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.     

A pair of orthogonal frames

We start with a characterization of a pair of frames to be orthogonal in a shift-invariant space and then give a simple construction of a pair of orthogonal shift-invariant frames. This is applied to obtain a construction of a pair of Gabor orthogonal frames as an example. This is also developed further to obtain constructions of a pair of orthogonal wavelet frames.     

Square classes of totally positive units

In this article, we investigate some conditions for a real cyclic extension K over Q to satisfy the property that every totally positive unit of K is a square. As an application, we give a partial answer to Taussky's conjecture. We then extend our result to real abelian extensions of certain type.     

Luminescence enhancement of Eu-doped calcium magnesium silicate blue phosphor for UV-LED application

(Ca_1−x,Eu_x)MgSi_2yO_6+δ blue phosphor was prepared by spray pyrolysis and the photoluminescence properties were optimized by controlling concentration of Si element and the activator content. At y=1.0, the concentration quenching in the luminescent intensity appeared when the Eu²⁺ content (x) was 0.01 (1 at%). Such quenching concentration was changed with the concentration of silicon (y), which was increased with an increase in the quantity of excess Si (y>1.0). The highest luminescent intensity was achieved when the Eu²⁺ content (x) and the Si concentration (y) were 0.04 and 1.3, respectively. According to X-ray diffraction (XRD) analysis, the tetragonal SiO₂ phase was formed as a minor phase when the y value was larger than 1.3. The formation of SiO₂ phase, however, did not reduce but increased the luminescent intensity when the Eu²⁺ content was optimized again. As a result, the luminescent intensity of the phosphor particles optimized in the content of both Si and Eu²⁺ was about 150% improved compared with that of the CaMgSi₂O₆:Eu sample (x=0.01, y=1.0).     

Fabrication of low OH loss holey fibers with varying air hole sizes and their optical properties

We experimentally investigate a flexible fabrication technique for low OH and transmission losses holey fibers with a Ge-doped core and air holes in a silica cladding region. Versatile holey fibers of different size, pitch, and shape of air holes were achieved by controlling the temperature and heating time of the holey fiber preform. In addition, we suppress the OH loss of less than ∼0.323 dB/km at 1383 nm. After fabricating holey fibers, we measure their optical properties including cut-off wavelength, mode field diameter, splicing loss, dispersion, bending loss, and polarization dependent loss based on the size of air holes. The total transmission loss was measured to be ∼0.226 dB/km at 1550 nm by improving the fabrication process. After fabricating optical patch cord based on holey fibers, we measured the long-term stability of the fabricated holey fiber by using the temperature cycling technique for 24 and obtained low power fluctuation of 0.2 dB. We achieve the high quality holey fiber with a low bending loss of ∼0.04 dB/turn under a bending radius of 2.5 mm at 1550 nm. We also obtain a tunable band rejection filter with a number of bending turns.     

Game theoretic analysis of the bargaining process over a long-term replenishment contract

This paper presents supplier–buyer models to describe the bargaining process between a supplier and a buyer over a long-term replenishment contract. Two different models are developed: one for the situation where the supplier has superior bargaining power over the buyer, and the other for the reverse situation. For each model, a method is derived that employs game theory-based analysis to determine the best strategy for each agent. A computational experiment is conducted to estimate the efficiency of the methods and to determine the economic implications of the results. The result indicates that each algorithm is very efficient compared to other strategies. We also verify that the solutions derived from each model are Nash equilibrium. Significantly improved outcomes are obtained for both agents by agreeing to the terms generated by the algorithms over the terms selected in the usual manner.     

Periodic Solutions of Classical Hamiltonian Systems without Palais-Smale Condition

In this paper, we study the existence of periodic solutions for classical Hamiltonian systems without the Palais-Smale condition. We prove that the information of the potential function contained in a finite domain is sufficient for the existence of periodic solutions. Moreover, we establish the existence of infinitely many periodic solutions without any symmetric condition on the potential function V.     

Simultaneous jumps in two two-level atoms

We demonstrate the importance of collective behaviour in two identical two-level atoms. When the atoms become very close together a cascade three-level atom analysis can be adopted to show the increasing possibility of simultaneous jumps. Due to the dipole-dipole interaction the intermediate one-atom excited state is detuned by a large amount when the atoms are close together but leaving the upper two-atom excited state in two-photon resonance. The relative importance of multiple jumps compared with stepwise independent jumps is then changed dramatically.     

Analysis of creep due to grain-boundary diffusion in hexagonal microstructures

For steady-state deformation caused by grain-boundary diffusion in hexagonal microstructures, the stress distribution on grain boundaries and the macroscopic strain rates are analysed by taking the effects of viscous grain-boundary sliding into account. The maximum normal stress and the extent of stress concentration are shown to decrease as the grain-boundary viscosity increases. For infinite viscosity and/or extremely small grain sizes, the distribution of the normal stress becomes uniform on grain boundaries. The strain rates are predicted by both the stress analysis and the energy balance method, and the two strain rates are consistent with each other. The predicted strain rates also decrease as the grain-boundary viscosity increases. The present analysis reveals that the grain-size exponent is dependent on the grain size and the grain-boundary viscosity: the exponent becomes unity for small grain sizes and/or high viscosity, while it is three for large grain sizes and/or low viscosity. Recent experimental observations that the strain rates of nano-sized grain are much lower than those predicted by grain-boundary diffusion are explained by the increasing contribution of viscous grain-boundary sliding with decreasing grain size.