Algebraic geometry of the eigenvector mapping for a free rigid body

The present paper deals with the algebro-geometric aspects of the eigenvector mapping for a free rigid body. The eigenvector mapping is regarded as a rational mapping to the complex projective plane from the product of the elliptic curves, one of which is the integral curve and the other the spectral curve. This is the space of the necessary data to determine the eigenvectors. The eigenvector mapping admits a factorisation through a Kummer surface, which is a double covering of the projective plane branched along a sextic curve associated with the dynamics. The key of the argument is the Cremona transformation of the projective plane and some elliptic fibrations of the Kummer surface.     

Precise isomerization polymerization of alkenylcyclohexanes: stereoregular polymers containing six-membered rings along the polymer chain

Pd and Ni diimine complexes catalyze the isomerization polymerization of alkenylcyclohexanes to afford polymers composed of alternating trans-cyclohexane-1,4-diyl rings and oligomethylene spacers with high selectivity. The melting points of the polymers vary from 130 to 226 °C depending on length of the oligomethylene spacer.     

Adsorption of several gases on flexible metal organic framework [Cu(dhbc)2(4,4'-bpy)]·H2O

The adsorption of ten gases on the flexible metal organic framework material [Cu(dhbc)(2)(4,4'-bpy)]·H(2)O (Cu(db)) has been measured over a wide range of temperatures and pressures. The gate opening condition and driving force behind gate adsorption for Cu(db) were discussed by examining the adsorption isotherms. The adsorption isotherms for each adsorbate can be generalized to a characteristic curve using the adsorption potential energy (ε) and the adsorption volume. The adsorption potential (ε(gate)) at gate opening is almost constant over a wide range of temperatures; thus, the gate pressure at a desired temperature can be deduced using the ε(gate) evaluated from one adsorption isotherm. The gate opening capacity of the gases was arranged in the order: CO(2)≒N(2)O>C(2)H(4)≒Xe>CH(4)>CO>O(2)>Ar≒N(2)>H(2), which is governed by the interaction energy between the outer surface of Cu(db) and the adsorbate. It is suggested that the gate effect is brought about when the integral interaction energy of adsorbates with the Cu(db) surface exceeds a defined limit correlating with the π-π stacking energy of Cu(db) layers.     

Compression behaviors of binary skutterudite CoP3 in noble gases up to 40 GPa at room temperature

The binary skutterudite CoP(3) has a large void at the body-centered site of each cubic unit cell and is, therefore, called a nonfilled skutterudite. We investigated its room-temperature compression behavior up to 40.4 GPa in helium and argon using a diamond-anvil cell. High-pressure in situ X-ray diffraction and Raman scattering measurements found no phase transition and a stable cubic structure up to the maximum pressure in both media. A fitting of the present pressure-volume data to the third-order Birch-Murnaghan equation of state yields a zero-pressure bulk modulus K(0) of 147(3) GPa [pressure derivative K(0)' of 4.4(2)] and 171(5) GPa [where K(0)' = 4.2(4)] in helium and argon, respectively. The Gru?neisen parameter was determined to be 1.4 from the Raman scattering measurements. Thus, CoP(3) is stiffer than other binary skutterudites and could therefore be used as a host cage to accommodate large atoms under high pressure without structural collapse.     

Significant substitution effects in dipolar and non-dipolar supercritical fluids

Vibrational Raman spectra of C=C stretching modes of ethylene derivates (cis-C(2)H(2)Cl(2), cis-stilbene, and trans-stilbene) were measured in supercritical fluids along an isotherm as functions of their densities. The substitution effect of the Raman shift is so significant that a difference among three solutes can be 20 times and is observed similarly in dipolar (CHF(3)) and non-dipolar (CO(2)) fluids. In particular, the shifts of trans-stilbene were enormously large among all systems for studies of vibrational spectroscopies of supercritical fluids and were equivalent to those of typical hydrogen-bonded fluids. Such large shifts arising from the significant attractive energy between solute and solvent molecules were attributed to a site-selective solvation around a phenyl group, which was driven by a dispersion force in the absence of steric hindrance. We found that the absence of steric hindrance causes the significant local density augmentation. To the best of our knowledge, Raman experiments and their theoretical analysis are the first ones quantifying how the difference of steric hindrance produces solvation structures in solution as well as supercritical solutions.     

Alkynylation of benzotriazole with silylethynyliodonium triflates. Regioselective synthesis of 2-ethynyl-2H-benzotriazole derivatives

Phenyl(trimethylsilylethynyl)iodonium and tert-butyldimethylsilylethynyl(phenyl)iodonium triflates were applied to alkynylation of benzotriazole. Treatment of the silylethynyliodonium triflates with the potassium salt of benzotriazole ion in (t)BuOH and CH(2)Cl(2) gave 2-(trimethylsilylethynyl)-2H-1,2,3-benzotriazole and 2-(tert-butyldimethylsilylethynyl)-2H-1,2,3-benzotriazole in 74% and 76% yields, respectively. The regioisomers, 1-silylethynyl-1H-1,2,3-benzotriazole derivatives, were minor. In both cases of the silyl-substitued ethynyliodonium salts, novel regioselective alkynylation of benzotriazole at the 2 position was observed.     

Synthesis of oxosumanenes through benzylic oxidation

Oxosumanenes were synthesized through benzylic oxidation. The electronic and redox properties were revealed to exhibit the expanded π-conjugation compared to sumanene. Single-crystal X-ray analysis of monooxosumanene showed columnar π-stacking in a concave-convex fashion. Stereoselective trimethylation of the trioxo derivative was performed via 1,2-addition to the carbonyl groups.     

Halichonines A, B, and C, novel sesquiterpene alkaloids from the marine sponge Halichondria okadai Kadota

Novel sesquiterpene alkaloids, halichonines A (1), B (2), and C (3), were identified from the marine sponge Halichondria okadai Kadota. By spectroscopic analyses and synthesis, their structures were revealed to include a 6,6-bicyclic ring system and two prenylated amine moieties. In addition, 2 induced apoptosis in HL60 human leukemia cells.     

Fluorescent trimethyl-substituted naphthyridine as a ligand for C-C mismatch detection in CCG trinucleotide repeats

We report on the selective binding of 2-amino-5,6,7-trimethyl-1,8-naphthyridine (ATMND) to C-C mismatch present in the hairpin structures of (CCG)(n) trinucleotide repeats that are associated with neurological diseases; this binding is accompanied by significant fluorescence quenching of ATMND.