a new analytic function for modeling partially penetrating wells a new analytic function is presented to model three dimensional flow near a partially penetrating well the function represents a sink distribution along the well axis whereby equipotential conditions along the well perimeter are approximately satisfied by adjusting several degrees of freedom of the function this procedure is well known and has led to rather accurate solutions provided a sufficient number of free parameters were incorporated the values for these parameters are obtained by solving a system of linear equations the function presented in this paper achieves the same accuracy as past solutions with a significant reduction in the number of degrees of freedom required and hence fewer equations to be solved this increased efficiency is of little consequence when the well is modeled by itself however when combined with the solutions to the many other flow features in a regional aquifer the savings become significant in fact if each of the individual solutions would have many degrees of freedom the resulting system of equations may become unmanageable thus restricting applications to demonstrate the use of the new function a hypothetical groundwater contamination problem is solved whereby contaminants are intercepted by a partially penetrating well

fft formulations of adaptive fourier decomposition adaptive fourier decomposition afd has been found to be among the most effective greedy algorithms afd shows an outstanding performance in signal analysis and system identification as compensation of effectiveness the computation complexity is great that is especially due to maximal selections of the parameters in this paper we explore the discretization of the 1 d afd integration via with discrete fourier transform dft incorporating fast fourier transform fft we show that the new algorithm called fft afd reduces the computational complexity from o mn2 to o mnlogn the latter being the same as fft through experiments we verify the effectiveness accuracy and robustness of the proposed algorithm the proposed fft based algorithm for afd lays a foundation for its practical applications

chebyshev centers and some geometric properties of banach spaces abstract in this paper we study two properties p 1 and p 2 introduced in the literature for studying the existence and stability of relative chebyshev centers we reformulate these properties in a way that leads naturally to our results we mainly relate these properties with some geometric properties of banach spaces in particular reflexive spaces having the kadec klee property are characterized in terms of property p 1 and uniform convexity is characterized in terms of property p 2 some continuity results for the center map are also presented

on approximation of stable linear dynamical systems using laguerre and kautz functions approximation of stable linear dynamical systems by means of so called laguerre and kautz functions which are the laplace transforms of a class of orthonormal exponentials is studied since the impulse response of a stable finite dimensional linear dynamical system can be represented by a sum of exponentials times polynomials it seems reasonable to use basis functions of the same type assuming that the transfer function of a system is bounded and analytic outside a given disc it is shown that laguerre basis functions are optimal in a mini max sense this result is extended to the two parameter kautz functions which can have complex poles while the poles of laguerre functions are restricted to the real axis by conformai mapping techniques the two parameter kautz approximation problem is recast as two laguerre approximation problems thus the well developed theory of laguerre functions can be applied to analyze kautz approximations unilateral shifts are used to further develop the connection between laguerre functions and kautz functions results on 2 and approximation using kautz models are given furthermore the weighted l2 kautz approximation problem is shown to be equivalent to solving a block toeplitz matrix equation

orthogonal rational functions for system identification numerical aspects recently there has been a growing interest in the use of orthogonal rational functions orfs in system identification there are many advantages over more classical techniques probably due to a known explicit expression for the basis functions when the orthogonality weight is uniformly equal to 1 the so called malmquist basis the attention has been on the development of methods using this basis however for some discrete identification problems this choice of the orthogonality weight may still lead to serious numerical problems due to the ill conditioning of the linear system of equations to be solved in this note we give an algorithm based on a more general system of orf to overcome the numerical problem and which allows for a fast order update of the estimate

off spectral analysis of bergman kernels the asymptotic analysis of bergman kernels with respect to exponentially varying measures near emergent interfaces has attracted recent attention such interfaces typically occur when the associated limiting bergman density function vanishes on a portion of the plane the off spectral region this type of behavior is observed when the metric is negatively curved somewhere or when we study partial bergman kernels in the context of positively curved metrics in this work we cover these two situations in a unified way for exponentially varying weights on the complex plane we obtain a uniform asymptotic expansion of the coherent state of depthn rooted at an off spectral point which we also refer to as the root function at the point in question the expansion is valid in the entire off spectral component containing the root point and protrudes into the spectrum as well this allows us to obtain error function transition behavior of the density of states along the smooth interface previous work on asymptotic expansions of bergman kernels is typically local and valid only in the bulk region of the spectrum which contrasts with our non local expansions

analytic formulation of cauchy integrals for boundaries with curvilinear geometry a general framework for analytic evaluation of singular integral equations with a cauchy kernel is developed for higher order line elements of curvilinear geometry this extends existing theory which relies on numerical integration of cauchy integrals since analytic evaluation is currently published only for straight lines and circular and hyperbolic arcs analytic evaluation of cauchy integrals along straight elements is presented to establish a context coalescing new developments within the existing body of knowledge curvilinear boundaries are partitioned into sectionally holomorphic elements that are conformally mapped from a local curvilinear z plane to a straight line in the graphic 1 plane cauchy integrals are evaluated in these planes to achieve a simple representation of the complex potential using chebyshev polynomials and a taylor series expansion of the conformal mapping bell polynomials and the faa di bruno formula provide this taylor series for mappings expressed as inverse mappings and or compositions examples illustrate application of the general framework to boundary value problems with boundaries of natural coordinates bezier curves and b splines strings formed by the union of adjacent curvilinear elements form a large class of geometries along which dirichlet and or neumann conditions may be applied this provides a framework applicable to a wide range of fields of study including groundwater flow electricity and magnetism acoustic radiation elasticity fluid flow air flow and heat flow 1 embed inline graphic 1 gif

the solution of a class of free boundary problems mellin transform and wiener hopf techniques are used to solve several free boundary problems occurring in groundwater flow this is a novel application of a technique not usually associated with free boundary problems here it is advocated as a powerful alternative to methods relying on conformal mappings in particular analytical methods can now be applied to classes of problems whose explicit solution is otherwise unobtainable relatively simple integral representations are also provided for a class of problems that otherwise require complicated analysis involving hypergeometric functions the problems are formulated in an intermediate complex plane and the mellin transform is used to solve the problems directly in this plane alternative methods require a hodograph plane to be formulated this is then conformally mapped to the intermediate plane if the conformal mapping can be done then the full solution is determined as a byproduct of this analysis the conformal mappings of some curvilinear polygons to a half plane are found to perform such mappings directly for non trivial problems involving more than three singular points requires the solution of fuchsian differential equations that involve accessory parameters and unknown points apart from degenerate cases there appears to be no constructive method of obtaining solutions to such fuchsian differential equations as a result few practical problems whose representation in the hodograph plane involves curvilinear quadrangles have been solved this paper has the aim of developing and demonstrating a simple coherent strategy for tackling the free boundary problems that lead to a class of these more complicated situations this substantially extends the range of problems that can be treated the method presented sidesteps the difficulties associated with the free point and accessory parameter and the solution for a problem where the hodograph plane is a curvilinear quadrangle with one vertex angle of 2 pi is found in the physical plane this corresponds to a point of inflection on the free surface hence it is possible to conformally map a class of curvilinear quadrangles to an upper half plane using the analytic methods developed here and this resolves an open question in conformal mapping theory two illustrative examples are also solved one involving three singular points and this provides a comparison with previous techniques the other illustrates the occurrence of a point of inflection in a relatively simple situation the alternative method advocated here is compared to the other analytical techniques available these are briefly reviewed to place the mellin transform wiener hopf approach in context

partial linearization for planar nonautonomous differential equations abstract we prove a partial linearization theorem for planar nonautonomous differential equations with one center like direction and one hyperbolic direction gap conditions are formulated in terms of the dichotomy spectral intervals the result is applied to the duffing van der pol oscillator under a nonautonomous parametric perturbation

system identification using kautz models in this paper the problem of approximating a linear time invariant stable system by a finite weighted sum of given exponentials is considered system identification schemes using laguerre models are extended and generalized to kautz models which correspond to representations using several different possible complex exponentials in particular linear regression methods to estimate this sort of model from measured data are analyzed the advantages of the proposed approach are the simplicity of the resulting identification scheme and the capability of modeling resonant systems using few parameters the subsequent analysis is based on the result that the corresponding linear regression normal equations have a block toeplitz structure several results on transfer function estimation are extended to discrete kautz models for example asymptotic frequency domain variance expressions

distances on probability measures and random variables in this paper we lift fundamental topological structures on probability measures and random variables in particular the weak topology convergence in law and finite dimensional convergence to an isometric level this allows for an isometric quantitative study of important concepts such as relative compactness tightness stochastic equicontinuity prohorov s theorem and smoothness in doing so we obtain numerical results which allow for the development of an intrinsic approximation theory and from which moreover all classical topological results follow as easy corollaries

stein s method and a quantitative lindeberg clt for the fourier transforms of random vectors abstract we use a multivariate version of stein s method to establish a quantitative lindeberg clt for the fourier transforms of random n vectors we achieve this conceptually mainly by constructing a natural approach structure on n random vectors overlying the topology of weak convergence and technically mainly by deducing a specific integral representation for the hessian matrix of a solution to the stein equation with test function e t x exp i k 1 n t k x k where t x r n

effective boundary conditions for the laplace equation with a rough boundary the problem of replacing dirichlet or neumann conditions on a stochastically embossed surface by approximate effective conditions on a smooth surface is studied for potential fields satisfying the laplace equation a combination of ensemble averaging and multiple scattering techniques is used it is shown that for the dirichlet case the effective boundary condition becomes mixed and establishes a relation between the averaged field and its normal derivative for the neumann problem the normal derivative on the smooth surface equals a suitable combination of first and second order derivatives tangent to the surface explicit results are given for small boss concentration and illustrated with the examples of spheroidal and spherical bosses for the dirichlet case with hemispherical bosses direct numerical simulation results are presented up to area coverages of 75 an application of the results to the calculation of the added mass of a rough sphere in potential flow of the capacitance of a rough spherical conductor and of the transmission and reflection of long water waves at a smooth rough bottom transition aids in their physical interpretation

a class of algorithms for identification in h abs traet in this paper a class of algorithms for the problem of system identification in are investigated these algorithms are characterized by a two stage structure and involve a class of window functions some conditions in terms of properties of the window functions are derived which guarantee robust convergence of the algorithms identification errors are analyzed for several common window functions this leads to some insights into the trade off between the error induced by approximation and that due to noise

exterior powers of the adjoint representation and the weyl ring of e8 abstract i derive explicitly all polynomial relations in the character ring of e 8 of the form k e 8 p k 1 8 0 where k e 8 is an arbitrary exterior power of the adjoint representation and i is the ith fundamental character this has simultaneous implications for the theory of relativistic integrable systems seiberg witten theory quantum topology orbifold gromov witten theory and the arithmetic of elliptic curves the solution is obtained by reducing the problem to a large but finite dimensional linear problem which is amenable to an efficient solution via distributed computation

rational basis functions for robust identification from frequency and time domain measurements this paper investigates the use of general bases with fixed poles for the purposes of robust estimation these bases which generalise the common fir laguerre and two parameter kautz ones are shown to be fundamental in the disc algebra provided a very mild condition on the choice of poles is satisfied it is also shown that by using a min max criterion these bases lead to robust estimators for which error bounds in different norms can be explicitly quantified the key idea facilitating this analysis is to re parameterise the chosen model structures into a new one with equivalent fixed poles but for which the basis functions are orthonormal in h 2 d

smooth invariant manifolds in banach spaces with nonuniform exponential dichotomy we establish the existence of smooth stable manifolds for semiflows defined by ordinary differential equations v a t v f t v in banach spaces assuming that the linear equation v a t v admits a nonuniform exponential dichotomy our proof of the ck smoothness of the manifolds uses a single fixed point problem in the unit ball of the space of ck functions with holder continuous kth derivative this is a closed subset of the space of continuous functions with the supremum norm by an apparently not so well known lemma of henry see proposition 3 the estimates showing that the functions maintain the original bounds when transformed under the fixed point operator are obtained through a careful application of the faa di bruno formula for the higher derivatives of the compositions see 31 and 35 as a consequence we obtain in a direct manner not only the exponential decay of solutions along the stable manifolds but also of their derivatives up to order k when the vector field is of class ck

ultradistributional boundary values of harmonic functions on the sphere abstract we present a theory of ultradistributional boundary values for harmonic functions defined on the euclidean unit ball we also give a characterization of ultradifferentiable functions and ultradistributions on the sphere in terms of their spherical harmonic expansions to this end we obtain explicit estimates for partial derivatives of spherical harmonics which are of independent interest and refine earlier estimates by calderon and zygmund we apply our results to characterize the support of ultradistributions on the sphere via abel summability of their spherical harmonic expansions

a slender wing theory in potential flow consider uniform steady potential flow past a slender wing by considering a horseshoe vortex in the limit as us where is the circulation u is the uniform stream velocity and s is the span a model representing a vortex sheet is obtained from which the lift on the slender wing can be determined this is in contrast to the textbook approach of batchelor and katz plotkin who discretize the vortex sheet with horseshoe vortices in the limit as us but then relate the vortex strength to lift by using the two dimensional limit us 0 we shall argue that using these different limits in the same analysis is inconsistent and leads to an incorrect result the resulting potential term is shown to be the same as the potential term of the lift oseenlet in oseen flow in the limit of high reynolds number flow only half the contribution to the lift integral comes from the potential velocity part of the lift oseenlet the other half comes from the vortex wake velocity part of the lift oseenlet we therefore assume potential flow everywhere except at the vortex sheet along which we allow a singular vortex wake velocity term of the lift oseenlet from this a slender wing theory is presented together with integral expressions for the lift and change in lift over the wing surface applications to slender bodies and large aspect ratio wings in particular the lanchester prandtl lifting line are then considered

stream surfaces in two dimensional and three dimensional divergence free flows it is demonstrated that two dimensional flows and three dimensional flows have fundamentally different influences on stream surfaces an element that generates a two dimensional flow only can affect the angle of intersection between two stream surfaces locally an element that generates a three dimensional flow may affect this angle regionally one consequence is that stream functions for three dimensional flows may not in general be chosen such that their basis vectors are everywhere mutually orthogonal another consequence is that the deformation of stream surfaces produced by a three dimensional element does not approach that produced by a two dimensional element at large distances from the element a two dimensional model cannot reproduce stream surfaces that occur in a three dimensional flow

ancillary solutions for curved crack stress analysis a method to generate a weight function for use in the stress analysis of arbitrarily shaped cracks with arbitrary boundary conditions and mixed mode loading is presented the method only involves the numerical resolution of a singular integral equation with a cauchy type kernel whose singularity is straight forward to remove the generation of the weight function is done through the superposition of a fundamental solution and a complementary solution the fundamental solution obeys the complex bueckner formula asymptotically and has a finite traction potential along the curved crack the complementary solution is made up of a distributed load plus a simple crack solution such that the weight function is stress free along the crack and has the right boundary conditions only the simple crack solution needs to be solved using the numerical resolution of a singular integral equation with a cauchy type kernel a numerical example is added to illustrate the method

2d partial unwinding a novel non linear phase decomposition of images this paper aims at proposing a novel 2d non linear phase decomposition of images which performs the image processing tasks better than the traditional fourier transformation linear phase decomposition but further it has additional mathematical properties allowing more effective image analysis including adaptive decomposition components and positive instantaneous phase derivatives 1d unwinding blaschke decomposition has recently been proposed and studied through factorization it expresses arbitrary 1d signal into an infinite linear combination of blaschke products it offers fast converging positive frequency decomposition in the form of rational approximation however in the multi dimensional cases the usual factorization mechanism does not work as a consequence there is no genuine unwinding decomposition for multi dimensions in this paper a 2d partial unwinding decomposition based on algebraic transforms reducing multi dimensions to the 1d case is proposed and analyzed the result shows that the fast convergence offers efficient image reconstruction the tensor type decomposing terms are mutually orthogonal giving rise to 2d positive frequency decomposition the comparison results show that the proposed method outperforms the standard greedy algorithm and the most commonly used methods in the fourier category an application in watermarking is presented to demonstrate its potential in applications

frequency domain identification with generalized orthonormal basis functions a method is considered for the identification of linear parametric models based on a least squares identification criterion that is formulated in the frequency domain to this end use is made of the empirical transfer function estimate etfe identified from time domain data as a parametric model structure use is made of a finite expansion sequence in terms of recently introduced generalized basis functions being generalizations of the classical pulse and laguerre and kautz types of bases an asymptotic analysis of the estimated models is provided and conditions for consistency are formulated explicit and transparent bias and variance expressions are established the latter ones also valid in a situation of undermodeling

approximate solutions and micro regularity in the denjoy carleman classes abstract we begin with a sequence m of positive real numbers and we consider the denjoy carleman class c m we show how to construct m approximate solutions for complex vector fields with c m coefficients we then use our construction to study micro local properties of boundary values of approximate solutions in general m involutive structures of codimension one where the approximate solution is defined in a wedge whose edge where the boundary value exists is a maximally real submanifold we also obtain a c m version of the edge of the wedge theorem

comparison of fast boundary element methods on parametric surfaces we compare fast black box boundary element methods on parametric surfaces in r3 these are the adaptive cross approximation the multipole method based on interpolation and the wavelet galerkin scheme the surface representation by a piecewise smooth parameterization is in contrast to the common approximation of surfaces by panels nonetheless parametric surface representations are easily accessible from computer aided design cad and are recently topic of the studies in isogeometric analysis especially we can apply two dimensional interpolation in the multipole method a main feature of this approach is that the cluster bases and the respective moment matrices are independent of the geometry this results in a superior compression of the far field compared to other cluster methods

a new algorithm for computing the multivariate faa di bruno s formula abstract a new algorithm for computing the multivariate faa di bruno s formula is provided we use a symbolic approach based on the classical umbral calculus that turns the computation of the multivariate faa di bruno s formula into a suitable multinomial expansion we propose a maple procedure whose computational times are faster compared with the ones existing in the literature some illustrative applications are also provided

divided differences of implicit functions under general conditions the equation g x y 0 implic itly denes y locally as a function of x in this article we express divided dierences of y in terms of bivariate divided dierences of g generalizing a recent result on divided dierences of inverse functions

on backward shift algorithm for estimating poles of systems abstract in this paper we present an algorithm for estimating poles of linear time invariant systems by using the backward shift operator we prove that poles of rational functions including zeros and multiplicities are solutions to an algebraic equation which can be obtained by taking backward shift operator to the shifted cauchy kernels in the unit disc case the algorithm is accordingly developed for frequency domain identification we also prove the robustness of this algorithm some illustrative examples are presented to show the efficiency in systems with distinguished and multiple poles

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

a vector potential and exact flux through surfaces using lagrange and stokes stream functions a vector potential is obtained for two dimensional flow fields using the lagrange stream function and for axisymmetric flow fields using the stokes stream function the flux through surfaces bounded by straight line segments with arbitrary orientation is obtained using the line integral of the tangential component of the vector potential along the boundary of the surface integration of the lagrange stream function results for surfaces in two dimensional flow a cauchy integral of the stokes stream function follows for axisymmetric flow the process of assembling vector potentials and developing closed form expressions to provide exact flux through surfaces is illustrated for a partially penetrating well with uniform flow in a horizontal aquifer a virtual flux is generated through vortex sheets where the lagrange stream function is discontinuous and through singular vortex lines where the stokes stream function is non zero on the axis of symmetry this virtual flux must be accounted for to obtain exact flux the unifying framework presented here to assemble vector potentials obtained using lagrange and stokes stream functions and to compute flux is applicable to three dimensional divergence free steady flow fields that can be decomposed into two dimensional and axisymmetric components

system identification by discrete rational atoms a novel adaptive frequency domain system identification method for linear time invariant systems is proposed in this paper it finds poles for discrete rational atoms with discrete frequency responses the theoretical foundation including adaptive decomposition principle and decomposition convergence rate is established the algorithm of the adaptive pursuit is also provided in this paper

asymptotic expansion of multivariate conservative linear operators in this paper we study the asymptotic expansion of the partial derivatives of a sequence of linear conservative operators we find sufficient conditions on the sequence that guarantee that such an expansion can be derived from the asymptotic formula for the nondifferentiated sequence our results are valid even if the operators of the sequence present difficult conservative properties different form the classical preservation of the usual convexities we use our theorems to obtain the complete asymptotic expansions and voronovskaja formulae for the partial derivatives of multivariate versions of the meyer konig and zeller operators and the bleimann butzer and hahn operators

laguerre methods and h identification of continuous time systems abstract h identification of stable continuous time systems is studied using generalized laguerre series methods the theoretical basis of generalized laguerre series methods in h identification is established by giving several results on frequency unweighted and frequency weighted approximations of different classes of infinite dimensional systems an h identification technique based on step response data and laguerre methods is given and analysed generalized laguerre series methods are shown to provide h identification techniques which allow for frequency weighting furthermore it is demonstrated that the theory of generalized laguerre polynomials solves certain approximation problems in an analytical fashion for a class of delay systems

the fundamental role of general orthonormal bases in system identification the purpose of this paper is threefold firstly it is to establish that contrary to what might be expected the accuracy of well known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure secondly it is to derive new variance expressions that can provide greatly improved accuracy while also making explicit the influence of any fixed poles or zeros this is achieved by employing certain new results on generalized fourier series and the asymptotic properties of toeplitz like matrices in such a way that the new variance expressions presented here encompass pre existing ones as special cases via this latter analysis a new perspective emerges on recent work pertaining to the use of orthonormal basis structures in system identification namely that orthonormal bases are much more than an implementational option offering improved numerical properties in fact they are an intrinsic part of estimation since as shown here orthonormal bases quantify the asymptotic variability of the estimates whether or not they are actually employed in calculating them

brief paper frequency domain identification an algorithm based on an adaptive rational orthogonal system this paper presents a new adaptive algorithm for frequency domain identification the algorithm is related to the rational orthogonal system takenaka malmquist system this work is based on an adaptive decomposition algorithm previously proposed for decomposing the hardy space functions in which a greedy sequence is obtained according to the maximal selection criterion we modify the algorithm through necessary changes for system identification

drawdown and capture zone topology for nonvertical wells 1 an analytic framework is developed to model the three dimensional steady flow generated by wells placed at general nonvertical orientations within a horizontal aquifer this framework uses closed form solutions for a distribution of point sinks and point doublets along the centerline of the well and semi infinite panel elements each with piecewise linearly varying strengths this extends previously published implementations and enables a boundary condition of uniform head along the cylindrical face of the well to be accurately matched the resulting model is used to examine the drawdown and capture zone topology for wells spanning orientations ranging from vertical to horizontal scaling relationships are developed for wells perpendicular to flow that are invariant with respect to drawdown and to the strength of elements the capture zone geometry for such wells is variant with respect to a dimensionless pumping rate going through transition from two dimensional flow in a plane perpendicular to the well to two dimensional flow in a horizontal plane

an application of approach theory to the relative hausdorff measure of non compactness for the wasserstein metric abstract after shortly reviewing the fundamentals of approach theory as introduced by r lowen in 1989 we show that this theory is intimately related to the well known wasserstein metric on the space of probability measures with a finite first moment on a complete and separable metric space more precisely we introduce a canonical approach structure called the contractive approach structure and prove that it is metrized by the wasserstein metric the key ingredients of the proof of this result are dini s theorem ascoli s theorem and the fact that the class of real valued contractions on a metric space has some nice stability properties we then combine the obtained result with prokhorov s theorem to establish inequalities between the relative hausdorff measure of non compactness for the wasserstein metric and a canonical measure of non uniform integrability

a unifying construction of orthonormal bases for system identification this paper develops a general and very simple construction for complete orthonormal bases for system identification this construction provides a unifying formulation of many previously studied orthonormal bases since the common fir and recently popular laguerre and two parameter kautz model structures are restrictive special cases of the construction presented here however in contrast to these special cases the basis vectors in the unifying construction of this paper can have arbitrary placement of pole position according to the prior information the user wishes to inject results characterizing the completeness of the bases and the accuracy properties of models estimated using the bases are provided

a vector potential for a partly penetrating well and flux in an approximate method of images a vector potential is formulated for three dimensional steady groundwater flow within a framework that is consistent with the lagrange stream function for twodimensional flow analytical expressions are developed for vector potentials of a point sink and a line sink of both finite and infinite length a previously unpublished vector potential for a partly penetrating well in a horizontal confined aquifer is obtained using the method of images where an infinite series of image line sinks is approximated using a finite number of images and two semi infinite elements singularities and discontinuities within these vector potentials are interpreted as producing a virtual discharge connecting vortex lines into continuous loops over infinity the vector potential is used to accurately and efficiently compute the net flux through surfaces containing singularities in the specific discharge this net flux quantifies errors in the elevation of streamlines associated with a finite number of images and provides a measure to ensure a relatively seamless link between local three dimensional flow and farfield two dimensional flow

a multivariate faa di bruno formula with applications a multivariate faa di bruno formula for computing arbitrary partial derivatives of a function composition is presented it is shown by way of a general identity how such derivatives can also be expressed in the form of an infinite series applications to stochastic processes and multivariate cumulants are then delineated

analysis of the domain mapping method for elliptic diffusion problems on random domains in this article we provide a rigorous analysis of the solution to elliptic diffusion problems on random domains in particular based on the decay of the karhunen loeve expansion of the domain perturbation field we establish decay rates for the derivatives of the random solution that are independent of the stochastic dimension for the implementation of a related approximation scheme like quasi monte carlo quadrature stochastic collocation etc we propose parametric finite elements to compute the solution of the diffusion problem on each individual realization of the domain generated by the perturbation field this simplifies the implementation and yields a non intrusive approach having this machinery at hand we can easily transfer it to stochastic interface problems the theoretical findings are complemented by numerical examples for both stochastic interface problems and boundary value problems on random domains

a kam theorem for finitely differentiable hamiltonian systems abstract given l 2 2 d 4 we prove the persistence of a cantor family of kam tori of measure o e 1 2 l for any non degenerate nearly integrable hamiltonian system of class c l d t d where 1 is the diophantine power of the frequencies of the persistent kam tori and d r d is a bounded domain provided that the size e of the perturbation is sufficiently small this extends a result by d salamon in 25 according to which we do have the persistence of a single kam torus in the same framework moreover as for the persistence of a single torus the regularity assumption is essentially optimal

existence of chebyshev centers best n nets and best compact approximants in this paper we investigate the existence and continuity of chebyshev centers best n nets and best compact sets some of our positive results were obtained using the concept of quasi uniform convexity furthermore several examples of nonexistence are given e g a sublattice m of c o 1 and a bounded subset b c m is constructed which has no chebyshev center no best n net and not best compact set approximant

the fbi transforms and their use in microlocal analysis abstract using a more general class of fbi transforms introduced by s berhanu and j hounie in 12 we completely characterize regularity and microregularity in denjoy carleman non quasi analytic classes which includes the gevrey classes and m christ version of the fbi transform defined in 22 as examples we also exhibit a result on microlocal regularity for solutions of first order partial differential equations in these classes that do not seem possible to prove using the classical fbi transform

the continuation approach a general framework for the analysis and evaluation of singular and near singular integrals the continuation approach presented in this paper is a simple and unified framework for analyzing and computing a large class of singular and near singular integrals such as those that arise in the boundary element method the analysis formulates singular and near singular integrals consistently as instances of a single phenomenon with all types of algebraic singularities treated in a similar way for domains of arbitrary dimension singular integrals are viewed merely as continuations of nonsingular but perhaps near singular ones by placing the singularity of the integrand outside the integration domain and taking the limit as it approaches the domain the technique exploits the functional homogeneity shared by the green s functions of many physical problems for flat surfaces this allows the integral to be mapped to the contour of the integration domain curved surfaces are handled by projecting the integration domain to a tangent hyperplane where the singular components of the integral can be

modeling three dimensional flow in confined aquifers by superposition of both two and three dimensional analytic functions a technique is presented to incorporate three dimensional flow in a dupuit forchheimer model the method is based on superposition of approximate analytic solutions to both two and three dimensional flow features in a confined aquifer of infinite extent three dimensional solutions are used in the domain of interest while farfield conditions are represented by two dimensional solutions approximate three dimensional solutions have been derived for a partially penetrating well and a shallow creek each of these solutions satisfies the condition that no flow occurs across the confining layers of the aquifer because of this condition the flow at some distance of a three dimensional feature becomes nearly horizontal consequently remotely from a three dimensional feature its three dimensional solution is replaced by a corresponding two dimensional one the latter solution is trivial as compared to its three dimensional counterpart and its use greatly enhances the computational efficiency of the model as an example the flow is modeled between a partially penetrating well and a shallow creek that occur in a regional aquifer system