Tax-Adjusted Replacement Models

The 1984 UK Finance Act introduced changes in tax legislation with consequences for both capital and revenue expenditure on plant. The one- and two-cycle rent models for capital equipment replacement and the infinite-cycle discounted-cost model are extended here to incorporate the new tax features. A specific replacement problem is used as the basis of an analyis of the sensitivity of the optimal replacement period to parameters. Whilst all these models are consistently insensitive to the new tax legislation, there is no consistency across models with respect to which parameters dominate choice of optimal replacement period.     

A Systems Model of Underwater Inspection Operations

The paper reports on the development of a systems model of the sub-sea inspection of an offshore structure in the North Sea. Diving practices, weather conditions, topside management procedures and inspection techniques are incorporated into the model, along with support-vessel capabilities. The model provides a research tool capable of indicating and quantifying ways of increasing the efficiency of inspection diving. Characteristic distributions of many of the variables involved are presented, along with an indication of the consequences of changes in decision and operational parameters. The study indicates that a significant increase in sub-sea inspection efficiency will come from synchronization of topside and sub-sea activities.     

An Operational Research Approach to Planned Maintenance: Modelling P.M. for a Vehicle Fleet

A methodology is advanced for modelling the problem of planned preventive maintenance, thereby relating plant performance to maintenance activity. Ideas are discussed and developed within the context of a P.M. system for the maintenance of a vehicle fleet. Three specific questions are addressed: first, the omission of any desirable activities from the P.M. schedule, secondly, the presence of redundant items in the schedule, and thirdly, the consequences of different frequencies of application of the P.M. schedule. A fleet model is obtained relating the P.M. period to measures such as proportion of breakdown repairs and the cost per vehicle year.     

Inverse Hölder inequalities in one and several dimensions

We study certain functionals and obtain an inverse Hölder inequality for n functions f₁^a1,…,f_n^an (f_k concave, 1 dimension).We also prove a multidimensional inverse Hölder inequality for n functions f₁,…,f_n, where $\text{?}{}^2\text{f}{}_{\mathrm{k}}\text{?x}{}_{\mathrm{i}}{}^2\text{? 0, i = 1,…, d, k = 1,…, n}$.Finally we give an inverse Minkowski inequality for concave functions.     

Integral inequalities for generalized concave or convex functions

Let ψ be convex with respect to ?, B a convex body in Rⁿ and f a positive concave function on B. A well-known result by Berwald states that $\text{1}\text{¦B¦}\text{∝}{}_{\mathrm{B}}\text{ψ(f(x)) dx ? n ∝}{}_0{}^1\text{ψ(ξt)(1 ? t)}{}^{\mathrm{n\; ?\; 1)}}\text{dt}$ (1) if ξ is chosen such that $\text{1}\text{¦B¦}\text{∝}{}_{\mathrm{B}}\text{?(f(x)) dx = n ∝}{}_0{}^1\text{?(ξt)(1 ? t)}{}^{\mathrm{n\; ?\; 1)}}\text{dt}$.The main purpose in this paper is to characterize those functions f : B → R₊ such that (1) holds.     

A new algorithm for meromorphic Nevanlinna-Pick interpolation

Summary. Let D be be the open unit disc, H₀ the space of all bounded analytic functions in D and H_k the set of all functions of the form f(z)/(z–z₁)...(z–z_k) where z₁,...,z_k D and f H₀. Given {z₁,...,z_n},{w₁,...,w_n}, where z_i D,w_i and z_iz_j if ij, we show for 0kn–1, under certain assumptions, how to construct the unique interpolating function B_kH_k, B_k(z_j)=w_j, of minimal essential supremum norm on D by solving an eigenvalue problem defined by the interpolation data. The function B_k is a scaled quotient of two finite Blaschke products.Mathematics Subject Classification (2000): 65E05, 30D50, 30E05Acknowledgement We are very indebted to Professor Martin Gutknecht for pointing out the necessity of Assumption A and for providing us with a translation of [A]. Also valuable discussions with Professors Olof Staffans and Göran Högnäs are acknowledged. The research of the second named author was supported by the Academy of Finland Project 51906.     

A high-yielding supramolecular reaction

The X-ray crystal structure determinations of twelve cocrystals involving iso-nicotinamide and a variety of carboxylic acids have revealed a very consistent pattern of hydrogen-bond preferences. The combination of a monocarboxylic acid, an amide, and a pyridine moiety leads, in every case, to discrete "supermolecules" (consisting of two molecules of iso-nicotinamide and two molecules of the relevant carboxylic acid) with well-defined and robust connectivity. The two dominant (regularly occurring) supramolecular synthons in these crystal structures are (1) the heteromeric carboxylic acid.pyridine hydrogen bond and (2) a self-complementary amide.amide hydrogen-bond interaction, both of which prevail in the presence of widely differing chemical functionalities. In four of these cocrystals, a dicarboxylic acid is employed, which alters the structural outcome from discrete entities to infinite assemblies (or to a hexameric complex in a "U-shaped" dicarboxylic acid), which is fully expected since the two primary supramolecular synthons remain intact. This structural study shows that iso-nicotinamide is a supramolecular reagent that can produce well-defined supermolecules (containing carboxylic acids) in very high yields.     

Supramolecular reagents: versatile tools for non-covalent synthesis

The design and modular synthesis of three ternary co-crystals with desired connectivity, assembled using tailor-made pyridyl/benzimidazol-1-yl-based supramolecular reagents, are described.     

Analysis of tobacco-specific N-nitrosamines in snuff by ethyl acetate extraction and liquid chromatography-tandem mass spectrometry

A rapid, selective and sensitive method for routine analysis of the four tobacco-specific N-nitrosamines, N'-nitrosonornicotine, N'-nitrosoanatabine, N'-nitrosoanabasine and 4-(methyl-nitrosamino)-1-(3-pyridyl)-1-butanone in snuff has been developed. The nitrosamines were isolated by ethyl acetate extraction and analysed by LC-MS-MS. Except for evaporation and filtration, no additional clean-up steps are needed in the proposed method. The detection limits for standard in solvent are between 0.0005 and 0.001 microg/ml (0.005 and 0.01 microg/g).     

Testing the Gouy-Chapman theory by means of surface tension measurements for SDS-NaCl-H2O mixtures

Surface tension isotherms were measured for sodium dodecyl sulfate (SDS) at different concentrations of added salt (NaCl). The free energy of the surfactant monolayer was assessed by invoking the Gouy-Chapman theory for the charged head groups, the hydrophobic (Tanford) free energy of transfer of the hydrocarbon chain, and the hydrocarbon chain configurational free energy according to Gruen's calculations and finally macroscopic contact terms. In particular, the effect of an increased salt concentration in bulk was examined. Theoretical predictions compare well with the experimental findings, and good agreement was found with respect to both the variation of free energy of the monolayer and the surface pressure behavior. Thus, at least for a liquid-expanded monolayer of SDS, the Gouy-Chapman model yields a satisfactory account of the electrostatic contribution to the thermodynamic properties at different salt concentrations of NaCl.