kato class measures of symmetric markov processes under heat kernel estimates abstract we establish the coincidence of two classes of kato class measures in the framework of symmetric markov processes admitting upper and lower estimates of heat kernel under mild conditions one class of kato class measures is defined by way of the heat kernel another is defined in terms of the green kernel depending on some exponents related to the heat kernel estimates we also prove that p th integrable functions on balls with radius 1 having a uniformity of its norm with respect to centers are of kato class if p is greater than a constant related to the estimate under the same conditions these are complete extensions of some results for the brownian motion on euclidean space by aizenman and simon our result can be applicable to many examples for instance symmetric relativistic stable processes jump processes on d sets brownian motions on riemannian manifolds diffusions on fractals and so on

recovering exponential accuracy from collocation point values of smooth functions with end point singularities gibbs phenomenon is the particular manner how a global spectral approximation of a piecewise analytic function behaves at the jump discontinuity the truncated spectral series has large oscillations near the jump and the overshoot does not decay as the number of terms in the truncated series increases there is therefore no convergence in the maximum norm and convergence in smooth regions away from the discontinuity is also slow in gottlieb and shu 1995 5 a methodology is proposed to completely overcome this difficulty in the context of spectral collocation methods resulting in the recovery of exponential accuracy from collocation point values of a piecewise analytic function in this paper we extend this methodology to handle spectral collocation methods for functions which are analytic in the open interval but have singularities at end points with this extension we are able to obtain exponential accuracy from collocation point values of such functions similar to gottlieb and shu 1995 5 the proof is constructive and uses the gegenbauer polynomials c n l x the result implies that the gibbs phenomenon can be overcome for smooth functions with endpoint singularities

an asymptotic solution for two phase flow in the presence of capillary forces 1 under the assumption of smoothly varying background properties i derive an asymptotic solution for two phase flow this formulation partitions the modeling of two phase flow into two subproblems an arrival time calculation and a saturation amplitude computation the asymptotic solution itself is defined along a trajectory though the model if gravitational forces are not important and the flow field is independent of changes in the background saturation the trajectory may be identified with a streamline and the asymptotic approach provides a mathematical basis for streamline simulation the evolution of the saturation amplitude is governed by a generalization of burgers equation defined along the trajectory if the capillary properties are uniform and gravitational forces are negligible one can derive self similar solutions for the three limiting behaviors of a two phase front asymptotic solutions were found to deviate by less than 5 from saturations calculated using a numerical simulator the numerical results indicate that changes in capillary properties can introduce significant variations in the arrival time of a specific aqueous fraction a more robust definition of arrival time appears to be the time associated with the peak rate of change in aqueous phase fraction the greatest slope of the breakthrough curve

on the gibbs phenomenon i recovering exponential accuracy from the fourier partial sum of a nonperiodic analytic function it is well known that the fourier series of an analytic and periodic function truncated after 2n 1 terms converges exponentially with n even in the maximum norm it is also known that if the function is not periodic the rate of convergence deteriorates in particular there is no convergence in the maximum norm although the function is still analytic this is known as the gibbs phenomenon in this paper we show that the first 2n 1 fourier coefficients contain enough information about the function so that an exponentially convergent approximation in the maximum norm can be constructed the proof is a constructive one and makes use of the gegenbauer polynomials c n x it consists of two steps in the first step we show that the first m coefficients of the gegenbauer expansion based on c n x for 0 n m of any l2 function can be obtained within exponential accuracy provided that both and m are proportional to but smaller than n in the second step we construct the gegenbauer expansion based on c n 0 n m from the coefficients found in the first step we show that this series converges exponentially with n provided that the original function is analytic though nonperiodic thus we prove that the gibbs phenomenon can be completely overcome

an averaging method for the fourier approximation to discontinuous functions both the truncated fourier integral and the truncated fourier series approximations for a discontinuous function bring about the inevitable oscillating error say the gibbs phenomenon most basic filtering methods for the gibbs phenomenon like the fejer averaging method and the lanczos averaging method have a disadvantage that the rise time is very slow even though the filtering effect is prominent away from the discontinuity in this paper we propose a new averaging method of polynomial type which improves the rise time of the existing method the present method can be regarded as a generalization of the traditional lanczos averaging method by several numerical examples we show the efficiency of the present method

advection diffusion past a strip i normal incidence the concentration p x y of particles moving by diffusion and advection or drift is analyzed the motion is impeded by an impenetrable strip that is parallel to the z axis it is assumed that p satisfies the linear advection diffusion equation with a boundary condition on the strip it is also assumed that p 1 at infinity this problem is solved asymptotically for vl d 1 where v is the drift velocity d is the diffusion coefficient and 2l is the strip width it is found that p is large on the side of the strip facing the incident flow that p is small in the shadow behind the strip and that p is nearly constant elsewhere the case of a strip normal to the incident flow is rather different from that of a strip oblique to the flow methods of asymptotic analysis are used

ray theory for high peclet number convection diffusion asymptotic methods based on those of geometrical optics are applied to some steady convection diffusion streamed flows at a high peclet number even with the assumption of inviscid irrotational flow past a body with uniform ambient conditions the rays from which the solution is constructed can only be found after local analyses have been carried out near the stagnation points in simple cases the temperature away from the body is the sum of contributions from each stagnation point

relativistic schrodinger operators asymptotic behavior of the eigenfunctions nonrelativistic schrodinger operators are perturbations of the negative laplacian and the connection with stochastic processes and brownian motion in particular is well known and usually goes under the name of feynman and kac we present a similar connection between a class of relativistic schrodinger operators and a class of processes with stationary independent increments in particular we investigate the decay of the eigenfunctions of these operators and we show that not only exponential decay but also polynomial decay can occur

absorption semigroups their generators and schrodinger semigroups on presente des resultats de perturbations pour des c 0 semi groupes on considere le probleme aux valeurs initiales pour l equation de la chaleur avec absorption avec une solution dans l p r v avec une mauvaise fonction v r r on considere le meme probleme dans l 2 r pour l equation de schrodinger

on schrodinger semigroups and related topics abstract this paper deals with two related subjects in the first part we give generation theorems relying on weak compactness arguments for perturbed positive semigroups in general ordered banach spaces with additive norm on the positive cone the second part provides new functional analytic developments on semigroup theory for schrodinger operators in l p spaces with l 1 bounded potentials without restriction on the l 1 bound in particular our formalism enlarges a priori the classical kato class and its subsequent refinements the connection with form perturbation theory is also dealt with

a strategy for choosing gegenbauer reconstruction parameters for numerical stability the gegenbauer reconstruction method was first proposed in 1992 but in early studies no attempts were made to optimize the relevant parameters of this method these parameters were allowed to grow proportionally with the number of nodes which in many cases resulted in exponential convergence for a selected range of the proportionality constants early studies also made clear that very large error bounds could be expected if these key parameters were not chosen carefully subsequent studies then pointed out that although unrelated to the method s analytically predictable domains of poor accuracy round off errors could also sabotage the method s accuracy the challenge of successfully implementing a gegenbauer reconstruction then rests on understanding the performance trade offs we can expect when choosing the key parameters in accordance with different objectives in this study we propose a new strategy for choosing optimal parameters in the chebyshev gegenbauer reconstruction method specifically to achieve numerical stability this strategy is based on asymptotic analysis as well as minimization problems in one and two dimensions the effectiveness of our approach which could also be applied to a wider selection of polynomials is then illustrated with results from numerical experiments

resolution properties of the fourier method for discontinuous waves in this paper we discuss the wave resolution properties of the fourier approximations of a wave function with discontinuities it is well known that a minimum of two points per wave is needed to resolve a periodic wave function using fourier expansions for chebyshev approximations of a wave function a minimum of points per wave is needed see numerical analysis of spectral methods theory and applications by d gottlieb and s orszag here we obtain an estimate for the minimum number of points per wave to resolve a discontinuous wave based on its fourier coefficients in our recent work on overcoming the gibbs phenomenon we have shown that the fourier coefficients of a discontinuous function contain enough information to reconstruct with exponential accuracy the coefficients of a rapidly converging gegenbauer expansion we therefore study the resolution properties of a gegenbauer expansion where both the number of terms and the order increase

a full bayesian approach to parameter inference from tracer travel time moments and investigation of scale effects at the cape cod experimental site a method for inverting the travel time moments of solutes in heterogeneous aquifers is presented and is based on peak concentration arrival times as measured at various samplers in an aquifer the approach combines a lagrangian rubin and dagan 1992 solute transport framework with full bayesian hydrogeological parameter inference in the full bayesian approach the noise values in the observed data are treated as hyperparameters and their effects are removed by marginalization the prior probability density functions pdfs for the model parameters horizontal integral scale velocity and log k variance and noise values are represented by prior pdfs developed from minimum relative entropy considerations analysis of the cape cod massachusetts field experiment is presented inverse results for the hydraulic parameters indicate an expected value for the velocity variance of log hydraulic conductivity and horizontal integral scale of 0 42 m d 0 26 and 3 0 m respectively while these results are consistent with various direct field determinations the importance of the findings is in the reduction of confidence range about the various expected values on selected control planes we compare observed travel time frequency histograms with the theoretical pdf conditioned on the observed travel time moments we observe a positive skew in the travel time pdf which tends to decrease as the travel time distance grows we also test the hypothesis that there is no scale dependence of the integral scale with the scale of the experiment at cape cod we adopt two strategies the first strategy is to use subsets of the full data set and then to see if the resulting parameter fits are different as we use different data from control planes at expanding distances from the source the second approach is from the viewpoint of entropy concentration no increase in integral scale with distance is inferred from either approach over the range of the cape cod tracer experiment

detection of edges in spectral data ii nonlinear enhancement we discuss a general framework for recovering edges in piecewise smooth functions with finitely many jump discontinuities where f x f x f x neq 0 our approach is based on two main aspects localization using appropriate concentration kernels and separation of scales by nonlinear enhancement to detect such edges one employs concentration kernels k epsilon cdot depending on the small scale epsilon it is shown that odd kernels properly scaled and admissible in the sense of having small w 1 infty moments of order cal o epsilon satisfy k epsilon f x f x cal o epsilon thus recovering both the location and amplitudes of all edges as an example we consider general concentration kernels of the form k sigma n t sum sigma k n sin kt to detect edges from the first 1 epsilon n spectral modes of piecewise smooth f s here we improve in generality and simplicity over our previous study in a gelb and e tadmor appl comput harmon anal 7 1999 pp 101 135 both periodic and nonperiodic spectral projections are considered we identify in particular a new family of exponential factors sigma exp cdot with superior localization properties the other aspect of our edge detection involves a nonlinear enhancement procedure which is based on separation of scales between the edges where k epsilon f x sim f x neq 0 and the smooth regions where k epsilon f cal o epsilon sim 0 numerical examples demonstrate that by coupling concentration kernels with nonlinear enhancement one arrives at effective edge detectors

legendre pseudospectral viscosity method for nonlinear conservation laws in this paper the legendre spectral viscosity sv method for the approximate solution of initial boundary value problems associated with nonlinear conservation laws is studied the authors prove that by adding a small amount of sv bounded solutions of the legendre sv method converge to the exact scalar entropy solution the convergence proof is based on compensated compactness arguments and therefore applies to certain 2 times 2 systems finally numerical experiments for scalar as well as the one dimensional system of gas dynamics equations are presented which confirm the convergence of the legendre sv method moreover these numerical experiments indicate that by post processing the sv approximation one can recover the entropy solution within spectral accuracy

conditional estimation of solute travel time in heterogeneous formations impact of transmissivity measurements solute transport through heterogeneous formations is modeled by the travel time approach i e the time it takes a solute particle to travel from the source to a control plane due to uncertainty is a random variable characterized by its cumulative probability density function g this function is used by regulatory agencies in pollution site assessment the main aim of the present study is to examine the impact of data namely measured transmissivities upon g and reduction of uncertainty this is achieved for two dimensional steady flow of average uniform head gradient by using a lagrangian approach developed in the past dagan 1982 1984 1989 rubin 1990 1991 the impact of data is seen in conditioning on measured values and in estimation of parameters characterizing flow and formation properties the approach is illustrated by a simulation based on synthetic data the results show how uncertainty is reduced by increasing the density of measurements for a control plane sufficiently far from the source

on the gibbs phenomenon and its resolution the nonuniform convergence of the fourier series for discontinuous functions and in particular the oscillatory behavior of the finite sum was already analyzed by wilbraham in 1848 this was later named the gibbs phenomenon this article is a review of the gibbs phenomenon from a different perspective the gibbs phenomenon as we view it deals with the issue of recovering point values of a function from its expansion coefficients alternatively it can be viewed as the possibility of the recovery of local information from global information the main theme here is not the structure of the gibbs oscillations but the understanding and resolution of the phenomenon in a general setting the purpose of this article is to review the gibbs phenomenon and to show that the knowledge of the expansion coefficients is sufficient for obtaining the point values of a piecewise smooth function with the same order of accuracy as in the smooth case this is done by using the finite expansion series to construct a different rapidly convergent approximation

numerical trajectory calculations for the efficient inversion of transient flow and tracer observations 1 we introduce a trajectory based method for the inversion of flow and transport observations the approach operates on the output of a standard numerical simulator and is applicable under very general conditions using only head and concentration histories we efficiently construct the model parameter sensitivities required for solving the inverse problem a single simulation or forward calculation is required in order to take a step in the inversion our formulation based on asymptotic solutions for flow and transport partitions the inverse problem into an arrival time and an amplitude matching problem because the model parameter sensitivities are defined along trajectories both inverse problems scale very well with respect to model size at the migration experimental site of the grimsel rock laboratory in switzerland we utilized transient head and tracer arrival times to constrain the hydraulic conductivity between a suite of boreholes the squared data misfit is reduced by over an order of magnitude in 30 iterations of our inversion algorithm each iteration requires two runs of our numerical simulator tough2 one for each experiment to construct the trajectories and associated model parameter sensitivities we find a high conductivity channel curving in a roughly east west direction in agreement with two previous studies estimates of model parameter resolution indicate that we can image the large scale conductivity variations within the array of boreholes

perturbation of dirichlet forms lower semiboundedness closability and form cores we study perturbations e e qu of dirichlet forms e on some l2 space l2 m given by quadratic forms q g g d with a signed borel measure whose positive and negative parts are smooth measures with respect to the given dirichlet form we give necessary and sufficient conditions for e to be a lower semibounded closed quadratic form with a unique associated continuous semigroup pt on l2 m we also study the associated resolvent semigroup as well as the relation between e and the largest closed quadratic form which is smaller than e in particular we exhibit form cores

a probabilistic principle and generalized schrodinger perturbation abstract we present a probabilistic principle for an additive functional of certain markov processes its smallness with time is equivalent to its smalness with space and apply it to a perturbation problem for relativistic schrodinger operators

on subordinated holomorphic semigroups if e is a uniformly bounded c0 semigroup on a complex banach space x then a 0 a 1 generates a holomorphic semigroup on x and e is subordinated to e through the levy stable density function this was proved by yosida in 1960 by suitably deforming the contour in an inverse laplace transform representation using other methods we exhibit a large class of probability measures such that the subordinated semigroups are always holomorphic and obtain a necessary condition on the measure s laplace transform for that to be the case we then construct probability measures that do not have this property

fast marching methods fast marching methods are numerical schemes for computing solutions to the nonlinear eikonal equation and related static hamilton jacobi equations based on entropy satisfying upwind schemes and fast sorting techniques they yield consistent accurate and highly efficient algorithms they are optimal in the sense that the computational complexity of the algorithms is o n log n where n is the total number of points in the domain the schemes are of use in a variety of applications including problems in shape offsetting computing distances from complex curves and surfaces shape from shading photolithographic development computing first arrivals in seismic travel times construction of shortest geodesics on surfaces optimal path planning around obstacles and visibility and reflection calculations in this paper we review the development of these techniques including the theoretical and numerical underpinnings provide details of the computational schemes including higher order versions and demonstrate the techniques in a collection of different areas

analysis and application of fourier gegenbauer method to stiff differential equations the fourier gegenbauer fg method introduced by gottlieb shu solomonoff and vandeven icase report 92 4 hampton va 1992 is aimed at removing the gibbs phenomenon that is recovering the point values of a nonperiodic function from its fourier coefficients in this paper we discuss some numerical aspects of the fg method related to its em pseudospectral implementation in particular we analyze the behavior of the gegenbauer series with a moderate several hundred number of terms suitable for computations we also demonstrate the ability of the fg method to get a spectrally accurate approximation on small subintervals for rapidly oscillating functions or functions having steep profiles bearing on the previous analysis we suggest a high order spectral fourier method for the solution of nonperiodic differential equations it includes a polynomial subtraction technique to accelerate the convergence of the fourier series and the fg algorithm to evaluate derivatives on the boundaries of nonperiodic functions the present hybrid fourier gegenbauer hfg method possesses better resolution properties than the original fg method the precision of this method is demonstrated by solving stiff elliptic problems with steep solutions

impossibility of fast stable approximation of analytic functions from equispaced samples it is shown that no stable procedure for approximating functions from equally spaced samples can converge exponentially for analytic functions to avoid instability one must settle for root exponential convergence the proof combines a bernstein inequality of 1912 with an estimate due to coppersmith and rivlin in 1992

on the gibbs phenomenon iv recovering exponential accuracy in a subinterval from a gegenbauer partial sum of a piecewise analytic function we continue the investigation of overcoming gibbs phenomenon i e obtaining exponential accuracy at all points including at the discontinuities themselves from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function we show that if we are given the first n expansion coefficients of an l 2 function f x in terms of either the trigonometrical polynomials or the chebyshev or legendre polynomials we can construct an exponentially convergent approximation to the point values of f x in any sub interval in which it is analytic

on the gibbs phenomenon v recovering exponential accuracy from collocation point values of a piecewise analytic function this paper presents a method to recover exponential accuracy at all points including at the discontinuities themselves from the knowledge of an approximation to the interpolation polynomial or trigonometrical polynomial we show that if we are given the collocation point values or a highly accurate approximation at the gauss or gauss lobatto points we can reconstruct an uniform exponentially convergent approximation to the function f x in any sub interval of analyticity the proof covers the cases of fourier chebyshev legendre and more general gegenbauer collocation methods a numerical example is also provided

the resolution of the gibbs phenomenon for spherical harmonics spherical harmonics have been important tools for solving geophysical and astrophysical problems methods have been developed to effectively implement spherical harmonic expansion approximations however the gibbs phenomenon was already observed by weyl for spherical harmonic expansion approximations to functions with discontinuities causing undesirable oscillations over the entire sphere recently methods for removing the gibbs phenomenon for one dimensional discontinuous functions have been successfully developed by gottlieb and shu they proved that the knowledge of the first n expansion coefficients either fourier or gegenbauer of a piecewise analytic function f x is enough to recover an exponentially convergent approximation to the point values of f x in any subinterval in which the function is analytic here we take a similar approach proving that knowledge of the first n spherical harmonic coefficients yield an exponentially convergent approximation to a spherical piecewise smooth function f in any subinterval 1 2 0 2 where the function is analytic thus we entirely overcome the gibbs phenomenon

review of parameter identification procedures in groundwater hydrology the inverse problem the purpose of this survey is to review parameter identification procedures in groundwater hydrology and to examine computational techniques which have been developed to solve the inverse problem parameter identification methods are classified under the error criterion used in the formulation of the inverse problem the problem of ill posedness in connection with the inverse problem is addressed typical inverse solution techniques are highlighted the review also includes the evaluation of methods used for computing the sensitivity matrix statistics which can be used to estimate the parameter uncertainty are outlined attempts have been made to compare and contrast representative inverse procedures and direction for future research is suggested

spectrally accurate solution of nonperiodic differential equations by the fourier gegenbauer method it is well known that the fourier partial sum of an analytic nonperiodic function supported on a finite interval converges slowly inside the interval and exhibits o 1 spurious oscillations near the boundaries the gibbs phenomenon an effective algorithm which allows one to completely overcome the gibbs phenomenon was developed in j comput appl math 43 1992 pp 81 92 the basic concept of this approach consists of the re expansion of the fourier partial sums into the rapidly convergent gegenbauer series in this paper we extend the fourier gegenbauer f g method of j comput appl math 43 1992 pp 81 92 to the evaluation of the spatial derivatives of a piecewise analytic function also we apply this method to the solution of nonperiodic boundary value problems although the derivatives of a discontinuous function are not in l2 the exponential convergence of the truncated gegenbauer series can be proved and the rate of convergence can be estimated the solution of differential equations is accomplished in two steps first a particular solution with arbitrary boundary conditions is constructed using the f g method this particular solution is then corrected to satisfy the prescribed boundary conditions of the problem by adding a proper linear combination of homogeneous solutions for boundary layer problems the intermediate particular solution has steep profiles near the boundaries these steep regions introduce a large error into the final solution which presumably has a smooth profile on the whole interval a method which compensates for this loss of accuracy by using the appropriately constructed homogeneous solutions is proposed

geostatistical inverse modeling of transient pumping tests using temporal moments of drawdown 1 pumping tests belong to the most common techniques of hydrogeological site assessment while the steady state drawdown is determined by the distribution of transmissivity alone the transient behavior is also influenced by the storativity field in geostatistical inverse modeling the spatial distributions of both transmissivity and storativity are inferred from the drawdown curves and prior information on the spatial correlation of the parameter fields so far however transient data have hardly been analyzed by geostatistical inverse methods because the computational effort is rather high in the present study we characterize the drawdown by its temporal moments we present moment generating equations and corresponding equations to compute the sensitivity of the temporal moments of drawdown with respect to the distributions of transmissivity and storativity we utilize these equations to infer the transmissivity and storativity fields from transient pumping tests using the quasi linear geostatistical approach of inverse modeling considering temporal moments rather than full drawdown curves drastically reduces the computational effort of the estimation procedure in test cases we show that the first two temporal moments are sufficient to characterize the drawdown curves we investigate how erroneous assumptions regarding the spatial variability of storativity affect the estimate of the transmissivity field and we analyze the effect of truncating the measured drawdown curves

determining analyticity for parameter optimization of the gegenbauer reconstruction method the gegenbauer reconstruction method effectively eliminates the gibbs phenomenon and restores exponential accuracy to the approximations of piecewise smooth functions recent investigations show that its success depends upon choosing parameters in such a way that the regularization and the truncation error estimates are equally considered this paper shows that the underlying analyticity of the function in smooth regions plays a critical role in the regularization error estimate hence we develop a technique that first analyzes the behavior of the function in its regions of smoothness and then applies this knowledge to refine the regularization error estimate such refinement yields better parameter choices for the gegenbauer reconstruction method and is confirmed both by better accuracy and more robustness in the approximation of piecewise smooth functions

perturbation theory for convolution semigroups abstract we deal with convolution semigroups not necessarily symmetric in l p r n and provide a general perturbation theory of their generators by indefinite singular potentials such semigroups arise in the theory of levy processes and cover many examples such as gaussian semigroups stable semigroups relativistic schrodinger semigroups etc we give new generation theorems and feynman kac formulas in particular by using weak compactness methods in l 1 we enlarge the extended kato class potentials used in the theory of markov processes in l 2 setting dirichlet form perturbation theory is finely related to l 1 theory and the extended kato class measures is also enlarged finally various perturbation problems for subordinate semigroups are considered

the resolution of the gibbs phenomenon for spliced functions in one and two dimensions abstract in this paper we study approximation methods for analytic functions that have been spliced into nonintersecting subdomains we assume that we are given the first 2n 1 fourier coefficients for the functions in each subdomain the objective is to approximate the spliced function in each subdomain and then to glue the approximations together in order to recover the original function in the full domain the fourier partial sum approximation in each subdomain yields poor results as the convergence is slow and spurious oscillations occur at the boundaries of each subdomain thus once we glue the subdomain approximations back together the approximation for the function in the full domain will exhibit oscillations throughout the entire domain recently methods have been developed that successfully eliminate the gibbs phenomenon for analytic but nonperiodic functions in one dimension these methods are based on the knowledge of the first 2n 1 fourier coefficients and use either the gegenbauer polynomials gottlieb et al or the bernoulli polynomials abarbanel gottlieb cai et al and eckhoff we propose a way to accurately reconstruct a spliced function in a full domain by extending the current methods to eliminate the gibbs phenomenon in each nonintersecting subdomain and then gluing the approximations back together we solve this problem in both one and two dimensions in the one dimensional case we provide two alternative options the bernoulli method and the gegenbauer method as well as a new hybrid method the gegenbauer bernoulli method in the two dimensional case we prove for the very first time exponential convergence of the gegenbauer method and then we apply it to solve the spliced function problem

global optimization in hilbert space we propose a complete search algorithm for solving a class of non convex possibly infinite dimensional optimization problems to global optimality we assume that the optimization variables are in a bounded subset of a hilbert space and we determine worst case run time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set because these run time bounds are independent of the number of optimization variables and in particular are valid for optimization problems with infinitely many optimization variables we prove that the algorithm converges to an varepsilon suboptimal global solution within finite run time for any given termination tolerance varepsilon 0 finally we illustrate these results for a problem of calculus of variations

solving the estimation identification problem in two phase flow modeling in this paper a procedure is presented to solve the estimation identification problem in two phase flow modeling given discrete observations made on the system response an optimum parameter set is derived for an appropriate conceptual model by solving the inverse problem using standard optimization techniques subsequently a detailed error analysis is performed and nonlinearity effects are considered we discuss the iterative process of model identification and parameter estimation for a ventilation test performed at the grimsel rock laboratory switzerland a numerical model of the ventilation drift and the surrounding crystalline rock matrix is developed evaporation of moisture at the drift surface and the propagation of the unsaturated zone into the formation are simulated a sensitivity analysis is performed to identify the parameters to be estimated absolute permeability and two parameters of van genuchten s characteristic curves are subsequently determined based on measurements of negative water potentials evaporation rates and gas pressure data the performance of the minimization algorithm and the system behavior for the optimum parameter set are discussed the study shows that a field experiment conducted under two phase flow conditions can be successfully reproduced by taking into account a variety of physical processes and that it is possible to reliably determinemore the two phase hydraulic properties that are related to the given conceptual model 32 refs 8 figs 7 tabs less

potential theory of geometric stable processes in this paper we study the potential theory of symmetric geometric stable processes by realizing them as subordinate brownian motions with geometric stable subordinators more precisely we establish the asymptotic behaviors of the green function and the levy density of symmetric geometric stable processes the asymptotics of these functions near zero exhibit features that are very different from the ones for stable processes the green function behaves near zero as 1 x d log 2 x while the levy density behaves like 1 x d we also study the asymptotic behaviors of the green function and levy density of subordinate brownian motions with iterated geometric stable subordinators as an application we establish estimates on the capacity of small balls for these processes as well as mean exit time estimates from small balls and a harnack inequality for these processes

trouble with gegenbauer reconstruction for defeating gibbs phenomenon runge phenomenon in the diagonal limit of gegenbauer polynomial approximations to defeat gibbs phenomenon in fourier and chebyshev series gottlieb et al d gottlieb c w shu a solomonoff h vandeven on the gibbs phenomenon i recovering exponential accuracy from the fourier partial sum of a nonperiodic analytic function j comput appl math 43 1992 81 98 developed a gegenbauer reconstruction the partial sums of the fourier or other spectral series are reexpanded as a series of gegenbauer polynomials c n m x recovering spectral accuracy even in the presence of shock waves or other discontinuities to achieve a rate of convergence which is exponential in n however gegenbauer reconstruction requires increasing the order m of the polynomials linearly with the truncation n of the series m bn for some constant b 0 when the order m is fixed it is well known that the gegenbauer series converges as n everywhere on x 1 1 if f x the function being expanded is analytic on the interval but what happens in the diagonal limit in which m n tend to infinity simultaneously we show that singularities of f x off the real axis can destroy convergence of this diagonal approximation process in the sense that the error diverges for subintervals of x 1 1 gegenbauer reconstruction must therefore be constrained to use a sufficiently small ratio of order m to truncation n this off axis singularity constraint is likely to impair the effectiveness of the reconstruction in some applications

determination of optimal parameters for the chebyshev gegenbauer reconstruction method we propose a new strategy for choosing the optimal parameters for the gegenbauer reconstruction method based on chebyshev spectral coefficients under different assumptions on the smoothness of the function f these parameters are optimal in the sense that the bounds on the truncation and regularization errors were forced to be equal this strategy is independent on the number of terms n in the chebyshev expansion of the function f and guarantees exponential convergence as n rightarrow infty of the gegenbauer series to f on the intervals of smoothness the effectiveness of this strategy and exponential convergence are confirmed by numerical examples for functions with varying degrees of smoothness

spectral vanishing viscosity method for nonlinear conservation laws we propose a new spectral viscosity sv scheme for the accurate solution of nonlinear conservation laws it is proved that the sv solution converges to the unique entropy solution under appropriate reasonable conditions the proposed sv scheme is implemented directly on high modes of the computed solution this should be compared with the original nonperiodic sv scheme introduced by maday ould kaber and tadmor in siam j numer anal 30 1993 321 342 where sv is activated on the derivative of the sv solution the new proposed sv method could be viewed as a correction of the former and it offers an improvement which is confirmed by our numerical experiments a postprocessing method is implemented to greatly enhance the accuracy of the computed sv solution the numerical results show the efficiency of the new method

a bayesian approach to stochastic capture zone delineation incorporating tracer arrival times conductivity measurements and hydraulic head observations this paper presents a methodology to invert tracer arrival times and to incorporate travel time data in the delineation of well capture zones within a bayesian framework the observed arrival times are used to obtain probability based weights for each realization of the hydraulic conductivity field realizations that closely reproduce the observed arrival times are more likely to represent the true or real conductivity field than realizations yielding worse predictions and are consequently characterized by a higher conditional probability in the prediction of the capture zones the realizations are weighted by their respective probability we combine the arrival time data with conductivity measurements and head observations to delineate stochastic capture zones the conductivity measurements update the prior distributions specified for the unknown structural parameters of the conductivity field and are used as conditioning data in the generation of conditional conductivity fields the parameter values used to generate the conductivity realizations are sampled by monte carlo from the updated parameter distributions the head and travel time observations are subsequently used to assign probability based weights to the conductivity realizations by applying bayes theorem the hyperparameters of the error model are assumed unknown and their effect is accounted for by marginalization a synthetic flow setup consisting of a single extraction well in a fully confined aquifer under a regional gradient is used to illustrate the method we evaluate the relative worth of the different data types by introducing them sequentially in the inverse methodology results indicate that the different data types are complementary and that the travel time data are essential to improve the predictions of the capture zones this is confirmed by the results for the case where uncertainty in the homogeneous porosity is accounted for

on the direct fourier method for computer tomography considers the direct fourier methods dfm s for reconstructing an image from its given x ray projections the main purpose here is to use concepts from numerical analysis to estimate the errors in the methods the authors also suggest an alternative to the interpolations involved in the dfm s and estimate the number of terms involved realizing that one of the main reasons for the degradation of the quality of the reconstruction is the gibbs phenomenon the authors suggest a way to overcome this difficulty and give numerical evidence of its efficacy