Fractional extensions of some boundary value problems in oil strata

In the present paper, we solve three boundary value problems related to the temperature field in oil strata — the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional generalization of the incomplete lumped formulation in the radial case. By using the Caputo differintegral operator and the Laplace transform, the solutions are obtained in integral forms where the integrand is expressed in terms of the convolution of some auxiliary functions of Wright function type. A generalization of the Laplace transform convolution theorem, known as Efros’ theorem is widely used.     

Allocation of jobs and identical resources with two pooling centers

We examine the resource allocation problem of partitioning identical servers into two parallel pooling centers, and simultaneously assigning job types to pooling centers. Each job type has a distinct Poisson arrival rate and a distinct holding cost per unit time. Each pooling center becomes a queueing system with an exponential service time distribution. The goal is to minimize the total holding cost. The problem is shown to be polynomial if a job type can be divided between the pooling centers, and NP-hard if dividing job types is not possible. When there are two servers and jobs cannot be divided, we demonstrate that the two pooling center configuration is rarely optimal. A heuristic which checks the single pooling center has an upper bound on the relative error of 4/3. The heuristic is extended for the multiple server problem, where relative error is bounded above by the number of servers.      

Impact of demand uncertainty on coordinating supply chain inventories through common replenishment epochs

Prior studies have shown that inventories in a one vendor, multi-buyer supply chain with deterministic demands can be coordinated effectively through the use of common replenishment epochs (CRE). In this paper, we study the impact of demand uncertainty on the effectiveness of coordinating such a supply chain. We develop a model to analyse the coordination mechanism using CRE in a one-vendor, multi-buyer supply chain, when the demand faced by the buyers is stochastic. Our numerical study based on the model found that coordination through CRE may not always be beneficial when the demand variance is high. We also investigate a strategy of advance order processing by the vendor to improve the effectiveness of coordination through CRE.     

‘Doing the right problem’ <Emphasis Type="Italic">versus</Emphasis> ‘doing the problem right’: problem structuring within a Land Force environment

The essential first step of any OR investigation is to ensure that the ‘right problem’ is studied. Our approach is to propose a set of six ‘rights’ or questions whereby achievement against particular aspects of a problem space is made and these provide the basis for scoping the context, understanding the system, and proposing sound options to the decision-maker. This style of problem structuring is an essential element of the Defence problem domain, and especially so for the Land Force, where there exist multiple degrees of freedom for poorly defined problems in an environment of uncertainty and ambiguity. Central to this is performing conceptual rather than analytical modelling, as perturbations then provide a basis for exploring a space, rather than solving a problem.     

Correlation between luminescent properties and structure organization in AlGaN/GaN superlattices annealed after erbium ion implantation

The evolution of the structure organization of MOCVD-grown AlGaN/GaN superlattices subjected to erbium ion implantation with an energy of 1 MeV and dose of 3 × 10¹⁵ cm^?2 and subsequent annealing is correlated with their photoluminescent properties. The structure organization is quantitatively estimated using parameter Δ (degree of violation of local symmetry), which is found via multifractal analysis of surface morphology patterns obtained with atomic force microscopy. It is shown that the implantation not only causes Ga segregation on the surface, but also changes the structure organization, which shows up in the finer grain structure compared with the starting one and disordering, as well as in an increase in Δ. As the annealing temperature rises from 700 to 800°C, Δ declines, indicating that the structure organization is improved, and the intensity of the dominating photoluminescence peak due to Er³⁺ ions (1.542 μm) grows. With a further increase in the annealing temperature to 1050°C, the structure organization degrades, domains get larger, voids 100–200 nm deep form, and the photoluminescence intensity drops. The formation of voids during high-temperature annealing is also substantiated by data for 230-keV proton scattering. It is thus established that the improvement of the superlattice structure organization activates erbium and causes the erbium-ion-related luminescence intensity to grow.     

Electrodeposition of molybdenum oxide and its structural characteristics

The cathodic processes in electroplating of compact molybdenum oxide coatings onto supports made of 12Cr18Ni9Ti steel and aluminum are considered along with the physicochemical characteristics determining their service properties.     

Bis(2-hydroxyacetophenone)ethylenediimine as a neutral carrier in a coated-wire membrane electrode for lead(II).

A coated-wire ion-selective electrode (CWISE), based on a Schiff base as a neutral carrier, was successfully developed for the detection of Pb(II) in aqueous solution. CWISE exhibited a linear response with a Nernstian slope of 29.4 +/- 0.5 mV/decade within the concentration range of 1.0 x 10(-5) - 1.0 x 10(-1) M lead ion. CWISE has shown detection limits of 5.0 x 10(-6) M. The electrode exhibited good selectivity over a number of alkali, alkaline earth, transition and heavy metal ions. This sensor yielded a steady potential within 10 to 20 s at a linear dynamic range. The electrode was suitable for use in aqueous solutions in a pH range of 2.0 to 5.0. Applications of this electrode for the determination of lead in real samples and as indicator electrode for potentiometric titration of Pb2+ ion using K2CrO4 are reported.     

Synthetic modeling of the active site of native metalloenzymes by trimethylacetatozinc complexes

Synthetic approaches are discussed to a preparation of binuclear trimethylacetatozinc complexes containing an M₂(μ-OOCR)₂L₄ binuclear fragment, which is found in the active site of native metalloenzymes.     

The standard enthalpies of formation of nitro compounds with small rings

The energies of combustion and standard enthalpies of formation of 1-nitrospiro[2.3]hexane, 7-nitrodispiro[3.0.3.1]nonane, and 1,1-dinitrocyclopropane were determined experimentally.