ALBERT

Notes: Abstract We consider the slotted ALOHA protocol on a channel with a capture effect. There are M 〈 ∞ users each with an infinite buffer. If in a slot, i packets are transmitted, then the probability of a successful reception of a packet is q i. This model contains the CDMA protocols as special cases. We obtain sufficient rate conditions, which are close to necessary for stability of the system, when the arrival streams are stationary ergodic. Under the same rate conditions, for general regenerative arrival streams, we obtain the rates of convergence to stationarity, finiteness of stationary moments and various functional limit theorems. Our arrival streams contain all the traffic models suggested in the recent literature, including the ones which display long range dependence. We also obtain bounds on the stationary moments of waiting times which can be tight under realistic conditions. Finally, we obtain several results on the transient performance of the system, e.g., first time to overflow and the limits of the overflow process. We also extend the above results to the case of a capture channel exhibiting Markov modulated fading. Most of our results and proofs will be shown to hold also for the slotted ALOHA protocol without capture.

Notes: Abstract An ADI scheme for solving three-dimensional parabolic equations withfirst-order derivatives and variable coefficients has been developed basedon our previous papers and the idea of the modified upwind differencescheme. This ADI scheme is second-order accurate and unconditionallystable. Further, a small parameter can be chosen which makes it suitablefor simulating fast-transient phenomena or for computations on fine spatialmeshes. The method is illustrated with numerical examples.

Notes: Abstract We consider a four-class two-station network with feedback, with fluid inputs and a head-of-the-line generalized processor sharing discipline at each station. We derive the Skorokhod Problem associated with the network and obtain algebraic sufficient conditions for Lipschitz continuity of the associated Skorokhod Map. This provides the first example of a multiclass network with feedback for which the associated Skorokhod Problem has been proved to be regular. As an elementary application, we show that under the conditions which guarantee Lipschitz continuity the network is stable if and only if the usual load conditions apply.

Notes: Abstract Bifurcation phenomena from standing pulse solutions of the problem $$\varepsilon \tau u_t = \varepsilon ^2 u_{xx} + f(u,v),{\text{ }}v_t = v_{xx} + g(u,v)$$ is considered. ε(〉0) is a sufficiently small parameter and τ is a positive one. It is shown that there exist two types of destabilization of standing pulse solutions when τ decreases. One is the appearance of travelling pulse solutions via the static bifurcation and the other is that of in-phase breathers via the Hopf bifurcation. Furthermore which type of destabilization occurs first with decreasing τ is discussed for the piecewise linear nonlinearities f and g.

Notes: Abstract The viability of irrigated systems in the Senegal River Valley is being brought into question today due to their under‐utilization. We assume that their viability depends largely on the way their different components behave and interact. We therefore sought to examine in greater depth today's knowledge of the structure of these systems and activities performed within them. This led to the development of a multi‐agent system model, a kind of virtual irrigated system, with a special focus on rules in use for access to credit, water allocation and cropping season assessment as well as organization and coordination of farmers. The purpose of this paper is to show how this kind of tool is relevant to the study of irrigated systems' viability. As an example it is used to examine the influence of existing social networks on the viability of irrigated systems.

Notes: Abstract In this paper, we propose a Hausdorff metric to measure the “distance” between two linear inequality systems on a real normed space X. For this topology, which comes through a pseudo-metric in the set Σ of linear inequality systems, the closedness of the feasible set mapping is studied, and at the same time a characterization of the stability of the subset Σ c of consistent sytems is given.

Notes: Abstract The bond portfolio management problem is formulated as a multiperiod two-stage or multistage stochastic program based on interest rate scenarios. These scenarios depend on the available market data, on the applied estimation and sampling techniques, etc., and are used to evaluate coefficients of the resulting large scale mathematical program. The aim of the contribution is to analyze stability and sensitivity of this program on small changes of the coefficients – the (scenario dependent) values of future interest rates and prices. We shall prove that under sensible assumptions, the scenario subproblems are stable linear programs and that also the optimal first-stage decisions and the optimal value of the considered stochastic program possess acceptable continuity properties.

Notes: Abstract We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.

Notes: Abstract We construct A‐stable and L‐stable diagonally implicit Runge–Kutta methods of which the diagonal vector in the Butcher matrix has a minimal maximum norm. If the implicit Runge–Kutta relations are iteratively solved by means of the approximately factorized Newton process, then such iterated Runge–Kutta methods are suitable methods for integrating shallow water problems in the sense that the stability boundary is relatively large and that the usually quite fine vertical resolution of the discretized spatial domain is not involved in the stability condition.

Notes: Abstract It has been recently shown that large growth factors might occur in Gaussian Elimination with Partial Pivoting (GEPP) also when solving some plausibly natural systems. In this note we argue that this potential problem could be easily solved, with much smaller risk of failure, by very small (and low cost) modifications of the basic algorithm, thus confirming its inherent robustness. To this end, we first propose an informal model with the goal of providing further support to the comprehension of the stability properties of GEPP. We then report the results of numerical experiments that confirm the viewpoint embedded in the model. Basing on the previous observations, we finally propose a simple scheme that could be turned into (even more) accurate software for the solution of linear systems.

Notes: Abstract This paper studies the stability and convergence properties of general Runge-Kutta methods when they are applied to stiff semilinear systems y′(t) = J(t)y(t) + g(t, y(t)) with the stiffness contained in the variable coefficient linear part. We consider two assumptions on the relative variation of the matrix J(t) and show that for each of them there is a family of implicit Runge-Kutta methods that is suitable for the numerical integration of the corresponding stiff semilinear systems, i.e. the methods of the family are stable, convergent and the stage equations possess a unique solution. The conditions on the coefficients of a method to belong to these families turn out to be essentially weaker than the usual algebraic stability condition which appears in connection with the B-stability and convergence for stiff nonlinear systems. Thus there are important RK methods which are not algebraically stable but, according to our theory, they are suitable for the numerical integration of semilinear problems. This paper also extends previous results of Burrage, Hundsdorfer and Verwer on the optimal convergence of implicit Runge-Kutta methods for stiff semilinear systems with a constant coefficients linear part.

Notes: Abstract This paper is devoted to the numerical analysis of ill-posed problems of evolution equations in Banach spaces using certain classes of stochastic one-step methods. The linear stability properties of these methods are studied. Regularisation is given by the choice of the regularisation parameter as α = $$\sqrt {\tau _n }$$ , where τ n is the stepsize and provides the convergence on smooth initial data. The case of the approximation of well-posed problems is also considered.

Notes: Abstract Legged-climbing robot is considered. Each foot of the robot has an electromagnet system for robot"s holding on a metal surface. This surface can be both vertical and inclined, including negative slope. Analytical calculation of robot stability under turn over or sliding conditions has been made. Critical slopes have been determined. One of these slopes corresponds to minimal reserve of robot stability towards sliding and another to minimal reserve of robot stability towards turning-over. As total reserve of stability of a robot is always equal to the minimal one of these reserves. Additional support elements of elastic material with high coefficient of friction, along with electromagnet, allows to increase minimal reserve of robot stability towards sliding. The use of such support elements leads to redistributing force of normal support reaction between electromagnet (which surface has low coefficient of friction) and additional support element (which surface has high coefficient of friction). It is just what leads to increasing the total friction force and as a consequence to increasing of minimal reserve of robot stability towards sliding.

Notes: Abstract We suggest a simple but general method of establishing symmetry properties of stable solutions of nonlinear elliptic equations. The method relies on characterization of symmetry breaking with a help of zero modes and on a generalization of the Perron–Frobenius theory.

Notes: Abstract Based on the description of shear horizontal (SH) wave propagation in arbitrarily oriented transversely isotropic media, radiation characteristics of ultrasonic transducers for this wave type are determined. The radiated wavefields are obtained by point source superposition, making use of an analytical relationship for the wave propagation direction as a function of the spatial coordinates. Approximate formulae are given for the radiation characteristics of circular and rectangular transducers in the far-field, which are in a form similar to the isotropic material case. Focusing on transversely isotropic weld metal specimens and unidirectional composites, numerical evaluation is performed for normal-incidence probes as well as for electromagnetic acoustic transducers.

Notes: Abstract In this paper, we study the stability of functional equations that has its origins with S. M. Ulam, who posed the fundamental problem 60 years ago and with D. H. Hyers, who gave the first significant partial solution in 1941. In particular, during the last two decades, the notion of stability of functional equations has evolved into an area of continuing research from both pure and applied viewpoints. Both classical results and current research are presented in a unified and self-contained fashion. In addition, related problems are investigated. Some of the applications deal with nonlinear equations in Banach spaces and complementarity theory.

Notes: Abstract A second-order accurate numerical method has been proposed for the solution of a coupled non-linear oscillator featuring in chemical kinetics. Although implicit by construction, the method enables the solution of the model initial-value problem (IVP) to be computed explicitly. The second-order method is constructed by taking a linear combination of first-order methods. The stability analysis of the system suggests the existence of a Hopf bifurcation, which is confirmed by the numerical method. Both the critical point of the continuous system and the fixed point of the numerical method will be seen to have the same stability properties. The second-order method is more competitive in terms of numerical stability than some well-known standard methods (such as the Runge–Kutta methods of order two and four).

Notes: Abstract Large-scale steady-state groundwater flow in atoll carbonate platforms results from temperature and salinity-induced density gradients. Atolls are built on top of a basaltic substrate that provides geothermal heating from beneath. Moreover, they are immersed in the tropical ocean where temperature decreases rapidly with depth. Groundwater circulation in these platforms has long been associated with the geothermal heat flux because it is capable of generating inward and upward flow of oceanic origin water by buoyancy effects. This study shows that hydraulic circulation occurs even in the absence of a geothermal flux because the combination of the cold subsurface ocean waters with the warm surface conditions is sufficient to maintain a convection cell within the carbonate platform. Using a one-dimensional analytical model, validated by more sophisticated two-dimensional simulations, we can investigate the interaction between these two driving forces. The flow rate inside the platform is, in fact, a function of the ratio of the geothermal flux to the temperature gradient in the ocean. It increases with the geothermal flux but decreases with the oceanic temperature gradient. This one-dimensional model also shows that taking salinity effects on density into account increases the flow rates transiting through the platform by a third.

Notes: Abstract We consider the modified conjugate gradient procedure for solving A $$\underline x $$ = $$\underline b $$ in which the approximation space is based upon the Krylov space associated with A 1/p and $$\underline b $$ , for any integer p. For the square-root MCG (p=2) we establish a sharpened bound for the error at each iteration via Chebyshev polynomials in $$\sqrt A$$ . We discuss the implications of the quickly accumulating effect of an error in $$\sqrt A$$ $$\underline b $$ in the initial stage, and find an error bound even in the presence of such accumulating errors. Although this accumulation of errors may limit the usefulness of this method when $$\sqrt A$$ $$\underline b $$ is unknown, it may still be successfully applied to a variety of small, “almost-SPD” problems, and can be used to jump-start the conjugate gradient method. Finally, we verify these theoretical results with numerical tests.

Notes: Abstract A generalization of the Little–Hopfield neural network model for associative memories is presented that considers the case of a continuum of processing units. The state space corresponds to an infinite dimensional euclidean space. A dynamics is proposed that minimizes an energy functional that is a natural extension of the discrete case. The case in which the synaptic weight operator is defined through the autocorrelation rule (Hebb rule) with orthogonal memories is analyzed. We also consider the case of memories that are not orthogonal. Finally, we discuss the generalization of the non deterministic, finite temperature dynamics.

Notes: Abstract We have been interested in Automatic Guided Vehicles (AGV) for several years. In this paper, we synthesize controllers for AGV applications using monocular vision. In particular, we are interested in road following and direction change tasks, and in analyzing the influence of extrinsic camera parameter perturbations on vehicle behavior. We use the bicycle as the kinematic vehicle model, and we choose the position of the white band on the road as the sensor signal. We define an interaction between the camera, which is mounted inside the vehicle, and the white band detected in the image space. Using this kind of interaction, we present how to use a pole assignment technique to solve the servoing task. We show the simulation and experimental results (1/10 scale demonstrator) with and without perturbations. We then investigate the use of a robust controller to slow down the effect of perturbations on the behavior of the vehicle.

Notes: Abstract This paper describes a novel knowledge-based approachfor helping workflow process designers andparticipants better manage the exceptions (deviationsfrom an ideal collaborative work process caused byerrors, failures, resource or requirements changesetc.) that can occur during the enactment of aworkflow. This approach is based on exploiting ageneric and reusable body of knowledge concerning whatkinds of exceptions can occur in collaborative workprocesses, and how these exceptions can handled(detected, diagnosed and resolved). This work buildsupon previous efforts from the MIT Process Handbookproject and from research on conflict management incollaborative design.

Notes: Abstract Problem-based learning is a constructivist approach toprofessional education stressing the use of real lifeproblems in education. Several previous attempts tounderstand the intricacies of learning in theproblem-based context have led to a causal model,elements of which were tested in the present study.The focus of the investigation was on the students' motivation to committhemselves to studying in a problem-based healthsciences curriculum, expressed in term of levels ofattendance at tutorial meetings. Data were collectedregarding functioning of the tutorial group, tutorfunctioning, level of prior knowledge, quality of theinstructional problems, time spent on individualstudy, academic achievement and increased interest.These data were analyzed using a structural equationsmodeling approach. As hypothesized, commitment appears to bea potent determinant of achievement. In fact, itrepresents one of the strongest determinants oflearning in the model tested.

Notes: Abstract Ecosystem Management (EM) is a new holistic approach to the management of natural resources. It integrates the scientificknowledge on ecological interrelationships and the complex socioeconomic and political frame of values, aiming at the long-term sustainability of a region, i.e., the ecosystem. Itincludes the human, biological and natural dimensions, and canregulate the internal structures and functions of the ecosystem,and the inputs and outputs from it, so that solutions to development and protection problems can be achieved and be socially well-accepted. It has been given attention since 1991,mainly in the U.S.A., where the existing legal framework formeda basis for EM. The former experience of programs based on the traditional methods of management, the goal of sustainable development stated by many governmental, public or private agencies, and the advent of scientific knowledge, permitted the development of a theoretical basis for EM. Today, a significant number of EM programs have been established and are in progressin the U.S.A. Here the concept, general principles and methodology of EM are reviewed, and the EM program in the Stateof Florida in the U.S.A. is presented, which is considered a successful case study. In addition, the examples of managementof two very important ecosystems in Northern Greece are critically presented for comparison, in order to evaluate if they have EM characteristics.

Notes: Abstract Two-dimensional, vertically-averaged hydrodynamic and sediment transport models were developed and applied as part of a PCB fate and transport modeling study of Thompson Island Pool (TIP), Upper Hudson River. Mechanistic formulations were used to simulate cohesive and non-cohesive suspended load transport; site-specific data were extensively used to determine model inputs. This modeling approach is compared and contrasted to non-mechanistic solids transport sub-models used in other contaminant fate studies. A minimum number of model parameters were adjusted to calibrate the sediment transport model using data collected during the 1994 spring flood. The model was validated during the 1997 spring flood and for a 22-year (1977–1998) period. Successful calibration and validation of the model showed that: (1) deposition and resuspension processes were realistically and accurately formulated in the model; (2) the model is an effective diagnostic tool for quantitatively evaluating net deposition and erosion from various areas of TIP; and (3) sediment transport results can be coupled with a PCB fate model with a high degree of confidence.

Notes: Abstract The development, testing and application of a dynamic two-dimensional (longitudinal-vertical) mass balance model for dissolved oxygen (DO) and chlorophyll (Chl) for rivers is documented that for the first time accommodates both the oxygen demand and filtering effects of zebra mussels. The test system is a phytoplankton-rich section (∼ 15 km long) of the Seneca River, NY, that is believed to represent an upper bound of the impact of this exotic invader. Changes in common measures of water quality of the river brought about by the zebra mussel invasion are reviewed and related longitudinal patterns in DO, Chl, and Secchi disc transparency are documented. Model testing is supported by comprehensive measurements of DO, Chl, and various forcing conditions over a three-month period, and independent determinations of several model coefficients. Wide variations in the areal consumption rate of DO (ZOD; g·m−2·d−1) and filtering rate (m3·m−2·d−1) of zebra mussels, as determined through model calibration, occurred over the study period. Values of ZOD in areas with dense zebra mussel populations at times (e.g., 〉 50 g·m−2·d−1) were an order of magnitude greater than the sediment oxygen demand associated with organically enriched deposits. The value of determinations of these fluxes from model calibration procedures is evaluated within the context of the limitations of protocols presently available to support independent specification of these rates. Model analyses are conducted to evaluate the relative magnitude of source and sink processes for DO and Chl, the potential operation and implications of feedback from low DO levels on oxygen consumption by zebra mussels, and the sensitivity of model simulations to selected sources of uncertainty and variability. Model projections of oxygen resources of the river are presented in a probabilistic format in evaluating reductions in zebra mussel biomass that would be necessary to eliminate violations of standards and regain assimilative capacity.

Notes: Abstract We explore a computationally efficient method of simulating realistic networks of neurons introduced by Knight, Manin, and Sirovich (1996) in which integrate-and-fire neurons are grouped into large populations of similar neurons. For each population, we form a probability density that represents the distribution of neurons over all possible states. The populations are coupled via stochastic synapses in which the conductance of a neuron is modulated according to the firing rates of its presynaptic populations. The evolution equation for each of these probability densities is a partial differential-integral equation, which we solve numerically. Results obtained for several example networks are tested against conventional computations for groups of individual neurons. We apply this approach to modeling orientation tuning in the visual cortex. Our population density model is based on the recurrent feedback model of a hypercolumn in cat visual cortex of Somers et al. (1995). We simulate the response to oriented flashed bars. As in the Somers model, a weak orientation bias provided by feed-forward lateral geniculate input is transformed by intracortical circuitry into sharper orientation tuning that is independent of stimulus contrast. The population density approach appears to be a viable method for simulating large neural networks. Its computational efficiency overcomes some of the restrictions imposed by computation time in individual neuron simulations, allowing one to build more complex networks and to explore parameter space more easily. The method produces smooth rate functions with one pass of the stimulus and does not require signal averaging. At the same time, this model captures the dynamics of single-neuron activity that are missed in simple firing-rate models.

Notes: Abstract The Kyoto Protocol requires the U.S.to reduce the rate of emissions of six greenhousegases (GHG) to 93% of their 1990 rate and to achievethis target by the 2008 to 2012 commitment period. This study assesses the magnitude of change needed inthe U.S. economy and, specifically, in the U.S. energysector, to achieve and maintain the target establishedby the Kyoto Protocol. A simple carbon (C)emissions-energy model is explained in this analysisusing four key variables. Current and future trendsin C emissions are explained by: the carbon/energy(C/E) ratio, Gross Domestic Product growth, energyprices and an energy trend variable. Potential GHGmitigation policy actions affect C emissionsindirectly by affecting at least one of these keyvariables. The analysis concludes that reducingfossil energy use in the U.S. to meet the Kyoto GHGemissions reduction target would be very costly. Technological progress that reduces C emissions wouldnot be fully sufficient without prematurely abandoningproductive capital equipment. Energy price increasesof about 14% per year, or declines in economic growthof almost 5% per year, could reduce energy demand andassociated C emissions enough to achieve the terms ofthe Kyoto Protocol.

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 The International Life SciencesInstitute (ILSI) Risk Science Institute (RSI) convenedan expert panel of scientists to developrecommendations for a comprehensive monitoring programfor the Croton and Catskill/Delaware watersheds, whichprovide drinking water to New York City's residents. This effort was conducted as part of efforts topreserve and enhance the quality of New York City'sreservoir system through a watershed protectionprogram. The panel developed recommendations for astrategic framework on which to construct a monitoringprogram. As part of this activity, the paneldetermined whether existing monitoring activities weredeficient and, where activities were deficient, thepanel developed recommendations for additionalinformation that should be collected.The panel recommended the development and use of anintegrated approach to watershed monitoring, whichdraws on modeling, risk-based planning and analysis,statistical sampling and design, and basic compliancemonitoring. The approach should be designed toprovide an assessment of natural and anthropogenicsources of stress to the system as well as anassessment of water quality trends in response tostresses acting in concert, both over the long termand over the five-year New York City Memorandum ofAgreement (MOA) assessment time frame. It should alsoprovide an assessment of the human health andenvironmental risks posed by a variety of stressors,and the impact of management actions implemented toameliorate stressors.

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 To assess the impact of acid deposition on forestedloess and clay soils in the Netherlands, changes inbase saturation and soil solution concentrations weresimulated with the dynamic soil acidification modelReSAM for 38 loess soils and 16 clay soils. Theselected locations represent the range in geographicalposition and diversity in parent material occurring inforested loess and clay soils in the Netherlands. Twodeposition scenarios were used for the period1992–2050: a business as usual scenario (BAU) and ascenario in which deposition was reduced according topresent Dutch policy plans (MV-3). A comparison ofsimulated and measured soil solution concentrationsand base saturation in 1992/1993 showed that the modelsimulated concentrations and base saturation in theloess soils quite good. However, the model tended tooverestimate acidification in the top (0–10 cm) of theclay soils. Despite the reasonable agreement betweenmeasured and simulated data some uncertainty in thevalidity of the model predictions remains because timetrends to validate the model were not available. Themodel predicted a small but ongoing acidificationduring the BAU scenario in the loess soils asindicated by a decline in median base saturation andpH in the topsoil in 2050. Present policy plans (MV-3)lead to a slight recovery of the base saturation in2050 and a decline in Al concentrations. In the claysoils a strong decline in base saturation is simulatedin the topsoil, whereas an increase in base saturationis predicted for the subsoil.

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 dynamical stability of a homogeneous, simple supported column, subjected to a periodic axial force, is investigated. The viscoelastic material is assumed to obey the Leaderman nonlinear constitutive relation. The equation of motion was derived as a nonlinear integro-partial-differential equation, and was simplified into a nonlinear integro-differential equation by the Galerkin method. The averaging method was employed to carry out the stability analysis. Numerical results are presented to compare with the analytical ones. Numerical results also indicate that chaotic motion appears.

Notes: Abstract The governing equation of solid-liquid couple vibration of pipe conveying fluid on the elastic foundation was derived. The critical velocity and complex frequency of pipe conveying fluid on Winkler elastic foundation and two-parameter foundation were calculated by power series method. Compared with pipe without considering elastic foundation, the numerical results show that elastic foundation can increase the critical flow velocity of static instability and dynamic instability of pipe. And the increase of foundation parameters may increase the critical flow velocity of static instability and dynamic instability of pipe, thereby delays the occurrence of divergence and flutter instability of pipe. For higher mass ratio β, in the combination of certain foundation parameters, pipe behaves the phenomenon of restabilization and redivergence after the occurrence of static instability, and then coupled-mode flutter takes place.

Notes: Abstract The spatial stability equation of moving jet containing dense suspended solid particles was derived out by means of the continuum phase-coupled model. The stability curves of moving jet for different downstream distances, Reynolds number of flow-field, particle properties and velocities of jetting device are got by the finite difference method based on the asymptotic method and the Eulerian conservative difference scheme. Founded on the analysis of the obtained stability curves it is found that the positive velocity of jetting device widens the unstable frequency range of flow-field but the effect of the negative one is contrary. In addition, particles existing in the flow-field curb the instability of flow-field and the effect enhances with the decrease of Reynolds number of flow-field. These conclusions benefit learning the development of moving two-phase jet.

Notes: Abstract By adopting the energy method, a new method to calculate the stability of the composite shell of revolution is presented. This method takes the influence of nonlinear prebuckling deformations and stresses on the buckling of the shell into account. The relationships between the prebuckling deformations and strains are calculated by nonlinear Kármán equations. The numerical method is used to calculate the energy of the total system. The nonlinear equations are solved by combining gradient method and amendatory Newton iterative method. The computer program is also developed. An example is given to demonstrate the accuracy of the method presented.

Notes: Abstract The recursive least square is widely used in parameter identification. But it is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. It is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.

Notes: Abstract Topology optimization design of continuum structures that can take account of stress and displacement constraints simultaneously is difficult to solve at present. The main obstacle lies in that, the explicit function expressions between topological variables and stress or displacement constraints can not be obtained using homogenization method or variable density method. Furthermore, large quantities of design variables in the problem make it hard to deal with by the formal mathematical programming approach. In this paper, a smooth model of topology optimization for continuum structures is established which has weight objective considering stress and displacement constraints based on the independent-continuous topological variable concept and mapping transformation method proposed by Sui Yunkang and Yang Deqing. Moreover, the approximate, explicit expressions are given between topological variables and stress or displacement constraints. The problem is well solved by using dual programming approach, and the proposed element deletion criterion implements the inversion of topology variables from the discrete to the continuous. Numerical examples verify the validity of proposed method.

Notes: Abstract We are concerned with ∈-mixed solutions for weak Stackelberg problems corresponding to two-player nonzero-sum noncooperative games. Two cases are considered: (i) mixed strategies for only the second player; (ii) mixed strategies for both players. After giving basic results relating convergence of functions and weak convergence of probability measures, we establish existence and stability results for ∈-mixed solutions under general assumptions of minimal character without any convexity assumption. Our results improve previous work of Mallozzi and Morgan (Refs. 1–2).

Notes: Abstract The adsorption of copper, chromate, and arsenate (CCA)onto iron-oxide-coated sand (IOCS) was examined insingle-metal and mixed-metal systems. Copper andarsenate were strongly adsorbed or formed inner-spheresurface complexes with the IOCS surface while chromatewas weakly adsorbed or formed an outer-sphere surfacecomplex with the IOCS surface. Copper adsorption byIOCS slightly increased in the presence of arsenatebut was not affected by the presence of chromate. Arsenate adsorption was not affected by the presenceof copper and/or chromate. Chromate adsorptionincreased in the presence of copper by the combinationof electrostatic effects and possiblesurface-copper-chromate ternary complex formation. The presence of arsenate significantly decreasedchromate adsorption due to competition for adsorptionsites and electrostatic effects. Using inner-spheresurface complexation constants for copper and arsenateand outer-sphere surface complexation constants forchromate, the triple-layer model (TLM) was successfulin describing adsorption of copper, chromate, andarsenate in single-solute systems. The modelindicated that each metal uses a different number ofadsorption sites. For CCA metals-IOCS systems, theequilibrium constants determined from single-solutesystems were not able to predict adsorption frommulti-solute systems. The TLM does not currentlyaccount for the heterogeneity of oxide surface sitesand the formation of ternary complexes and/or solidphases that do not exist in single-solute systems.

Notes: Abstract The paper investigates the problem of the robust stability of Schur polynomials. Recently, a new approach based on the Rouche theorem of classical complex analysis has been adopted for the solution of this problem. In this paper, an improvement of the previous solution is presented. This is the optimum solution of the robust stability problem for Schur polynomials, which is obtained by solving a minimization problem and is better than other methods in robust stability literature. Three numerical examples are given to illustrate the proposed method.

Notes: Abstract In this paper, the concept of extended well-posedness of scalar optimization problems introduced by Zolezzi is generalized to vector optimization problems in three ways: weakly extended well-posedness, extended well-posedness, and strongly extended well-posedness. Criteria and characterizations of the three types of extended well-posedness are established, generalizing most of the results obtained by Zolezzi for scalar optimization problems. Finally, a stronger vector variational principle and Palais-Smale type conditions are used to derive sufficient conditions for the three types of extended well-posedness.

Notes: Abstract In this note, the problem of the robust stability for a two-dimensional (two-variable) Schur polynomial which is the characteristic polynomial of a discrete-time linear time-invariant system is investigated. A new approach based on the Rouché theorem is adopted. The extension to the robust stability for multidimensional (multivariable) polynomials is also provided. Interesting sufficient conditions for such robust stability are derived. A two-dimensional example is included to support the theoretical result.

Notes: Abstract In vector optimization, several authors have studied the upper and lower semicontinuity for mappings involving constraints in topological vector spaces partially ordered through a cone with nonempty interior. In this paper, we give conditions about the upper and lower semicontinuity in the case that the ordering cone in the parameter space has possibly empty interior, as it happens in many function spaces and seqence spaces.

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 A mathematical model is presented for four-wheel-steeringvehicles, with the time delay in driver's response and the nonlinearityin lateral tyre forces taken into account. It is proved that thevehicle-driver system has a trivial steady state motion, as well aseight non-trivial steady state motions due to the nonlinearity of tyreforces. The asymptotic stability and Hopf bifurcation of the trivialsteady state are analyzed for two control strategies ofrear-wheel-steering. It is shown through the numerical simulations thatthe four-wheel-steering technique based on the bilinear control strategyworks better when the driver's response involves time delay.

Notes: Abstract To study the stability of the stochastic "dangling spider" model, the second Lyapunov method is substantiated for stochastic differential functional equations with the whole previous history.

Notes: Abstract To study the stability of the stochastic "dangling spider" model, the second Lyapunov method is substantiated for stochastic differential functional equations with the entire previous history.

Notes: Abstract A lack of consensus on the general adaptive significance of energetic efficiency can be shown to exist in ecology and anthropology. After briefly reviewing key studies in optimal foraging theory and ecological anthropology, a model is presented which includes the following elements: (1) an equation of adaptive success with reproductive fitness, within an optimality framework; (2) a definition of energy limitation consistent with this framework; (3) a distinction between efficiency of energy capture and efficiency of energy use in achieving other goals; (4) a multiple definition of energetic efficiency that distinguishes purely energetic measures (output/input) from rate measures (energy captured per unit time); (5) the inclusion of time budgeting as a primary adaptive constraint; (6) a quantitative demonstration that increased output/input ratios do not consistently predict an increase in net energy captured, and are poor measures where time is a constraint. The general conclusion is that where energy is limiting, increased efficiency in the rate of energy capture will be adaptive because more net energy will be made available; where energy is not limiting, an increased net capture rate may still confer increased adaptive success, since time and labor energy are freed from energy-capture activities and can be devoted to achieving other adaptive goals. But while energetic efficiency, properly defined, is shown to have general adaptive significance in all cases where time or energy are constraints, considerations of adaptive optimality preclude the general equation of energetic efficiency and adaptive success.

Notes: The Petrov-Galerkin projection method is outlined for the solution of the linear elliptic equation Lu = f with homogeneous boundary conditions. By choosing appropriate finite dimensional trial and test spaces, the methods of weighted residuals, collocation, and H1 Galerkin can be interpreted within the Petrov-Galerkin projection method framework.The important question of how best to choose the trial and test functions to suit a particular type of problem is then discussed. Objective criteria associated with the matrix which governs the Petrov-Galerkin numerical process are proposed.

Notes: Solutions to the backwards heat equation are approximated by solutions of a pseudo-heat equation. Solutions to this modified equation are constructed by means of a fundamental solution and potential theory, and it is shown that the fundamental solution can be approximated by various expansions in special functions.

Notes: In this paper we consider a free boundary problem of general type for the heat equation in one space dimension. We formulate this problem as an optimal control problem and derive necessary conditions for a solution of it. In order to compute a solution of the control problem, we apply the projection-gradient-method. Simple numerical examples illustrate the results.

Notes: The interior initial-boundary value problem for Maxwell's equations is considered for certain homogeneous boundary conditions and currents which satisfy corresponding compatibility conditions. Under the assumption that a solution exists, it is shown by means of suitable normed spaces that the sequence of discrete solutions obtained from the horizontal line method converges discretely to this solution. A priori estimations are given both for the discrete solutions and the solution of the given problem.

Notes: A new proof of the sampling theorem for non-bandlimited signals is presented. It leads to better rates of convergence for the envolved approximation process. Furthermore, the order of convergence is given for an extended class of functions.

Notes: The semiclassical equations describing a ring laser show two successive bifurcations, one stationary and one Hopf bifurcation. This phenomenon is analyzed mathematically. The initial value problem for the laser equations and the stability of the stationary solutions are discussed in detail. The transition to ultrashort laser pulses is shown to be a Hopf bifurcation. The direction of the bifurcation is determined for a numerical example. It turns out that it depends on the parameters of the system.

Notes: Although the plane boundary value problem for the Laplacian with given Dirichlet data on one part Γ2 and given Neumann data on the remaining part Γ2 of the boundary is the simplest case of mixed boundary value problems, we present several applications in classical mathematical physics. Using Green's formula the problem is converted into a system of Fredholm integral equations for the yet unknown values of the solution u on Γ2 and the also desired values of the normal derivatie on Γ1. One of these equations has principal part of the second kind, whereas that one of the other is of the first kind. Since any improvement of constructive methods requires higher regularity of u but, on the other hand, grad u possesses singularities at the collision points Γ1 ∩ Γ2 even for C∞ data, u is decomposed into special singular terms and a regular rest. This is incorporated into the integral equations and the modified system is solved in appropriate Sobolev spaces. The solution of the system requires to solve a Fredholm equation of the first kind on the arc Γ2 providing an improvement of regularity for the smooth part of u. Since the integral equations form a strongly elliptic system of pseudodifferential operators, the Galerkin procedure converges. Using regular finite element functions on Γ1 and Γ2 augmented by the special singular functions we obtain optimal order of asymptotic convergence in the norm corresponding to the energy norm of u and also superconvergence as well as high orders in smoother norms if the given data are smooth (and not the solution).

Notes: With the maximum principle for differential equations asymptotic estimates are made for a class of linear elliptic singular perturbation problems with resonant turning point behaviour in some of the independent variables. The method is applied to the stationary solution of the Kolmogorov backward equation in population genetics.

Notes: For the one-dimensional Nernst-Planck equations of the theory of ion-transport in thin layers or membranes which mathematically represent a nonlinear coupled parabolic integro-differential system some global existence and uniqueness theorems for inner and outer problems are given using a priori estimates of the maximum principle type.

Notes: The secondary wave motion in the free Ekman layer, on which a constant shear stress acts, is examined by an analytic method. The results show, that the waves move away from the center of rotation.

Notes: The initial value problem for the modified Vlasov equation with a mollification parameter δ 〉 0, as introduced by Batt, has a unique global solution in the weak sense whenever f0 ε L1 and f0 ≧ 0 λ-a.e. Assuming boundedness of f0 and boundedness of the kinetic energy, it is shown that, as δ → 0, there are subsequences δn → 0 such that the corresponding solutions converge weakly in the measure-theoretical sense. The limits are shown to be global weak solutions of the initial value problem for Vlasov's equation, and these solutions are seen to be weakly continuous with respect to t. For the plasma physical case, boundedness of the kinetic energy is a consequence of energy conservation.

Notes: This paper discusses a finite element approximation for an integral equation of the second kind deduced from a potential theory boundary value problem in two variables. The equation is shown to admit a unique solution, to be variational and coercive in the Hilbert space of functions σ ε H1/2(Γ), frd γ = 0. The Galerkin method with finite elements as trial functions is shown to lead to an optimal rate of convergence.

Notes: We describe in this paper a finite element method for the solution of viscous incompressible flow problems which incorporates an approximate form of the incompressibility condition automatically into the finite element basis. Several examples of such finite elements are presented and applied to a simple test problem.

Notes: The treatment of boundary value problems for Helmholtz equation and for the time harmonic Maxwell's equations by boundary integral equations leads to integral equations of the second kind which are uniquely solvable for small positive frequencies λ. However, the integral equations obtained in the limiting case λ = 0 which are related to boundary value problems of potential theory in general are not uniquely solvable since the corresponding boundary value problems are not. By first considering in a general setting of a Banach space X the limiting behaviour of solutions φλ to the equation φλ - K λ φ λ = fλ as λ → 0 where {Kλ: X → X, λ ∊ (0,α)}, α 〉 0, denotes a family of compact linear operators such that I - Kλ (I identity) is bijective for λ∊(0,α) whilst I - K0 is not and ‖ Kλ - K0‖ →, 0, ‖fλ - f0‖ → 0, λ → 0, and then applying the results to the boundary integral operators, the limiting behaviour of the integral equations is considered. Thus, the results obtained by Mac Camey for the Helmholtz equation are extended to the case of non-connected boundaries and Werner's results on the integral equations for the Maxwell's equations are extended to the case of multiply connected boundaries.

Notes: Let A be a selfadjoint uniformly elliptic differential operator. Let the underlying domain be bounded. Eigenvalue problems can be solved then, and an arbitrary square integrable function may be developed in a Fourier series relative to the eigenfunctions. In general elliptic differential operators have a continuous spectrum, if the underlying domain is unbounded. In this case the spectral theorem provides a representation of a given function by an integral transformation. The spectral projector can be calculated, if the outgoing and incoming solutions are known (radiation condition). Thus integral transformations may be derived very easily. Four examples will be given: the Fourier sine transform, the Lebedev transform, the transformation belonging to the Dirichlet problem of the plate equation and, finally, the Fourier transformation.

Notes: Mixed boundary value problems for the wave-equation in the x-y-plane, with boundaries parallel to the x-axis, are usually treated by Laplacetransformation. To use this method numerically we present it here by means of the Mikusiński-calculus. In this paper our main interest lies in the treatment of mixed initial-boundary value problems arising in unsteady subsonic cascade flow.

Notes: This paper deals with so-called general linear stochastic processes (GLSP), defined by T. Kawata in 1972 in generalization of work of R. Lugannani and J. B. Thomas of 1967/71. These second order processes (which are not necessarily stationary nor have independent increments) are described by rather weak requirements, so that several processes such as some random noise and pulse train processes are specific models of these GLSP. Part I is concerned with two general theorems giving asymptotic expansions (including those for the density function) in the central limit theorem for such GLSP, together with error rates. The assumptions for the corresponding θ- and o-error estimates seem rather natural: in the former, apart from assumptions on the inherent structure of such GLSP, the existence of certain moments of higher order as well as a Cramer-type condition are assumed, in the latter in addition a Lindeberg-type condition of higher order. Fourier analytic machinery is used for the proofs.

Notes: This part is concerned with the applications of the theorems on error estimates for asymptotic expansions in the central limit theorem for general linear stochastic processes of Part I to two important typical models. These are the general random noise process and a class of pulse train processes that occur in stochastic signal theory and in a variety of digital communication schemes. The assumptions on the inherent structure of the general theorems turn out to be simple here.

Notes: In this paper boundary controllability of one-dimensional vibrating system such as the vibrating string or the vibrating beam is studied. In particular we are concerned with the question whether it is possible to transfer a given initial state of vibration into rest within a given time such that the system stays in rest when the control is turned off.This problem is rephrased as a typical trigonometric moment problem which is solved within the framework of an abstract moment problem in a Hilbert space. The results of null-controllability which are obtained are substantially based on classical results of Ingham and Redheffer concerning trigonometric inequalities and incompleteness of certain sequences of trigonometric functions, respectively. The representation of the general statements follows closely the lines of a paper of Russell. Besides a special case is treated where explicit representations of boundary controls can be given that transfer the system to a permanent rest position. This special case includes amplitude boundary control of the vibrating string and the freely supported beam.

Notes: Given a semilinear reaction-diffusion equation. If the corresponding ordinary differential equation admits a convex compact positively invariant set and the boundary data assume their values in this set then the first and third boundary value problem have stationary solutions. The proofs are based on Weinberger's strong invariance principle, some related tools and the Leray-Schauder degree. The theorem is applied to several equations from theoretical biology, also in the case of distinct diffusion rates.

Notes: For any differential operator L, separable in some coordinate system, we construct a set of commuting operators Si such that 1) each Si maps solutions of Lu = 0 into solutions, and 2) the separated solutions of Lu = 0 are simultaneous eigenfunctions of Si. Moreover, a certain description of the separable coordinate system by Si is possible. The paper generalizes results obtained by W. Miller and others on many equations of mathematical physics.

Notes: We consider a family of semilinear evolution equations in Hilbert space of the form with, in general, unbounded operators *A(λ), F(λ·) depending analytically on a real parameter λ. We assume that the origin is a stationary solution, i.e. F(λ,0) = 0, for all λ ε R and that the linearization (with respect to u) at the origin is given by du/dt + A(λ)u = 0. Our essential assumption is the following: A(λ) possesses one pair of simple complex conjugate eigenvalues μ(λ) = Re μ(λ) ± i Im μ(λ) such that Im μ(0) 〉 0 and for some m ε N or If m = 1 the curves of eigenvalues μ(λ) cross the imaginary axis transversally at ±i Im μ(0). In this case a unique branch of periodic solutions emanates from the origin at λ = 0 which is commonly called Hopf bifurcation. If μ(λ) and the imaginary axis are no longer transversal, i.e. m 〉 1, we call a bifurcation of periodic solutions, if it occurs, a generalized Hopf bifurcation. It is remarkable that up to m such branches may exist. Our approach gives the number of bifurcating solutions, their direction of bifurcation, and its asymptotic expansion. We regain the results of D. Flockerzi who established them in a completely different way for ordinary differential equations.

Notes: Pulse mode sonar operation is analyzed under the assumption that the scattering object Γ lies in the far fields of both the transmitter and the receiver. It is shown that, in this approximation, the sonar signal is a plane wave s(x · θ0 - t) near Γ, where θ0 is a unit vector directed from the transmitter toward Γ, and similarly the echo is a plane wave e(x · θ - t) near the receiver, where θ is a unit vector directed from Γ toward the receiver. Moreover, if Γ is stationary with respect to the sonar system then it is shown that where š(ω) is the Fourier transform of S(τ) and T+(ωθ,ωθ0) is the scattering amplitude in the direction θ due to the scattering by Γ of a time-harmonic plane wave with frequence ω and propagation direction θ0. A generalization of this relation is derived for moving scatterers.

Notes: The existence of periodic solutions of general first order nonlinear difference-differential equations is shown using an appropriate cone of initial data and an asymptotic fixed point theorem.

Notes: We consider a simple model of a jet engine inlet consisting of two coaxial cylinders. The inner cylinder extends in both directions to infinity and represents the hub of a jet engine. The outer cylinder is assumed to be semiinfinite representing the engine's jacket. This arrangement is approached by a compressible and invisced gas moving at a velocity U less than the speed of sound. Two problems are formulated. In problem A a normal speed distribution is given in the compressor-inlet plane, in problem B we are given a pressure distribution. We look for the induced pressure and velocity fields. Using the acoustical approximation of the fundamental equations the Wiener-Hopf-method is applied then leading, after a multiplicative and additive decomposition procedure, to an infinite system of linear equations. These involve the expansion coefficients of the solution with respect to the eigenfunctions of the concentric cylindrical duct. Applying arguements from perturbation theory it is possible to extract the essential information from this system of equations. Apart from the possible exception of a denumerable set of values of the distance L of the blade-row from the inlet the problem has a unique solution.

Notes: If A is a symmetric 2 × 2-matrix, then the initial value problem describes the evolution in time of a fictive gas whose particles can move only with the velocities u1 and v2. It is proved that, for continuous initial values vanishing at infinity, (1) has a global solution if an H-Theorem holds for the gas described by (1). The validity of an H-Theorem is expressed by the properties of A.

Notes: In connection with the free boundary value problem of determining the earth's surface from measurements of gravitational potential and force-field (“the geodetic boundary problem”), an oblique derivative problem arises, where D0 is some bounded domain, star shaped with respect to the origin. In order to prove a uniquencess theorem for the geodetic boundary problem, it is essential to give estimates for (weighted) L2-norms of the second derivatives of the solutions so that their bounds can be estimated numerically if bounds for the function describing the boundary are known. In this paper a Fredholm inverse for the above problem is constructed and the second derivatives of the solutions are estimated in the desired form.

Notes: In plane domains with corners for the Bilaplacian a uniquely solvable conform variational principle is studied on weighted Sobolev spaces which is equivalent to the standard Dirichlet problem in the weak form. Clamped plates under point forces near corners are handled by this approach. With weighted Hsieh-Clough-Tocher elements on regular triangulations as conform C1-finite elements a new error analysis is performed without higher regularity assumptions on the exact solution than given by the data and the boundary. The rate of convergence of the error depends on the eigenvalue with smallest imaginary part of a clamped infinite wedge since this eigenvalue describes the singularity of the exact solution in a sector with same angle. Using different spaces of trial and test functions in the standard Galerkin procedure it is shown that the error in the weighted energy norm does not pollute. For convex corners asymptotic error estimates, are proved yielding convergence for a mixed method in hydrodynamics where the solution of a system of 2nd order and its Laplacian are approximated simultaneously by C0-finite elements being piecewise polynomials.

Notes: As, in general, the projections of characteristics into the x-space intersect for finite values of t, the global solution of a conservation law cannot be determined from the characteristic system of the equation, is considered. Only in the linear case, this equation coincides with the equation of the projections of characteristics. For convex h and all x0 this equation has a solution almost everywhere, and the properties of this solution permit to construct a global solution of the conservation law using strips, in the same way as this is done for linear problems by the method of characteristics.

Notes: The three-dimensional fluid flow of a steady or unsteady moving incompressible continuous medium is considered. Several Crocco-type transformations are applied which reduce the system of three equations of the Prandtl boundary layer to a system of two strongly coupled parabolic equations.

Notes: A bifurcation analysis is given for the generalized Bénard problem near the critical value of the Grashoff number. In contrast to earlier investigations where symmetry arguments were used to reduce the boundary-value-problem to a simple-eigenvalue-bifurcation, we only require double periodicity and treat high multiplicity bifurcation. It is shown that solutions of a yet unknown type exist.

Notes: We describe an iteration procedure in a Banach space which is quadratically convergent like Newton's method. In fact, it is a modification of the latter. The inverted derivatives are replaced by so-called contractors which are constructed recursively. Moreover, this method is extended to a scale of Banach spaces. It turns out that the rate of convergence remains quadratic, even if the norms of the contractors are increasing exponentially. A hard implicit function theorem results. In particular, this theorem can be applied to prove existence of quasiperiodic solutions for the Lorenz model of stationary convection.

Notes: We look for solutions of systems of nonlinear elliptic equations with nonlinear boundary conditions and values in some compact convex set M. If the nonlinear terms satisfy a sign condition on the boundary of M and the inhomogeneous terms assume their values in this set existence of solutions is proved.The proof is based on the homotopy invariance of the Leray-Schauder degree and Weinberger's strong maximum principle.

Notes: Ordinary bifurcation problems of the form (1) typically have at most one nontrivial, nonnegative solution for λ 〉 0. The paper shows that this is in general not true for discrete analogues to (1) no matter how small the step width h 〉 0 is chosen.

Notes: A minimal positive solution of the Thomas-Fermi problem ẅ = λt-1/2 w3/2, w(0) = 1, w(1) = w(1) is shown to exist for each λ 〉 0. It is proved that all positive solutions, for a given value of λ, are strictly ordered and that the minimal positive solution wλ is a decreasing function of λ. Upper and lower analytic bounds for wλ are given and these bounds are shown to initiate sequences of Picard and Newton iterates which converge monotonically to wλ. A comparative analysis of the efficiency of the iteration schemes is presented. The methods used are of a general nature and can be applied to a variety of nonlinear boundary value problems of convex type [14].

Notes: Bifurcation from the continuous spectrum of a linearized operator is of interest in many physical problems. For example it occurs in the nonlinear Klein-Gordon equation and in nonlinear integrodifferential equations as the Choquard problem; it further appears in nonlinear integral equations of the convolution type.A general theory enclosing all these problems is not yet known. To understand the basic phenomena, we therefore consider monotone differential operators whose linearisations have a purely continuous spectrum. It is shown that in fact the lowest point of the continuous spectrum is a bifurcation point, if the nonlinearity grows sufficiently strong.

Notes: Abstract Effects of different forest management policies on long-term vegetation development are incorporated into a computer simulation of a western Washington watershed. The response of a Rocky Mountain elk(Cervus canadensis nelsoni) population to these vegetation changes is simulated using information on their differential use of vegetation types. Simulations include: 1) a cessation of timber harvesting leading to an immediate decline in elk members resulting from a reduction in summer habitats; 2) a stable elk population, similar to the present one, resulting from a constant timber harvesting rate, and 3) initial increases in herd size, followed within 50 years by a sharp decrease, resulting from cutting all old growth timber within the next decade and then a cessation of timber harvestings.