Rotating Navier-Stokes Equations in $${\mathbb R}^{3}_{+}$$ with Initial Data Nondecreasing at Infinity: The Ekman Boundary Layer Problem

We prove time local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary solution called the Ekman spiral. We choose initial data in the vector-valued homogeneous Besov space for 2 <  p <  ∞. Here the L ^p -integrability is imposed in the normal direction, while we may have no decay in tangential components, since the Besov space contains nondecaying functions such as almost periodic functions. A crucial ingredient is theory for vector-valued homogeneous Besov spaces. For instance we provide and apply an operator-valued bounded H ^∞-calculus for the Laplacian in for a general Banach space .     

Soft-sputtering of insulin films in argon-cluster secondary ion mass spectrometry

In secondary ion mass spectrometry (SIMS) of organic substances, the dissociation of the sample molecules is crucial. We have developed SIMS equipment capable of bombardment, where the primary ions are argon cluster ions with kinetic energy per atom controllable down to 1 eV. We previously reported the detection of intact ions of insulin and cytochrome C using this equipment. In this paper, we present a detailed characterization of the emission of secondary ions from insulin, focusing on the difference in secondary ion yield between intact ions and fragment ions by varying the incident angle of the cluster ions. The emission intensity of the intact ions was changed drastically due to the exposed dosage and incident angle of the cluster ions in contrast to the fragment ions. We discuss these results based on the manner in which the argon-cluster ions collide with the organic solid.     

Third-order nonlinear optical properties of open-shell supermolecular systems composed of acetylene linked phenalenyl radicals

The third-order nonlinear optical (NLO) properties, at the molecular level, the static second hyperpolarizabilities, γ, of supermolecular systems composed of phenalenyl and pyrene rings linked by acetylene units are investigated by employing the long-range corrected spin-unrestricted density functional theory, LC-UBLYP, method. The phenalenyl based superethylene, superallyl, and superbutadiene in their lowest spin states have intermediate diradical characters and exhibit larger γ values than the closed-shell pyrene based superpolyene systems. The introduction of a positive charge into the phenalenyl based superallyl radical changes the sign of γ and enhances its amplitude by a factor of 35. Although such sign inversion is also observed in the allyl radical and cation systems in their ground state equilibrium geometries, the relative amplitude of γ is much different, that is, |γ(regular allyl cation)/γ(regular allyl radical)| = 0.61 versus |γ(phenalenyl based superallyl cation)/γ(phenalenyl based superallyl radical)| = 35. In contrast, the model ethylene, allyl radical/cation, and butadiene systems with stretched carbon-carbon bond lengths (2.0 ?), having intermediate diradical characters, exhibit similar γ features to those of the phenalenyl based superpolyene systems. This exemplifies that the size dependence of γ as well as its sign change by introducing a positive charge on the phenalenyl based superpolyene systems originate from their intermediate diradical characters. In addition, the change from the lowest to the highest π-electron spin states significantly reduces the γ amplitudes of the neutral phenalenyl based superpolyene systems. For phenalenyl based superallyl cation, the sign inversion of γ (from negative to positive) is observed upon switching between the singlet and triplet states, which is predicted to be associated with a modification of the balance between the positive and negative contributions to γ. The present study paves the way toward designing a variety of open-shell NLO supermolecular systems composed of phenalenyl radical building blocks.     

Collective dynamics of supercritical water

Inelastic X-ray scattering experiments on sub- and supercritical water were performed to investigate collective dynamics of this unique solvent. Analysis within a generalized Langevin formalism shows that the positive dispersion of the sound velocity, as compared to the hydrodynamic value, first decreases (1.0<ρ<0.8 g cm⁻³) at all measured momentum transfers (1.3-10.7 nm⁻¹), and then increases (0.7<ρ<0.26 g cm⁻³) again only at higher momentum transfers. We suggest the initial decrease is due to approaching the percolation limit in the number of hydrogen bonds, and the subsequent increase is due to the formation of rigid dimers in sub- and supercritical water.     

Photochemistry of 2-(1-naphthyl)-2H-azirines in matrixes and in solutions: wavelength-dependent C-C and C-N bond cleavage of the azirine ring

The photochemistry of 3-methyl-2-(1-naphthyl)-2H-azirine (1a) was investigated by the direct observation of reactive intermediates in matrixes at 10 K and by the characterization of reaction products in solutions. As already reported, the photolysis of the azirine 1a with the short-wavelength light (>300 nm) caused the C-C bond cleavage of the 2H-azirine ring to produce the nitrile ylide 2. However, the products derived from the C-N bond cleavage were exclusively obtained in the irradiation of 1a with the long-wavelength light (366 nm) both in matrixes and in solutions. When 1a was irradiated in the presence of O(2) with the long-wavelength light, acetonitrile oxide (6) was produced through the capture of the biradical 4 generated by the C-N bond cleavage of 1a with O(2). An introduction of a nitro group into the naphthyl ring of 1a resulted in an acceleration of the decomposition in the long-wavelength irradiation and an extension of the wavelength region where the products derived from the C-N bond cleavage were selectively obtained. On the basis of molecular orbital calculations with the INDO/S method, the reason for the wavelength-dependent selective C-C and C-N bond cleavage of the azirine ring of 1a is discussed.     

Determination of germanium by hydride generation with reducing tube followed by graphite furnace atomic absorption spectrometry using CH4/Ar as sweeper gas

Summary A sensitive method for the hydride generation and graphite tube furnace atomic absorption spectrometric measurements with a reducing tube using mixed gas (CH₄ 10% + Ar 90%) as sweeper gas has been developed for the determination of germanium. Germanium hydrides were generated in a horizontal glass tube, in which a pellet of NaBH₄ was placed. 0.61/min of sweeper gas flow rate, 2,700° C of atomization temperature and 2.5–3 M of acidity range were the best experimental conditions. The strong supression of the germanium signal by Ni and Co was effectively eliminated with 1,10-phenanthroline and thiosemicarbazide was comparatively effective for Au. The reducing tube used in this technique is extremely simple and can be connected to all the types of graphite furnaces. A detection limit of 2 ng was obtained with a precision of 3–4%

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Germaniumbestimmung durch Hydriderzeugung im Reduktionsrohr und nachfolgende Graphitofen-AAS mit CH₄/Ar als Spülgas

Zusammenfassung Bei dem beschriebenen Verfahren werden die Hydride in einem horizontalen Glasrohr erzeugt, das eine NaBH₄-Perle enthält. Als optimale experimentelle Bedingungen ergaben sich: Spülgas (0,61/min) aus 10% CH₄ und 90% Ar, Atomisierungstemperatur 2700° C, 2,5–3 M Säure. Die starke Beeinflussung des Ge-Signals durch Ni und Co wurde mit Hilfe von 1,10-Phenanthrolin eliminiert, die Störung durch Au mit Hilfe von Thiosemicarbazid. Das verwendete Reduktionsrohr ist sehr einfach und kann für alle Arten von Graphitöfen benutzt werden. Die Nachweisgrenze beträgt 2 ng, die Reproduzierbarkeit 3–4%.

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Paper read at the Meeting of the Japan Society for Analytical Chemistry, June 1982     

Non-linear laws of echoic memory and auditory change detection in humans

Background  

The detection of any abrupt change in the environment is important to survival. Since memory of preceding sensory conditions is necessary for detecting changes, such a change-detection system relates closely to the memory system. Here we used an auditory change-related N1 subcomponent (change-N1) of event-related brain potentials to investigate cortical mechanisms underlying change detection and echoic memory.