Bifurcation phenomena associated to a class of p-Laplacian like operators

 Global bifurcation of positive solutions for some degenerate quasilinear elliptic problems is considered. The uniform estimate of the gradient of weak solutions is given. This estimate is crucial in our arguments. Received: 10 August 2001 Supported in part by Grant-in-Aid for Scientific Research (No. 11640207), Ministry of Education, Science, Sports and Culture, Japan. Mathematics Subject Classification (2000): 35B32, 35J25, 35J70     

New Preparation of Cyclic Acyloxyphosphorane by Reaction of Glyoxylic Acid with Phosphorus(III) Compounds

We have recently found that the reaction of α-keto acids (1) with phosphorus (III) compounds (3) yielded cyclic acyloxyphosphoranes(C-AOPs, 4), a new class of pentacovalent phosphorus species having a P-OC(O) group.^{1, 2)} The present paper deals with a new reaction of glyoxylic acid (2) with 3 to give C-AOPs (5) having no substituent at the C-3 position. 1 is an α-keto acid whereas 2 can be taken as an α-formyl acid. Although it is well known in the field of organic chemistry that the formyl group often behaves differently from a keto group, the reaction of 2 with 3 provides an example in which both groups behave in a similar manner.     

Growth of undoped and Zn-doped GaN nanowires

Undoped and Zn-doped GaN nanowires were synthesized by chemical vapor deposition (CVD), and the effects of substrates, catalysts and precursors were studied. A high density of GaN nanowires was obtained. The diameter of GaN nanowires ranged from 20 nm to several hundreds of nm, and their length was about several tens of μm. The growth mechanism of GaN nanowires was discussed using a vapor–liquid–solid (VLS) model. Furthermore, room-temperature cathodoluminescence spectra of undoped and Zn-doped GaN nanowires showed emission peaks at 364 and 420 nm, respectively.     

Effect of the chemical species of arsenic on sensitivity in graphite furnace atomic absorption spectrometry.

The sensitivity of graphite furnace atomic absorption spectrometry (GFAAS) to arsenobetaine (AB) was 1.3-times higher than to inorganic As. In order to understand the mechanism underlying this observation, the atomization processes for both chemical species were investigated in terms of the enthalpy change (DeltaH) during the atomization process in GFAAS. The enthalpy change of AB was slightly lower than that of inorganic As, which suggested that AB was atomized more efficiently than was inorganic As. Moreover, it was observed that some co-existing organic materials enhanced the analytical sensitivity of inorganic As. The sensitivity difference between inorganic As and AB depended upon the mechanisms of their atomization processes.     

Preparation and certification of arsenate [As(V)] reference material, NMIJ CRM 7912-a

Arsenate [As(V)] solution reference material, National Metrology Institute of Japan (NMIJ) certified reference material (CRM) 7912-a, for speciation of arsenic species was developed and certified by NMIJ, the National Institute of Advanced Industrial Science and Technology. High-purity As₂O₃ reagent powder was dissolved in 0.8 M HNO₃ solution and As(III) was oxidized to As(V) with HNO₃ to prepare 100 mg kg^-1 of As(V) candidate CRM solution. The solution was bottled in 400 bottles (50 mL each). The concentration of As(V) was determined by four independent analytical techniques—inductively coupled plasma mass spectrometry, inductively coupled plasma optical emission spectrometry, graphite furnace atomic absorption spectrometry, and liquid chromatography inductively coupled plasma mass spectrometry—according to As(V) calibration solutions, which were prepared from the arsenic standard of the Japan Calibration Service system and whose species was guaranteed to be As(V) by NMIJ. The uncertainties of all the measurements and preparation procedures were evaluated. The certified value of As(V) in the CRM is (99.53 ± 1.67) mg kg^-1 (k = 2).     

On distorted probabilities and m-separable fuzzy measures

Fuzzy measures are used in conjunction with fuzzy integrals for aggregation. Their role in the aggregation is to permit the user to express the importance of the information sources (either criteria or experts). Due to the fact that fuzzy measures are set functions, the definition of such measures requires the definition of 2ⁿ parameters, where n is the number of information sources. To make the definition easier, several families of fuzzy measures have been defined in the literature.In this paper m-separable fuzzy measures are introduced. We present some results on this type of measures and we relate them to some of the previous existing ones. We study generating functions for m-separable fuzzy measures and some properties related to these generating functions.     

Conditions for Choquet integral representation of the comonotonically additive and monotone functional

If the universal set X is not compact but locally compact, a comonotonically additive and monotone functional (for short c.m.) on the class of continuous functions with compact support is not represented by one Choquet integral, but represented by the difference of two Choquet integrals. The conditions for which a c.m. functional can be represented by one Choquet integral are discussed.     

Determination of cadmium in grains by isotope dilution ICP–MS and coprecipitation using sample constituents as carrier precipitants

A coprecipitation method using sample constituents as carrier precipitants was developed that can remove molybdenum, which interferes with the determination of cadmium in grain samples via isotope dilution inductively coupled plasma mass spectrometry (ID-ICPMS). Samples were digested with HNO₃, HF, and HClO₄, and then purified 6 M sodium hydroxide solution was added to generate colloidal hydrolysis compounds, mainly magnesium hydroxide. Cadmium can be effectively separated from molybdenum because the cadmium forms hydroxides and adsorbs onto and/or is occluded in the colloid, while the molybdenum does not form hydroxides or adsorb onto the hydrolysis colloid. The colloid was separated by centrifugation and then dissolved with 0.2 M HNO₃ solution to recover the cadmium. The recovery of Cd achieved using the coprecipitation was >97%, and the removal efficiency of Mo was approximately 99.9%. An extremely low procedural blank (below the detection limit of ICPMS) was achieved by purifying the 6 M sodium hydroxide solution via Mg coprecipitation using Mg(NO₃)₂ solution. The proposed method was applied to two certified reference materials (NIST SRM 1567a wheat flour and SRM 1568a rice flour) and CCQM-P64 soybean powder. Good analytical results with small uncertainties were obtained for all samples. This method is simple and reliable for the determination of Cd in grain samples by ID-ICPMS. Figure Overview of a coprecipitation method using sample constituents     

Optical properties of MOVPE-grown a-plane GaN and AlGaN

a-Plane GaN and AlGaN were grown on r-plane sapphire by low-pressure metal-organic vapor epitaxy (LP-MOVPE), and the effects of reactor pressure (from 40 to 500 Torr) and growth temperature (from 1020 to 1100 °C) on the crystalline quality and surface morphology of a-plane GaN were studied. The a-plane GaN grown under 40 Torr had a smooth-surface morphology but a poor crystalline quality; however, the a-plane GaN grown under 500 Torr had higher crystalline quality and optical properties, whose full-width at half-maximum of the X-ray rocking curve (XRC-FWHM) and intensity of yellow luminescence (YL) were smaller. Furthermore, the optical properties of a-plane GaN were investigated by photoluminescence (PL) in detail. We also studied the emission properties of a-plane Al_0.35Ga_0.65N grown at room temperature.