Planar pursuit-evasion with variable speeds, part 1, extremal trajectory maps

Pursuit evasion in a plane is formulated with both players allowed to vary their speeds between fixed limits. A suitable choice of real-space coordinates confers open-loop optimality on the game. The solution in the small is described in terms of the individual players'' extremal trajectory maps (ETM). Each map is independent of role, adversary, and capture radius. An ETM depicts the actual real-space trajectories. A template method of generating constant control arcs is described. Examples of ETM for an aircraft flying at a constant altitude with fixed and varying speeds are presented.

Planar pursuit-evasion with variable speeds, part 2, barrier sections

An iterative method of constructing sections of the game surfaces from the players'' extremal trajectory maps is discussed. Barrier sections are presented for aircraft pursuit-evasion at constant altitude, with one aircraft flying at sustained speed and the other varying its speed.

A note on the evaluation of dielectric dispersion parameters of non-debije type liquids

A simple method for evaluating dielectric relaxation parameters ie given whioh can be used for analyeing the arelaxation times of a liquid into two absorptions.

A Comparative Study of Electrochemical Kinetic Parameters by the Potential Step Method. Electrode Reactions of CyDTA and EDTA Complexes of Cu(II) at DME

By using the same current-time (I-t) curves, electrochemical kinetic parameters are determined by two methods, (a) using the ratio of current at a given potential to the diffusion-controlled limiting current and (b) curve fitting method, for the reduction of Cu(II)–CyDTA complex. The analysis by the method (a) shows that the rate determining step involves only one electron although the overall reduction of the complex involves two electrons suggesting thereby the stepwise reduction of the complex. The nature of I-t curves suggests the adsorption of intermediate species at the electrode surface. Under these circumstances more reliable kinetic parameters can be obtained by the method (a) compared to that of (b). Similar observations are found in the case of reduction of Cu(II)–EDTA complex.

Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.

The problem of liquid droplet combustion-reexamination

The simple quasi-steady analysis of the combustion of a liquid fuel droplet in an oxidising atmosphere provides unsatisfactory explanations for several experimental observations. It's prediction of values for the burning constant (K), the flame-to-droplet diameter ratio ( ) and the flame temperature (Tf) have been found to be amgibuous if not completely inaccurate. A critical survey of the literature has led us to a detailed examination of the effects of unsteadiness and variable properties. The work published to date indicates that the gas-phase unsteadiness is relatively short and therefore quite insignificant.A new theoretical analysis based on heat transfer within the droplet is presented here. It shows that the condensed-phase unsteadiness lasts for about 20â??25% of the total burning time. It is concluded that the discrepancies between experimental observations and the predictions of the constant-property quasi-steady analysis cannot be attributed either to gas-phase or condensed-phase unsteadiness.An analytical model of quasi-steady droplet combustion with variable thermodynamic and transport properties and non-unity Lewis numbers will be examined. Further findings reveal a significant improvement in the prediction of combustion parameters, particularly of K, when consideration is given to variations of cp and λ with the temperature and concentrations of several species. Tf is accurately predicted when the required conditions of incomplete combustion or low ( ) at the flame are met. Further refinement through realistic Lewis numbers predicts ( ) meaningfully.

An imprecise fuzzy risk approach for water quality management of a river system

Uncertainty plays an important role in water quality management problems. The major sources of uncertainty in a water quality management problem are the random nature of hydrologic variables and imprecision (fuzziness) associated with goals of the dischargers and pollution control agencies (PCA). Many Waste Load Allocation (WLA)problems are solved by considering these two sources of uncertainty. Apart from randomness and fuzziness, missing data in the time series of a hydrologic variable may result in additional uncertainty due to partial ignorance. These uncertainties render the input parameters as imprecise parameters in water quality decision making. In this paper an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system subject to uncertainty arising from partial ignorance. In a WLA problem, both randomness and imprecision can be addressed simultaneously by fuzzy risk of low water quality. A methodology is developed for the computation of imprecise fuzzy risk of low water quality, when the parameters are characterized by uncertainty due to partial ignorance. A Monte-Carlo simulation is performed to evaluate the imprecise fuzzy risk of low water quality by considering the input variables as imprecise. Fuzzy multiobjective optimization is used to formulate the multiobjective model. The model developed is based on a fuzzy multiobjective optimization problem with max-min as the operator. This usually does not result in a unique solution but gives multiple solutions. Two optimization models are developed to capture all the decision alternatives or multiple solutions. The objective of the two optimization models is to obtain a range of fractional removal levels for the dischargers, such that the resultant fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision making. The methodology is demonstrated with a case study of the Tunga-Bhadra river system in India.

A thymine-related mutation system in immunoglobulin variable regions

Abstract is not available.

An approximate mathematical procedure for the determination of characteristic parameters for a general case in three dimensional photoelasticity

In cases whazo zotatLon of the seoondazy pztncipal 8tzo,ae axes along tha light path ,exists, it is always poaeible to detezmlna two dizactions along which plane-polazlaad light ,antazlng the model ,amerCe8 as plene-pela~l,aed light fzom the model. Puzth,az the nat zstazdatton Pot any light path is dlff,azant Prom the lntsgtatad zetazd,ation Pat the l£ght path nogZsctlng the ePfsct or z,atation.

On the stabilization of uniformly decoupled systems by state variable feedback

Conditions under which the asymptotic stabilization of uniformly decoupled time-varying multivariate systems is possible are explored. This is accomplished by developing a canonical form for integrator uniformly decoupled system in which the coefficient matrices have a simple structure. The procedures developed rely on certain conditions on the given system and yield explicit expressions for the stabilization compensators.

A Finite Variable Difference Relaxation Scheme for hyperbolic-parabolic equations

Using the framework of a new relaxation system, which converts a nonlinear viscous conservation law into a system of linear convection-diffusion equations with nonlinear source terms, a finite variable difference method is developed for nonlinear hyperbolic-parabolic equations. The basic idea is to formulate a finite volume method with an optimum spatial difference, using the Locally Exact Numerical Scheme (LENS), leading to a Finite Variable Difference Method as introduced by Sakai [Katsuhiro Sakai, A new finite variable difference method with application to locally exact numerical scheme, journal of Computational Physics, 124 (1996) pp. 301-308.], for the linear convection-diffusion equations obtained by using a relaxation system. Source terms are treated with the well-balanced scheme of Jin [Shi Jin, A steady-state capturing method for hyperbolic systems with geometrical source terms, Mathematical Modeling Numerical Analysis, 35 (4) (2001) pp. 631-645]. Bench-mark test problems for scalar and vector conservation laws in one and two dimensions are solved using this new algorithm and the results demonstrate the efficiency of the scheme in capturing the flow features accurately.

On the relationship of thermodynamic parameters with the buried surface area in protein-ligand complex formation

Prediction of thermodynamic parameters of protein-protein and antigen-antibody complex formation from high resolution structural parameters has recently received much attention, since an understanding of the contributions of different fundamental processes like hydrophobic interactions, hydrogen bonding, salt bridge formation, solvent reorganization etc. to the overall thermodynamic parameters and their relations with the structural parameters would lead to rational drug design. Using the results of the dissolution of hydrocarbons and other model compounds the changes in heat capacity (DeltaCp), enthalpy (DeltaH) and entropy (DeltaS) have been empirically correlated with the polar and apolar surface areas buried during the process of protein folding/unfolding and protein-ligand complex formation. In this regard, the polar and apolar surfaces removed from the solvent in a protein-ligand complex have been calculated from the experimentally observed values of changes in heat capacity (DeltaCp) and enthalpy (DeltaH) for protein-ligand complexes for which accurate thermodynamic and high resolution structural data are available, and the results have been compared with the x-ray crystallographic observations. Analyses of the available results show poor correlation between the thermodynamic and structural parameters. Probable reasons for this discrepancy are mostly related with the reorganization of water accompanying the reaction which is indeed proven by the analyses of the energetics of the binding of the wheat germ agglutinin to oligosaccharides.

Effect of soil variability on the bearing capacity of clay and in slope stability problems

Site-specific geotechnical data are always random and variable in space. In the present study, a procedure for quantifying the variability in geotechnical characterization and design parameters is discussed using the site-specific cone tip resistance data (qc) obtained from static cone penetration test (SCPT). The parameters for the spatial variability modeling of geotechnical parameters i.e. (i) existing trend function in the in situ qc data; (ii) second moment statistics i.e. analysis of mean, variance, and auto-correlation structure of the soil strength and stiffness parameters; and (iii) inputs from the spatial correlation analysis, are utilized in the numerical modeling procedures using the finite difference numerical code FLAC 5.0. The influence of consideration of spatially variable soil parameters on the reliability-based geotechnical deign is studied for the two cases i.e. (a) bearing capacity analysis of a shallow foundation resting on a clayey soil, and (b) analysis of stability and deformation pattern of a cohesive-frictional soil slope. The study highlights the procedure for conducting a site-specific study using field test data such as SCPT in geotechnical analysis and demonstrates that a few additional computations involving soil variability provide a better insight into the role of variability in designs.

The pulse response of non-linear third order systems

The response of a third order non-linear system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form in which the method of variation of parameters is applicable for the solution of the problem. The method is applied to a single axis gyrostabilized platform subjected to an exponentially decaying pulse. The analytical results are compared with digital and analog computer solutions.