The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

Compositional changes of Australia-grown Western Schley pecans [Carya illinoinensis (Wangenh.) K. Koch] during maturation

Changes in composition during the maturation of Western Schley pecans [Carya illinoinensis (Wangenh.) K. Koch] grown in Australia were investigated. Pecans of different maturity levels were collected at monthly intervals between March and June in. 1999 and 2000 and analyzed for the concentrations of moisture, total lipid, sucrose, raffinose, protein, and the minerals aluminum, boron, calcium, copper, iron, potassium, magnesium, manganese, sodium, phosphorus, sulfur, and zinc. Moisture, total lipid, and calcium contents changed significantly (p < 0.05) with harvest time and maturity, whereas the other components did not. Western Schley pecans grown in Australia should be harvested after the shuck has opened and it is either green or brown in color to maximize total lipid content and quality. This occurred after May 11 in 1999 and after May 17 in 2000.

Sensor scheduling in electronic support using Markov chains

In electronic support, receivers must maintain surveillance over the very wide portion of the electromagnetic spectrum in which threat emitters operate. A common approach is to use a receiver with a relatively narrow bandwidth that sweeps its centre frequency over the threat bandwidth to search for emitters. The sequence and timing of changes in the centre frequency constitute a search strategy. The search can be expedited, if there is intelligence about the operational parameters of the emitters that are likely to be found. However, it can happen that the intelligence is deficient, untrustworthy or absent. In this case, what is the best search strategy to use? A random search strategy based on a continuous-time Markov chain (CTMC) is proposed. When the search is conducted for emitters with a periodic scan, it is shown that there is an optimal configuration for the CTMC. It is optimal in the sense that the expected time to intercept an emitter approaches linearity most quickly with respect to the emitter's scan period. A fast and smooth approach to linearity is important, as other strategies can exhibit considerable and abrupt variations in the intercept time as a function of scan period. In theory and numerical examples, the optimum CTMC strategy is compared with other strategies to demonstrate its superior properties.

Vehicle routing and crew scheduling for metropolitan mail distribution at Australia Post

This paper presents a new multi-depot combined vehicle and crew scheduling algorithm, and uses it, in conjunction with a heuristic vehicle routing algorithm, to solve the intra-city mail distribution problem faced by Australia Post. First we describe the Australia Post mail distribution problem and outline the heuristic vehicle routing algorithm used to find vehicle routes. We present a new multi-depot combined vehicle and crew scheduling algorithm based on set covering with column generation. The paper concludes with a computational investigation examining the affect of different types of vehicle routing solutions on the vehicle and crew scheduling solution, comparing the different levels of integration possible with the new vehicle and crew scheduling algorithm and comparing the results of sequential versus simultaneous vehicle and crew scheduling, using real life data for Australia Post distribution networks.

Compositional analysis of teas from Australian supermarkets

Caffeine, total amino acids, water extract and moisture content are considered to be quality indicators for leaf teas and teabags. These analyses were examined in 20 leaf teas and 36 teabags sampled from Australian supermarkets. About 70% of the analysed samples showed a moisture content higher than Vie maximum accepted level, 6.5%, for tea storage and marketing by the tea industries and traders. Water appropriate extract of 15 samples out of 36 teabags was lower than that of the teas without teabags, which indicates that the quality of the paper used for teabags needs to be evaluated. Moreover, one of the black leaf tea samples was found to have a water extract below the lower limit of international standards. Four green and black teas of the same brand, claimed to contain less than 3% caffeine, were found to have 3-4%, the same as the other samples analysed in this study. The mean total contents of amino acids were 2.50% and 1.76% in black leaf teas and the teabags, respectively, whereas they were 3.44% and 2.28% in green leaf teas and the teabags, respectively. Furthermore, the weights of 28 teabags out of 36 samples were found to lie outside of the proposed +/- 2% variation accepted by the tea industries and traders, and 4 samples showed even larger variation, 10% being out of the proposed weights. This investigation also showed that the solubility of caffeine and water extract was affected by the permeability of teabags, whereas total amino acids were very variable. These results suggest that an efficient and practical quality control system for both imported and Australian-made teas in the Australian supermarkets should be developed, implemented and enforced. Chemical analysis should be a part of the system for establishing an objective assessment for the quality control. (c) 2004 Elsevier Ltd. All rights reserved.

Cluster scheduling and load balancing via TCP options

This paper describes an experiment in designing, implementing and testing a Transport layer cluster scheduling and dispatching architecture. The motivation for the experiment was the hypothesis that a Transport layer clustering solution may offer advantantages over the existing industry-standard Network layer and Data Link Layer approaches. The critical success factors initially established to guide and evaluate the experiment were reduced dispatcher work load, reduced dispatcher internal state memory requirements, distributed denial of service resilience, and cluster software design simplicity. The functional design stage of the experiment produced a Transport layer strategy for scheduling and load balancing based on the specification of two new TCP options. Implementation required the introduction of the newly specified TCP options into the Linux (2.4) kernel. The implementation produced an extended Linux Socket API to facilitate user-process access to the additional TCP capability. The testing stage of the experiment confirmed the operational efficiency of the solution.

Compositional class refinement in object-Z

Object-Z allows coupling constraints between classes which, on the one hand, facilitate specification at a high level of abstraction, but, on the other hand, make class refinement non-compositional. The consequence of this is that refinement is not practical for large Systems. This paper overcomes this limitation by introducing a methodology for compositional class refinement in Object-Z. The key step is an equivalence transformation of an arbitrary Object-Z specification to one in which introduced constraints prohibit non-compositional refinements. The methodology also allows the constraints which couple classes to be refined yielding an unrestricted approach to compositional class refinement.