The Depot Siting Problem with Discontinuous Delivery Cost<Superscript>†</Superscript>

Discontinuities may occur in the distribution cost function for a variety of reasons. Some of these, notably discontinuous trunking costs and depot costs dependent on location, have been examined in the literature. In this paper the problem which arises when discontinuities occur in the local delivery cost function is examined and a method of solution incorporating heuristics is described. An illustrative example is given.     

Radial jet in rotating outer flow

The rotating radial jet formed by fluid introduced radially outwards into a rotating environment is studied by the momentum integral method and by perturbation for weak swirl, assuming incompressible laminar flow. For non-swirling outer fluid, the results slightly extend previously published results. For swirling outer fluid, the jet is characterized by a finite radial penetration distance. Its development over that distance is divided into three regions: an initial adjustment, a central pseudo-similarity region, and a final decay.     

Modelling of flow pattern in a shallow aquifer affected by reservoirs

A compartmental model is developed to estimate flow parameters of a shallow aquifer affected by water loads in surface reservoirs and to evaluate its nonsteady flow distribution. The method incorporates temporal piezometric head measurements and sampling of water for dissolved chemicals and isotopes analyses. Each compartment is governed by a set of equations describing the conservation of linear momentum and mass balance expressions for water, isotopes, and dissolved chemicals. The number of compartmental balance expressions always must be greater than that of the unknown flow parameters associated with each compartment. An optimization method is described to yield spatial distribution of aquifer storativity, transmissivity, porosity, leakage, and compliance coefficients and fluxes leaking into an aquifer's lower boundary. Future predictions of an aquifer's piezometric head distribution in a compartmental system is formulated on the basis of the estimated flow parameters and the leakage components.Compartmental modelling which incorporates concentrations of environmental tracers, may yield efficiency in computing resources and accuracy enhancement for predicting an aquifer's flow regime.     

Sampling Procedures for Risk Simulation

Risk simulation has become a standard alternative to the utilization of single estimates for input data to investment appraisal models. Under the risk simulation approach managers define probability distributions for relevant input factors. During this process management may consciously or subconsciously assume certain relationships between the input variables. These interdependencies are often omitted from the models, however, under the justification that they are accounted for implicitly in the values attributed to the variables by management. It is demonstrated in this paper that such omissions may lead to significant errors in the observed distributions of the selected appraisal criteria. Various forms of discriminate sampling are introduced and an example is cited for which certain discriminate schemes are shown to be more accurate than traditional independent sampling.     

Economic Batch-Size Determination for Multi-Product Scheduling

In the determination of batch-sizes in batch production, different criteria can be used as guiding principles, depending on the specified objectives. In a production schedule consisting of several products, an optimum solution for the whole production schedule is sought. At the same time it is necessary to ensure that the total production costs of each individual product will not exceed a certain pre-determined value. Solutions for overall optimization of the schedule with respect to maximum profit per batch, or with respect to maximum return on the total cost of production of the batch, have already been published. This paper suggests a method for determining the economic batch-sizes when it is desirable to maximize the rate of return per unit time for a multi-product schedule.     

The modified stochastic game

We present a new tool for the study of multiplayer stochastic games, namely the modified game, which is a normal-form game that depends on the discount factor, the initial state, and for every player a partition of the set of states and a vector that assigns a real number to each element of the partition. We study properties of the modified game, like its equilibria, min–max value, and max–min value. We then show how this tool can be used to prove the existence of a uniform equilibrium in a certain class of multiplayer stochastic games.     

Moderately branched ultra‐high molecular weight polyethylene by using N,N′‐nickel catalysts adorned with sterically hindered dibenzocycloheptyl groups

Five examples of unsymmetrical 1,2‐bis (arylimino) acenaphthene ( L1 – L5 ), each containing one N‐2,4‐bis (dibenzocycloheptyl)‐6‐methylphenyl group and one sterically and electronically variable N‐aryl group, have been used to prepare the N,N′‐nickel (II) halide complexes, [1‐[2,4‐{(C₁₅H₁₃}₂–6‐MeC₆H₂N]‐2‐(ArN)C₂C₁₀H₆]NiX₂ (X = Br: Ar = 2,6‐Me₂C₆H₃ Ni1 , 2,6‐Et₂C₆H₃ Ni2 , 2,6‐i‐Pr₂C₆H₃ Ni3 , 2,4,6‐Me₃C₆H₂ Ni4 , 2,6‐Et₂–4‐MeC₆H₂ Ni5 ) and (X = Cl: Ar = 2,6‐Me₂C₆H₃ Ni6 , 2,6‐Et₂C₆H₃ Ni7 , 2,6‐i‐Pr₂C₆H₃ Ni8 , 2,4,6‐Me₃C₆H₂ Ni9 , 2,6‐Et₂–4‐MeC₆H₂ Ni10 ), in high yield. The molecular structures Ni3 and Ni7 highlight the extensive steric protection imparted by the ortho‐dibenzocycloheptyl group and the distorted tetrahedral geometry conferred to the nickel center. On activation with either Et₂AlCl or MAO, Ni1 – Ni10 exhibited very high activities for ethylene polymerization with the least bulky Ni1 the most active (up to 1.06  ×  10⁷ g PE mol^?1(Ni) h^?1 with MAO). Notably, these sterically bulky catalysts have a propensity towards generating very high molecular weight polyethylene with moderate levels of branching and narrow dispersities with the most hindered Ni3 and Ni8 affording ultra‐high molecular weight material (up to 1.5  ×  10⁶ g mol^?1). Indeed, both the activity and molecular weights of the resulting polyethylene are among the highest to be reported for this class of unsymmetrical 1,2‐bis (imino)acenaphthene‐nickel catalyst.     

cis‐Dicarbonyl‐cis‐dichlorido‐trans‐bis(triphenylphosphine‐κP)iridium(III) tetrafluoridoborate,formed by reaction of (cycloocta‐1,5‐diene)bis(triphenylphosphine)iridium tetrafluoridoborate with carbonyl fluoride in dichloromethane solution

The reaction between carbonyl fluoride and [Ir(COD)(PPh₃)₂]BF₄ (COD is cycloocta‐1,5‐diene) in dichloromethane solution affords the novel title iridium salt, [IrCl₂(C₁₈H₁₅P)₂(CO)₂]BF₄. The cation lies across a twofold rotation axis in the space group P2₁2₁2 and its structure confirms the presence in a cis relationship of two metal‐bound chlorides, while the phosphine ligands occupy a trans pair of sites. The anion also lies across a twofold rotation axis, and the F atoms are disordered over two sets of sites.