Chemical Reactivity of Tetrasulfur Tetranitride: Synthesis,Physical Properties,and Structural Characterization of the Amorphous Phase Cu7S4N4

Tetrasulfur tetranitride, S₄N₄, reacts with elemental Cu within inert solvents to a black‐blue material of approximate composition Cu₇S₄N₄ which is totally amorphous to X‐rays and which cannot be made crystalline by either thermal treatment or electron radiation. Cu₇S₄N₄ explodes if heated above 234 °C or when subjected to mechanical shock to eventually yield copper(I) sulfide; this together with the characteristic infrared spectrum of Cu₇S₄N₄ indicates the presence of molecular S₄N₄ units inside the amorphous phase. The metastable nature of Cu₇S₄N₄ is also mirrored by electron microscopy which furthermore allows the structural characterization of its degradation products. Based on experimental EXAFS data offering characteristic Cu—N and Cu—S distances, a theoretical crystalline approximant of Cu₇S₄N₄ was suggested and structurally optimized by density‐functional total‐energy calculations including periodic boundary conditions. This model incorporates a central S₄N₄ unit bonded to three shells of Cu atoms of different functionalities; in addition, a partial rupture of the S₄N₄ unit is likely to allow for a lowering of the total energy of the metastable phase. The latter observation supports the impossibility to make Cu₇S₄N₄ crystallize using ₄N₄ crystallize using whatever kind of measures.     

Near-optimal design of Global Positioning System (GPS) networks using the Tabu Search technique

This paper describes an optimization technique based on an heuristic procedure which is applied to analyse and improve the efficiency of the design of Global Positioning System (GPS) surveying networks. GPS is a valuable survey tool because of its ability to increase the accuracy, speed and flexibility of a survey. A GPS network can be defined as a number of stations, which are co-ordinated by a series of sessions, formed by placing receivers on stations. The goal is to select the best order in which these sessions can be organised to give the best possible schedule. Generally, solving large networks to optimality requires impractical computational time. This paper proposes a Tabu Search technique which provides optimal or near-optimal solutions for large networks with an acceptable amount of computational effort. Computational results for several case studies with known and unknown optimal schedules have been presented to assess the performance of the proposed technique.     

Hydroformylation in fluorous solvents

The hydroformylation of long chain alkenes under fluorous biphase conditions and in neat perfluorocarbon solvents is reviewed. Special emphasis is placed upon the authors' evaluation of the steric and electronic influence of perfluoroalkylation on catalyst activity, regioselectivity and retention in the fluorocarbon phase.     

The use of temporary tethers in the meta photocycloaddition reaction

The use of temporary tethers in facilitating meta photocycloaddition reactions between phenol and allyl alcohol derivatives has been investigated. The merits of silicon, carbonate and methylene acetal tethers were assessed, whilst considering strategies for the preparation of the natural products gymnomitrol and gelsemine. The photoadducts were epoxidised, and then subjected to acid catalysed fragmentation with concomitant cleavage of the tether. Depending on whether water or methanol was used during the fragmentation stage of the methylene tethers, the methylene group was either removed altogether or transformed into a MOM group.     

An abstract Szeg? theorem

Given a semi-group U(t) of bounded linear operators with bounded self-adjoint generator A we estimate the logarithm of the section determinants of U(t) in terms of A. When A is subject to an additional condition, which is related to so-called Følner sequences of orthogonal projections, this estimate implies a Szeg? type theorem for bounded, self-adjoint, and strictly positive operators. We show that the condition mentioned is satisfied when A is a Toeplitz operator or a compact operator.     

An Analogue of the Cramér–Lundberg Approximation in the Optimal Investment Case

We consider ruin probabilities for an insurance company, which can also invest in the stock market. The risk process is modeled by a compound Poisson process and the stock price by geometric Brownian motion. We show that if the tails of the claims are light tailed, then the optimal strategy is asymptotically given by holding a constant $-value in the stock position. Furthermore, we show that a kind of Cramér–Lundberg approximation holds for the minimal ruin probability. Everything is shown under assumptions, which are analogous to the assumptions in the case of the classical Cramér–Lundberg approximation without investment.     

Embedding partial Steiner triple systems so that their automorphisms extend

It is shown that there is a function g on the natural numbers such that a partial Steiner triple system U on u points can be embedded in a Steiner triple system V on ν points, in such a way that all automorphisms of U can be extended to V, for every admissible ν satisfying ν > g(u). We find exponential upper and lower bounds for g. © 2005 Wiley Periodicals, Inc. J Combin Designs.     

Polysiloxanol condensation and disproportionation in the presence of a superacid

Kinetics studies of the condensation of model hydroxyl-terminated oligosiloxanes, pentamethyldisiloxane-1-ol (MDH) and heptamethyltrisiloxane-1-ol (MD₂H), catalysed by protic complex of tetrakis(pentafluorophenyl)borate in the toluene solution were performed. The dominating reaction was condensation, which was accompanied by disproportionation of oligosiloxanols. Water released in the condensation forms separate dispersed phase, but the phase separation and the presence of water does not affect the rate of the polycondensation. Both processes, condensation and disproportionation, show analogous kinetic laws being first order in silanol and half order in catalyst. They exhibit also similar values of activation parameters. The kinetics are explained by the formation of a reactive protic complex of silanol with borate being in fast preequilibrium with an unreactive complex including two borate molecules and the silanol molecules. The equilibrium lies to the side of the unreactive borate complex.