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.     

Asymptotic Behavior of Loss Probability in GI/M/1/K Queue as K Tends to Infinity

We obtain an asymptotic behavior of the loss probability for the GI/M/1/K queue as K for cases of <1, >1 and =1.     

Lower functions for processes with stationary independent increments

Summary Let {X _t } be aR ¹-valued process with stationary independent increments and . In this paper we find a sufficient condition for there to exist nonnegative and nondecreasing functionh(t) such that lim infA _t /h(t)=C a.s. ast0 andt, for some positive finite constantC whenh(t) takes a particular form. Also two analytic conditions are considered as application.This research is partially supported by Korea Science & Engineering Foundation     

The law of the iterated logarithm for local time of a Lévy process

Summary Let {X _t } be a one-dimensional Lévy process with local timeL(t, x) andL ^*(t)=sup{L(t, x): x }. Under an assumption which is more general than being a symmetric stable process with index >1, we obtain a LIL forL*(t). Also with an additional condition of symmetry, a LIL for range is proved.This research is supported by a grant from Korea Science and Engineering Foundations     

Lower functions for asymmetric Lévy processes

Summary Let {X _t } be a ¹ process with stationary independent increments and its Lévy measurev be given byv{yy>x}=x ^–L ₁ (x), v{yy<–x}=x ^–L ₂ (x) whereL ₁,L ₂ are slowly varying at 0 and and 0<1. We construct two types of a nondecreasing functionh(t) depending on 0<<1 or =1 such that lim inf a.s. ast 0 andt for some positive finite constantC.This research is partialy supported by a grant from Korea University     

Exact Convergence Rate for the Distributions of GI/M/c/K Queue as K Tends to Infinity

We obtain the exact convergence rate of the stationary distribution ^(K) of the embedded Markov chain in GI/M/c/K queue to the stationary distribution of the embedded Markov chain in GI/M/c queue as K. Similar result for the time-stationary distributions of queue size is also included. These generalize Choi and Kim's results of the case c=1 by nontrivial ways. Our results also strengthen the Simonot's results [5].     

Facile Syntheses of 7,7-Dimethyl-6,8-Dioxabicyclo[3.2.1]octane,A Constituent of the Japanese Hop Oil,and Frontalin Via Hetero Diels-Alder Reaction Using Dilution Method

A constituent of the Japanese hop oil, Humulus lupulus, and frontalin has been prepared as racemates in short and the most convenient pathway via hetero Diels-Alder reaction using dilution method.     

Stability for multidimensional jump-diffusion processes

The aim of this work is to obtain sufficient conditions for stability of multidimensional jump-diffusion processes in the sense of stability in distribution and stability at the equilibrium solution. The technique employed is to construct appropriate Lyapunov functions.     

Recurrence and transience for jump–diffusion processes

The purpose of this work is to obtain sufficient conditions for transience and recurrence of multidimensional jump–diffusion processes, which are driven by Brownian motion and Poisson random measure. The approach adopted here is to construct appropriate Lyapounov functions     

Ab initio studies of three-membered ring formation through intramolecular nucleophilic substitution

Three-membered ring (3MR) forming processes of ⁻X(SINGLE BOND)CH₂(SINGLE BOND)CH₂(SINGLE BOND)F and ⁻CH₂(SINGLE BOND)C((SINGLE BOND)Y)(SINGLE BOND)CH₂(SINGLE BOND)F (X(DOUBLE BOND)CH₂, O, or S and Y(DOUBLE BOND)0 or S) through a gas phase neighboring group mechanism (S_Ni) are studied theoretically using the ab initio molecular orbital method with the 6–31+G* basis set. When electron correlation effects are considered, the activation (ΔG^≠) and reaction energies (ΔG⁰) are lowered by ca. 10 kcal mol⁻¹, indicating the importance of the electron correlation effect in these reactions. The contribution of entropy of activation (−TΔS^≠) at 298 K to ΔG^≠ is very small, and the reactions are enthalpy controlled. The ΔG^≠ and ΔG⁰ values for these ring closure processes largely depend on the stabilities of the reactants and the heteroatom acting as a nucleophilic center. The Bell–Evans–Polanyi principle applies well to all these reaction series. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1773–1784, 1997