The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

Regularization of time-varying descriptor systems by the asvd

We study linear variable coefficient control problems in descriptor form. Based on a behaviour approach and the general theory for linear differential algebraic systems we give the theoretical analysis and describe numerically stable methods to determine the structural properties of the system.

Response of plant-pollinator communities to fire: changes in diversity, abundance and floral reward structure

Globally, plant-pollinator communities are subject to a diverse array of perturbations and in many temperate and semi-arid systems fire is a dominant structuring force. We present a novel and highly integrated approach, which quantifies, in parallel, the response to fire of pollinator communities, floral communities and floral reward structure. Mt Carmel, Israel is a recognised bee-flower biodiversity hotspot, and using a chronosequence of habitats with differing post-fire ages, we follow the changes in plant-pollinator community organisation from immediately following a burn until full regeneration of vegetation. Initially, fire has a catastrophic effect on these communities, however, recovery is rapid with a peak in diversity of both flowers and bees in the first 2 years post-fire, followed by a steady decline over the next 50 years. The regeneration of floral communities is closely matched by that of their principal pollinators. At the community level we quantify, per unit area of habitat, key parameters of nectar and pollen forage known to be of importance in structuring pollinator communities. Nectar Volume, nectar water content, nectar concentration and the diversity of nectar foraging niches are all greatest immediately following fire with a steady decrease as regeneration proceeds. Temporal changes in energy availability for nectar, pollen, total energy (nectar + pollen) and relative importance of pollen to nectar energy show a similar general decline with site age, however, the pattern is less clear owing to the highly patchy distribution of floral resources. Changes in floral reward structure reflect the general shift from annuals (generally low-reward open access flowers) to perennials (mostly high-reward and restricted access flowers) as post-fire regeneration ensues. The impact of fire on floral communities and their associated rewards have clear implications for pollinator community structure and we discuss this and the role of other disturbance factors on these systems.

The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

Catchment phosphorous losses: an export coefficient modelling approach with scenario analysis for water management

This paper presents the development of an export coefficient model to characterise the rates and sources of P export from land to water in four reservoir systems located in a semi-arid rural region in southern of Portugal. The model was developed to enable effective management of these important water resource systems under the EU Water Framework Directive. This is the first time such an approach has been fully adapted for the semi-arid systems typical of Mediterranean Europe. The sources of P loading delivered to each reservoir from its catchment were determined and scenario analysis was undertaken to predict the likely impact of catchment management strategies on the scale of rate of P loading delivered to each water body from its catchment. The results indicate the importance of farming and sewage treatment works/collective septic tanks discharges as the main contributors to the total diffuse and point source P loading delivered to the reservoirs, respectively. A reduction in the total P loading for all study areas would require control of farming practices and more efficient removal of P from human wastes prior to discharge to surface waters. The scenario analysis indicates a strategy based solely on reducing the agricultural P surplus may result in only a slow improvement in water quality, which would be unlikely to support the generation of good ecological status in reservoirs. The model application indicates that a reduction of P-inputs to the reservoirs should first focus on reducing P loading from sewage effluent discharges through the introduction of tertiary treatment (P-stripping) in all major residential areas. The fully calibrated export coefficient modelling approach transferred well to semi-arid regions, with the only significant limitation being the availability of suitable input data to drive the model. Further studies using this approach in semi-arid catchments are now needed to increase the knowledge of nutrient export behaviours in semi-arid regions.

Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.

Optimal control of nonlinear systems represented by differential algebraic equations

An iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified simplified model based problem with parameter updating in such a manner that the correct solution of the original nonlinear problem is achieved.

Optimal control of nonlinear differential algebraic equation systems

A novel iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified linear quadratic model based problem with parameter updating in such a manner that the correct solution of the original non-linear problem is achieved. The resulting algorithm has a particular advantage in that the solution is achieved without the need to solve the differential algebraic equations . Convergence aspects are discussed and a simulation example is described which illustrates the performance of the technique. 1. Introduction When modelling industrial processes often the resulting equations consist of coupled differential and algebraic equations (DAEs). In many situations these equations are nonlinear and cannot readily be directly reduced to ordinary differential equations.

Performance analysis of AF cooperative systems with HPA nonlinearity in semi-blind relays

In this paper, dual-hop amplify-and-forward (AF) cooperative systems in the presence of high-power amplifier (HPA) nonlinearity at semi-blind relays, are investigated. Based on the modified AF cooperative system model taking into account the HPA nonlinearity, the expression for the output signal-to-noise ratio (SNR) at the destination node is derived, where the interference due to both the AF relaying mechanism and the HPA nonlinearity is characterized. The performance of the AF cooperative system under study is evaluated in terms of average symbol error probability (SEP), which is derived using the moment-generating function (MGF) approach, considering transmissions over Nakagami-m fading channels. Numerical results are provided and show the effects of some system parameters, such as the HPA parameters, numbers of relays, quadrature amplitude modulation (QAM) order, Nakagami parameters, on performance.

Effects of manure and fertilizer on grain yield, soil carbon and phosphorus in a 13-year field trial in semi-arid Kenya

Long-term indicators of soil fertility were assessed by measuring grain yield, soil organic carbon (SOC) and soil Olsen phosphorous for a P-deficient soil. In one set of treatments, goat manure was applied annually for 13 years at 0, 5 and 10 t ha(-1), and intercrops of sorghum/cowpea, millet/green gram and maize/pigeonpea were grown. Yield depended on rainfall and trends with time were not identifiable. Manure caused an upward trend in SOC, but 10 t ha(-1) manure did not give significantly more SOC than 5 t ha(-1). Only 10 t ha(-1) manure increased Olsen P. Measurements of both SOC and Olsen P are recommended. In another set of treatments, manure was applied for four years; the residual effect lasted another seven to eight years when assessed by yield, SOC and Olsen P Treatment with mineral fertilizers provided the same rates of N and P as 5 t hat manure and yields from manure and fertilizer were similar. Fertilizer increased Olsen P but not SOC. Management systems with occasional manure application and intermediate fertilizer applications should be assessed. Inputs and offtakes of C, N and P were measured for three years. Approximately 16, 25 and 11% of C, N and P respectively were stabilized into soil organic matter from 5 t ha(-1) a(-1) manure. The majority of organic P was fixed as soil inorganic P.

Reduced height (Rht) and photoperiod insensitivity (Ppd) allele associations with establishment and early growth of wheat in contrasting production systems

Near isogenic lines (NILs) varying for genes for reduced height (Rht) and photoperiod insensitivity (Ppd-D1a) in a cv. Mercia background (rht (tall), Rht-B1b, Rht-D1b, Rht-B1c, Rht8c + Ppd-D1a, Rht-D1c, Rht12) were compared at one field site but within contrasting ('organic' vs. 'conventional') rotational and agronomic contexts, in each of 3 years. In the final year, further NILs (rht (tall), Rht-B1b, Rht-D1b, Rht-B1c, Rht-B1b + Rht-D1b, Rht-D1b + Rht-B1c) in both Maris Huntsman and Maris Widgeon backgrounds were added together with 64 lines of a doubled haploid (DH) population [Savannah (Rht-D1b) x Renesansa (Rht-8c + Ppd-D1a)]. Assessments included laboratory tests of germination and coleoptile length, and various field measurements of crop growth between emergence and pre jointing [plant population, tillering, leaf length, ground cover (GC), interception of photosynthetically active radiation (PAR), crop dry matter (DM) and nitrogen accumulation (N), far red: red reflectance ratio (FR:R), crop height, and weed dry matter]. All of the dwarfing alleles except Rht12 in the Mercia background and Rht8c in the DHs were associated with reduced coleoptile length. Most of the dwarfing alleles (depending on background) reduced seed viability. Severe dwarfing alleles (Rht-B1c, Rht-D1c and Rht12) were routinely associated with fewer plant numbers and reduced early crop growth (GC, PAR, DM, N, FR:R), and in 1 year, increased weed DM. In the Mercia background and the DHs the semi-dwarfing allele Rht-D1b was also sometimes associated with reductions in early crop growth; no such negative effects were associated with the marker for Rht8c. When significant interactions between cropping system and genotype did occur it was because differences between lines were more exaggerated in the organic system than in the conventional system. Ppd-D1a was associated positively with plant numbers surviving the winter and early crop growth (GC, FR:R, DM, N, PAR, height), and was the most significant locus in a QTL analysis. We conclude that, within these environmental and system contexts, genes moderating development are likely to be more important in influencing early resource capture than using Rht8c as an alternative semi-dwarfing gene to Rht-D1b.

Effects of cultural system (organic and conventional) on growth, photosynthesis and yield components of sweet corn (zea mays L.) under semi-arid environment

Organic sweet maize consists of a new industrial crop product. Field experiment was conducted to determine the effects of cultural systems on growth, photosynthesis and yield components of sweet maize crop (Zea mays L. F-1 hybrid 'Midas'). A randomized complete block design was employed with four replicates per treatment (organic fertilization: cow manure (5, 10 and 20 t ha(-1)), poultry manure (5, 10 and 20 t ha(-1)) and barley mulch (5, 10 and 20 t ha(-1)), synthetic fertilizer (240 kg N ha(-1)): 21-0-0 and control). The lowest dry weight, height and leaf area index and sod organic matter were measured in the control treatment. Organic matter content was proportionate to the amount of manure applied. The control plots had the lowest yield (1593 kg ha(-1)) and the double rate cow manure plots the had,greatest one. (6104 kg ha(-1)). High correlation between sweet corn yield and organic matter was registered. Moreover, the lowest values of 1000-grain weight were obtained with control plot. The fertilizer plot gave values which were similar to the full rate cow manure treatment. The photosynthetic race of the untreated control was significantly lower than that of the other treatments. The phorosynthetic rate increased as poultry manure and barley mulch ram decreased and as cow manure increased. Furthermore the untreated control had the lowest stomatal conductance and chlorophyll content. Our results indicated that sweet corn growth and yield in the organic plots was significantly higher than those in the conventional plots.

A semi-blind reception scheme based on ICA for multiuser MIMO-STBC system

When the orthogonal space-time block code (STBC), or the Alamouti code, is applied on a multiple-input multiple-output (MIMO) communications system, the optimum reception can be achieved by a simple signal decoupling at the receiver. The performance, however, deteriorates significantly in presence of co-channel interference (CCI) from other users. In this paper, such CCI problem is overcome by applying the independent component analysis (ICA), a blind source separation algorithm. This is based on the fact that, if the transmission data from every transmit antenna are mutually independent, they can be effectively separated at the receiver with the principle of the blind source separation. Then equivalently, the CCI is suppressed. Although they are not required by the ICA algorithm itself, a small number of training data are necessary to eliminate the phase and order ambiguities at the ICA outputs, leading to a semi-blind approach. Numerical simulation is also shown to verify the proposed ICA approach in the multiuser MIMO system.

Regularization of descriptor systems by output feedback

Conditions are given under which a descriptor, or generalized state-space system can be regularized by output feedback. It is shown that under these conditions, proportional and derivative output feedback controls can be constructed such that the closed-loop system is regular and has index at most one. This property ensures the solvability of the resulting system of dynamic-algebraic equations. A reduced form is given that allows the system properties as well as the feedback to be determined. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way.