An interpolation approximation for the GI/G/1 queue based on multipoint Padé approximation

The performance evaluation of many complex manufacturing, communication and computer systems has been made possible by modeling them as queueing systems. Many approximations used in queueing theory have been drawn from the behavior of queues in light and heavy traffic conditions. In this paper, we propose a new approximation technique, which combines the light and heavy traffic characteristics. This interpolation approximation is based on the theory of multipoint Padé approximation which is applied at two points: light and heavy traffic. We show how this can be applied for estimating the waiting time moments of the ^GI/G/1 queue. The light traffic derivatives of any order can be evaluated using the MacLaurin series analysis procedure. The heavy traffic limits of the ^GI/G/1 queue are well known in the literature. Our technique generalizes the previously developed interpolation approximations and can be used to approximate any order of the waiting time moments. Through numerical examples, we show that the moments of the steady state waiting time can be estimated with extremely high accuracy under all ranges of traffic intensities using low orders of the approximant. We also present a framework for the development of simple analytical approximation formulas. This revised version was published online in June 2006 with corrections to the Cover Date.     

ContributionsSign-balanced covering matrices

A q × n array with entries from 0, 1,…,q − 1 is said to form a difference matrix if the vector difference (modulo q) of each pair of columns consists of a permutation of [0, 1,… q − 1]; this definition is inverted from the more standard one to be found, e.g., in Colbourn and de Launey (1996). The following idea generalizes this notion: Given an appropriate δ (-[−1, 1]^t, a λq × n array will be said to form a (t, q, λ, Δ) sign-balanced matrix if for each choice C₁, C₂,…, C_t of t columns and for each choice = (₁,…,_t) Δ of signs, the linear combination ∑_j=1^t _jC_j contains (mod q) each entry of [0, 1,…, q − 1] exactly λ times. We consider the following extremal problem in this paper: How large does the number k = k(n, t, q, λ, δ) of rows have to be so that for each choice of t columns and for each choice (₁, …, _t) of signs in δ, the linear combination ∑_j=1^t _jC_j contains each entry of [0, 1,…, q t- 1] at least λ times? We use probabilistic methods, in particular the Lovász local lemma and the Stein-Chen method of Poisson approximation to obtain general (logarithmic) upper bounds on the numbers k(n, t, q, λ, δ), and to provide Poisson approximations for the probability distribution of the number W of deficient sets of t columns, given a random array. It is proved, in addition, that arithmetic modulo q yields the smallest array - in a sense to be described.     

灰色模型的最优化及其参数的直接求法

基于灰色模型的内涵表达式和白化方程响应式均为等比级数的观点,提出了一种不用求ago值、均值,不涉及灰色微分方程,白化微分方程概念,直接求灰色模型参数a,c的方法,通过此方法建立的新模型不仅从理论上可保证是在满足给定评价标准为模拟绝对误差平方和最小(或模拟相对误差平方和最小)、给定精度条件下的最优化模型,从而结束了灰色模型只有更优,没有最优的历史.并从理论上证明了新模型具有白化指数律重合性、白化系数律重合性,伸缩变换一致性.最后通过实例编程验证该方法具有可操作性,且预测精度高,效果好.     

Isolation and Structure Elucidation of Nortriterpenoids from Schisandra rubriflora

Seven new highly oxygenated nortriterpenoids, rubriflorins D–J ( 1 – 7 ), were isolated from the leaves and stems of Schisandra rubriflora, and their structures were elucidated on the basis of extensive analysis of spectroscopic data. These new compounds feature the opening of ring A compared with related known nortriterpenoids isolated from the genus Schisandra and showed weak activity against HIV‐1.     

Low-energy ion-assisted control of interfacial structures in metallic multilayers

A molecular dynamics method has been used to simulate the argon ion-assisted deposition of Cu/Co/Cu multilayers and to explore ion beam assistance strategies that can be used during or after the growth of each layer to control interfacial structures. A low-argon ion energy of 5–10 eV was found to minimize a combination of interfacial roughness and interlayer mixing (alloying) during the ion-assisted deposition of multilayers. However, complete flattening with simultaneous ion assistance could not be achieved without some mixing between the layers when a constant ion energy approach was used. It was found that multilayers with lower interfacial roughness and intermixing could be grown either by modulating the ion energy during the growth of each metal layer or by utilizing ion assistance only after the completion of each layers deposition. In these latter approaches, relatively high-energy ions could be used since the interface is buried and less susceptible to intermixing. The interlayer mixing dependence upon the thickness of the over layer has been determined as a function of ion energy.     

Synthesis of 5‐Radioiodoarabinosyl Uridine Analog for Probing the HSV‐1 Thymidine Kinase Gene

Tumor cells transduced with herpes simplex virus thymidine kinase gene have been intensively applied to the field of positron emission tomography via imaging of its substrate. As a pilot synthesis approach, a facile preparation of 5‐[¹²⁵I] iodoarabinosyl uridine starting from commercially available uridine is reported herein.     

Synthesis and characterization of poly(higher‐α‐olefin)s with a nickel(α‐diimine)/methylaluminoxane catalyst system: Effect of chain running on the polymer properties

Homopolymerization of octadecene‐1 at different reaction conditions has been studied. Significant chain running can be seen at higher polymerization temperatures. Interestingly, insertion of octadecene‐1 into a sterically hindered nickel‐cation/carbon (secondary) bond is observed. The microstructure of the polymer was established using NMR spectroscopy. The effects of chain running on polymer melting, crystallization behavior, and dynamic mechanical thermal properties were studied using DSC and DMTA. The extent of chain running (i.e., 2,ω‐, 1,ω‐enchainments) decreases with an increase in the carbon number of α‐olefins. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 191–210, 2007     

Gradient- and Sensitivity-Enhanced TOCSY Experiments

A pulsed field gradient version of the sensitivity-enhanced 2D TOCSY experiment is proposed which yields high-quality spectra with improved sensitivity and a minimum of two scans pert₁increment. For rapid acquisition of 1D TOCSY spectra, the 1D DPFGSE–TOCSY experiment was modified to include phase-encoded multiple-selective excitation followed by a simple spectral editing. Combination of these two building blocks is used in a sensitivity-enhanced 2D analog of the 3D TOCSY–TOCSY experiment which provides an efficient tool for resolving severely overlapped signals of oligomers in short experimental time.     

Multinuclear magnetic resonance study of some mesoionic oxatriazoles containing nitrogenous exocyclic groups

¹H,¹³C,¹⁴N and¹⁵N NMR measurements are reported for four mesoionic 1-oxa-2, 3, 4-triazoles containing exocyclic nitrogenous groups. The NMR signal assignments are discussed and compared with those previously published for some corresponding oxatriazoles. The results obtained support the proposed cyclic mesoionic structures for the compounds studied. The questions of possible charge delocalization and valence tautomerism are addressed. Compound with N^– H as a exocyclic group (Fig. 1) is found to be relatively unstable, this is attributed to proton migration in the corresponding non-cyclic form of this molecule.Published in Khimiya Geterotsikiicheskikh Soedinenii, No. 9, pp. 1260–1263, September, 1995.     

Fluorinated,crosslinkable terpolymers based on vinylidene fluoride and bearing sulfonic acid side groups for fuel‐cell membranes

The radical terpolymerization of 8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene with vinylidene fluoride (VDF) and perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride is presented. Changing the feed compositions of these three fluorinated comonomers enabled us to obtain different random‐type poly[vinylidene fluoride‐ter‐perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride‐ter‐8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene] terpolymers containing various sulfonyl fluoride and brominated side groups. Yields higher than 70% were reached in all cases. The hydrolysis of the sulfonyl fluoride group into the ? SO₃Li function in the presence of lithium carbonate was quantitatively achieved without the content of VDF being affected, and so dehydrofluorination of the VDF base unit was avoided. These original terpolymers were then crosslinked via dangling bromine atoms in the presence of a peroxide/triallyl isocyanurate system, which produced films insoluble in organic solvents such as acetone and dimethylformamide (which totally dissolved uncured terpolymers). The acidification of ? SO₃Li into the ? SO₃H function enabled protonic membranes to be obtained. The thermal stabilities of the crosslinked materials were higher than those of the uncured terpolymers, and their electrochemical performances were investigated. According to the contents of the sulfonic acid side functions, the ion‐exchange capacities ranged from 0.6 to 1.5 mequiv of H⁺/g, whereas the water uptake and conductivities ranged from 5–26% (±11%) and from 0.5 to 6.0 mS/cm, respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4566–4578, 2006