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     

Computation of multiple eigenvalues of infinite tridiagonal matrices

In this paper, it is first given as a necessary and sufficient condition that infinite matrices of a certain type have double eigenvalues. The computation of such double eigenvalues is enabled by the Newton method of two variables. The three-term recurrence relations obtained from its eigenvalue problem (EVP) subsume the well-known relations of (A) the zeros of ; (B) the zeros of ; (C) the EVP of the Mathieu differential equation; and (D) the EVP of the spheroidal wave equation. The results of experiments are shown for the three cases (A)-(C) for the computation of their ``double pairs'.

     

Gas chromatographic analysis of the thermally unstable dimethyl methylphosphonate carbanion via trimethylsilyl derivatization

An HPLC method to quantitate phytometallophores (phytosiderophores) exuded from roots of barley (Hordeum vulgare L.) growing in nutrient solution culture was developed. 9-Fluorenylmethyl chloroformate (FMOC) derivatives of phytometallophores were separated on a C18 reverse-phase column using a sodium acetate (pH 7.2) and acetonitrile-methanol gradient over 20 min followed by fluorescence detection. Detection limits ranged from 15 to 370 pmol depending on the particular phytometallophore. The effectiveness of this method was demonstrated using the response of barley seedlings to Fe-sufficient and Fe-deficient nutrient solution conditions. Phytometallophores collected in root washings of Fe-deficient barley seedlings increased with plant age while phytometallophore release from Fe-adequate roots was negligible.     

Comparison of total fluorine, extractable organic fluorine and perfluorinated compounds in the blood of wild and pefluorooctanoate (PFOA)-exposed rats: Evidence for the presence of other organofluorine compounds

The widespread occurrence and environmental persistence of perfluorinated compounds (PFCs) received worldwide attention recently. Exhaustive analysis of all fluorinated compounds in an environmental sample can be daunting because of the constraints in the availability of analytical standards and extraction methods. Combustion ion chromatographic technique for trace fluorine analysis was used to assess the concentrations of known PFCs (e.g., PFOS, PFOA) and total fluorine (TF) in the blood of wild rats collected from Japan. The technique was further validated using tissues from PFOA-exposed rats. Six PFCs (PFOS, PFOSA, PFUnDA, PFDA, PFNA, and PFOA) were detected in all of the wild rat blood samples. Concentrations of extractable organic fluorine (EOF) in fraction 1 (Fr1; MTBE extraction) of wild rats ranged 60.9-134 ng F mL⁻¹, while those in fraction 2 (Fr2; hexane) were below LOQ (32 ng F mL⁻¹); TF concentrations in the blood of wild rats ranged from 59.9-192 ng F mL⁻¹. The contribution of known PFCs in EOF-Fr1 (MTBE) varied from 9% to 89% (56% on average), and known PFC concentrations in TF content were less than 25%. In contrast, TF concentrations in the blood of PFOA-exposed rats ranged from 46900 to 111000 ng F mL⁻¹, with PFOA contributing over 90% of TF. A comparison of results from the samples analyzed in this study and the literature revealed three distinct groups with PFOA/known PFC and TF levels (i.e., wild rats and general population, occupationally exposed workers, and PFOA-exposed laboratory rats). The mass balance analysis of the different forms of fluorine in blood suggested the presence of other forms of organic fluorine in addition to known PFCs.     

Heterodimerization of olefins. 1. Hydrovinylation reactions of olefins that are amenable to asymmetric catalysis

Through a systematic examination of ligand and counterion effects, new protocols for a nearly quantitative and highly selective codimerization of ethylene and various functionalized vinylarenes have been discovered. In a typical reaction, 4-bromostyrene and ethylene undergo codimerization in the presence of 0.0035 equiv each of [(allyl)NiBr]2, triphenylphosphine, and AgOTf in CH2Cl2 at -56 degrees C to give 3-(4-bromophenyl)-1-butene in >98% yield and selectivity. Corresponding reactions with [(allyl)PdX]2 are much less efficient and less selective and may require further optimization before a viable system can be identified. Another useful protocol that gives comparable yield and selectivity involves the use of a single-component catalyst prepared from allyl 2-diphenylphosphinobenzoate, Ni(COD)2, and (C6F5)3B. Recognition of a synergistic relationship between a chiral hemilabile ligand (for example, (R)-2-methoxy-2'-diphenylphosphino-1,1'-binaphthyl, MOP) and a highly dissociated counteranion (BARF or SbF6) in an enantioselective version of the Ni-catalyzed reaction raises the prospects of developing a practical route for the synthesis of 3-arylbutenes. Several pharmaceutically relevant compounds, including widely used 2-arylpropionic acids, can be synthesized from these key intermediates. This reaction appears to be quite general. Synthesis of several new 2-diphenylphosphino-1,1-binaphthyl derivatives, prepared to probe the effect of hemilabile coordination on the efficiency and selectivity of the reaction, are also described.     

Mesoporous Silica Particles as Topologically Crosslinking Fillers for Poly(N‐isopropylacrylamide) Hydrogels

Here it is demonstrated that mesoporous silicas (MPSs) can be used as effective “topological crosslinkers” for poly(N‐isopropylacrylamide) (PNIPA) hydrogels to improve the mechanical property. Three‐dimensional bicontinuous mesporous silica is found to effectively reinforce the PNIPA hydrogels, as compared to nonporous silica and two‐dimensional hexagonally ordered mesoporous silica.     

Analysis of trifluoroacetic acid and other short-chain perfluorinated acids (C2-C4) in precipitation by liquid chromatography-tandem mass spectrometry: comparison to patterns of long-chain perfluorinated acids (C5-C18)

This paper provides analytical chemical information on selected new molecular entities (NMEs) which are drugs that have recently been approved by the FDA. These are the antiretroviral drugs, atazanavir, indinavir and emtricitabine, the antibacterial gemifloxacin, rosuvastatine which is a cholesterol-lowing drug, the anti-cancer drug gefitinib and aprepitant for neurological disorders. Electrospray ionisation-quadrupole ion trap mass spectrometry (ESI-MSⁿ) was employed to generate tandem mass spectrometric (MS²) data of the drugs studied and structural assignments of product ions were supported by quadrupole time-of-flight mass spectrometry (QToF-MS/MS). These fragmentation studies were then utilised in the development and validation of a specific and sensitive liquid chromatographic method (LC–ESI-MS²) to identify and determine these drugs at therapeutic concentration levels in serum after a single protein precipitation procedure with acetonitrile. In addition, this method was compared to the application of gas liquid chromatography-flame ionisation detection (GLC-FID) and differential pulse polarography (DPP) for the analysis of these NMEs in serum.