Stochastic differential games with multiple modes

We have studied two person stochastic differential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the nonzero-sum case we have proved the existence of a Nash equilibrium.

Evolutionary games with two timescales

We consider a two timescale model of learning by economic agents wherein active or 'ontogenetic' learning by individuals takes place on a fast scale and passive or 'phylogenetic' learning by society as a whole on a slow scale, each affecting the evolution of the other. The former is modelled by the Monte Carlo dynamics of physics, while the latter is modelled by the replicator dynamics of evolutionary biology. Various qualitative aspects of the dynamics are studied in some simple cases, both analytically and numerically, and its role as a useful modelling device is emphasized.

Differential Games of Mixed Type with Control and Stopping Times

We study a zero sum differential game of mixed type where each player uses both control and stopping times. Under certain conditions we show that the value function for this problem exists and is the unique viscosity solution of the corresponding variational inequalities. We also show the existence of saddle point equilibrium for a special case of differential game.

A comparison of the molecular orbital (ab initio, CNDO and EHT) methods applied to the conformational study of thiocarbonohydrazide in its basic and diprotonated forms

Conformational preferences of thiocarbonohydrazide (H2NNHCSNHNH2) in its basic and N,N′-diprotonated forms are examined by calculating the barrier to internal rotation around the C---N bonds, using the theoretical LCAO—MO (ab initio and semiempirical CNDO and EHT) methods. The calculated and experimental results are compared with each other and also with values for N,N′-dimethylthiourea which is isoelectronic with thiocarbonohydrazide. The suitability of these methods for studying rotational isomerism seems suspect when lone pair interactions are present.

Multiresolution Area-based Fractal Dimension Estimation of Signals Applied to EEG Data

In this paper, we present an approach to estimate fractal complexity of discrete time signal waveforms based on computation of area bounded by sample points of the signal at different time resolutions. The slope of best straight line fit to the graph of log(A(rk)A / rk(2)) versus log(l/rk) is estimated, where A(rk) is the area computed at different time resolutions and rk time resolutions at which the area have been computed. The slope quantifies complexity of the signal and it is taken as an estimate of the fractal dimension (FD). The proposed approach is used to estimate the fractal dimension of parametric fractal signals with known fractal dimensions and the method has given accurate results. The estimation accuracy of the method is compared with that of Higuchi's and Sevcik's methods. The proposed method has given more accurate results when compared with that of Sevcik's method and the results are comparable to that of the Higuchi's method. The practical application of the complexity measure in detecting change in complexity of signals is discussed using real sleep electroencephalogram recordings from eight different subjects. The FD-based approach has shown good performance in discriminating different stages of sleep.

Incompressible boundary layer for longitudinal flow over a cylinder with an applied magnetic field

The flow, heat and mass transfer problem for a steady laminar incompressible boundary layer flow in an electrically conducting fluid over a longitudinal cylinder with an applied magnetic field has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The results are found to be strongly dependent on the magnetic field and dissipation parameter. The effect of the mass transfer is more pronounced on the skin friction than on the heat transfer. The results have been compared with those of the series solution, the asymptotic solution, the Glauert and Lighthill's solution, local similarity, local nonsimilarity and difference-differential methods. Good agreement is found with all of them, except with the results of the local similarity and series solution methods.

Multi-time scale analysis applied to long time simulation of power systems

The results are presented of applying multi-time scale analysis using the singular perturbation technique for long time simulation of power system problems. A linear system represented in state-space form can be decoupled into slow and fast subsystems. These subsystems can be simulated with different time steps and then recombined to obtain the system response. Simulation results with a two-time scale analysis of a power system show a large saving in computational costs.

Support vector machine applied to settlement of shallow foundations on cohesionless soils

The determination of settlement of shallow foundations on cohesionless soil is an important task in geotechnical engineering. Available methods for the determination of settlement are not reliable. In this study, the support vector machine (SVM), a novel type of learning algorithm based on statistical theory, has been used to predict the settlement of shallow foundations on cohesionless soil. SVM uses a regression technique by introducing an ε – insensitive loss function. A thorough sensitive analysis has been made to ascertain which parameters are having maximum influence on settlement. The study shows that SVM has the potential to be a useful and practical tool for prediction of settlement of shallow foundation on cohesionless soil.

Hormones and Cuscuta development: IAA uptake transport and metabolism in relation to growth in the absence and presence of applied cytokinin

Transport of 1-14C-IAA in successive stem segments of Cuscuta was strictly basipetal in growing and non growing regions of the vine with a flux velocity of 10-12 mm/h (intercept method). This transport showed a distinct peaked profile, increasing from a low value at 10 mm from the apex to a maximum between 50 and 90 mm before declining to a low value again around 160 mm at which elongation growth ceased. The IAA transport profile paralleled the in vivo growth rate profile, though the latter peaked ahead of transport. A better correlation was observed between the profile of growth responsiveness of the vine to exogenous IAA application and the profile of IAA transport. Growth responsiveness was determined as the differential in growth rate of stem segments in vitro in the absence and presence of growth optimal concentration of IAA (10 μm). Retention of exogenous IAA in the stem was maximal where transport decreased, and this coincided with the region of maximal conjugation of applied 1-14C-IAA to aspartic acid to form indoleacetylaspartate (IAAsp). In addition to aspartate, IAA was conjugated to a small extent to an unidentified compound. IAA destruction by decarboxylation was greatest where transport was low, particularly in the nongrowing region, where lignification occurred (i.e., beyond 180 mm). At concentrations up to 20 μM, a pulse of 1-14C-IAA chased by "cold" IAA moved as a peak (with a peak displacement velocity of 12-18 mm/h) in the "growth" region of the vine, but became diffusionlike where growth either fell off steeply or ceased. At a higher (50 μM) IAA concentration, though uptake was not saturated, transport in the growth region became diffusionlike, indicating saturation of the system. Reduced IAA flux in the region where growth responsiveness to IAA declined coincided with the region of increased IAA conjugation. However, it cannot be concluded whether increased IAA conjugation was the cause or effect of decreased IAA flux. Application of benzyladenine to the vines in vivo, a treatment that elicited haustoria formation by 72 h, resulted in the inhibition of both IAA transport and elongation growth rate in the subapical region. In vitro treatment of vine segments with BA similarly increased IAA retention and decreased IAA transport. IAA loss was suppressed, and conjugation to IAAsp was enhanced. © 1989 Springer-Verlag New York Inc.

Solution concepts in two-person multicriteria games

In this paper, we propose new solution concepts for multicriteria games and compare them with existing ones. The general setting is that of two-person finite games in normal form (matrix games) with pure and mixed strategy sets for the players. The notions of efficiency (Pareto optimality), security levels, and response strategies have all been used in defining solutions ranging from equilibrium points to Pareto saddle points. Methods for obtaining strategies that yield Pareto security levels to the players or Pareto saddle points to the game, when they exist, are presented. Finally, we study games with more than two qualitative outcomes such as combat games. Using the notion of guaranteed outcomes, we obtain saddle-point solutions in mixed strategies for a number of cases. Examples illustrating the concepts, methods, and solutions are included.

High temperature mechanical properties of thermal barrier coated superalloy applied to combustor liner of aero engines

High temperature load controlled fatigue, hot tensile and accelerated creep properties of thermal barrier coated (TBC) Superni C263 alloy used as a candidate material in combustor liner of aero engines are highlighted in this paper. Acoustic emission technique has been utilised to characterise the ductile-brittle transition teperature the bond coat. Results revealed that the DBTT (ductile to brittle transition temperature) of this bond coat is around 923 K, which is in close proximity to the value reported for CoCrAlY type of bond coat. Finite element technique, used for analysing the equivalent stresses in the bond coat well within the elastic limit, revealed the highest order of equivalent stress at 1073 K as the bond coat is ductile above 923 K. The endurance limit in fatigue and the life of TBC coated composite under accelerated creep conditions are substantially higher than those of the substrate material. Fractographic features at high stresses under fatigue showed intergranular cleavage whereas those at low stresses were transgranular and ductile in nature. Delamination of the bond coat and spallation of the TBC at high stresses during fatigue was evident. Unlike in the case of fatigue, the mode of fracture in the substrate at very high stresses was transgranular whereas that at low stresses was intergranular in creep.

Multicriterion differential games with applications to combat problems

In this paper a theory for two-person zero sum multicriterion differential games is presented. Various solution concepts based upon the notions of Pareto optimality (efficiency), security and equilibrium are defined. These are shown to have interesting applications in the formulation and analysis of two target or combat differential games. The methods for obtaining outcome regions in the state space, feedback strategies for the players and the mode of play has been discussed in the framework of bicriterion zero sum differential games. The treatment is conceptual rather than rigorous.