On Spectral Polynomials of the Heun Equation. II

The well-known Heun equation has the form

Detection Limits of Grazing-Exit EPMA for Particle Analysis

 In conventional electron probe microanalysis (EPMA), the electron-induced X-rays are measured at large take-off angles of about 45°. In the grazing exit EPMA (GE-EPMA) method, they are measured at small angles (< 1°). X-rays emitted from deep positions can not be detected at grazing exit angles due to refraction effects at sample-vacuum interface; therefore, it is possible to measure X-rays emitted only from near the surface with a low background. GE-EPMA is especially suitable for the analysis of particles deposited on a flat sample carrier. The detection limits of GE-EPMA were investigated for artificial particles (Al₂O₃, Fe₂O₃ and PbO₂ , particle sizes: 1 ∼ 18 μm) deposited on flat sample carriers of Au thin films–Si wafers. The detection limits improved with decreasing exit angle. The detection limits for characteristic X-rays at an exit angle of approximately 1.1° were 2–4 times lower than at 45°. A minimum detection limit of ca. 0.1% was obtained for Al in small particles.     

A theoretical study on the ionization of OCS with an analysis of vibrational structures of the photoelectron spectrum

 Ab initio calculations have been performed to study the molecular structures and vibrational levels of the four low-lying ionic states (1, 2²Π, and 1, 2²Σ⁺) of carbonyl sulfide. The global regions of the potential-energy surfaces have been obtained by multireference single and double excitation configuration interaction calculations. Vibrational calculations using explicit vibrational Hamiltonians have been used for vibrational analysis. The equilibrium molecular structures and a vibrational analysis of the four ionic states are presented. The theoretical ionization intensity curves including the vibrational structures of the ionic states are also presented and are compared with the photoelectron spectrum. Received: 20 January 2001 / Accepted: 22 August 2001 / Published online: 30 October 2001     

The Heun Equation and the Calogero-Moser-Sutherland System I: The Bethe Ansatz Method

 We propose and develop the Bethe Ansatz method for the Heun equation. As an application, holomorphy of the perturbation for the BC ₁ Inozemtsev model from the trigonometric model is proved. Received: 28 September 2001 / Accepted: 31 October 2002 Published online: 31 January 2003 Communicated by L. Takhtajan     

1.5 μm emission from InAs quantum dots with InGaAsSb strain-reducing layer grown on GaAs substrates

InGaAsSb strain-reducing layers (SRLs) are applied to cover InAs quantum dots (QDs) grown on GaAs substrates. The compressive strain induced in InAs QDs from the GaAs is reduced due to the tensile strain induced by the InGaAsSb SRL, because the lattice constant of InGaAsSb is closer to InAs lattice constant than that of GaAs, resulting in a significant red shift of photoluminescence peaks of the InAs QDs. The emission wavelength from InAs QDs can be controlled by changing the Sb composition of the InGaAsSb SRL. The 1.5 μm band emissions were achieved in the sample with an InGaAsSb SRL whose Sb compositions were above 0.3. The calculation of the electron and the hole wave functions using the transfer matrix method indicates that the electron and the hole were localized around InAs QDs and InGaAsSb SRL.     

Permeation of aromatic compounds in aqueous solutions through thin,dense cellulose acetate membranes

The partition and diffusion coefficients of aqueous solutions of aromatic compounds through a thin, dense cellulose acetate membrane were measured at 20°C. The water content and the thickness of the prepared membranes varied from 0.121 to 0.610 by volume fraction and from 17 to 88 μm, respectively. The aromatic solutes used were phenol, aniline, hydroquinone and p-chlorophenol. The solute concentration ranged between 9.0 x 10^-5 and 1.0 x 10^-3 mol/l. The partition coefficients had the following order: p-chlorophenol, phenol, aniline, hydroquinone; they were experimentally correlated with the water content of the swollen membranes.The dependence of the diffusion coefficients on the water content of the membrane was examined using as basis a pore model and a free volume model, respectively. The diffusion coefficients were adequately correlated with the water content of the membrane according to the relation given by the free volume model.     

Analytic continuation of eigenvalues of the Lamé operator

Eigenvalues of the Lamé operator are studied as complex-analytic functions in period τ of an elliptic function. We investigate the branching of eigenvalues numerically and clarify the relationship between the branching of eigenvalues and the convergent radius of a perturbation series.     

Iron‐Catalyzed Aminative Cyclization/Intermolecular Homolytic Aromatic Substitution Using Oxime Esters and Simple Arenes

Intermolecular C?H alkylation of simple arenes in the presence of an iron catalyst has been achieved in a cascade manner with an aminative cyclization triggered by N?O bond cleavage of an alkene‐tethered oxime ester. Various arenes, including electron‐rich and electron‐poor arenes, and heteroarenes can be employed in the reaction system. Regioselectivity and radical trapping experiments support the involvement of alkyl radical species, which undergo a homolytic aromatic substitution (HAS) to afford the arylation products.     

用封闭循环反应器对碳与二氧化碳气化反应中碱金属催化作用的研究

用封闭循环式反应器考察了在K_2CO_3存在下用二氧化碳气化碳的反应,并在反应进行过程中测定了吸附于焦表面的氧量,并对焦表面吸附氧量与K_2CO_3添加量和气化反应速率的关系以及反应温度和压力对焦表面吸附氧量的影响进行了研究。结果表明,反应过程中的焦表面吸附氧量与K_2CO_3添加量成正比,气化速率随反应时间的变化与焦表面吸附氧量随时间的变化具有很好的对应关系。根据实验结果,认为在反应过程中CO_2首先在催化金属形成的活性中心被解离吸附,形成表面氧化物,气化反应速率由该表面氧化物的数量决定,并认为碳与CO_2的反应是以包括有非催化反应的表面金属氧化物的氧化还原机理进行。     

Stable hydrocarbon diradical, an analogue of trimethylenemethane

Hydrocarbon diradical 1, a new stable, 3-fold symmetric analogue of trimethylenemethane (TMM) with no heteroatom perturbation, is prepared and studied. Such diradicals should provide new building blocks for high-spin hydrocarbon polyradicals with very strong net ferromagnetic coupling. Magnetic studies (SQUID) and EPR spectroscopy indicate that 1 in tetrahydrofuran-d8 (THF-d8) possesses a triplet (S = 1) ground state, with strong ferromagnetic coupling. After annealing at room temperature, the EPR spectra of 1 (approximately 0.02 M in frozen THF-d8) consist of a single narrow resonance (deltaH(pp) < 1 G), and intermolecular antiferromagnetic coupling is increased by 1 order of magnitude. This behavior is consistent with the presence of exchange narrowing, thus suggesting aggregation of 1 in THF-d8. Blue solutions of 1 in THF-d8 possess a strong UV-vis absorption band at lambda(max) approximately 640 nm. Diradical 1 in THF-d8 is stable (or persistent) at room temperature, with no detectable decomposition for at least 2 days.