18,21-dien-3β-yl acetate (4), and (17S)-17,18-seco-lup-19(21)-ene-3,18,22-trione (5), named officinatrione, as well as 16 known compounds from the roots of Taraxacum officinale collected in Takatsuki city, Osaka, Japan. Of the above compounds, 5 was the first lupane-type triterpene, of which the D-ring was open to form a nine-membered ring. Compounds 2 and 5 exhibited moderate cytotoxic activities against L1210 cell line (IC₅₀ 10.5 and 10.1 μM).     

The effect of phenoxy oxygen atoms on extremely high extraction ability and less separation efficiency of trivalent rare earth elements with tetraphosphonic acid derivative of calix[4]arene

A cone confomational p-t-octylcalix[4]arene with four methylenephosphonic acids at the lower rim as well as its monomeric analog have been synthesized as a new extraction reagent to investigate the extraction behavior of the nine trivalent rare earth elements: Y, La, Pr, Nd, Sm, Eu, Gd, Ho and Er. The new calix[4]arene exhibited significantly higher extraction capacity than not only the monomeric derivative and the commercial extraction reagent, 2-ethylhexyl hydrogen 2-ethylhexylphosphonate, but also the cone conformational calix[4]arene extractants employed in our previous work, composed of a tetrapropylenephosphonic acid with a longer spacer, a tetraphosphonic acid at the upper rim, and tetraacetic acid at the lower rim. A dependence on the pH was observed for the new extractant in the highly acidic region, and the extraction took place via a simple ion-exchange mechanism. Using slope analysis, the stoichiometries of tetrameric and monomeric extractants to rare earth metal ions were determined to be 2:1 and 3:1, respectively. Using the proposed extraction equations, extraction equilibrium constants and separation factors were estimated. The extremely high extraction ability and moderate separation efficiency were attributed to the chelating effect of the phosphonic acid and the phenoxy oxygen atom. The effect of the phenoxy oxygen atom on extraction ability and separation efficiency of calix[4]arene derivatives was found to be significant.     

Rhodium(I)‐Catalyzed Cyclization of Allenynes with a Carbonyl Group through Unusual Insertion of a CO Bond into a Rhodacycle Intermediate

Rhodium(I)‐catalyzed cyclization of allenynes with a tethered carbonyl group was investigated. An unusual insertion of a C?O bond into the C(sp²)–rhodium bond of a rhodacycle intermediate occurs via a highly strained transition state. Direct reductive elimination from the obtained rhodacyle intermediate proceeds to give a tricyclic product containing an 8‐oxabicyclo[3.2.1]octane skeleton, while β‐hydride elimination from the same intermediate gives products that contain fused five‐ and seven‐membered rings in high yields.     

Rhodium-Catalyzed Highly Diastereo- and Enantioselective Synthesis of a Configurationally Stable S-Shaped Double Helicene-Like Molecule

An S-shaped double helicene-like molecule (>99 % ee), possessing stable helical chirality, has been synthesized by the rhodium(I)/difluorphos complex-catalyzed highly diastereo- and enantioselective intramolecular double [2+2+2] cycloaddition of a 2-naphthol- and benzene-linked hexayne. The collision between two terminal naphthalene rings destabilizes the helical chirality of the S-shaped double helicene-like molecule, but the introduction of two additional fused benzene rings significantly increases the configurational stability. Thus, no epimerization and racemization were observed even at 100 °C. The enantiopure S-shaped double helicene-like molecule forms a trimer through the multiple C−H⋅⋅⋅π and C−H⋅⋅⋅O interactions in the solid-state. The trimers stack to form columnar packing structures, in which neighboring stacks have opposite dipole directions. The accumulation of helical structures in the same direction in the S-shaped double helicene-like molecule enhanced the chiroptical properties.