ALBERT

Notes: Abstract We present an approach to compute optimal control functions in dynamic models based on one-dimensional partial differential algebraic equations (PDAE). By using the method of lines, the PDAE is transformed into a large system of usually stiff ordinary differential algebraic equations and integrated by standard methods. The resulting nonlinear programming problem is solved by the sequential quadratic programming code NLPQL. Optimal control functions are approximated by piecewise constant, piecewise linear or bang-bang functions. Three different types of cost functions can be formulated. The underlying model structure is quite flexible. We allow break points for model changes, disjoint integration areas with respect to spatial variable, arbitrary boundary and transition conditions, coupled ordinary and algebraic differential equations, algebraic equations in time and space variables, and dynamic constraints for control and state variables. The PDAE is discretized by difference formulae, polynomial approximations with arbitrary degrees, and by special update formulae in case of hyperbolic equations. Two application problems are outlined in detail. We present a model for optimal control of transdermal diffusion of drugs, where the diffusion speed is controlled by an electric field, and a model for the optimal control of the input feed of an acetylene reactor given in form of a distributed parameter system.

Notes: Abstract We consider the problem of determining an optimal driving strategy in a train control problem with a generalised equation of motion. We assume that the journey must be completed within a given time and seek a strategy that minimises fuel consumption. On the one hand we consider the case where continuous control can be used and on the other hand we consider the case where only discrete control is available. We pay particular attention to a unified development of the two cases. For the continuous control problem we use the Pontryagin principle to find necessary conditions on an optimal strategy and show that these conditions yield key equations that determine the optimal switching points. In the discrete control problem, which is the typical situation with diesel-electric locomotives, we show that for each fixed control sequence the cost of fuel can be minimised by finding the optimal switching times. The corresponding strategies are called strategies of optimal type and in this case we use the Kuhn–Tucker equations to find key equations that determine the optimal switching times. We note that the strategies of optimal type can be used to approximate as closely as we please the optimal strategy obtained using continuous control and we present two new derivations of the key equations. We illustrate our general remarks by reference to a typical train control problem.

Notes: Abstract We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upper bound on the work-in-process, the problem is formulated as a stochastic dynamic program. We then establish a verification theorem and a partial characterization of the optimal control policy if it exists.

Notes: Abstract We study two continuity concepts for set-valued maps that play central roles in quantitative stability analysis of optimization problems: Aubin continuity and Lipschitzian localization. We show that various inverse function theorems involving these concepts can be deduced from a single general result on existence of solutions to an inclusion in metric spaces. As applications, we analyze the stability with respect to canonical perturbations of a mathematical program in a Hilbert space and an optimal control problem with inequality control constraints. For stationary points of these problems, Aubin continuity and Lipschitzian localization coincide; moreover, both properties are equivalent to surjectivity of the map of the gradients of the active constraints combined with a strong second-order sufficient optimality condition.

Notes: Abstract In this paper we explain that various (possibly discontinuous) value functions for optimal control problem under state-constraints can be approached by a sequence of value functions for suitable discretized systems. The key-point of this approach is the characterization of epigraphs of the value functions as suitable viability kernels. We provide new results for estimation of the convergence rate of numerical schemes and discuss conditions for the convergence of discrete optimal controls to the optimal control for the initial problem.

Notes: Abstract We consider first nonlinear systems of the form x=A(x)x+B(x)u together with a standard quadratic cost functional and replace the system by a sequence of time-varying approximations for which the optimal control problem can be solved explicitly. We then show that the sequence converges. Although it may not converge to a global optimal control of the nonlinear system, we also consider a similar approximation sequence for the equation given by the necessary conditions of the maximum principle and we shall see that the first method gives solutions very close to the optimal solution in many cases. We shall also extend the results to parabolic PDEs which can be written in the above form on some Hilbert space.

Notes: Abstract A new methodology is presented in thisarticle for computing the optimal operation of soilaquifer treatment systems. The mathematical problemis stated as a discrete-time optimal control problemto maximize infiltration subject to various physicaland operation constraints. The methodology is basedupon solving the discrete-time optimal control problemusing a successive approximation linear quadraticregulator interfaced with a simulator. Theunsaturated flow model HYDRUS is modified to simulatethe water content distribution, the infiltrationprocess, and the draining process. A penalty functionmethod is used to treat the bound constraints on thewater content and the cycle time. Sample problems aregiven to illustrate the capability of the model tosolve the optimal operation of soil aquifer treatment systems.

Notes: Abstract The statistical distribution of von Mises stress in the trabeculae of human vertebral cancellous bone was estimated using large-scale finite element models. The goal was to test the hypothesis that average trabecular von Mises stress is correlated to the maximum trabecular level von Mises stress. The hypothesis was proposed to explain the close experimental correlation between apparent strength and stiffness of human cancellous bone tissue. A three-parameter Weibull function described the probability distribution of the estimated von Mises stress (r2) 〉 0.99 for each of 23 cases). The mean von Mises stress was linearly related to the standard deviation (r2=0.63) supporting the hypothesis that average and maximum magnitude stress would be correlated. The coefficient of variation (COV) of the von Mises stress was nonlinearly related to apparent compressive strength, apparent stiffness, and bone volume fraction (adjusted r2=0.66, 0.56, 0.54, respectively) by a saturating exponential function [COV=A+B exp(−x/C)]. The COV of the stress was higher for low volume fraction tissue (〈0.12) consistent with the weakness of low volume fraction tissue and suggesting that stress variation is better controlled in higher volume fraction tissue. We propose that the average stress and standard deviation of the stress are both controlled by bone remodeling in response to applied loading. © 2000 Biomedical Engineering Society. PAC00: 8719Rr

Notes: Abstract It is indicated that up to the year 2030, the annual average temperatures in China will increase by 0.88 to 1.2°C, with increments in the south less than in the north. Annual average precipitation would raise slightly, but the increment could be 4% in northeastern China. The increment of annual mean runoff could rise over 6% in the northeastern area, and decrease in the other regions 1.4 to 10.5%. The increased water shortage due to climate change could achieve 160 to 5090 million m3 in some areas of China. Financial loss due to the lack of water could reach 1300 million yuan, and up to 4400 million yuan in serious drought years in the Beijing-Tianjin-Tangshan area.

Notes: Abstract We prove the maximum principle for an optimal control problem governed by the system $$y'(t) + A(t)y(t) = f(t,y(t),u(t)),{\text{ }}u(t) \in U(t), $$ with state constraint $$(y(0),y(T)) \in C \subset H \times H $$ , under three different hypotheses: (H1) C is a convex set with nonempty interior; (H2) $$C = \{ y_0 \} \times C_{0,} {\text{ with }}C_0 $$ a convex set with nonempty interior in H and the evolution system satisfying compactness hypotheses; (H3) the periodic case $$y(0) = y(T)$$ , with the evolution system satisfying compactness hypotheses. We do not assume the controls to be bounded. We give some examples for distributed control problems.

Notes: Abstract We consider a production planning problem for a dynamic jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are assumed to be finite-state Markov chains. As the rates of change of the machine states approach infinity, an asymptotic analysis of this stochastic manufacturing systems is given. The analysis results in a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. The long-run average cost for the original problem is shown to converge to the long-run average cost of the limiting problem. The convergence rate of the long-run average cost for the original problem to that of the limiting problem together with an error estimate for the constructed asymptotic optimal control is established.

Notes: Abstract This work deals with the necessary conditions of optimality for some optimal control problems governed by elliptic variational inequalities. Boundary control and state constrained problems are considered. The techniques used are based on those in Ref. 1 and a new penalty functional is defined in this paper.

Notes: Abstract An important and numerous literature argues that nonconcavity (often convexity with respect to the state) of the Hamiltonian leads to multiple steady states, instability, and a threshold. This threshold property provides a powerful paradigm to explain history dependency and hysteresis. This paper shows that economically relevant properties (in particular, multiple steady states and thresholds) are possible in strict concave models too. Two corresponding necessary conditions with intuitive economic interpretation are derived.

Notes: Abstract The migration of vinyl chloride monomer (VCM) from unplasticizedpolyvinyl chloride (uPVC) pipes was investigated using locallymanufactured pipes. Specimens of 33 cm long were used throughoutthe research. The investigation was carried out under differentconditions of water temperature, pH and total dissolved solidsconcentration and at different durations of exposure. The VCMconcentration in the water was evaluated using the gaschromotography (GC)/head-space technique. A VCM concentration ofmore than 2.5 ppb was detected after 30 days of exposure at45 °C. The initial VCM concentration in the uPVC pipewas predicted using equations derived from Fick's first law ofdiffusion. Water tenperature did not affect the migration ofVCM, unless it was raised to high values (i.e. 45 °C).Total dissolved solids (TDS) and pH of water were found toaffect the release of VCM from uPVC pipes. Diffusion rate of VCMwas predicted as a function of pH or TDS values.

Notes: Abstract Long-term charcoal production in small private charcoal kilns (CK) in Eastern Bieszczady Mts. (SE Poland) can cause local smoke contamination of the ambient forest environment. Responses of model soil systems, contaminated or not contaminated by CK smoke, to contrasting combinations of hydrothermic regimes were compared in laboratory microcosms (respiration of soil community, decomposition rate of soil organic matter and cotton stripes, herb seeds germination were studied). The majority of the obtained data show a markedly higher level of soil biological activity in the CK versus the control series. In some cases CK and control soil systems show different patterns of reactions to the tested combinations of microclimate regime. These phenomena should at least partly be attributed to the effects of CK pollution.

Notes: Abstract Adaptation in response to anthropogenic climate change seeks to maintain viability by maximising benefits and minimising losses. It is necessary because some climatic change is now inevitable, despite the international focus on mitigation measures. Indeed, the measures agreed at Kyoto would by themselves result in only a small reduction in the climate changes to be expected over the next century. Discussion of the expected changes and possible impacts leads to the following conclusions regarding climate change scenarios in relation to impacts and adaptation: • Climate change in the foreseeable future will not be some new stable "equilibrium" climate, but rather an ongoing "transient" process; • Climate change predictions relevant to impacts on most sectors and ecosystems are still highly uncertain; • There is a need for a greater focus on developing countries and tropical regions, and on relevant key variables, including the magnitude and frequency of extreme events; • The focus should shift from single predictions, or extreme ranges of uncertainty, to risk assessment; • Thresholds critical to impacted sectors and ecosystems should be identified, and expressed as functions of climatic variables; • Planned adaptations will be necessary to cope with multiple stresses, including those due to non-climatic changes; • A major task of adaptation science is to identify the limits of adaptation, i.e., to identify "dangerous levels of greenhouse gases" beyond which adaptation becomes impractical or prohibitively expensive.

Notes: Abstract If current trends continue, human activities will drastically alter most of the planet's remaining natural ecosystems and their composite biota within a few decades. Compounding the impacts on biodiversity from deleterious management practices is climate variability and change. The Intergovernmental Panel on Climate Change (IPCC) recently concluded that there is ample evidence to suggest climate change is likely to result in significant impacts on biological diversity. These impacts are likely to be exacerbated by the secondary effects of climate change such as changes in the occurrence of wildfire, insect outbreaks and similar disturbances. Current changes in climate are very different from those of the past due to their rate and magnitude, the direct effects of increased atmospheric CO2 concentrations and because highly modified landscapes and an array of threatening processes limit the ability of terrestrial ecosystems and species to respond to changed conditions. One of the primary human adaptation option for conserving biodiversity is considered to be changes in management. The complex and overarching nature of climate change issues emphasises the need for greatly enhanced cooperation between scientists, policy makers, industry and the community to better understand key interactions and identify options for adaptation. A key challenge is to identify opportunities that facilitate sustainable development by making use of existing technologies and developing policies that enhance the resilience of climate-sensitive sectors. Measures to enhance the resilience of biodiversity must be considered in all of these activities if many ecosystem services essential to humanity are to be sustained. New institutional arrangements appear necessary at the regional and national level to ensure that policy initiatives and research directed at assessing and mitigating the vulnerability of biodiversity to climate change are complementary and undertaken strategically and cost-effectively. Policy implementation at the national level to meet responsibilities arising from the UNFCCC (e.g., the Kyoto Protocol) and the UN Convention on Biological Diversity require greater coordination and integration between economic sectors, since many primary drivers of biodiversity loss and vulnerability are influenced at this level. A case study from the Australian continent is used to illustrate several key issues and discuss a basis for reform, including recommendations for facilitating adaptation to climate variability and change.

Notes: Abstract Global climate change is likely to have a range of consequences for human health as a result of disturbance or weakening of the biosphere's natural or human-managed life support systems. The full range of potential human health impacts of global climate change is diverse and would be distributed differentially spatially and over time. Changes in the mortality toll of heatwaves and changes in the distribution of vector-borne infectious diseases may occur early. The public health consequences of sea level rise and of regional changes in agricultural productivity may not occur (or become apparent) for several decades. Vulnerability is a measure of both sensitivity to climate change and the ability to adapt in anticipation of, or in response to, its impacts. The basic modes of adaptation to climate-induced health hazards are biological, behavioural and social. Adaptation can be undertaken at the individual, community and whole-population levels. Adaptive strategies should not introduce new health hazards. Enhancement of the acknowledged public health infrastructure and intervention programmes is essential to reduce vulnerability to the health impacts of climate change. In the longer-term, fundamental improvements in the social and material conditions of life and in the reduction of inequalities within and between populations are required for sustained reduction in vulnerability to environmental health hazards.

Notes: Abstract A mechanism has been established to improve integration of international climate-related programmes. Known as the Climate Agenda it outlines a programme, that in a cost-effective way, responds to national obligations to respond to international agreements as well as their national needs for social and economic development. The paper briefly describes the Climate Agenda and the incorporation within it of studies of climate impact assessments and response strategies to reduce vulnerability. The need for increased emphasis on climate impact assessment and for the development of effective adaptation measures is emphasised following the elaboration of a Kyoto Protocol to the United Nations Framework Convention on Climate Change (UNFCCC). UNEP's efforts to identify national programmes contributing to the Climate Agenda are described. The response from developing countries has, however, been very disappointing, even from countries where we know work is ongoing through funding by GEF or US Country Studies Program and other bilateral programmes. Initial compilation of information available so far shows that many developed countries are putting a lot into the area of impact assessment of not just climate change, but also climate variability. There remain some research gaps, especially in the area of assessment of climate impacts on ecosystems, hydrological systems, etc. Considerable efforts are presently being directed at reduction of emissions of greenhouse gases and in the case of developing countries, most efforts are being directed towards completing national communications and providing baseline data for future studies. The paper refers to early activities by UNEP in cooperation with other international organizations to undertake integrated assessments of the impacts of climate change on important socio-economic sectors and the later incorporation of lessons learned into the IPCC Guidelines for Assessing Impacts of Climate Change. Later sections outline the development of a handbook on methods for climate change impact assessment and adaptation strategies as a practical approach to national assessments and the development of appropriate and cost-effective response to climate change. The initiation of a GEF-funded project to apply the methods contained in the handbook and improve the results based on national studies is also described for both developed and developing countries. Working in collaboration with a team of international experts under the coordination of the Institute of Environmental Studies at Vrije University (Amsterdam), the goal of this ongoing project is to develop a valuable methodological tool that Parties to the UNFCCC may apply to develop national climate change impact and adaptation assessments. Development of these guidelines was linked to a series of country studies in Antigua and Barbuda, Estonia, Cameroon and Pakistan funded under a UNEP/GEF project. The application of the first version of the UNEP Handbook by national study teams in these four countries is making valuable technical and practical contributions and will ensure that the next version of the Handbook will be a more useful tool for experts in developing countries undertaking similar studies in the future. The methods contained in the Handbook are also the basis for similar assessments funded under bilateral development programmes in other countries. These and similar studies elsewhere are coordinated with the UNEP programme and will eventually aim to create reliable and comparable assessments, a compatible set of tools for such purpose and the identification of realistic adaptation options for incorporation into national planning for adapting to climate change. The paper also addresses how climate impact assessment and response strategies are undertaken as part of national enabling activities carried out in co-operation with UNEP.

Notes: Abstract Many developing countries, especially in Africa, contribute only very small amounts to the world total of greenhouse gas emissions. For them, the reduction of such emissions is not a priority, and the more important issue is to find ways to reduce their vulnerability to the projected climate change which is being imposed upon them largely as a result of emissions from developed countries. This priority does not accord with the ultimate objective of the United Nations Framework Convention on Climate Change, which is to achieve stabilization of greenhouse gas emissions. This paper reports upon studies in Uganda designed to help in the development of a national adaptation strategy, and addresses the need to reconcile such a strategy with the global priority accorded to mitigation and with national economic development priorities. Some features of a national climate change adaptation strategy are identified and questions are raised about the need for an international regime to facilitate and support adaptation.

Notes: Abstract Climate change impacts on African human settlements arise from a number of climate change-related causes, notably sea level changes, impacts on water resources, extreme weather events, food security, increased health risks from vector home diseases, and temperature-related morbidity in urban environments. Some coastlines and river deltas of Africa have densely populated low-lying areas, which would be affected by a rise in sea level. Other coastal settlements will be subjected to increased coastal erosion. Recent flooding in East Africa highlighted the vulnerability of flood plain settlements and the need to develop adaptive strategies for extreme weather events management and mitigation. In the semi arid and arid zones many settlements are associated with inland drainage water sources. Increases in drought will enhance water supply related vulnerabilities. Inter-basin and international water transfers raise the need for adequate legal frameworks that ensure equity among participating nations. Similarly, water supply and irrigation reservoirs in seasonal river catchments might fail, leading to poor sanitation in urban areas as well as food shortage. Hydroelectric power generation could be restricted in drought periods, and where it is a major contributor to the energy budget, reduced power generation could lead to a multiplicity of other impacts. States are advised to develop other sources of renewable energy. Temperature changes will lead to altered distribution of disease vectors such as mosquitoes, making settlements currently free of vector borne diseases vulnerable. Rapid breeding of the housefly could create a menace associated with enteric disorders, especially in conditions of poor sanitation. The dry savannahs of Africa are projected as possible future food deficit areas. Recurrent crop failures would lead to transmigration into urban areas. Pastoralists are likely to undertake more trans-boundary migrations and probably come into conflict with settled communities. Adaptive measures will involve methods of coastal defences (where applicable), a critical review of the energy sector, both regionally and nationally, a rigorous adherence to city hygiene procedures, an informed agricultural industry that is capable of adapting to changing climate in terms of cropping strategies, and innovations in environment design to maximise human comfort at minimum energy expenditure. In the savannah and arid areas water resource management systems will be needed to optimise water resource use and interstate co-operation where such resources are shared. Climate change issues discussed here raise the need for state support for more research and education in impacts of climate change on human settlements in Africa.

Notes: Abstract The sodium arsenite method developed by Jacobs andHochheiser is one of the most widely used manualmethods for nitrogen dioxide (NO2) monitoring inambient air, particularly in developing countries. Asreported, the method gives 82% NO2 absorptionefficiency (NAE) in the concentration range from 40 to750 μg/m3, when only one impinger tube isemployed in the sampling train at a flow rate of 0.2lpm and for 24 h sampling duration. Accordingly,a uniform correction factor (0.82) is used indenominator to calculate the ultimate concentration ofNO2 in ambient air.In the present investigation, the effect oftemperature on absorption efficiency of NO2 isstudied employing four impinger tubes in series tocollect the maximum NO2 generated in the gasstream. The study conducted at 16, 26 and 36 °Ctemperatures shows maximum absorption efficiency(average) of 87.8% at 26°C in 1st impingertube. At lower and higher temperatures, it is foundconsiderably less. A suitable correction factor,therefore, must be applied to estimate actual NO2concentration in ambient air using arsenite method, intropical countries like India, where atmospherictemperature variations are large (less than 5°Cin winter and more than 45°C in summer).

Notes: Abstract The optimal control problem of nonholonomic motion planning of space manipulator was discussed. Utilizing the method of wavelet analysis, the discrete orthogonal wavelets were introduced to solve the optimal control problem, the classical Fourier basic functions were replaced by the wavelet expansion approximation. A numerical algorithm of optimal control was proposed based on wavelet analysis. The numerical simulation shows, the method is effective for nonholonomic motion planning of space manitulator.

Notes: Abstract This paper derives some optimization results for bilinear systems using a higher-order method by characterizing them over matrix Lie groups. In the derivation of the results, first a bilinear system is transformed to a left-invariant system on matrix Lie groups. Then, the product of exponential representation is used to express this system in canonical form. Next, the conditions for optimality are obtained by the principles of variational calculus. It is demonstrated that closed-form analytical solutions exist for classes of bilinear systems whose Lie algebra are nilpotent.

Notes: Abstract The optimal expenditure pattern for a double-path engineering project, i.e., a project composed of a nonroutine risky R&D path and a routine nonrisky preparatory path, manufacturing related or marketing related, is studied via the calculus of variations to derive a set of twin second-order nonlinear differential equations whose solution yields the optimal joint expenditure. Assuming independence between the risky and nonrisky paths, a constant return per unit time, a gamma-type unimodal conditional-completion density function for the R&D activity, and the principle of diminishing returns on the effort, we find an interesting interplay between the two paths for the peak position and termination of the expenditures. Counterintuitively, we find that the peak expenditure of the R&D path does not necessarily precede that of the preparatory path, although both path expenditure peaks obey the well-known Kamien–Schwartz theorem. That is, for both paths, the expenditure peak positions precede always the peak of the conditional-completion density function of the R&D path.

Notes: Abstract For a general fixed-duration optimal control problem, the proximal aiming technique of nonsmooth analysis is employed in order to construct a discontinuous feedback law, whose Euler solutions are all optimal to within a prescribed tolerance, universally for all initial data in a prescribed bounded set. The technique is adapted in order to construct universal near-saddle points for two-player fixed-duration differential games of the Krasovskii–Subbotin type.

Notes: Abstract It is shown in this paper that the finite-time optimal control of polynomial systems can be obtained by solving a sequence of optimal control problems for the linearized problem. The paper provides proof of convergence as well as illustration of the procedure by two examples.

Notes: Abstract The objective of this paper is to present a useful application of the theory of regularity of systems of nonlinear partial differential equations to the solution of stochastic differential games with N players. It is particularly interesting to notice that the structure of games fits perfectly with what is requested to prove the regularity property which is needed.

Notes: Abstract In this paper, the value function for an optimal control problem with endpoint and state constraints is characterized as the unique lower semicontinuous generalized solution of the Hamilton-Jacobi equation. This is achieved under a constraint qualification (CQ) concerning the interaction of the state and dynamic constraints. The novelty of the results reported here is partly the nature of (CQ) and partly the proof techniques employed, which are based on new estimates of the distance of the set of state trajectories satisfying a state constraint from a given trajectory which violates the constraint.

Notes: Abstract This paper deals with the optimal control problem for the Lyapunov exponents of stochastic matrix products when these matrices depend on a controlled Markov process with values in a finite or countable set. Under some hypotheses, the reduced process satisfies the Doeblin condition and the existence of an optimal control is proved. Furthermore, with this optimal control, the spectrum of the system consists of only one element.

Notes: Abstract The purpose of this paper is an integrated overview of bilinear systems (BLS) research which has evolved over the past few decades, and a new result on control of flexible a.c. transmission systems (FACTS) is presented. BLS may be derived in many cases from principles of physics, chemistry, biology, socioeconomics, and engineering. In other cases, BLS are more accurate approximations to nonlinear systems than are traditional linear systems, as shown for example by the added bilinear terms (in state and control) for the Taylor series. While an appropriately designed linear control system may be optimum relative to some quadratic performance index without added constraints, bilinear or parametric control can be designed to improve more global performance and indeed to increase the region of attainable states. Such controllability and stabilization of BLS and of a series line-capacitor controlled FACTS is presented.

Notes: Abstract The influence of thermal discharges on thephytoplankton community from a coastal zone of theGulf of Mexico was evaluated through their structureand photosynthetic behaviour focusing on responses tochanges in light and temperature. Biological andphysicochemical parameters were measured over a periodof two years in an area with permanent hot waterdischarges from a thermoelectric plant. Thetemperature in the sampling area ranged from 23.5 to36 °C with differences between the coldest andthe hottest station from 5.3 to 9.2 °C.Photosynthetically active radiation (PAR) were reducedin the discharge area water column, due to turbulence.One hundred and one different taxa were identifiedwith a strong predominance of Diatoms. The chlorophylla concentration ranged from 0.3 to 6.1 μgL-1, with highest values of thephaeophytin:chlorophyll ratio found at the hottest station.The community structure did not show significativedifferences among sampling stations with respect totemperature variations. However, in the algalassemblages influenced by thermal discharges, it waspossible to observe alterations in the photosynthesisbehaviour. Phytoplankton response to short termphotosynthesis experiments was segregated according tocomposition and origin of microalgal assemblages.Samples with larger heterogeneous composition had moreconsistent oxygen production responses. Algalcommunities exposed to hot effluent showed differentdegrees of photosynthesis rate reduction,higher light requirements (〉500 μE m2 s-1)and lower temperature (25 °C) to achieve Pmaxthan algae sampled in sites without such exposure.

Notes: Abstract Bleaching in stony-corals is the result of disruption of symbiosis between the coral hosts and photosynthetic microalgal endosymbionts (zooxanthellae). Coral bleaching events of unprecedented frequency and global extent have been reported during the last two decades. Recently, we demonstrated that bleaching of the coral Oculina patagonica in the Mediterranean Sea is caused by the bacterium Vibrio shiloi, when seawater temperature rises and allows the bacterium to become virulent. The first step in the infection process is host-specific adhesion of V. shiloi to O. patagonica via a β-galactoside receptor on the coral surface. The bacterium then penetrates into the coral tissue and produces extracellular materials which rapidly inhibit photosynthesis of zooxanthellae and bleach and lyse the algae. The inhibition of pothosynthesis is due to a low molecular weight, heat stable toxin and ammonia. Bleaching and lysis are due to a heat-labile, high molecular weight materials, probably lytic enzymes. Elevated temperature induces different virulence factors within the infectious agent of the disease, V. shiloi. Adhesion was found to be temperature-regulated. When the bacteria were grown at 16°C there was no adhesion to corals maintained at either 25°C or 16°. However, when the bacteria were grown at 25°C they adhered avidly to corals maintained at 16°C and 25°C. In addition, the production of lytic enzymes and the photosynthesis inhibitor was also found to be temperature dependent. Production of the latter toxin was ten times greater at 29°C than at 16°C, and extracellular protease was 5-fold higher in cultures grown at 29°C than at 16°C. The data presented here suggest an explanation for the correlation between elevated seawater temperatures and seasonal coral bleaching.

Notes: Abstract This paper presents an optimal endogenous growth model with pollutionaccumulation and abatement activities which analyzes the implications ofpollution accumulation irreversibility on the existence of sustainablegrowth paths. This model studies different pollution-decay functions whichpresent, among others, the feature that a sufficiently high pollution stocklevel can reduce the rate of decay to zero. This study shows that this newfeature, which gains support for the biological literature, significantlyalters the traditional results on the properties of sustainable endogenousgrowth by reducing the field of existence and strengthening the role ofindividual preferences.

Notes: Abstract A strategy is proposed to solve the fixed final state optimalcontrol problem using the simple cell mapping method. A non-uniform timestep simple cell mapping is developed to create a general database fromwhich solutions of various optimal control problems can be obtained. Atwo-stage backward search algorithm is proposed to eliminate degeneratedpaths often associated with the simple cell mapping. The proposed methodcan accurately delineate the switching curves and eliminate false limitcycles in the solution. The method is applied to two optimal controlproblems with bang-bang control. The well-known minimum time controlproblem of moving a point mass from any initial condition to the originof the phase plane is studied first. This example has exact solutionsavailable which provide a yardstick to examine the accuracy of themethod. The cell size dependence of the solution accuracy is studiednumerically. The second example is a variable stiffness feedback controlproblem with tuning range saturation. The strategy proposed is able toprovide the switching curves in the phase plane. This result has notbeen obtained before.