Stability criteria for controlled queueing systems

We give an almost complete classification of ergodicity and transience conditions for a general multi-queue system with the following features: arrivals form Poisson streams and there are various routing schemes for allocating arrivals to queues; the servers can be configured in a variety of ways; completed jobs can feed back into the system; the exponential service times and feedback probabilities depend upon the configuration of the servers (this model includes some types of multi-class queueing system); switching between service regimes is instantaneous. Several different levels of control of the service regimes are considered. Our results for the N-queue system require randomisation of service configurations but we have studied the two queue system in situations where there is less control. We use the semi-martingale methods described in Fayolle, Malyshev and Menshikov [3] and our results generalise Kurkova [8] and complement Foley and McDonald [4] and [5]. AMS 2000 subject classification: Primary: 90B22; Secondary: 60J10 90B15     

Effect of Mn substitution on the delicate balance between structure and properties of Gd1.4Ce0.6Sr2RuCu2O10

Some new members of a ruthenocuprate(2212) series have been synthesized by Mn substitution for Ru in Gd_1.4Ce_0.6Sr₂RuCu₂O₁₀. Characterization by x-ray diffraction (XRD) phase analysis has been carried out. Changes in structural features on substitution, including a significant change in lattice parameter for a very low substitution level, have been observed. Four-probe resistivity studies indicate the coexistence of superconductivity and magnetism for the pristine compound and a semiconductor-like upturn in resistivity and the absence of superconductivity even for very low levels of Mn substitution. AC susceptibility measurements show a progressive suppression of the magnetic transition temperature as well as a smearing of the magnetic transition as a function of Mn substitution. Possible reasons for the absence of superconductivity have been discussed.     

Quantitative oxygen imaging in an engine

Simultaneous imaging of laser-induced fluorescence of toluene and 3-pentanone was used to determine the local absolute oxygen and residual gas concentrations present within an engine. The technique utilizes the different sensitivities of the laser-excited molecules to quenching by molecular oxygen as a means to determine quantitative images of in-cylinder oxygen concentrations. The difference in the amount of oxygen available between two operating conditions was investigated. Results are in agreement with measurements in the exhaust gas. Received: 4 June 2002 / Published online: 8 August 2002     

An improved linearization strategy for zero-one quadratic programming problems

We present a new linearized model for the zero-one quadratic programming problem, whose size is linear in terms of the number of variables in the original nonlinear problem. Our derivation yields three alternative reformulations, each varying in model size and tightness. We show that our models are at least as tight as the one recently proposed in [7], and examine the theoretical relationship of our models to a standard linearization of the zero-one quadratic programming problem. Finally, we demonstrate the efficacy of solving each of these models on a set of randomly generated test instances.     

A two-echelon base-stock inventory model with Poisson demand and the sequential processing of orders at the upper echelon

We consider a two-echelon inventory system with a number of non-identical, independent ‘retailers’ at the lower echelon and a single ‘supplier’ at the upper echelon. Each retailer experiences Poisson demand and operates a base stock policy with backorders. The supplier manufactures to order and holds no stock. Orders are produced, in first-come first-served sequence, with a fixed production time. The supplier therefore functions as an M/D/1 queue. We are interested in the performance characteristics (average inventory, average backorder level) at each retailer. By finding the distribution of order lead time and hence the distribution of demand during order lead time, we find the steady state inventory and backorder levels based on the assumption that order lead times are independent of demand during order lead time at a retailer. We also propose two alternative approximation procedures based on assumed forms for the order lead time distribution. Finally we provide a derivation of the steady state inventory and backorder levels which will be exact as long as there is no transportation time on orders between the supplier and retailers. A numerical comparison is made between the exact and approximate measures. We conclude by recommending an approach which is intuitive and computationally straightforward.     

On the interpretation of the racemic states of the B 2 phase of banana-shaped mesogens

We show that the racemic states of the B 2 phase of liquid crystals composed of banana-shaped molecules do not satisfy the Curie principle. Thus it is argued that these states cannot exist in bulk samples and the homochiral states constitute the only stable microscopic structures. A reinterpretation of the racemic states with the same macroscopic optical behaviour is proposed in terms of mixtures of the homochiral structures.     

On embedding numbers into quaternion orders

A generalization of the chevalley-Hasse-Noether theorem from maximal orders to arbitrary Eichler orders in quaternion algebras is given. A stability property for the numbers of orbits for unit groups in quaternion orders acting on optimal embeddings of quadratic orders is proved. The results are applied to Siegel's meanvalue of integral representations by genera of integral definite ternary quadratic forms.     

Surface analysis and surface measuring techniques in firearm offences

Summary When a shot is fired, the projectile and the cartridge case are released from the weapon, as well as components of the priming charge and propellant, the so-called powder-gunshot residues. In order to solve firearm offences, it is therefore very important to determine the topography of trace-bearing areas on the bullet and the cartridge case, as well as the chemical composition of gunshot residue particles. Gunshot residue particles are made visible with the scanning electron microscope (SEM) and are analysed by means of energy-dispersive X-ray spectroscopy (EDXS) and lately also by means of wavelength-dispersive X-ray spectroscopy (WDXS). In addition to this, analyses of these particles are displayed by means of Auger electron spectroscopy (AES) and secondary ion mass spectroscopy (SIMS) and depth profiles are prepared. To determine the local distributions of gunshot residue elements with regard to their quantity, the direct Zeeman atomic absorption spectroscopy (DZ-AAS) is employed. Besides the determination of the chemical composition, the topography of the trace-bearing areas on the bullet and cartridge case plays an important part. For the detection of these surfaces, light optical and electron-optical methods are employed. Moreover, the use of opto-electronical testing systems has been attracting more and more attention recently.