estimation of discontinuous coefficients in parabolic systems applications to reservoir simulation we present spline based techniques for estimating spatially varying parameters that appear in parabolic distributed systems typical of those found in reservoir simulation problems in particular we discuss the problem of determining discontinuous coefficients estimating both the functional shape and points of discontinuity for such parameters in addition our ideas may also be applied to problems with unknown initial conditions and unknown parameters appearing in terms representing external forces convergence results and a summary of numerical performance of the resulting algorithms are given

estimation of parameters in two dimensional transport equations a general approximation framework based on bicubic splines is developed for estimating temporally and spatially varying parameters in two dimensional transport equations the parameter estimation problem is first cast as an abstract infinite dimensional minimization problem then a sequence of approximate finite dimensional minimization problems is defined which yields a sequence of parameter estimates since convergence results relating the approximate problems to the full infinite dimensional problem are presented in 6 and 17 this paper will focus only on the computer implementation of our technique and the results of numerical tests using analytically generated data the technique is also applied to the analysis of actual biological data from an insect dispersal experiment in which the movement of cabbage root flies in the presence of a cabbage crop was studied

cubic spline approximation techniques for parameter estimation in distributed systems approximation schemes employing cubic splines in the context of a linear semigroup framework are developed for both parabolic and and hyperbolic second order partial differential equation parameter estimation problems convergence results are established for problems with linear and nonlinear systems and a summary of numerical experiments with the techniques proposed is given

estimation of nonlinearities in parabolic models for growth predation and dispersal of populations a convergence theory is given for approximation techniques to treat inverse problems involving systems of nonlinear parabolic partial differential equations these techniques can be used to estimate density dependent dispersal coefficients in population models as well as nonlinear growth and predation terms numerical experiences with the resulting algorithms on both conventional scalar and vector computers are reported along with an indication of performance of the methods with field data from prey predator experiments

a diffusion problem on a semi infinite interval approximate solutions and parameter estimations on considere le probleme de diffusion canonique pour x 0 t 0 u t x t k 2 q u xx x t f q x t u u x o f x q u o t 0 u x t dans l 2 0 q estun vecteur fixe et peut representer des parametres inconnus

fundamental triangular norm based tribes and measures abstract we complete the results of butnariu and klement about t s tribes and t s measures where t s s 0 is a frank s fundamental triangular norm for a denumerable universum x we show that any t s tribe is a semigenerated one and hence any t s measure is a generated one

free vibrations of a non uniform beam with general elastically restrained boundary conditions abstract a simple and efficient method is presented to study the problem of free vibration of a non uniform bernoulli euler beam with general elastic restraints at boundary points with one set of particularly chosen fundamental solutions of the system the frequency equation is derived and expressed in concise form if the closed form fundamental solutions of the system are not available the approximate fundamental solutions can be obtained through a newly developed algorithm which is shown to be efficient convenient and accurate finally several limiting cases of the general system are examined and some examples are presented to illustrate the validity and accuracy of the proposed method

entropy of fuzzy partitions a general model abstract the entropy of fuzzy partitions with regard to a fuzzy measure is analyzed a general model based on pseudo arithmetical operations and g functions will be created the entropy of fuzzy partitions introduced by ruspini inform and control 15 1969 22 and dumitrescu j math anal appl 176 1993 359 is shown to be reasonable only up to an isomorphism

frequency domain sample maximum likelihood estimation for spatially dependent parameter estimation in pdes the identification of the spatially dependent parameters in partial differential equations pdes is important in both physics and control problems a methodology is presented to identify spatially dependent parameters from spatio temporal measurements local non rational transfer functions are derived based on three local measurements allowing for a local estimate of the parameters a sample maximum likelihood estimator smle in the frequency domain is used because it takes noise properties into account and allows for high accuracy consistent parameter estimation confidence bounds on the parameters are estimated based on the noise properties of the measurements this method is successfully applied to the simulations of a finite difference model of a parabolic pde with piecewise constant parameters

an algebraic generalization of the notion of tribe tribes became a successful basis of measure theory on fuzzy sets during their investigation new requirements arose we discuss possible modifications of the original definition of a tribe we suggest a more general structure which admits to apply different triangular norms in different parts emphasis is put on point free notions

estimation of variable coefficients in the fokker planck equations using moving node finite elements inverse problems are considered for the estimation of temporally and spatially varying coefficients in the fokker planck or forward kolmogorov equation that often arise in size age structured population models these are difficult problems even for simulation studies since they share certain numerical difficulties with transport dominated diffusion convection problems of fluid dynamics these difficulties stem from the fact that when the convection is large compared to the diffusion both traditional finite difference or finite element methods produce erroneous oscillatory solutions in this paper computational techniques are presented that combine a variation of the moving finite element method with spline approximations for the parameter estimation problems computational details of our numerical algorithm along with theoretical convergence results are presented several numerical examples illustrating the effectiveness of the method are also given

fitting numerical solutions of differential equations to experimental data a case study and some general remarks summary a simple and efficient algorithm for least squares estimation of the parameters of a numerically solved diffusion model is presented the algorithm has been specially developed for the analysis of data obtained by vitreous fluorophotometry a method in clinical eye research but it has several straightforward generalizations which are also outlined in the paper it happens that these equations are difficult or impossible to solve explicitly and that numerical methods are employed often it is desired to estimate the parameters of such models from experimental data using the method of least squares or one of its relatives the main body of differential equation models in biometry consists of initial value problems for systems of ordinary differential equations such as occur in compartment models but also partial differential equations appear banks and kareiva 1983 discuss the transport of glucose in the cat brain as well as deterministic population dynamic models for insect dispersal the current study deals with the transport of a fluorescent dye in the vitreous body of the human eye and in general questions of diffusion or heat transfer involve similar equations further applications might include fluid flow problems or equations of elasticity in biomechanics since numerical methods for the solution of partial differential equations are computationally demanding it is important to choose an efficient algorithm for the estimation of model parameters particularly in situations where the algorithm is to be applied many times for instance when several curves are to be fitted for each examination of each patient as part of an interactive routine for coordination of data from different sources the current study deals with vitreous fluorophotometry a method in clinical eye research where the model involves the diffusion equation and the parameters are the diffusion coefficient in the vitreous body of the eye and the permeability of the blood retinal barrier the data are concentration measurements in the vitreous body we have found that for this

an approximation theory for nonlinear partial differential equations with applications to identification and control approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations these ideas are used to establish theoretical convergence results for parameter identification using modal eigenfunction approximation techniques results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given

pseudofundamental triangular norms and g t tribes abstract we generalize the theory of t tribes of butnariu and klement this generalization may serve as a basis of a common theory of t measures and decomposable measures of fuzzy events

reduction of distributed system identification complexity using intelligent sensors abstract the identification problems of distributed parameter systems dps is dealt with a special method of data collection by using moving sensors is proposed the sensors are intelligent in the sense that they are able to track the positions of the exiremum values of a system state at each time instant it is shown how to reduce the identification problem for dps to that of identifying a certain system described by ordinary differential equations ode the proposed approach is applicable to the dps described by quasi linear partial differential equations of the hyperbolic type attention is focused on the problem of reduction while the identification of the resulting ode is not considered in detail since it is an easier task

an iterative procedure for estimation of variable coefficients in a hyperbolic system a parameter estimation problem for the acoustic wave equation in a multidimensional bounded domain with absorbing boundary conditions depending on the parameter is solved by using quasilinearization techniques results on the frechet differentiability of the solution with respect to the parameter are derived by applying the energy method an iterative procedure employing quasilinearization at each iteration step is given to solve the estimation problem results on the convergence of the method are presented numerical examples illustrate the application of our algorithm

estimation of variable coefficients in parabolic distributed systems we present techniques based on cubic spline approximations for estimating coefficients e g diffusion convector velocity etc depending on time and the spatial variable in parabolic distributed systems such as those that arise in transport models convergence results and a summary of numerical performance of the resulting algorithms are given

a characterization of the ordering of continuous t norms abstract given two t norms t 1 and t 2 it is quite often difficult or even impossible to check directly whether t 1 t 2 in schweizer and sklar 1983 a necessary and sufficient condition is given for continuous archimedean t norms to be comparable we simplify this result proving a sufficient condition which involves only one argument of a one place function rather than two arguments this result is applied to show the monotonicity of some well known classes of t norms next we generalize the result of schweizer and sklar to the case of all continuous t norms and present also a sufficient condition which is again easier to check