Unique and faithful embeddings of projective-planar graphs

A graph G is uniquely embeddable in a surface F² if for any two embeddings f₁,f₂: G → F², there exists an isomorphism σ: G → G and a homeomorphism h: F² → F² for which h → f₁ = f₂ σ. A graph G is faithfully embeddable in a surface F² if G admits an embedding f: G → F² such that for any isomorphism σ: G → G, there is a homeomorphism h: F² → F² with h → f = f → σ. It will be shown that if a projective-planar graph G is 5-connected and contains a subdivision of the complete graph K₆ as its subgraph, then G is uniquely embeddable in a projective plane, and that moreover if G is not isomorphic to K₆, then G is faithfully embeddable in a projective plane.     

Optical characteristics of an afterglow extracted from an inductively coupled plasma

An inductively coupled plasma is extracted into a quartz vacuum chamber through an orifice to observe optical characteristics of the extracted afterglow. The Mach disk, the barrel shock and the zone of silence, which are familiar in supersonic molecular beam experiments with neutral gases, are clearly observed. Axial profiles of the emission of various lines are measured with a photodiode array spectrometer. Intensities of ionic lines as well as atomic lines are stronger at the Mach disk than in the zone of silence. The location of the Mach disk with varying chamber presure is in conformity with an experimental equation obtained in supersonic molecular beam experiments.     

Measurement of thickness of a thin film by means of laser interference at many incident angles

An optical method for directly measuring the thickness of a thin transparent film has been proposed by means of multi-wave laser interference at many incident angles, and confirmed experimentally by means of equipment made on an experimental basis. Two methods are available: one can be used when an index of refraction of the film, a wavelength λ, and two successive angles of incidence at which the sinusoidal light intensity has minimum values, are known (Method I), and another can be used without an index of film refraction when three successive angles of incidence and a wavelength are known (Method II). The smallest measurable thickness is 1.43λ for Method I, and 2.5λ for Method II. The largest measurable thickness is about 100λ for both methods. The measurement error by means of numerical calculation is Δh/h−1.01×10⁻², and that obtained experimentally with an angular resolution of incident light of 0.3° is Δh/h7×10⁻² for Method I. The refractive index can also be measured by means of Method II.     

Chemical release control: Sulfonate esters from perfume and herbicide alcohols and p-styrenesulfonyl chloride

p-Styrenesulfonate esters of primary and secondary perfume alcohols and phenols, including citronellol, 1-menthol, borneol, β-phenethyl alcohol, eugenol, p-anisyl alcohol, cinnamyl alcohol, and geraniol, and herbicide alcohols such as 2,4-dichloro- and 2,4,5-trichlorophenoxy-ethanols were synthesized using p-styrenesulfonyl chloride in the presence of bases such as pyridine, triethylamine, sodium hydrogen carbonate, and sodium hydride. The hydrolytic behavior of sulfonate ester monomers and their copolymers with N-vinyl-2-pyrrolidone to liberate perfume and herbicide alcohols was structure-dependent, thereby affording chemical release control.     

Anomalous volumetric behavior of water-hexane and water-decane mixtures in the vicinity of the critical region as studied by infrared spectroscopy

Infrared spectra of binary mixtures of water with hexane and decane were measured at temperatures and pressures in the 473-648 K and 70-350 bar ranges, respectively. Volumetric concentrations of water and the hydrocarbons in the mixtures were obtained from absorption intensities of the fundamental OH stretching band of HDO and combination transitions of the hydrocarbons. Using both the concentrations, densities of the aqueous mixtures were estimated and compared with densities before mixing, which were calculated using literature densities of the neat liquids. It is found that anomalously large volume expansion on mixing occurs in the vicinity of the critical region of the mixtures.     

Total Synthesis of Mallotusinin

The total synthesis of mallotusinin, which bears a tetrahydroxydibenzofuranoyl (THDBF) bridge between the 2-oxygen and 4-oxygen of glucose on corilagin with a 3,6-O-(R)-hexahydroxydiphenoyl (HHDP) bridge, is described. The key features of the total synthesis are: 1) improvements of our previously reported method to synthesize corilagin; 2) establishment of the THDBF skeleton via an unusual intramolecular S_NAr reaction of an HHDP analogue, and 3) the application of a two-step bislactonization strategy for a HHDP bridge construction into the 2,4-O-THDBF bridge. Oxidative phenol coupling of 1,2,4-orthoacetyl-3,6-di-(4-O-benzylgalloyl)-α-d -glucopyranose and the orthoester cleavage of the coupling product without the pyranose-furanose ring transformation are key reactions for the improved synthesis of corilagin, which enabled the adequate supply of a corilagin precursor that was required to develop the mallotusinin synthesis. These established methods are expected to help develop the synthesis of other ellagitannins with a bridge between the two oxygens of corilagin.     

Conductance of nano-systems with interactions coupled via conduction electrons: effect of indirect exchange interactions

A nano-system in which electrons interact and in contact with Fermi leads gives rise to an effective one-body scattering which depends on the presence of other scatterers in the attached leads. This non local effect is a pure many-body effect that one neglects when one takes non interacting models for describing quantum transport. This enhances the non-local character of the quantum conductance by exchange interactions of a type similar to the RKKY-interaction between local magnetic moments. A theoretical study of this effect is given assuming the Hartree-Fock approximation for spinless fermions of Fermi momentum k_F in an infinite chain embedding two scatterers separated by a segment of length L_c. The fermions interact only inside the two scatterers. The dependence of one scatterer onto the other exhibits oscillations of period π/k_F which decay as 1/L_c and which are suppressed when L_c exceeds the thermal length L_T. The analytical results given by the Hartree-Fock approximation are compared with exact numerical results obtained with the embedding method and the DMRG algorithm.