The explicit solution of a diffusion equation with singularity

We give the explicit solution of the Cauchy problem for the diffusion equation with a singular term:

where . We construct the solution on the basis of a generalization of the Fourier transform. We next show that the solution is expressed by an analytic semigroup, and examine smoothness of and continuity of .

     

A note on complete intersections of height three

Let be a field of characteristic 0. If is a complete intersection generated by three homogeneous elements of degrees with , then the reduction of by a general linear form is minimally generated by three elements if and only if .

     

Diastereomixture and racemate of myo-inositol derivatives, stronger organogelators than the corresponding homochiral isomers

Contrary to the usually accepted phenomena, an optically heterogeneous 1:1 diastereomixture of DS and LS and a racemate of LS and DR obtained, respectively, from a racemic myo-inositol derivative and (S)- and racemic O-acetylmandelic acid formed stronger organogels, especially with aromatic fluids, than those formed from homochiral isomers, DS and LS. One of the plausible reasons for the formation of the stronger diastereomeric gel is shown to be the complementary interaction of two diastereomers.     

Structure-activity relationship of yohimbine and its related analogs in blocking alpha-1 and alpha-2 adrenoceptors: a comparative study of cardiovascular activities

We investigated the selectivities and structure requirements for alpha-1 and alpha-2 adrenoceptor blocking activities of yohimbine (YO) and its 12 related analogs, such as beta-yohimbine (beta-YO), dihydrocorynantheine (DHC) and (-)indoloquinolizidine ((-)IQ). The affinity of YO analogs to alpha-adrenoceptor was assessed by measuring their blockade of pressor responses to epinephrine in pithed rats. Among YO structure groups, the potency order was YO greater than DHC = beta-YO greater than geissoschizine methylether greater than 14 beta-hydroxy YO greater than 14 beta-benzoyloxy YO (inactive). (-)IQ was slightly less potent than YO, but much stronger than (+)IQ. Among (+/-)IQ structure groups, the potency order was (+/-)IQ greater than (+/-)1,12b-trans-1-hydroxy IQ much greater than (+/-)1,12b-cis-1-hydroxy IQ (inactive). (+/-)Borrerine was active, but (+/-)desmethylborrerine was inactive. The alpha-1 blocking activities of the four compounds YO, beta-YO, DHC and (-)IQ, were assessed in experiments of pressor responses to methoxamine in pithed rats and contractile responses to methoxamine in the rat vas deferens. The potency order was (-)IQ greater than YO greater than DHC greater than beta-YO. Furthermore, the alpha-2 blocking activities of the four analogs were assessed in experiments of pressor responses to clonidine and inhibition of electrically driven cardioacceleration by clonidine, in pithed rats. The potency order was YO greater than beta-YO greater than (-)IQ greater than DHC. Based on the potency ratio between alpha-1 and alpha-2 blocking activities, DHC or YO was most selective for alpha-1 or alpha-2 subtype, respectively, among the four YO analogs.(ABSTRACT TRUNCATED AT 250 WORDS)     

Palladium-catalyzed borylation of aryl halides or triflates with dialkoxyborane: A novel and facile synthetic route to arylboronates

A direct borylation of aryl halides or triflates with dialkoxyborane was investigated. The coupling reaction of pinacolborane with aryl halides or triflates in the presence of a catalytic amount of PdCl(2)(dppf) together with a base provided arylboronates in high yields. The product distributions were strongly dependent on the base employed, and the tertiary amine, especially Et(3)N, was effective for the selective formation of the boron-carbon bond. The reaction conditions were so mild that arylboronates having a variety of functional groups such as carbonyl, cyano, and nitro groups were readily prepared.     

A non-ionic surfactant as a new solvent for liquid-liquid extraction of zinc(II) with 1-(2-pyridylazo)-2-naphthol

A new method for extracting zinc(II) with 1-(2-pyridylazo)-2-naphthol (PAN) has been developed, based on the fact that a micellar solution of a non-ionic surfactant separates into two phases above a certain temperature, defined as the cloud point. Polyoxyethylene nonyl phenyl ether, (PONPE-7.5; average number of ethylene oxide units 7.5) was used as the surfactant. The cloud point of a 0.40% PONPE-7.5 solution is 1 degrees , and hence the solution is turbid at room temperature. The two phases can be separated by centrifuging for 8 min at room temperature. The zinc chelate of PAN is quantitatively extracted from 50g of the solution into a small volume (about 1 ml) of the lower (surfactant-rich) phase over the pH range 8.0-11.5. After most of the supernatant solution has been removed, the amount of final solution is adjusted to 2.00 g with 0.5 g of 10% of PONPE-20 solution and water. This mixture is transparent at room temperature. The absorbance is measured as 535 nm. Concentration factors of up to 25 can be obtained by choosing appropriate amounts of final ( 2.0 g) and initial solution ( 50 g). This new technique has been applied to the determination of zinc(II) in tap water.     

Polymorphism in Bi2WO6

The polymorphism of Bi₂WO₆ has been studied using differential dilatometry and differential thermal analysis with polycrystalline specimens prepared by sintering the oxides Bi₂O₃ and WO₃. Two reversible polymorphic transitions were observed, one at 662°C and one at 962°C. The former transition showed a very small change of enthalpy and very little dimensional change, while the latter showed a large thermal hysteresis, had a large change of enthalpy, and was accompanied by a sizable volume change. The high-temperature powder X-ray data indicated that the intermediate phase as well as the low-temperature form had orthorhombic symmetry and the high-temperature form had monoclinic symmetry. The 662°C transition is displacive and the 962°C transition reconstructive. A crystal structure of the high-temperature form is proposed and discussed in comparison with that of the low-temperature form.     

Evaluation of a commercial immunoassay for the detection of chlorfenapyr in agricultural samples by comparison with gas chromatography and mass spectrometric detection

A commercially available enzyme-linked immunosorbent assay (ELISA) kit with a high affinity monoclonal antibody was applied to residual analysis of insecticide chlorfenapyr in agricultural samples, and drawn a parallel between the ELISA and gas chromatography (GC) with mass spectrometry (MS). For standards prepared in water containing 5% (v/v) methanol, the sensitivity (I50 value), the dynamic range, and the limit of detection of the ELISA kit were 2.3, 1 - 10, and 0.1 ng/g, respectively. The used monoclonal antibody in the ELISA kit had a high selectivity. The ELISA kit was applied to the determination of chlorfenapyr in two kinds of fruits (apple and peach). The examination of the influence of these matrices on the reliability of the assay performance indicated that the ELISA could determine it in these samples near the regulation values in Japan simply by diluting the methanolic extract or by concentrating it, without any clean-up procedures. Recovery and precision of the proposed ELISA method were assessed by fortifying fruit samples with chlorfenapyr ranging from 0.05 to 1.5 microg/g. Mean recoveries were 94.2 and 90.3% for apple and peach, and coefficients of variation were below 16% in most cases. The results obtained from the proposed ELISA method correlate well the reference GC/MS method for both fruit samples (r > 0.98). These considerations make the ELISA kit very useful analytical tool for monitoring and regulatory programs, without the need of complex and expensive instrumentation.