Tail asymptotics for the fundamental period in the MAP/G/1 queue

This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail, and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result in (de Meyer and Teugels, J. Appl. Probab. 17: 802–813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions. I.-S. Wee’s research was supported by the Korea Research Foundation Grant KRF 2003-070-00008.     

Strongly countable dimensional compacta form the Hurewicz set

The hyperspaces of strongly countable dimensional compacta of positive dimension and of strongly countable dimensional continua of dimension greater than 1 in the Hilbert cube are homeomorphic to the Hurewicz set of all nonempty countable closed subsets of the unit interval [0,1]. These facts hold true, in particular, for covering dimension dim and cohomological dimension dimG, where G is any Abelian group.     

Moments of claims in a Markovian environment

This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace–Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.     

N‐Acetyl‐l‐tyrosine methyl ester monohydrate at 293 and 123 K

The crystal structure of a protected l ‐tyrosine, namely N‐acetyl‐l ‐tyrosine methyl ester monohydrate, C₁₂H₁₅NO₄·H₂O, was determined at both 293 (2) and 123 (2) K. The structure exhibits a network of O—H...O and N—H...O hydrogen bonds, in which the water molecule plays a crucial role as an acceptor of one and a donor of two hydrogen bonds. Molecules of water and of the protected l ‐tyrosine form hydrogen‐bonded layers perpendicular to [001]. C—H...π interactions are observed in the hydrophobic regions of the structure. The structure is similar to that of N‐acetyl‐l ‐tyrosine ethyl ester monohydrate [Soriano‐García (1993). Acta Cryst. C 49 , 96–97].     

Palladium-catalysed 5-endo-trig allylic (hetero)arylation

A palladium-catalysed intramolecular allylic (hetero)arylation strategy for the synthesis of fused cyclopentenes incorporated with all-carbon quaternary and spiro centres is described. The method is straightforward, shows broad scope, proceeds in synthetically useful yields, and provides a rare means to construct complex cyclopentanoids. The reaction is believed to involve a kinetically unfavourable 5-endo-trig carbocyclisation of the tethered (π-allyl)palladium system. Further, this method was successfully applied as the key step in the total synthesis of diterpene natural products taiwaniaquinone H and dichroanone.

A palladium-catalysed intramolecular allylic (hetero)arylation strategy for the synthesis of fused cyclopentenes incorporated with all-carbon quaternary and spiro centres is described.     

Cationic Heteroconjugation Constants in the OHN+ and NHO+ Systems in Propylene Carbonate: Dependence on Difference in Basicity

Cationic heteroconjugation equilibria of more than ninety systems consisting of substituted pyridines, their N-oxides, and trimethylamine N-oxide, i. e., in systems with mixed hydrogen bridges of type OHN⁺ (NHO⁺) were studied in propylene carbonate. Both experimental systems without proton transfer, BH⁺/B₁, and those with proton transfer, B₁H⁺/B, were explored. The stability of the mixed hydrogen bridges, OHN⁺ (NHO⁺), is compared with that of the OHC⁺-type bridges. The influence of the difference in basicity of the conjugate base of the proton donor and the proton acceptor on the presence of the proton transfer equilibria, and, consequently, the possibility of determination of the cationic heteroconjugation constant values is discussed.     

Synthesis and properties of azoles and their derivatives. 10. Synthesis of 3,5-diaryl-4-nitroisoxazoles

A method was proposed for the synthesis of 3,5-diaryl-4-nitroisoxazoles entailing the brominatian of potassium salts of the corresponding 3,5-diaryl-²-isoxazolinyl-4-nitronic acids. The method may be used for the conversions of both the trans and cis isomers of 3,5-disubstituted 4-nitro-²-isoxazolines.Communication 9, See [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 189–192, February, 1985.     

Spectrophotometric determination of Fe(II) in milligram solid samples

The analytical procedure of determination of Fe(II) in the presence of Fe(III) in milligram samples is proposed. A solid sample is dissolved in hydrochloric acid in argon atmosphere. Subsequently, the pH-value of the solution is fixed and Fe(III) complexed by phosphoric buffer. At the next step Fe(II) is oxidized by -molybdosilicic acid. Finally, the intensity of colouring caused by the reduced form of the acid is measured at the wavelength 770 nm. The proper treatment of the sample during oxidation, and immediately before, is decisive for the accuracy of the analysis. The method was verified by means of the analysis of synthetic magnetite. The theoretical content of Fe(II) was 24.12%, the determined one was 24.02 ± 0.10%. The method was applied to the determination of the homogeneity of an iron catalyst for ammonia synthesis.     

Mechanistic studies on the binding of nitric oxide to a synthetic heme-thiolate complex relevant to cytochrome p450

The synthetic heme-thiolate complex (SR) in methanol binds nitric oxide (k(on) = (2.7 +/- 0.2) x10(6) M(-)(1) s(-)(1) at 25 degrees C) to form SR(NO). The binding of NO to the SR complex in a noncoordinating solvent, such as toluene, was found to be almost 3 orders of magnitude faster than that in methanol. The activation parameters DeltaH(), DeltaS(), and DeltaV() for the formation of SR(NO) in methanol are consistent with the operation of a limiting dissociative mechanism, dominated by dissociation of methanol in SR(MeOH). In the presence of an excess of NO, the formation of SR(NO) is followed by subsequent slower reactions. The substantially negative activation entropy and activation volume values found for the second observed reaction step support an associative mechanism which involves attack of a second NO molecule on the thiolate ligand in the initially formed SR(NO) complex. The following slower reactions are strongly accelerated by a large excess of NO or by the presence of NO(2)(-) in the SR/NO reaction mixture. They can be accounted for in terms of dynamic equilibria between higher nitrogen oxides (NO(x)()) and reactive SR species, which lead to the formation of a nitrosyl-nitrite complex of SR(Fe(II)) as the final product. This finding is clearly supported by laser flash photolysis studies on the SR/NO reaction mixture, which do not reveal simple NO photolabilization from SR(Fe(III))(NO), but rather involve the generation of at least three photoinduced intermediates decaying with different rate constants to the starting material. The species formed along the proposed reaction pathways were characterized by FTIR and EPR spectroscopy. The results are discussed in terms of their relevance for the biological function of cytochrome P450 enzymes and in context of results for the reaction of NO with imidazole- and thiolate-ligated iron(III) hemoproteins.