A note on the positive solutions of second order differential equations

We obtain an existence theorem for monotone positive solutions of nonlinear second-order nonlinear differential equations via principal and nonprincipal solutions of the corresponding homogeneous equation.     

An approximate treatment of scattering based on the delta boundary operator

The development of a scheme to treat two-dimensional electromagneticscattering by electrically large, perfectly conducting bodiesis described. It incorporates the effects of surface curvatureand non-local phenomena and has the potential to provide thebasis for a general technique yielding more accurate predictionsthan the widely used physical optics method.     

Correction method for influence of tissue scattering for sidestream dark-field oximetry using multicolor LEDs

We have previously proposed an estimation method of intravascular oxygen saturation \(({\rm SO}_2)\) from the images obtained by sidestream dark-field (SDF) imaging (we call it SDF oximetry) and we investigated its fundamental characteristics by Monte Carlo simulation. In this paper, we propose a correction method for scattering by the tissue and performed experiments with turbid phantoms as well as Monte Carlo simulation experiments to investigate the influence of the tissue scattering in the SDF imaging. In the estimation method, we used modified extinction coefficients of hemoglobin called average extinction coefficients (AECs) to correct the influence from the bandwidth of the illumination sources, the imaging camera characteristics, and the tissue scattering. We estimate the scattering coefficient of the tissue from the maximum slope of pixel value profile along a line perpendicular to the blood vessel running direction in an SDF image and correct AECs using the scattering coefficient. To evaluate the proposed method, we developed a trial SDF probe to obtain three-band images by switching multicolor light-emitting diodes and obtained the image of turbid phantoms comprised of agar powder, fat emulsion, and bovine blood-filled glass tubes. As a result, we found that the increase of scattering by the phantom body brought about the decrease of the AECs. The experimental results showed that the use of suitable values for AECs led to more accurate \({\rm SO}_2\) estimation. We also confirmed the validity of the proposed correction method to improve the accuracy of the \({\rm SO}_2\) estimation.     

New homo- and heteroleptic derivatives of trivalent ytterbium containing radical anion 1,4-diazadiene ligands. Synthesis, properties, and crystal structures of the complexes (C9H7)2Yb[2-MeC6H4NC(Me)C(Me)NC6H4Me-2] and [PhNC(Ph)C(Ph)NPh]3Yb

The interaction of the ytterbium bis(indenyl) complex (C₉H₇)₂Yb^II(THF)₂ (1) with the 1,4-diazabutadiene 2-MeC₆H₄N=C(Me)-C(Me)=NC₆H₄Me-2 (^MeDAD) is accompanied by the oxidation of the metal atom to the trivalent state and results in a paramagnetic compound of the metallocene type (C₉H₇)₂Yb^III(^MeDAD^−·) (3) containing the radical anion of 1,4-diazabutadiene. The structure of the complex 3 was determined by X-ray diffraction analysis. The reactions of the bis(indenyl) (1) and bis(fluorenyl) (C₁₃H₉)₂Yb^II(THF)₂ (2) derivatives of divalent ytterbium with the 1,4-diazabutadiene PhN=C(Ph)-C(Ph)=NPh (^PhDAD) (with the molar ratio of the reactants 1:2) proceed with a complete cleavage of the bonds Yb-C and the oxidation of the ytterbium atom to the trivalent state and result in a homoligand complex (^PhDAD^−·)₃Yb (6) containing three radical anion 1,4-diazadiene ligands. Complex 6 was also obtained by an exchange reaction of YbCl₃ with ^PhDAD^−·K⁺ (1: 3) in THF. Complex 6 was characterized by X-ray diffraction analysis.     

Synthesis and properties of bis(indenyl) derivatives of ytterbium and lutetium. Molecular structures of the complexes (C9H7)2Ln(μ-Cl)2Li(Et2O)2 (Ln = Yb, Lu) and [(C9H7)2YbCl2][Li(DME)3]

The heterobimetallic bis(indenyl) chloride complexes of ytterbium and lutetium (C₉H₇)₂Ln(μ-Cl)₂Li(Et₂O)₂ (Ln = Yb or Lu) were synthesized by the metathesis reaction of LnCl₃ with two equivalents of indenyllithium in diethyl ether. In the case of ytterbium, the analogous reaction in 1,2-dimethoxyethane afforded the ionic complex [(C₉H₇)₂YbCl₂]⁻[Li(DME)₃]⁺. The reaction of YbCl₃ with indenylpotassium in a molar ratio of 1: 2 in THF is accompanied by reduction of the metal atom to give the bis(indenyl) derivative of Yb^II, (C₉H₇)₂Yb(THF)₂. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 39–44, January, 2008.     

Growth of 3,4,9,10-perylenetetracarboxylic-dianhydride (PTCDA) on Cu(110) studied by STM

. The structure of thin 3,4,9,10-perylenetetracarb-oxylic-dianhydride (PTCDA) films on Cu(110) was studied by scanning tunnelling microscopy (STM) from submonolayer to monolayer coverage. While no long-range ordering was found after deposition at room temperature, the formation of a well-defined superstructure is observed after thermal annealing. It appears that the formation of the superstructure is driven by the interaction between the oxygen atoms of the PTCDA and the copper atoms of the substrate. While the distance between the molecules fits well to the atomic lattice of the Cu(110) surface along the [1[`(^[¯])]1^[¯]\bar\Box1\Box]]0] direction, the mismatch along the [001] direction leads to a periodic buckling normal to the surface accompanied by a restructuring of the substrate.     

EPMA and Microstructural Characterization of Yttrium Doped BaTiO3 Ceramics

 Yttrium-doped BaTiO₃ ceramics have been studied as a potential material for positive temperature coefficient resistors (PTCR). The mechanism of Y incorporation into BaTiO₃ plays an important role for displaying good electrical properties. Determination of the amount of yttrium in the BaTiO₃ as well as microstructure characterization of the samples were performed using SEM, EDS and WDS analysis. An optimized trace element WDS quantitative analysis was applied to determine elemental concentrations for Ba, Ti and Y in the samples as accurately as possible. BaTiO₃ and Y₂O₃ were used as standards. Analysis was undertaken using a JEOL JXA 840A electron probe microanalyzer. WDS X-ray intensity measurements were performed under 20 kV, 50 nA beam current and 0.2% preset standard counting deviation (σ_c) using a PET crystal. Measured k-ratios were quantified by ZAF matrix correction. Average results of WDS quantitative analysis showed 20.17 ± 0.08 at % Ti, 19.95 ± 0.09 at % Ba, 0.22 ± 0.03 at % Y, and 59.66 at % O. The results suggest incorporation of yttrium in the BaTiO₃ preferentially at the Ba-sites, however partial incorporation of Y at Ti-sites could not be excluded.