Eigenvalue asymptotics for the Schrödinger operators on the hyperbolic plane

In this paper we consider the Schrödinger operator on the hyperbolic plane , where is the hyperbolic Laplacian and V is a scalar potential on . It is proven that, under an appropriate condition on V at ‘infinity’, the number of eigenvalues of H_V less than λ is asymptotically equal to the canonical volume of the quasi-classically allowed region as λ→∞. Our proof is based on the probabilistic methods and the standard Tauberian argument as in the proof of Theorem 10.5 in Simon (Functional Integration and Quantum Physics, Academic Press, New York, 1979).     

Ni-catalyzed, ZnCl(2)-assisted domino coupling of enones, alkynes, and alkenes

A Ni(0)/ZnCl(2) system effectively promotes the coupling of enones and alkene-tethered alkynes. In the reaction with 1,6-enynes, the oxidative cyclization of Ni(0) species on enones across the alkyne part followed by ZnCl(2)-promoted cleavage generates alkenylnickel intermediates. Subsequent migratory insertion of the tethered alkene occurs with 5-exo-cyclization. When the resulting sigma-alkylnickel intermediates have beta-hydrogen atoms, the reaction terminates by beta-hydrogen elimination to provide cyclopentane derivatives. On the other hand, a sigma-alkylnickel intermediate that does not have beta-hydrogen atoms undergoes the insertion of a second alkene unit to cause a domino effect via a three-fold C-C bond formation process with and without the cleavage of one C-C bond.     

Crystalline inclusion compounds constructed through self-assembly of isonicotinic acid and thiocyanato coordination bridges

The synthesis, crystal structures, inclusion ability, and structural robustness of novel crystalline inclusion compounds of [Ni(SCN)2(isoH)2].xG (isoH = isonicotinic acid; G = aromatic guest) are described. The inclusion compounds are constructed by stacking identical 2D host layers that consist of SCN-, isoH, and Ni2+ with van der Waals contact separation. In the layer, two types of rectangular cavities (A-type and B-type) are formed, and the guests are included in the former cavity. The inclusion compounds were categorized into four stacking modes according to the difference in the stacking mode of the layers. A systematic investigation of the crystal structures of the 21 inclusion compounds clarified the close relationship between the molecular structure of the guest and the resultant stacking mode of the layers.     

Harmonicity of totally geodesic maps into nonpositively curved metric spaces

We prove the harmonicity of totally geodesic maps from a Riemannian manifold to a nonpositively curved metric space in the sense of Alexandrov for both Korevaar-Schoen-type and Cheeger-type energies. This enables us to make many examples of harmonic maps of an unknown type. We also construct an example of totally geodesic map between CAT(0)-spaces which is not harmonic.Mathematics Subject Classification (2000): 53C22, 53C43, 58E20     

Adsorption and structure of methyl mercaptoacetate on Cu(1 1 1) surface by XPS and NEXAFS spectroscopy

Methyl mercaptoacetate (MA) on Cu(1 1 1) surface was investigated using synchrotron radiation-based X-ray photoelectron spectroscopy (XPS) and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. MA adsorbs on the surface via thiolate formation and weak interaction of the carbonyl group with the surface. Two different adsorption states previously reported for methanethiolate and ethanethiolate were confirmed, besides atomic sulfur. NEXAFS measurements support gauche-type conformation of MA whose skeleton lies on the surface.     

Development of a high-sensitivity chromatographic separation system for pyridylaminated aldopentoses and aldohexoses

A rare sugar is considered to be a monosaccharide rarely found in nature. To investigate their natural distribution and biological roles, a robust analytical system must be used to isolate, identify, and quantify them. Herein, we report the development of such a system that can specifically quantify and chromatographically separate four aldopentoses and eight aldohexoses tagged with 2-aminopyridine. Purified monosaccharides derivatized with a pyridylamino moiety (PA–monosaccharides) are first chromatographed over a high-performance anion-exchange resin. But, because two of the PA–aldohexoses used in this study, PA–talose and PA–idose, co-elute with the common saccharides, PA–glucose and PA–mannose, respectively, a second chromatographic step, reversed-phase high-performance liquid chromatography, is used to completely separate them. Thus, as shown by the results of this study, chromatographic separation of PA–monosaccharides is achievable and provides a quantitative measurement of common and rare isomeric aldopentoses and aldohexoses.     

Measurement of the solubility of metal complexes in supercritical carbon dioxide using a UV–vis spectrometer

A new apparatus based on the circulation method was developed to measure the solubility of metal complexes in supercritical carbon dioxide (scCO₂) at a wide range of temperatures and pressures. A UV–vis spectrometer, which was connected to a small saturation cell through optical fibers, was used to determine solubility. The solubilities of cobalt(III) acetylacetonate (Co(acac)₃) and chromium(III) acetylacetonate (Cr(acac)₃) in scCO₂ were measured to check the validity of both the apparatus and the method and to accumulate new solubility data. The solubility data for Cr(acac)₃ obtained in this study were in good agreement with the data reported in the literature.The measured solubilities of Co(acac)₃ and Cr(acac)₃ were also correlated with the empirical equation including the three adjustable parameters, based on the equation proposed by Chrastil. The parameters were determined by fitting the equation to the experimental data for each metal complex and the calculated results closely replicated the experimental data.     

Adsorption behavior of VII group elements on tertiary pyridine resin in hydrochloric acid solution

We investigated the adsorption behaviors of technetium and rhenium on tertiary pyridine resin in hydrochloric acid solution. Technetium has a little larger distribution coefficient in higher concentration of hydrochloric acid region than rhenium. However, the tendency of adsorption behavior of technetium and rhenium is similar. We concluded that the rhenium can be used as the substitute for technetium. Adsorption behaviors of platinum group elements were also investigated. The separation of technetium from platinum group elements is discussed.     

A note on chordal bound graphs and posets

We study relations between induced subgraphs and (n,m)-subposets. Using properties of (n,m)-subposets, we consider a characterization of chordal double bound graphs in terms of forbidden subposets. Furthermore, we deal with properties of a poset whose double bound graph is isomorphic to its upper bound graph or its comparability graph, etc.     

Total synthesis of fumitremorgin B

Total synthesis of fumitremorgin B, one of the potent tremorgic mycotoxins, was achieved in 7 steps.