Asymptotic analysis of the effect of arrival model uncertainties in some optimal routing problems

We study the effect of arrival model uncertainties on the optimal routing in a system of parallel queues. For exponential service time distributions and Bernoulli routing, the optimal mean system delay generally depends on the interarrival time distribution. Any error in modeling the arriving process will cause a model-based optimal routing algorithm to produce a mean system delay higher than the true optimum. In this paper, we present an asymptotic analysis of the behavior of this error under heavy traffic conditions for a general renewal arrival process. An asymptotic analysis of the error in optimal mean delay due to uncertainties in the service time distribution for Poisson arrivals was reported in Ref. 6, where it was shown that, when the first moment of the service time distribution is known, this error in performance vanishes asymptotically as the traffic load approaches the system capacity. In contrast, this paper establishes the somewhat surprising result that, when only the first moment of the arrival distribution is known, the error in optimal mean delay due to uncertainties in the arrival model is unbounded as the traffic approaches the system capacity. However, when both first and second moments are known, the error vanishes asymptotically. Numerical examples corroborating the theoretical results are also presented.This work was supported by the National Science Foundation under Grants ECS-88-01912 and EID-92-12122 and by NASA under Contract NAG 2-595.The authors wish to thank an anonymous referee for pointing out Ref. 20, thus avoiding the need for an explicit proof of convexity of the cost function considered in the paper.     

Photoinduced dissociative electron transfer (DET) interactions in methoxycalixarene–chloroalkane systems

Fluorescence quenching of methoxycalixarenes (MOCX) by chloroalkanes (CA) has been investigated in acetonitrile solutions. Observed quenching is attributed to photoinduced dissociative electron transfer (DET) interaction, which is supported by the characterization of the Cl⁻ ions and by the radical scavenging experiments. Comparing the Cl⁻ yields with different DET systems, it is inferred that both concerted and stepwise DET mechanisms operate simultaneously in MOCX–CA systems. A correlation of the quenching constants with the free-energy changes following a suitable DET theory supports the above inference.     

Kinetics and mechanism of the complex formation between oxalatopentaamminecobalt(III) and aluminium(III) and gallium(III); a comparative study

Summary The reversible complex formation between oxalatopentaammine cobalt(III), aluminium(III) and gallium(III) was investigated by the stopped flow technique at 30 ± 0.1 °C and I = 1.0 mol dm^–3. The reactivity sequence: Ga^III > Al^III is observed, however, the major path for gallium(III) was (NH3)₅CoC₂O₄H²⁺ + GaOH²⁺ (NH₃)₅CoC₂O₄-Ga⁴⁺ + H₂O. The formation and dissociation rate constants of the binuclear species have been compared with the analogous data for iron(III) and nickel(II) reported earlier. The results reflect the fact that the half-bonded exalato moiety of (NH₃)₅CoC₂O _inf4 ^p+ acts as a chelating agent for the metal ions.Author to whom all correspondence should be directed.     

High surface area silicon carbide from rice husk: A support material for catalysts

Ultrafine -SiC with high surface area (150 m² g^–1) has been synthesized by inflight processing of charred rice husk in a r.f. plasma reactor operating at atmospheric pressure. The plasma-synthesized particles were doped with platinum (1%) and tested as a catalytic support material. The catalyst (1% Pt doped -SiC) showed 100% conversion of CO to CO₂ at a temperature as low as 175°C.     

Charge and salt-driven reentrant order-disorder and gas-solid transitions in charged colloids

Monte Carlo simulations have been performed for aqueous charged colloidal suspensions as a function of effective charge density (sigma) on the particles and salt concentration C(s). We vary the effective charge density in our simulations over a range where a reentrant solid-liquid transition in suspensions of silica and polymer latex particles has been reported by Yamanaka et al. (Phys. Rev. Lett. 80 (1998) 5806). We show that at low ionic strengths a homogeneous liquid-like ordered suspension undergoes crystallization upon increasing sigma. Further increase in sigma resulted once again in a disordered state, which is in agreement with experimental observations. In addition to this reentrant order-disorder transition, we observe an inhomogeneous-to-homogeneous transition in our simulations when salt is added to the disordered inhomogeneous state. This inhomogeneous-to-homogeneous disordered transition is analogous to the solid-gas transition of atomic systems and has not yet been observed in charged colloids. The reported experimental observations on charged colloidal suspensions are discussed in the light of present simulation results.     

Determination of Hormones and Non-ionic Surfactant Degradation Products in Small-Volume Aqueous Samples from Soil Columns Using LC-ESI-MS-MS and GC-MS

The leaching of two estrogens, 17β-estradiol and estrone, and two degradation products of non-ionic surfactants, octylphenol and nonylphenol, through a soil column were studied to estimate their transport behavior. Different concentration methods (lyophilization, solid phase extraction, and liquid–liquid extraction) were evaluated for analyzing these compounds in small effluent fractions (30–50 mL) collected. Liquid chromatography-mass spectrometry (LC-MS-MS) and gas chromatography-mass spectrometry (GC-MS) were employed for quantitative analysis of these compounds. After comparison, the lyophilization-LC-MS-MS method was found to be best suited for the analysis of the two estrogen hormones and the liquid–liquid extraction-GC-MS method best for the analysis of the two phenols in small samples in the soil column study. Because of their high sorption capacity, these compounds were mostly sorbed in the upper part of the soil column and were difficult to detect in column effluent.     

Numerical solution of minimax problems of optimal control,part 1

This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P).For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.This research was supported by the National Science Foundation, Grant No. ENG-79-18667, and by Wright-Patterson Air Force Base, Contract No. F33615-80-C3000. This paper is a condensation of the investigations reported in Refs. 1–7. The authors are indebted to E. M. Coker and E. M. Sims for analytical and computational assistance.     

Aqueous polymerization of acrylonitrile initiated by the bromate–thiourea redox system

The aqueous polymerization of acrylonitrile initiated by an acidified bromate–thiourea redox system has been studied under nitrogen atmosphere. The rate of polymerization is independent of thiourea concentration over the range 2–9 × 10^?3M and reaches maximum at 9 × 10^?3M. The rate varies linearly with [monomer]. The initial rate of polymerization as well as the maximum conversion increases within the range of 4–22.5 × 10^?3M KBrO₃, but beyond 22.5 × 10^?3M the rate of polymerization decreases. The initial rate and the limiting conversion increases with increasing polymerization temperature in the range 30–45°C; and beyond 45°C they decrease. The effect of certain neutral salts, water-soluble solvents, and micelles of cationic, anionic, and nonionic surfactants on the rate of polymerization has been investigated.     

Purification and Characterization of Gum-Derived Polysaccharides of Moringa oleifera and Azadirachta indica and Their Applications as Plant Stimulants and Bio-Pesticidal Agents

Plant gums are bio-organic substances that are derived from the barks of trees. They are biodegradable and non-adverse complex polysaccharides that have been gaining usage in recent years due to a number of advantages they contribute to various applications. In this study, gum was collected from Moringa oleifera and Azadirachta indica trees, then dried and powdered. Characterizations of gum polysaccharides were performed using TLC, GC-MS, NMR, etc., and sugar molecules such as glucose and xylose were found to be present. Effects of the gums on Abelmoschus esculentus growth were observed through root growth, shoot growth, and biomass content. The exposure of the seeds to the plant gums led to bio stimulation in the growth of the plants. Poor quality soil was exposed to the gum polysaccharide, where the polysaccharide was found to improve soil quality, which was observed through soil analysis and SEM analysis of soil porosity and structure. Furthermore, the plant gums were also found to have bio-pesticidal activity against mealybugs, which showed certain interstitial damage evident through histopathological analysis.