Computation of the quasi-stationary distributions inM(n)/GI/1/K andGI/M(n)/1/K queues

In this paper, we provide numerical means to compute the quasi-stationary (QS) distributions inM/GI/1/K queues with state-dependent arrivals andGI/M/1/K queues with state-dependent services. These queues are described as finite quasi-birth-death processes by approximating the general distributions in terms of phase-type distributions. Then, we reduce the problem of obtaining the QS distribution to determining the Perron-Frobenius eigenvalue of some Hessenberg matrix. Based on these arguments, we develop a numerical algorithm to compute the QS distributions. The doubly-limiting conditional distribution is also obtained by following this approach. Since the results obtained are free of phase-type representations, they are applicable for general distributions. Finally, numerical examples are given to demonstrate the power of our method.     

Ion-interaction chromatography of several metallocyanide complexes stabilized by adding cyanide in a neutral mobile phase.

Standard solutions (at 10(-5) M levels) of Cu(I)- and Fe(II)-cyanide complexes were stabilized for at least 5 h using 0.5 mM cyanide solution (around pH 9) as a medium. Complexes of Cu(I)- and Fe(III)-cyanide also could be stabilized without any dissociation by adding 1 mM cyanide to an acetonitrile-water (18:82, v/v) mobile phase (pH 7.0) containing 10 mM tetra-n-propylammonium salt (TPA). Under the optimal conditions, the six complexes of Cu(I)-, Ag(I)-, Ni(II)-, Fe(II)-, Fe(III)- and Au(I)-cyanides were resolved from their mixtures within about 45 min, with well-shaped chromatographic peaks.     

Mechanism of gold adsorption by persimmon tannin gel.

Gold adsorption by persimmon tannin (PT) gel from a solution containing hydrogen tetrachloroaurate(III) was examined. A flow-rate examination in a column system indicated the reduction of Au(III) ion to Au(0). XRD patterns clarified the existence of Au(0) on the gel which adsorbed gold. The gel could also adsorb colloidal Au(0) prepared independently. A model consisting of ligand exchange, Au(III) reduction to Au(0), and resulting Au(0) adsorption by PT gel was presented for the gold adsorption mechanism.     

EFFECTS OF N-PHENYLIMIDE S-23142 AND N-METHYL MESOPORPHYRIN IX ON THE SYNTHESIS OF THE PHYTOCHROME CHROMOPHORE IN PEA EMBRYONIC AXES

Abstract Treatment of imbibed embryonic axes taken from seeds of Pisum sativum with N-phenylimide S-23142, a herbicide that has been suggested to inhibit protoporphyrin synthesis, or with N -methyl mesoporphyrin IX, an inhibitor of the iron chelatase for heme, resulted in a significant decrease in the amount of spectrophotometrically detectable phytochromc in the axes in both cases. However, the amount of immunochemically detectable phytochrome was not affected by either treatment. If S-23142 inhibits the synthesis of protoporphyrin IX in pea, it appears that the conversion of protoporphyrinogen IX to protoporphyrin IX is involved in the biosynthesis of the phytochrome chromophore. The conversion of protoporphyrin IX to heme (Fe-protoporpbyrin) also appears to be a step in the biosynthesis of the chromophore, since N -methyl mesoporphyrin IX prevented the synthesis of spectrophotometrically detectable phytochrome but did not affect the magnesium chelatase activity required for the synthesis of chlorophyll in pea embryonic axes. The results suggest that protoporphyrinogen IX, protoporphyrin IX and heme are intermediates in the biogenesis of the phytochromc chromophore. The pathway to phytochromobilin might become fixed after protoporphyrin IX, being directed toward the Fe branch for heme rather than to the Mg branch for chlorophyll.     

Highly regioselective nucleophilic carbon-carbon bond formation on furans and thiophenes initiated by pummerer-type reaction

[reaction: see text] The reactions of (phenylsulfinyl)furans or -thiophenes with carbon nucleophiles in the presence of trifluoroacetic anhydride allowed the nucleophilic installation of carbon functional groups on the furan and thiophene nuclei with complete regioselectivity.     

Synthesis of Indolones via Radical Cyclization of N‐(2‐Halogenoalkanoyl)‐Substituted Anilines

The radical reactions of N‐(2‐halogenoalkanoyl)‐substituted anilines (anilides) of type 1 have been investigated under various conditions. Treatment of compounds 1a – 1o with Bu₃SnH in the presence of (2,2′‐azobis(isobutyronitrile) (AIBN) afforded a mixture of the indolones (oxindoles) 2a – 2o and the reduction products 5a – 5o (Table 1). In contrast, the N‐unsubstituted anilides 1p – 1s, 1u , and 1v gave the corresponding reduction products exclusively (Table 1). Similar results were obtained by treatment of 1 with Ni powder (Table 2) or wth Et₃B (Table 3). Anilides with longer N‐(phenylalkyl) chains such as 6 and 7 were inert towards radical cyclization, with the exception of N‐benzyl‐2‐bromo‐N,2‐dimethylpropanamide ( 6b ), which, upon treatment with Ni powder in i‐PrOH, afforded the cyclized product 9b in low yield (Table 4). Upon irradiation, the extended anilides 6, 7, 10 , and 11 yielded the corresponding dehydrobromination products exclusively (Table 5).     

Synthesis of thermoplastic curdlan alkyl carbamates having hydrogen bonding ability

Rigid and little moldable curdlan, a linear β-1,3-glucan having intra- and interchain hydrogen bonds, was reacted with several alkyl isocyanates, which gave thermoplastic curdlan alkyl carbamates (CrdC) with degree of substitution about 2. The alkyl carbamation at hydroxy groups in the glucan skeleton effectively broke the interchain hydrogen bonds of curdlan and increased flexibility of CrdC, while the newly formed carbamate moieties could moderately keep the hydrogen bonding ability in CrdC. Elongating the alkyl groups in the carbamate side chains increased solubility in organic solvents and thermoplasticity of CrdC, which enabled to make homogeneous and free-standing films by both methods of solution-casting and hot-pressing.     

Enantioresolution of 2-methoxy-2-(1-naphtyl)propionic acid using diastereomeric salt formation with chiral phenylethylamine

An enantioresolution of 2-methoxy-2-(1-naphtyl)propionic acid (MαNP acid) using the diastereomeric salt with chiral (R)-phenylethylamine was achieved to give enantiopure (R)-MαNP acid in 29% yield with >99% ee based on rac-MαNP acid. X-ray crystallographic analysis of diastereomeric salt revealed that (R)-MαNP acid was tightly arranged by four independent hydrogen bonds and one CH–π interaction with (R)-phenylethylamine.     

meso–meso‐Linked Diarylamine‐Fused Porphyrin Dimers

A meso–meso‐linked diphenylamine‐fused porphyrin dimer and its methoxy‐substituted analogue were synthesized from a meso–meso‐linked porphyrin dimer by a reaction sequence involving Ir‐catalyzed β‐selective borylation, iodination, meso‐chlorination, and S_NAr reactions with diarylamines followed by electron‐transfer‐mediated intramolecular double C?H/C?I coupling. While these dimers commonly display characteristic split Soret bands and small oxidation potentials, they produced different products upon oxidation with tris(4‐bromophenyl)aminium hexachloroantimonate. Namely, the diphenylamine‐fused porphyrin dimer was converted into a dicationic closed‐shell quinonoidal dimer, while the methoxy‐substituted dimer gave a meso–meso, β‐β doubly linked porphyrin dimer.