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.     

Stationary remaining service time conditional on queue length

In Mandelbaum and Yechiali [The conditional residual service time in the M/G/1 queue, http://www.math.tau.ac.il/∼uriy/publications (No. 30a), 1979] and in Fakinos [The expected remaining service time in a single-server queue, Oper. Res. 30 (1982) 1014-1018] a simple formula is derived for the (stationary) expected remaining service time in a M/G/1 queue, conditional on the number of customers in the system. We give a short new proof of the formula using Rate Conservation Law, and generalize to handle higher moments.     

Bivariate Recursive Equations on Excess-of-loss Reinsurance

This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 （a, b） family, bivariate recursive equations for the joint distribution of the cedent＇s aggregate claims and the reinsurer＇s aggregate claims are obtained.     

Estimating tail probabilities of heavy tailed distributions with asymptotically zero relative error

Efficient estimation of tail probabilities involving heavy tailed random variables is amongst the most challenging problems in Monte-Carlo simulation. In the last few years, applied probabilists have achieved considerable success in developing efficient algorithms for some such simple but fundamental tail probabilities. Usually, unbiased importance sampling estimators of such tail probabilities are developed and it is proved that these estimators are asymptotically efficient or even possess the desirable bounded relative error property. In this paper, as an illustration, we consider a simple tail probability involving geometric sums of heavy tailed random variables. This is useful in estimating the probability of large delays in M/G/1 queues. In this setting we develop an unbiased estimator whose relative error decreases to zero asymptotically. The key idea is to decompose the probability of interest into a known dominant component and an unknown small component. Simulation then focuses on estimating the latter ‘residual’ probability. Here we show that the existing conditioning methods or importance sampling methods are not effective in estimating the residual probability while an appropriate combination of the two estimates it with bounded relative error. As a further illustration of the proposed ideas, we apply them to develop an estimator for the probability of large delays in stochastic activity networks that has an asymptotically zero relative error.      

Confirmation of sable QTL that modifies the effects of the Ay allele on yellow coat color on mouse chromosome 1

F₁-A^y mice between RR (aabbCC) and C57BL/6J-A^y (A^yaBBCC) have a much darker yellow coat color than do C57BL/6J-A^y. Quantitative trait locus (QTL) analysis was carried out to identify genes responsible for the darker modification of the yellow coat color (this has been traditionally termed “sable”). A significant sable QTL was identified on chromosome 1 (Dmyaq4, LOD score 15.5 for lightness, and 13.4 for color difference), in a chromosomal position similar to that of Dmyaq2, a sable QTL previously identified in C3H/HeJ. Another significant sable QTL was identified on chromosome 4 (Dmyaq5, LOD score 5.6 for lightness, and 4.3 for color difference) near the tyrosinase-related protein 1 (Tyrp1) locus. The effect of Dmyaq5 was significant only in the presence of the RR allele at Dmyaq4, suggesting that the Dmyaq4 (as well as Dmyaq2) is a novel coat color gene that may act up-stream of Tyrp1 signaling to increase eumelanin production.     

Stereoselective synthesis of trifluoromethyl-substituted 1,2-diamines by aza-Michael reaction with trans-3,3,3-trifluoro-1-nitropropene

Aza-Michael addition of optically pure 4-phenyl-2-oxazolidinone to 3,3,3-trifluoro-1-nitropropene proceeds smoothly at low temperature with a high yield. Diastereoselectivity of the addition depends on the base used and lithiated species proved to be highly efficient affording 92% de. Optically pure 1,2-diamino-3,3,3-trifluoropropane is prepared in 58% yield from the aza-Michael addition product through a three-step procedure.     

Decomposition mechanism of triethylindium (TEI) on a GaP(0 0 1)-(2×1) surface studied by LEED, AES, TPD and HREELS

Adsorption and decomposition of triethylindium (TEI: (C₂H₅)₃In) on a GaP(0 0 1)-(2×1) surface have been studied by low-energy electron diffraction (LEED), Auger electron spectroscopy (AES), temperature-programmed desorption (TPD) and high-resolution electron energy loss spectroscopy (HREELS). It is found from the TPD result that ethyl radical and ethylene are evolved at about 300–400 and 450–550 K, respectively, as decomposition products of TEI on the surface. This result is quite different from that on the GaP(0 0 1)-(2×4) surface. The activation energy of desorption of ethyl radical is estimated to be about 93 kJ/mol. It is suggested that TEI is adsorbed molecularly on the surface at 100 K and that some of TEI molecules are dissociated into C₂H₅ to form P–C₂H₅ bonds at 300 K. The vibration modes related to ethyl group are decreased in intensity at about 300–400 and 450–550 K, which is consistent with the TPD result. The TEI molecules (including mono- and di-ethylindium) are not evolved from the surface. Based on the TPD and HREELS results, the decomposition mechanism of TEI on the GaP(0 0 1)-(2×1) surface is discussed and compared with that on the (2×4) surface.     

One-Parameter Fixed-Point Theory and Gradient Flows of Closed 1-Forms

We use the one-parameter fixed-point theory of Geoghegan and Nicas to get information about the closed orbit structure of transverse gradient flows of closed 1-forms on a closed manifold M. We define a noncommutative zeta function in an object related to the first Hochschild homology group of the Novikov ring associated to the 1-form and relate it to the torsion of a natural chain homotopy equivalence between the Novikov complex and a completed simplicial chain complex of the universal cover of M.     

Mechanism of catalytic asymmetric hydrogenation of 2-formyl-1-methylene-1,2,3,4-tetrahydroisoquinoline using Ru(CH3COO)2[(S)-binap]

The mechanism of the asymmetric hydrogenation of 2-acyl-1-alkylidene-1,2,3,4-tetrahydroisoquinolines, the first reported reaction with the Noyori-Takaya Ru(CH₃COO)₂(binap) complex, has been investigated by means of deuterium labeling, kinetics, and NMR analysis. A series of experiments has revealed that (1) a monohydride-unsaturated mechanism operates involving the initial formation of RuH followed by reaction with the enamide substrate, (2) the hydride transfer from RuH to the olefinic double bond is endothermic and reversible, and (3) the rate is determined in the hydrogenolysis step. This view is consistent with that of proposed for the BINAP-Ru catalyzed Kagan reaction.     

Theoretical STM images of alkaline-earth metal adsorbed Si(1 1 1)3 × 2 surfaces

We have performed total-energy calculations to study theoretical scanning tunneling microscopy (STM) images of the Si(1 1 1)3 × 2 surfaces induced by the adsorption of alkaline-earth metals (AEMs). Previously, in a series of works on Ba/Si(1 1 1) system, we have found that the observed Si(1 1 1)3 × 1-Ba LEED phase indeed has a 3 × 2 periodicity with a Ba coverage of 1/6 ML and the HCC substrate structure. Based on results of the Ba case, we proposed that the HCC structure is also adopted for other AEM atoms, which was confirmed by our recent work. In this paper, we mainly report the STM simulations for different AEM systems to compare with existing experimental data. We discuss the difference in the detailed STM images for different AEM adsorbates. Especially, the difference in filled-state images between Mg and other AEM atoms is attributed to the strong Mg-Si interaction.