Integer programming formulations of vehicle routing problems

Various mathematical formulations are available for situations represented by vehicle routing problems. The assignment-based integer programming formulations of these problems are more common and easy to understand. Such formulations are discussed in this paper and a much simpler formulation for the vechicle routing problem is presented for the case, when all the vehicles have the same load capacity and maximum allowable cost per route.     

Tests of a “free-volume” model of gas permeation through polymer membranes. I. Pure CO2, CH4, C2H4, and C3H8 in polyethylene

Permeability coefficients have been measured for CO₂, CH₄, C₂H₄, and C₃H₈ in polyethylene membranes at temperatures of 5, 20, and 35°C and at applied gas pressures of up to 30 atm. The temperature and pressure dependence of the permeability coefficients was represented satisfactorily by an extension of Fujita's free-volume model of diffusion of small molecules in polymers. The results of the present steady-state permeability measurements provide further support for the conclusion reached from previous unsteady-state diffusivity measurements that Fujita's model is applicable to the transport of small molecules, such as CO₂, CH₄, C₂H₄, and C₃H₈, in polyethylene. It was previously thought that this model is applicable only to the transport of larger molecules, such as of organic vapors, in polymers.     

Positron annihilation in annealed and quenched teflon and in sulphur

The value (τ₂) and the intensity (I₂) of the delayed component in the lifetime spectra of positrons annihilating in annealed and quenched teflon and in sulphur and crystex (polymer sulphur), at room temperature and at 77° K are reported. These data and the X-ray diffraction patterns for these materials are discussed in terms of the free volume model for the formation and quenching of positronium atoms in molecular materials.     

Nature and properties of ultrathin nanocrystalline gold films formed at the organic-aqueous interface

Ultrathin nanocrystalline films of gold formed at different temperatures at the organic-aqueous interface have been investigated by X-ray diffraction, electron microscopy, atomic force microscopy, and electronic spectroscopy. The films are smooth and continuous over relatively large length scales and are generally approximately 100 nm thick. The size of the nanocrystals is sensitive to the reaction temperature, which also determines whether the film is metallic or an activated conductor. The surface plasmon band of gold is highly red-shifted in the films. Alkanethiols perturb the structure of the films, with the magnitude of the effect depending on the chain length. Accordingly, the position of the plasmon band and the electrical resistance of the films are affected by interaction with alkanethiols; the plasmon band approaches that of isolated nanocrystals in the presence of long-chain thiols.     

Del Pezzo orders on projective surfaces

In this paper, we generalise the notion of del Pezzo surfaces to orders on surfaces. We show that these del Pezzo orders have del Pezzo centre if the centre is normal Gorenstein and the order has finite representation type. We proceed to classify these del Pezzo orders. The main result is that if the centre is not or the quadric cone, then these del Pezzo orders can be obtained from del Pezzo orders on . Finally, we classify del Pezzo orders on and the quadric cone.     

Exploring chemical diversity of epoxyquinoid natural products: synthesis and biological activity of (-)-jesterone and related molecules

Enantioselective syntheses of the potent antifungal agent (-)-jesterone, its hydroxy epimer, and a dimeric quinone epoxide derivative are reported. The synthesis involves diastereoselective epoxidation of a chiral quinone monoketal derivative and regio- and stereoselective reduction of a quinone epoxide intermediate.     

Applications of SMP Bounds to Multi-class Traffic in High-speed Networks

In this paper, we consider the stochastic fluid-flow model of a single node in a high-speed telecommunication network handling multi-class traffic. The node has multiple buffers, one for each class of traffic. The contents of these buffers are multiplexed onto a single output channel using one of the service scheduling policies: the Timed Round Robin Policy or the Static Priority Service Policy. The Quality of Service requirements for each class are based on cell loss probabilities. Using effective bandwidth methodologies and the recently developed bounds for semi-Markov modulated traffic, we solve call admission control problems for the two service scheduling policies at this node. We compare the performance of the effective bandwidth methodologies and the SMP bounds technique. We also numerically compare the performance of the two service scheduling policies.     

Electron spin resonance from annealed titania nanotubes

Titania nanotubes were prepared using a hydrothermal method. Hydrogen titanate nanotubes (H-TNTs) with an anatase phase changed to anatase nanocrystals at about 500 °C, and then a rutile structure at ∼800 °C. A sharp and symmetrical electron spin resonance (ESR) signal (g=2.003), attributed to a single-electron-trapped oxygen-vacancy (SETOV), was obtained at the annealed H-TNTs (T<500 °C). The SETOV signal increased and maximized remarkably at about 400–500 °C. Then, the nanotube structure appeared to be demolished. Yet, when the vacuum-heated H-TNTs were sealed in N₂ or Ar ambient, some additional ESR signals appeared besides the SETOV signal. The broad asymmetric ESR signal (g=1.98) was attributed to a surface oxygen vacancy related to the Ti³⁺ sites in a reduced TiO₂ matrix. The vacuum-heated sodium titanate nanotubes (Na-TNTs) showed only the SETOV signal (T<500 °C). PACS 61.46.Fg; 61.72.Ji; 76.30.-v     

Three‐dimensional finite element modelling of coupled free/porous flows: applications to industrial and environmental flows

Conjunctive modelling of free/porous flows provides a powerful and cost‐effective tool for designing industrial filters used in the process industry and also for quantifying surface–subsurface flow interactions, which play a significant role in urban flooding mechanisms resulting from sea‐level rise and climate changes. A number of well‐established schemes are available in the literature for simulation of such regimes; however, three‐dimensional (3D) modelling of such flow systems still presents numerical and practical challenges. This paper presents the development of a fully 3D, transient finite element model for the prediction and quantitative analyses of the hydrodynamic behaviour encountered in industrial filtrations and environmental flows represented by coupled flows. The weak‐variational formulation in this model is based on the use of C⁰ continuous equal‐order Lagrange polynomial functions for velocity and pressure fields represented by 3D hexahedral finite elements. A mixed UVWP finite element scheme based on the standard Galerkin technique satisfying the Ladyzhenskaya–Babuska–Brezzi stability criterion through incorporation of an artificial compressibility term in the continuity equation has been employed for the solution of coupled partial differential equations. We prove that the discretization generates unified stabilization for both the Navier–Stokes and Darcy equations and preserves the geometrical flexibility of the computational grids. A direct node‐linking procedure involving the rearrangement of the global stiffness matrix for the interface elements has been developed by the authors, which is utilized to couple the governing equations in a single model. A variety of numerical tests are conducted, indicating that the model is capable of yielding theoretically expected and accurate results for free, porous and coupled free/porous problems encountered in industrial and environmental engineering problems representing complex filtration (dead‐end and cross‐flow) and interacting surface–subsurface flows. The model is computationally cost‐effective, robust, reliable and easily implementable for practical design of filtration equipments, investigation of land use for water resource availability and assessment of the impacts of climatic variations on environmental catastrophes (i.e. coastal and urban floods). The model developed in this work results from the extension of a multi‐disciplinary project (AEROFIL) primarily sponsored by the European aerospace industries for development of a computer simulation package (Aircraft Cartridge Filter Analysis Modelling Program), which was successfully utilized and deployed for designing hydraulic dead‐end filters used in Airbus A380.Copyright © 2012 John Wiley & Sons, Ltd.     

Synthesis of highly sulfonated polybenzimidazoles by direct copolymerization and grafting

A series of highly sulfonated, ether‐containing polybenzimidazoles (SOPBI) with controlled sulfonation degrees were synthesized from various stoichiometric ratio mixtures of sodium 6,6'‐oxybis(3‐carboxybenzenesulfonate) (SODBA), 4,4'‐oxydibenzoic acid (ODBA), and 3,3'‐diaminobenzidine (DAB) by solution copolycondensation in poly(phosphoric acid). The resulting sulfonated polymers were further sulfonated by grafting of pendant sulfonic acid chains via a reaction of 1,3‐propane sultone with lithiated‐N of the imidazole rings in the polymer backbone, yielding materials with high, absolute IEC values (3.42–4.15 meq g^?1). Due to self‐neutralization, the solid state polymers possessed “free” acid content of 1.40 to 2.15 meq g^?1, were soluble in organic solvents yet insoluble in aqueous solution, while displaying proton conductivites (11–47 mS cm^?1) at elevated temperatures (80 °C, 95% RH). © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3654–3666