On the computation of conjugacy classes of Chevalley groups

In this paper an algorithm is presented to determine the number of semisimple conjugacy classes for a given centralizertype for the Chevalley groupsSL _n(q) andSU _n(q). Moreover we give the exact number of regular semisimple classes of this groups and a summary of results on the generic classnumber of exceptional Chevalley groups of adjoint type.The first author acknowledges financial support by a grant of the Deutsche Forschungsgemeinschaft     

Irrigation Modelling in the Context of Basin Water Resources

Management practices for irrigation schemes can often be improved by modelling the behaviour of a scheme and by evaluating its efficiency statistics. However, looking at an irrigation scheme without regard for other water uses within the river basin may not be effective. Efficiencies computed in this way are local and, since water may be used many times within the same basin, may not be realistic. Changes in water uses (e.g. irrigation, industrial, power production, urban water supply, navigation, environmental, recreational) will often have effects on other uses; and changes in irrigation schemes (management,structural, crop pattern) may affect other users within the basin. In addition, all water users will be affected by external changes such as changes in land cover or in climate. As demand for water increases, these links become more important until, at some stage, there is insufficient water for all users and hard choices must be made. Hydrological modelling is a tool that can be used to relate irrigation schemes to the other water uses within a river basin and can help in assessing real productivities and in evaluating alternative patterns of water usage. This paper discusses the techniques available to simulate irrigation schemes within overall basin water resources using, as an example, an intensively utilized basin in western Turkey.     

Analysis of adaptive routing schemes in multirate loss networks

As technology evolves, it is now feasible to implement sophisticated adaptive routing schemes on networks which support different kinds of services with heterogeneous bandwidth characteristics. Adaptive routing can increase the network throughput by routing calls to less congested paths. It can also be used to bypass transmission facility failures. In this paper, we analyze and compare two adaptive routing schemes. The first is called theMaximum mean time to blocking (MTB) routing which is based on themean time to blocking measure of a link. This measure captures the traffic rates, bandwidth characteristic and link capacity information and reflects more accurately the congestion status of different paths. The second is theM ² routing, which is a modification of the least loaded routing (LLR). Aggregation of link status information can significantly reduce signalling traffic. We show in this paper that with properly designed aggregation, the aggregatedM ² and MTB routings can have performance that approach that of the non-aggregated schemes. The use of complete sharing and restricted access policies together with trunk reservation control in multirate loss networks are also studied.     

Measurement and prediction of pressure drop in two-phase flow

Experimental data for air–water two-phase co-current flow in two different pipe diameters were used to test the prediction of pressure drop by a number of existing theories and correlations. Several models are shown to be useful for prediction, particularly with the stratified regimes which have proved difficult to handle in the past. The model suggested by Olujic proved to be of particular value.     

Synthesis and characterisation of carboxylic acid and diphenylphosphine derivatives in the 1,3-diyne series: Spectral properties of polydiacetylene carboxylates

Symmetrically substituted 1,3-diynes containing hydroxyalkyl ( 1a-d ), bromoalkyl ( 1e-h ) (diphenylphosphinyl) ( 1i-k ) and carboxyalkyl ( 2a-d ) substituents have been prepared and characterised; the phosphine derivative ( 1k ) has been converted with alkyl iodides ( RI ; R = Me, Et) into bis(phosphonium) salts ( 1l and m ). During preparation of the diynedioic acid. ( 2a ), the non-centrosymmetrical diyne, HO₂CCH₂C?C—C?C(CH₂)₂OH ( 3 ), was also isolated. ⁶⁰Co γ-Irradiation of diacetylene monomers ( 2a – d ) and 10,12-tricosadiyn-1-oic acid gave the corresponding polydiacetylene derivatives ( 4a – d and 5 ), respectively. Rubidium salts of ( 4c ) and ( 4d ), a barium salt of ( 4c ), and a potassium salt of ( 5 ) were prepared and isolated; soluble potassium salts of the carboxylic acid polymers ( 4 ) were generated in aqueous solution. The effects of changes in pH on the UV/visible absorption spectra of aqueous solutions of selected carboxylic acid polydiacetylenes have been recorded, and are discussed.     

The rank one mixed μ problem and ‘kharitonov-type’ analysis

The general mixed μ problem has been shown to be NP hard, so that the exact solution of the general problem is computationally intractable, except for small problems. In this paper we consider not the general problem, but a particular special case of this problem, the rank one mixed μ problem. We show that for this case the mixed μ problem is equivalent to its upper bound (which is convex), and it can in fact be computed easily (and exactly). This special case is shown to be equivalent to the so-called ‘affine parameter variation’ problem (for a polynomial with perturbed coefficients) which has been examined in detail in the literature, and for which several celebrated ‘Kharitonov-type’ results have been proven.     

Remote sensing of species mixtures in conifer plantations using LiDAR height and intensity data

In even-aged, single species conifer plantations LiDAR height data can be modelled to provide accurate estimates of tree height and volume. However, it is apparent that growth models developed for single species stands are not directly transferable to a more general situation of mixed species plantations. This paper evaluates the ability of small footprint, dual-return, pulsed airborne LiDAR data to estimate the proportion of the productive species when mixed with a nurse crop in closed canopy plantations. A study area located in Galloway Forest District in Scotland is used as an example of Lodgepole pine and Sitka spruce mixed plantation; this area contains good examples of a wide range of pure and mixed species plantation types. Three species groups are studied: areas of pure Sitka spruce, areas of pure Lodgepole pine and areas where the two species have been planted together. Two approaches are assessed for detection of plantation mixtures: the first uses LiDAR intensity data to separate spruce and pine species and the second uses LiDAR-derived canopy density measures, coefficient of variation, skewness, percent of ground returns (which provides a measure of canopy openness) and the mean canopy height, which enables areas with height variations to be identified. From analysis of LiDAR data extracted from 54 study plots using logistic regression, the coefficient of variation and LiDAR intensity data provide the most useful predictors of the proportion of spruce in a pine/spruce mixture with coefficients of determination (R²) of 0.914 and 0.930 respectively. The method could be developed as a mapping tool, which in combination with existing inventory data should help to improve timber volume forecasting for mixed species even-aged plantations.