Recent developments in the chemistry of stable doubly bonded germanium compounds

During the last 10 years, several compounds of the type Ge=X (X = C, Ge, N, P, S) have been isolated as monomers. The stabilization of such derivatives, which are generally highly polymerizable, was achieved by using very bulky groups both on the germanium atom and on the heteroelement X. Conjugation (particularly in a few germenes and germaimines) and intramolecular or intermolecular coordination with oxygen or nitrogen, also contributes, in some cases, to the stabilization. The X-ray analyses of such compounds show a significant bond shortening of the double bond (8–10%) relative to the corresponding single bond and a planar or nearly planar germanium. These doubly bonded germanium derivatives are usually thermally stable but must be handled in an inert atmosphere because of their high sensitivity to oxygen and moisture; they are extremely reactive, much more than the corresponding carbon analogues. Nearly quantitative additions on the double bond have been observed with electrophiles and nucleophiles, and various types of cycloadditions also occur. Except in one case, a germylene behavior has not been observed, proving that such compounds retain their structural integrity in solution.     

Energy levels of small titanium oxide clusters obtained from SCF calculations

The energy levels of small titanium oxide clusters [(TiO₂)₂, and (TiO₂H)₃, and (TiO₂H)₂] have been calculated using ab initio SCF methods. Both crystal and relaxed geometries have been considered. Systematic changes in the valencelevel structure resulting from geometry relaxation are found, which may be related to band-gap changes experimentally observed for small titanium oxide particles. In addition, a Ti? OH local surface state is found to be well described within a limited cluster model. © 1994 John Wiley & Sons, Inc.     

Forecasting call frequency at a financial services call centre

A forecasting model is developed for the number of daily applications for loans at a financial services telephone call centre. The purpose of the forecasts and the associated prediction intervals is to provide effective staffing policies within the call centre. The model building process is constrained by the availability of only 2 years and 7 months of data. The distinctive feature of the data is that demand is driven in the main by advertising. The analysis given focuses on applications stimulated by press advertising. Unlike previous analyses of broadly similar data, where ARIMA models were used, a model with a dynamic level, multiplicative calendar effects and a multiplicative advertising response is developed and shown to be effective.     

Study of the charge-exchange reactions\pi ^ - p \to (\pi ^0 ,\eta ,\eta \prime )n at 63 GeV

Muon electron pairs were detected in an Al multiplate spark chamber, exposed to a neutrino beam from the CERN PS. The leptons were not accompanied by other particles, except occasionally by protons. The background came mainly from muon associated π⁰ production, with one decay gamma lost. It was determined empirically, together with the small contribution from υ _e reactions. For electron energies above 2 GeV the background is 5.7±1.5 events, whereas 18 (μe)-candidates have been observed. Hence the effect is established, with a rate of about 10^?4 as compared to the muonic reactions above 3 GeV. Charm creation as the origin of this (μe)-production process is excluded; heavy neutral lepton production does not fit the kinematics observed. Instead the events are compatible with the two-body decay of an object with variable invariant mass of order 1 GeV, possibly resulting from axion interactions.     

Issues in Managing Information Technology

This paper describes three case studies which investigated issues relating to the implementation and management of advanced information technology. The benefits derived from information technology were found to vary from one organization to another. These studies provide further evidence to support earlier research findings that senior management has an important role to play in the effective exploitation of information technology, and that the investment approach taken by an organization has a significant effect on the development of computer-based information systems. The effectiveness of a system depends not only on applying the appropriate technology, but also on how successfully technical and behavioural issues are resolved.     

An algebraic characterization ofB-convergent Runge-Kutta methods

Summary In the analysis of discretization methods for stiff intial value problems, stability questions have received most part of the attention in the past.B-stability and the equivalent criterion algebraic stability are well known concepts for Runge-Kutta methods applied to dissipative problems. However, for the derivation ofB-convergence results — error bounds which are not affected by stiffness — it is not sufficient in many cases to requireB-stability alone. In this paper, necessary and sufficient conditions forB-convergence are determined.This paper was written while J. Schneid was visiting the Centre for Mathematics and Computer Science with an Erwin-Schrödinger stipend from the Fonds zur Förderung der wissenschaftlichen Forschung     

A warehouse-based design model for reverse logistics

In this paper, an MILP formulation is proposed for the design of a reverse logistics network based on a warehouse location–allocation model, which optimizes, simultaneously, the forward and reverse networks. A single product model with unlimited capacity is first defined. Subsequently, the model is extended to a multi-product capacitated recovery network model, where capacity limitations and a multi-product system can be considered. The proposed model is compared to published work in the field, where different model assumptions have been proposed. Two cases are described so as to gain a better insight into the model and allow a comparative analysis.     

Stability of a Model of Relativistic Quantum Electrodynamics

The relativistic “no pair” model of quantum electrodynamics uses the Dirac operator, D(A) for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field A– in the Coulomb gauge. There are no positrons because the electron wave functions are constrained to lie in the positive spectral subspace of some Dirac operator, D, but the model is defined for any number, N, of electrons, and hence describes a true many-body system. In addition to the electrons there are a number, K, of fixed nuclei with charges ≤Z. If the fields are not quantized but are classical, it was shown earlier that such a model is always unstable (the ground state energy E=−∞) if one uses the customary D(0) to define the electron space, but is stable (E > − const.(N+K)) if one uses D(A) itself (provided the fine structure constant α and Z are not too large). This result is extended to quantized fields here, and stability is proved for α= 1/137 and Z≤ 42. This formulation of QED is somewhat unusual because it means that the electron Hilbert space is inextricably linked to the photon Fock space. But such a linkage appears to better describe the real world of photons and electrons. Received: 8 September 2001 / Accepted: 18 March 2002