On Cauchy differences of all orders

Summary This paper deals with the problem of characterizing higher order Cauchy differences of mappings on groups and semigroups. Symmetric, first order Cauchy differencesf(x + y)–f(x)–f(y) for mapsf between groups were characterized by Jessen, Karpf, and Thorup [8] through the use of first partial Cauchy differences. Our results are similar and extend their result to higher order differences. Our results also extend those of Heuvers [6] for mappings between vector spaces over the rationals.     

A higher-order Markov model for the Newsboy's problem

Markov models are commonly used in modelling many practical systems such as telecommunication systems, manufacturing systems and inventory systems. However, higher-order Markov models are not commonly used in practice because of their huge number of states and parameters that lead to computational difficulties. In this paper, we propose a higher-order Markov model whose number of states and parameters are linear with respect to the order of the model. We also develop efficient estimation methods for the model parameters. We then apply the model and method to solve the generalised Newsboy's problem. Numerical examples with applications to production planning are given to illustrate the power of our proposed model.     

Monotonic Solutions of a Functional Equation Arising from Simultaneous Utility Representations

The functional equation ?(h(x)) ? ?(h(y)) + ?(y) = ?(h(x ? y) + y) was solved by Aczél, Luce and Marley on the assumption that the functions are different iable. They posed the question of its strictly monotonic continuous solutions. The problem is solved using a uniqueness theorem. The continuity assumption on the functions is removed and the equation is also solved on a restricted domain.     

Poly[2,7‐(9,9‐dihexylfluorene)‐alt‐pyridine] with donor‐acceptor architectures: A new series of blue‐light‐emitting alternating copolymers

A novel series of well‐defined alternating poly[2,7‐(9,9‐dihexylfluorenyl)‐alt‐pyridinyl] (PDHFP) with donor‐acceptor repeat units were synthesized using palladium (0)‐catalyzed Suzuki cross‐coupling reactions in good to high yields. In this series of alternating polymers, 2, 7‐(9,9‐dihexylfluorenyl) was used as the light emitting unit, and the electron deficient pyridinyl unit was employed to provide improved electron transportation. These polymers were characterized by ¹H‐NMR and ¹³C‐NMR, gel permeation chromatography (GPC), thermal analyses, and UV‐vis and fluorescence spectroscopy. The glass transition temperature of copolymers in nitrogen ranged from 110 to 148 °C, and the copolymers showed high thermal stabilities with high decomposition temperatures in the range of 350 to 390 °C in air. The difference in linkage position of pyridinyl unit in the polymer backbone has significant effects on the electronic and optical properties of polymers in solution and in film phases. Meta‐linkage (3,5‐ and 2,6‐linkage) of pyridinyl units in the polymer backbone is more favorable to polymer for pure blue emission and prevention of aggregation of polymer chain than para‐linkage (2,5‐linkage) of the pyridinyl units. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4792–4801, 2004     

S‐[4‐(Tri­methyl­ammonio)­phenyl]thio­sulfate,an aromatic organic thio­sulfate

The title compound, C₉H₁₃NO₃S₂, exists as a zwitterion with crystallographic mirror symmetry. The central S atom of the S₂O₃ group adopts a slightly distorted tetrahedral coordination geometry. The S—S bond length is 2.1137 (7) Å, while the S—O bond lengths are in the range 1.4417 (12)–1.457 (2) Å. The zwitterions in the crystal adopt a head‐to‐tail arrangement, which leads to the formation of a three‐dimensional network through C—H⋯O hydrogen bonds.     

Rigorous approach to kinetic parameters: polymerization of styrene with benzoyl peroxide in carbon tetrachloride

Both the rate constant of initiator dissociation, k_d, and the chain transfer constant, C_x, are determined by monitoring the rates of monomer and transfer agent conversions in a chain polymerization. Statistical analysis that takes into account the errors of experimental variables has been used to treat the kinetic data for the polymerization of styrene initiated by benzoyl peroxide (Bz₂O₂) in carbon tetrachloride at 60°C. Values of k_d and C_x produced by this error-in-variable method (EVM) are in accordance with those reported in literature. More important, the EVM algorithm always results in the smallest standard deviations of estimates, and hence, it is superior to the usual least-squares calculations. Other distinct features of the method are outlined. The initiator efficiency for Bz₂O₂ is estimated to be 0.72 under the present conditions.     

Spatial variations in the stoichiometry of sputtered YBaCuO thin films: theory and experiment

A Monte Carlo simulation of the sputtering process is applied to the problem of the thickness and stoichiometry variations in the sputtering of YBaCuO superconducting targets. The theory predicts no strong spatial variations in stoichiometry due to the different scattering behaviour of the various constituents of the superconductor. The theory is compared with a systematic experimental study using both RF and DC sputtering in either argon or oxygen gases. The ratios Ba: Y and Cu: Y were determined as a function of radial distance by inductively coupled plasma analysis (ICP). In argon, both DC and RF sputtering gave a thickness distribution in reasonable agreement with theory. In oxygen, RF sputtering gave a thickness distribution very different to theory and gave no net deposition in an annular central region. Stoichiometry variations are interpreted in terms of etching processes. The role of oxygen ions in etching is discussed and a case made for the importance of oxygen positive ions in RF sputtering in oxygen.