optimized multidimensional nonoscillating deconvolution the paper presents a nonoscillating iterative method of gold deconvolution the method is generalized for multidimensional data from computational point of view the gold deconvolution is time consuming operation it requires a great number of numerical operations a new optimized algorithm aimed to reduce number of computer operations has been derived in the paper

a free boundary problem for the laplacian with a constant bernoulli type boundary condition we study a free boundary problem for the laplace operator where we impose a bernoulli type boundary condition we show that there exists a solution to this problem we use a beurling s technique by defining two classes of sub and supersolutions and a perron argument we try to generalize here a previous work of a henrot and h shahgholian we extend these results in different directions

numerical recovery of location and residue of poles of meromorphic functions we present a method able to recover location and residue of poles of functions meromorphic in a half plane from samples of the function on the real positive semi axis the function is assumed to satisfy appropriate asymptotic conditions including in particular that required by carlson s theorem the peculiar features of the present procedure are a it does not make use of the approximation of meromorphic functions by rational functions b it does not use the standard methods of regularization of ill posed problems the data required for the determination of the pole parameters i e location and residue are the approximate values of the meromorphic function on a finite set of equidistant points on the real positive semi axis we show that this method is numerically stable by proving that the algorithm is convergent as the number of data points tends to infinity and the noise on the input data goes to zero moreover we can also evaluate the degree of approximation of the estimates of pole location and residue which we obtain from the knowledge of a finite number of noisy samples

application of the tikhonov regularization technique to the equivalent magnetic currents near field technique the equivalent magnetic currents method can be used to characterize radiating structures and to obtain information about the current distribution on the radiating device under test dut in order to do so the system is assumed to be linear and inversion from near field measurements can be carried out using numerical techniques such as the singular value decomposition however this approach is very sensitive to modeling and measurement errors which is a consequence of the ill conditioned nature of the inversion process here we propose to account for the ill conditioning by using a tikhonov regularization technique to perform the inversion this technique requires a regularization parameter to be set to an appropriate value and we show that a generalized cross validation approach yields adequate determination of the regularization parameter directly from the measured data the proposed method can be tailored to account for specific characteristics of the dut this point is illustrated by the estimation of the current distribution of a bidimensional radiating structure for which prior information about the orientation of radiating edges is incorporated into the inversion method

regularized iterative image restoration with ringing reduction linear space invariant image restoration algorithms often introduce ringing effects near sharp intensity transitions it is shown that these artifacts are attributable to the regularization of the ill posed image restoration problem two possible methods to reduce the ringing effects in restored images are proposed the first method incorporates deterministic a priori knowledge about the original image into the restoration algorithm the second method locally regulates the severity of the noise magnification and the ringing phenomenon depending on the edge information in the image a regularized iterative image restoration algorithm is proposed in which both ringing reduction methods are included by making use of the theory of the projections onto convex sets and the concept of norms in a weighted hilbert space both the numerical performance and the visual evaluation of the results are improved by the use of ringing reduction

regularity of the free boundary for the porous medium equation with r m 1 m 1 when u 0 then f 0 and both of the above equations become degenerate this degeneracy results in the interesting phenomenon of the finite speed of propagation if the initial data u is compactly supported in 1ztn the solution u t will remain compactly supported for all time t in this work we will show that under rather general assumptions on the initial data the free boundary

new pocs algorithms for regularization of inverse problems abstract ill posed problems described by first kind fredholm equations appear in many interesting practical cases in engineering or mathematical physics such as deconvolution and require regularization techniques to get adequate solutions this paper presents under a projection operators onto convex sets pocs framework to introduce the needed regularization operations a series of non adaptive and adaptive pocs regularization algorithms which offer as main advantages besides including previously proposed methods a lower computational load and the possibility of including any kind of constraints linear and nonlinear a series of simulation examples serve to appreciate the high performance of the proposed techniques in a typical problem recovering the discontinuites of a sequence showing sharp edges

new extremal characterizations of generalized inverses of linear operators abstract in 1956 r penrose studied best approximate solutions of the matrix equation ax b he proved that a b where a is the moore penrose inverse is the unique matrix of minimal frobenius norm among all matrices which minimize the frobenius norm of ax b in particular a is the unique best approximate solution of ax i the vector version of penrose s result that is the fact that the vector a b is the best approximate solution in the euclidean norm of the vector equation ax b has long been generalized to infinite dimensional hilbert spaces in this paper an infinite dimensional version of penrose s full result is given we show that a straightforward generalization is not possible and provide new extremal characterizations in terms of the hermitian order of a and of the classes of generalized inverses associated with minimal norm solutions of consistent operator equations or with least squares solutions for a certain class of operators we can phrase our characterizations in terms of a whole class of norms including the hilbert schmidt and the trace norms thus providing new extremal characterizations even in the matrix case we treat both operators with closed range and with not necessarily closed range finally we characterize a as the unique inner inverse of minimal hilbert schmidt norm if a 2

stochastic dominance on unidimensional grids special stochastic dominance relations for probability distributions on a finite grid of evenly spaced points are considered the relations depend solely on iterated partial sums of grid point probabilities and are very computer efficient their corresponding classes of utility functions for expected utility comparisons consist of functions defined on the grid that mimic in the large the traditional continuous functions whose derivatives alternate in sign the first degree and second degree relations are identical to their traditional counterparts defined from iterated integrals of cumulative distribution functions the higher degree relations differ from the traditional relations in interesting and sometimes subtle ways the paper explores aspects of the partial sums relations including effects of grid refinements and extensions and describes their relationships to the traditional relations

concavity properties for elliptic free boundary problems abstract we prove some concavity properties connected to nonlinear bernoulli type free boundary problems in particular we prove a brunn minkowski inequality and an urysohn s type inequality for the bernoulli constant and we study the behavior of the free boundary with respect to the given boundary data moreover we prove a uniqueness result regarding the interior problem

serrin type overdetermined problems an alternative proof we prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations namely the hessian equations in the case of the poisson equation our proof is alternative to the proofs proposed by serrin moving planes and by weinberger moreover our proof makes no direct use of the maximum principle while it sheds light on a relation between the serrin problem and the isoperimetric inequality

on quasilinear elliptic equations in domains with coninal boundary points on etudie les solutions de l equation pseudo laplace au div u p 2 u f 1 p pres de points limites coniques

distributionally robust optimization under moment uncertainty with application to data driven problems stochastic programming can effectively describe many decision making problems in uncertain environments unfortunately such programs are often computationally demanding to solve in addition their solution can be misleading when there is ambiguity in the choice of a distribution for the random parameters in this paper we propose a model that describes uncertainty in both the distribution form discrete gaussian exponential etc and moments mean and covariance matrix we demonstrate that for a wide range of cost functions the associated distributionally robust or min max stochastic program can be solved efficiently furthermore by deriving a new confidence region for the mean and the covariance matrix of a random vector we provide probabilistic arguments for using our model in problems that rely heavily on historical data these arguments are confirmed in a practical example of portfolio selection where our framework leads to better performing policies on the true distribution underlying the daily returns of financial assets

partially overdetermined elliptic boundary value problems we consider semilinear elliptic dirichlet problems in bounded domains overdetermined with a neumann condition on a proper part of the boundary under different kinds of assumptions we show that these problems admit a solution only if the domain is a ball when these assumptions are not fulfilled we discuss possible counterexamples to symmetry we also consider neumann problems overdetermined with a dirichlet condition on a proper part of the boundary and the case of partially overdetermined problems on exterior domains

existence and geometric properties of solutions of a free boundary problem in potential theory let 0 g h l rn n 2 be two given density functions at least one of them bounded away from zero outside a compact set and g holder continuous we prove that for any compactly supported positive measure which is sufficiently concentrated e g has sufficiently high n 1 dimensional density there exists a bounded open set rn such that the newtonian potential of the measure hln ghn 1 agrees with that of outside some regularity of is obtained as well as several results on the geometry of example if h and g are constant then for any x the inward normal ray of at x if it exists intersects the closed convex hull of typeset by ams tex 1 2 bjorn gustafsson and henrik shahgholian

comments on fundamentals of thin wire integral equations with the finite gap generator in papers 1 2 the authors extend the so called effective current method to the hallen s and pocklington s equations with the finite gap generator fgg the indicated method considered earlier in 3 with a reference to 4 is associated with application of the method of auxiliary sources to the analysis of cylindrical dipole antennas 5 7 the purpose of these comments is to draw the authors and readers attention to the existence ofpaper 8 where the pocklington s equation with the fgg is solved for the axial current considered there to be auxiliary the equation is solved by the galerkin method using the piecewise sinusoidal basis and testing functions the auxiliary axial current is used further for calculation of the surface current which is referred to as the effective current in 1 4 and the surface current itself is used for calculation of the input impedance so in some respects papers 1 7 just repeat the main idea and technique of paper 8 although of course papers 1 7 also contain a lot of their own new interesting and useful analytical and numerical results

the inverse scattering problem for time harmonic acoustic waves the inverse scattering problem we are considering in this paper is to determine the shape of a sound soft bounded connected obstacle from a knowledge of the time harmonic incident wave with frequency in the resonance region and the far field pattern of the scattered wave after some introductory remarks we begin by describing the method of integral equations and the null field method for solving the direct scattering problem this enables us to define an operator t mapping the boundary of the scattering obstacle and the incident field onto the far field pattern the inverse scattering problem is to invert this operator in order to do this we first must examine the range of t i e to characterize the class of far field patterns and to establish the existence of t on the range of t i e to show the uniqueness of the solution to the inverse scattering problem this analysis shows that for a given measured far field pattern in general no solution exists to the inverse scattering problem and if a solution does exist it does not depend continuously on the measured data i e the problem is improperly posed this motivates us to consider a linearized model and to examine various methods for studying linearized improperly posed problems based on the ideas of a priori assumptions and compactness arguments we then consider a simple model problem that focuses on the nonlinear character of the inverse scattering problem and motivated by our study of the linearized model reformulate the inverse scattering problem as a problem in constrained optimization we conclude by considering the numerical solution of this nonlinear optimization problem approach your problems from the right end and begin with the answers then one day perhaps you will find the final question from the hermit clad in crane feathers in the chinese maze murders by r van gulik

a free boundary problem for p laplacian in the plane abstract we consider the following free boundary problem in an unbounded domain in two dimensions p u 0 in u 0 u n g 0 on j 0 u 1 u n g 1 on j 1 where j 0 j 1 we prove that if 0 u 1 in j i is the graph of a function in c loc 1 r and g i is a constant for each i 0 1 then the free boundary must be two parallel straight lines and the solution u must be a linear function the proof is based on maximum principle

inverse scattering method for one dimensional inhomogeneous layered media an inverse scattering method to reconstruct simultaneously the permittivity profile and the conductivity profile of one dimensional inhomogeneons medium which makes use of the transverse electric te wave and or transverse magnetic tm wave is proposed the medium is illuminated by the te and or tm plane wave at oblique incidence and the data are taken as the reflection coefficients for a set of discrete frequencies and or a finite number of incident angles furthermore the reflection coefficient data contain the gaussian noise the nonlinear integral equation relating the unknown constitutive parameter of the medium to the reflection coefficient for te wave and or tm wave is solved by the newton iteration method the inverse operator in the newton method is determined by the regularization method it is demonstrated in terms of the numerical examples that this method utilizing both polarizations and the incident angle of the incident plane wave is very effective even if the reflection coefficient contains the practical measurement error or the phase of the reflection coefficient is unknown moreover the relationships between the errors of reconstructed profile and the measured reflection coefficient are also discussed

field singularities at metal dielectric wedges the wedges discussed are the dielectric wedge the metallic 90 deg corner on a dielectric plane and the adjacent 90 deg metallic and dielectric corners the field components perpendicular to the edge may become infinite according to a law 1 r n numerical data are given for n and plots of lines of force of bar e or bar h are shown

a symmetry result for the torsion equation in an unbounded domain in 2d abstract we investigate an overdetermined problem for the torsion equation u 1 with two kinds of free boundary conditions in an unbounded domain and present a symmetry result in the case of 2d the proof is based on the maximum principle in the proof we use the sliding method and some convex arguments

a wavelet based method for solving discrete first kind fredholm equations with piecewise constant solutions the inverse problem of finding piecewise constant solutions to discrete fredholm integral equations of the first kind arises in many applied fields e g in geophysics this equation is usually an ill posed problem when it is considered in a hilbert space framework requiring regularization techniques to control arbitrary error amplifications and to get adequate solutions in this work we describe an iterative regularizing method for computing piecewise constant solutions to first kind discrete fredholm integral equations the algorithm involves two main steps at each iteration 1 approximating the solution using a new signal reconstruction algorithm from its wavelet maxima which involves a previous step of detecting discontinuities by estimation of its local holder exponents and 2 obtaining a regularized solution of the original equation using the a priori knowledge and the above approximation in order to check the behaviour of the proposed technique we have carried out a statistical study from a high number of simulations obtaining excellent results their comparisons with the results coming from using classical tikhonov regularization by the multiresolution support total variation tv regularization and piecewise polynomial truncated singular value decomposition pp tsvd algorithm serve to illustrate the advantages of the new method copyright 2003 john wiley sons ltd

choice of initial conditions in the ml reconstruction of fan beam transmission with truncated projection data the authors investigate the effects of initial conditions in the iterative maximum likelihood ml reconstruction of fan beam transmission projection data with truncation in an iterative ml reconstruction the estimate of the transmission reconstructed image in the previous iteration is multiplied by some factors to obtain the current estimate normally a flat initial condition fic or an image with equal positive pixel values is used as initial condition for an ml reconstruction usage of fic has also been perceived as a way of preventing any bias on the reconstruction which may have come from the initial condition when projection data have truncation the authors show that using are fic in an ml iterative reconstruction can introduce a bias to the reconstruction inside the densely sampled region dsr whose projection data have no truncation at any angle to reduce this bias the authors propose to use the largest right singular vector lrsv of the system matrix as the initial condition and demonstrate that the bias can be reduced with the lrsv when data truncation is reduced the lrsv approaches the fic this result does not contradict to the use of fic when projection data are not truncated the authors also demonstrate that the reconstructed transmission image using lrsv as initial condition provides a more accurate attenuation coefficient distribution than that using fic however the improvement is mostly in the area outside the dsr

on the application of numerical methods to hallen s equation the so called hallen integral equation for the current on a finite linear antenna center driven by a delta function generator takes two forms depending on the choice of kernel the two kernels are usually referred to as the exact and the approximate or reduced kernel with the approximate kernel the integral equation has no solution nevertheless the same numerical method is often applied to both forms of the integral equation in this paper the behavior of the numerical solutions thus obtained is investigated and the similarities and differences between the two numerical solutions are discussed the numerical method is galerkin s method with pulse functions we first apply this method to the two corresponding forms of the integral equation for the current on a linear antenna of infinite length in this case the method yields an infinite toeplitz system of algebraic equations in which the width of the pulse basis functions enters as a parameter the infinite system is solved exactly for nonzero pulse width the exact solution is then developed asymptotically for the case where the pulse width is small when the asymptotic expressions for the case of the infinite antenna are used as a guide for the behavior of the solutions of the finite antenna the latter problem is greatly facilitated for the approximate kernel the main results of this paper carry over to a certain numerical method applied to the corresponding equation of the pocklington type

a harnack inequality approach to the regularity of free boundaries part ii flat free boundaries are lipschitz soit u une solution faible d un probleme aux limites libres du type u 0 sur u 0 et sur u 0 et soit le long de la frontiere libre f la relation u v g u x est satisfaite au sens faible alors si f est proche du graphe d une fonction de lipschitz dans la boule unite b 1 de r n f est le graphe d une fonction de lipschitz dans b 1 2

surface wave and superdirectivity aspects of effective current for linear antennas previous papers have defined the concept of effective current for linear antennas as a method of postprocessing the unphysical solutions obtained by applying discretization galerkin methods to the usual integral equations that employ the approximate or reduced kernel such an unphysical solution can be thought of as an auxiliary rapidly oscillating current located on the axis of the linear antenna while the effective current is the magnetic field due to the oscillating current at a distance equal to the antenna radius multiplied by a factor equal to the antenna circumference in the present paper we focus on the rapid decrease of the aforementioned magnetic field and point out similarities to surface waves to the well known phenomenon of superdirectivity and to the method of auxiliary sources mas our study sheds light on the unusual nature of electromagnetic waves generated by currents with very rapid spatial variations subject to the condition that the discretization is fine we treat th

the use of the frill generator in thin wire integral equations for a frill generator feed certain fundamental mathematical properties of hallen s and pocklington s equations with the approximate kernel are stated and derived for a particular moment method procedure galerkin s method with pulse functions applied to hallen s equation the consequences to the numerical solutions are carefully examined generalizations to other numerical methods with subsectional basis functions are discussed many of our results come from studying the simpler problem of the infinite dipole analytically and applying the understanding thus obtained to the case of the finite dipole

a symmetry result for the torsion equation in an unbounded domain in 3d abstract we investigate an overdetermined problem for the torsion equation u 1 in an unbounded domain in r 3 under some additional conditions we show that the solution is a one dimensional quadratic function and that the boundary of the domain is a pair of parallel planes the proof is based on the maximum principle

optimization with reference based robust preference constraints we propose an optimization model using a novel robust preference relationship reference based almost stochastic dominance rsd the concept of rsd addresses the two problems in utility based dec

regularization of the moment matrix solution by a nonquadratic conjugate gradient method inspired by tikhonov regularization a nonlinear conjugate gradient method is proposed with the purpose of simultaneously regularizing and solving the moment matrix equation the procedure is based on a nonquadratic conjugate gradient algorithm with exact line search restart and rescale applied to the problem of tm scattering by perfectly conducting rectangular cylinders the method is shown to exhibit a fast convergence rate

iterative inverse scattering method employing gram schmidt orthogonalization abstract an inverse scattering method is tested which appears to work very well it is an iterative procedure based on the distorted wave born approximation the resulting fredholm equation of the first kind is solved by a projection method that requires the construction of an orthonormal set of basis functions from the set of kernel functions this can be done by the spectral expansion method which entails matrix diagonalization or by gram schmidt orthogonalization the method is tested on a simple one dimensional optical wave inverse scattering problem both orthonormalization methods lead to a rapidly convergent and stable iteration the spectral expansion method gives somewhat better results but the gram schmidt orthogonalization method which is the novel aspect of our approach is much less time consuming we show how the projection method can be generalized to the case of acoustic wave scattering where the target must be characterized by more than a single independent function of position

operator theoretic and computational approaches to ill posed problems with applications to antenna theory a general framework for regularization and approximation methods for ill posed problems is developed three levels in the resolution processes are distinguished and emphasized philosophy of resolution regularization approximation schema and regularization algorithms dilemmas and methodologies of resolution of ill posed problems and their numerical implementations are examined in this framework with particular reference to the problem of finding numerically minimum weighted norm least squares solutions of first kind integral equations and more generally of linear operator equations with nonclosed range a common problem in all these methods is delineated each method reduces the problem of resolution to a nonstandard minimization problem involving an unknown critical parameter whose optimal value is crucial to the numerical realization and amenability of the method the nonstandardness results from the fact that one does not have explicitly or a priori the function to be minimized it has to built up using additional information convergence rate estimates and robustness conditions etc several results are developed that complement recent advances in numerical analysis and regularization of inverse and ill posed identification and pattern synthesis problems an emphasis is placed on the role of constraints function space methods the role of generalized inverses and reproducing kernels in the regularization and stable computational resolution of these problems the results will be applied specifically to problems of antenna synthesis and identification however the thrust of the paper is devoted to the interdisciplinary character of operator theoretic and numerical methods for ill posed problems

risk return skewness and preference this paper considers choice between individual projects and shows that when the choice set includes arbitrary distributions then any assumed relationship between expected utility theory and general moment preferences for individual decision makers is theoretically unsound in particular a risk averse investor with any common utility function may when choosing between two positive return opportunities prefer the project simultaneously having a lower mean higher variance and lower positive skewness moreover the decision maker can prefer opportunities with higher variance even when the opportunities are continuous unimodal and arbitrarily visually and statistically close to the normal distribution in shape our conclusions hold for any decision maker with a utility function whose derivatives alternate in sign being strictly positive or negative i e we exclude the uninteresting cases of quadratic and cubic utilities the method of analysis is based upon the theory of tchebychev systems of functions which deals with the expected value of utility functions of stochastic variables with known moments although we focus on the first three moments the results as presented here apply to all higher moments as well it is also shown that there can be extremely large deviations between the certainty equivalents of distributions having the same moments so this result is also pertinent to practical decision analysts as well the paper demonstrates that the properties of utility functions have implications which are much more subtle than previously recognized for evaluating distributions in terms of their moments

the one phase free boundary problem for the p laplacian with non constant bernoulli boundary condition our objective here is to generalize our earlier results on the existence of classical convex solution to a free boundary problem with a bernoulli type boundary gradient condition and with the p laplacian as the governing operator the main theorems of this paper assert that the exterior and the interior free boundary problem with a bernoulli law i e with a prescribed pressure a x on the free streamline of the flow have convex solutions provided the initial domains are convex the continuous function a x is subject to certain convexity properties in our earlier results we have considered the case of constant a x in the lines of the proof of the main results we also prove the semi continuity up to the boundary of the gradient of the p capacitary potentials in convex rings with c 1 boundaries

a class of utility functions containing all the common utility functions this paper presents a class of utility functions class a that contains all of the utility functions commonly used for mathematical modeling the class consisting of those utility functions whose derivatives alternate in sign a simple representation via mixtures of exponential utilities is provided for this class which is both mathematically convenient and conducive to functional operations a connection with laplace transforms and the resultant implications for preference relations aggregation and utility assessment are discussed

existence of classical solutions to a free boundary problem for the p laplace operator i the exterior convex case in this paper we prove under convexity assumptions for the data the existence of classical solutions for a bernoulli type free boundary problem with the p laplacian as the governing operator the method employed here originates from a pioneering work of a beurling where he proves the existence for the harmonic case in the plane though with no geometrical restrictions

hausdorff moments hardy spaces and power series in this paper we consider power and trigonometric series whose coefficients are supposed to satisfy the hausdorff conditions which play a relevant role in the moment problem theory we prove that these series converge to functions analytic in cut domains we are then able to reconstruct the jump functions across the cuts from the coefficients of the series expansions by the use of the pollaczek polynomials we can thus furnish a solution for a class of cauchy integral equations

optimization with stochastic dominance constraints we introduce stochastic optimization problems involving stochastic dominance constraints we develop necessary and sufficient conditions of optimality and duality theory for these models and show that the lagrange multipliers corresponding to dominance constraints are concave nondecreasing utility functions the models and results are illustrated on a portfolio optimization problem

image reconstruction and restoration overview of common estimation structures and problems developments in the theory of image reconstruction and restoration over the past 20 or 30 years are outlined particular attention is paid to common estimation structures and to practical problems not properly solved yet the problem of image reconstruction and restoration is first formulated some of the current regularization approaches used to solve the problem are then described the concepts of a priori information and compound criterion are introduced a bayesian interpretation of the regularization techniques is given which clarifies the role of the tuning parameters and indicates how they could be estimated the practical aspects of computing the solution first when the hyperparameters are known and second when they must be estimated are then considered conclusions are drawn and points that still need to be investigated are outlined

fundamentals of thin wire integral equations with the finite gap generator part ii we discuss certain fundamental properties of hallen s and pocklington s equations with the finite gap generator fgg which has long been used as a feed model for cylindrical antennas for the case of the exact kernel we focus on whether important quantities are finite or infinite and compare to corresponding quantities obtained using the delta function generator dfg for the approximate kernel we focus on the unsolvability of the two equations and the relation of unsolvability to the important phenomenon of unphysical oscillations we also extend to the fgg the so called effective current method this is an easy to apply remedy for the oscillatory solutions that allows one to obtain reasonable answers for important quantities such as current distributions and the input impedance it is shown here that these answers are close to those obtained with the exact kernel we show that in a certain sense the method is more advantageous to apply in the present fgg case than in the dfg case our discussions especially in part ii of this paper bring out similarities to 1 the phenomenon of superdirectivity and 2 recently discussed numerical phenomena occurring within the method of auxiliary sources

reconstructing the thermal green functions at real times from those at imaginary times by exploiting the analyticity and boundary value properties of the thermal green functions that result from the kms condition in both time and energy complex variables we treat the general non perturbative problem of recovering the thermal functions at real times from the corresponding functions at imaginary times introduced as primary objects in the matsubara formalism the key property on which we rely is the fact that the fourier transforms of the retarded and advanced functions in the energy variable have to be the unique carlsonian analytic interpolations of the fourier coefficients of the imaginary time correlator the latter being taken at the discrete matsubara imaginary energies respectively in the upper and lower half planes starting from the fourier coefficients regarded as data set we then develop a method based on the pollaczek polynomials for constructing explicitly their analytic interpolations

eliminating unphysical oscillations arising in galerkin solutions to classical integral equations of antenna theory an asymptotic study previous works have discussed in detail the difficulties occurring when one applies numerical methods to hallen s and pocklington s integral equations for the current distribution along a linear antenna when the so called approximate kernel is used the main difficulty is the appearance of unphysical oscillations near the driving point and or near the ends of the antenna another work has proposed an easy to apply possible remedy to overcome these unnatural oscillations the basic idea is to define a new current from the near magnetic field produced by the original oscillating current in the present paper for the case of an antenna center driven by a delta function generator we place this remedy on a much firmer basis by means of an asymptotic study for the case of the linear antenna of infinite length we provide specific connections of our study to actual finite length antennas

on the solution of a class of cauchy integral equations in a previous paper we have presented a new method for solving a class of cauchy integral equations in this work we discuss in detail how to manage this method numerically when only a finite and noisy data set is available particular attention is focused on the question of the numerical stability

the source identification problem in electromagnetic theory the problem of the identification of the electromagnetic source which produces an assigned radiation pattern is ill posed the solution is in general not unique and it does not depend continuously on the data in this paper we treat in detail these two aspects of the problem first of all we reconsider the radiation problem in the very general setting of the sobolev spaces in order to make more acceptable from a physical viewpoint the conditions which have to be imposed on the electromagnetic sources then by the use of the euclidean character of the hilbert spaces we decompose the sources into a radiating and a non radiating component we determine the subspace of the radiating sources and we find the basis spanning this subspace particular attention is then devoted to the case of the linear antenna in this case the solution of the problem is unique but it does not depend continuously on the data we may however implement the problem taking into account a bound on the ohmic losses this is sufficient to restore the continuity finally a method of variational regularization in the sense of tikhonov is discussed in detail

on partially and globally overdetermined problems of elliptic type we consider some elliptic pdes with dirichlet and neumann data prescribed on some portion of the boundary of the domain and we obtain rigidity results that give a classication of the solution and of the domain in particular we nd mild conditions under which a partially overdetermined problem is in fact globally overdetermined this enables to use several classical results in order to classify all the domains that admit a solution of suitable general partially overdetermined problems these results may be seen as solutions of suitable inverse problems that is to say given that an overdetermined system possesses a solution we nd the shape of the admissible domains models of these type arise in several areas of mathematical physics and shape optimization

tissue elasticity reconstruction using linear perturbation method a new method to reconstruct the elastic modulus of soft tissue subjected to an external static compression is presented in this approach the newton raphson method is used to vary a finite element fe model of the elasticity equations to fit in a least squared sense a set of axial tissue displacement fields estimated using a correlation technique applied to ultrasound signals the ill conditioning of the hessian matrix is eliminated using the tikhonov regularization technique this regularization provides a compromise between fidelity to the observed data and a priori information of the solution using an echographic image formation model it is shown that the method converges within a few iterations 8 10 and that strain images artifacts which are common in elastography are significantly reduced after the resolution of the inverse problem

some inverse problems around the tokamak tore supra we consider two inverse problems related to the tokamak textsl tore supra through the study of the magnetostatic equation for the poloidal flux the first one deals with the cauchy issue of recovering in a two dimensional annular domain boundary magnetic values on the inner boundary namely the limiter from available overdetermined data on the outer boundary using tools from complex analysis and properties of genereralized hardy spaces we establish stability and existence properties secondly the inverse problem of recovering the shape of the plasma is addressed thank tools of shape optimization again results about existence and optimality are provided they give rise to a fast algorithm of identification which is applied to several numerical simulations computing good results either for the classical harmonic case or for the data coming from textsl tore supra

high resolution boosted deconvolution of spectroscopic data the quality of the analysis of spectrometric data consists in correct identification of the existence of peaks and subsequently in good estimation of their positions in this paper we present high resolution deconvolution algorithms we propose an improvement in the efficiency by introducing a boosting operation into the deconvolution process

maximum entropy regularization in inverse synthetic aperture radar imagery the method of maximum entropy is applied to the regularization of inverse synthetic aperture radar isar image reconstructions this is accomplished by considering an ensemble of images with associated allowed probability density functions instead of directly considering the solution to be an image the author takes it to be the a posteriori probability density found by minimizing a regularization functional composed of the usual least squares term and a kullback cross entropy information difference term the desired image is then found as the expectation of this density the basic model of this approach is similar to that used in usual maximum a posteriori analysis and allows for a more general relationship between the image and its configuration entropy than is usually employed in addition it eliminates the need for inappropriate nonnegativity constraints on the generally complex valued image

on the use of nonsingular kernels in certain integral equations for thin wire circular loop antennas fundamental properties of certain popular integral equations for thin wire circular loop antennas with nonsingular kernels are studied the cornerstone of our study is a large asymptotic formula for the n th fourier coefficient of the nonsingular kernel four different methods of driving the circular loop are considered namely the delta function generator the finite gap generator a certain type of frill generator and the case of plane wave incidence the excitation model is crucial to our discussions since it determines the behavior of the solution convergence also discussed are associated difficulties that may arise when moment methods are applied to the aforementioned equations as well as a simple improvement to the fourier series method for determining the current in the case of the frill generator the main results herein closely parallel recent results for the case of the straight antenna and similarities and differences between the straight and circular cases are discussed

constant exchange risk properties this paper develops a methodology using risk properties to characterize the functional form of a utility measure for decision making under uncertainty the constant absolute risk property for example is known to be necessary and sufficient with appropriate regularity conditions for the utility function to have either a linear or an exponential form a new generalization of this property called the constant exchange risk property gives a characterization of six utility functions the linear function the exponential function the quadratic function the sum of two exponential functions the sum of a linear and an exponential function and the product of a linear and an exponential function since all of these functional forms have been used previously as approximations this methodology allows analysts to distinguish beforehand between alternative forms and thus properly specify the utility function in applications

on the existence of convex classical solutions for multilayer free boundary problems with general nonlinear joining conditions we prove the existence of convex classical solutions for a general multidimensional multilayer free boundary problem the geometric context of this problem is a nested family of closed convex surfaces except for the innermost and outermost surfaces which are given these surfaces are interpreted as unknown layer interfaces where the layers are the bounded annular domains between them each unknown interface is characterized by a quite general nonlinear equation called a joining condition which relates the first derivatives along the interface of the capacitary potentials in the two adjoining layers as well as the spatial variables a well known special case of this problem involves several stationary immiscible two dimensional flows of ideal fluid related along their interfaces by bernoulli s law

on a class of minimax stochastic programs for a particular class of minimax stochastic programming models we show that the problem can be equivalently reformulated into a standard stochastic programming problem this permits the direct use of standard decomposition and sampling methods developed for stochastic programming we also show that this class of minimax stochastic programs is closely related to a large family of mean risk stochastic programs where risk is measured in terms of deviations from a quantile

fast solutions of the 2d inverse scattering problem based on a tsvd approximation of the internal field for the forward model an alternative formulation of the microwave tomography problem is proposed in order to reduce the computation time of the inversion procedure the well known multiplicative regularized contrast source inversion method is used as reference algorithm our formulation is based on a truncated singular value decomposition of the matrix involved in the most computationally intensive operations of the inversion algorithm after theoretical and practical investigation of the behavior of the singular values it is shown that the corresponding approximation does not yield any significant degradation of the quality of the solutions even for large complex permittivity contrasts while the computation times are reduced by a factor ranging between 1 1 and 6 with respect to the original method

flattening results for elliptic pdes in unbounded domains with applications to overdetermined problems semilinear elliptic pdes are dealt with either in the half space or in overdetermined settings we obtain several new results and also give new proofs of celebrated theorems by exploiting some geometric analysis of level sets a geometric inequality and a pointwise gradient estimate

on two types of convergence in the method of auxiliary sources the method of auxiliary sources mas is often applied to problems involving an externally illuminated smooth perfect electric conductor pec one seeks to approximately satisfy the boundary condition on the pec surface using auxiliary sources located inside the pec surface usually the underlying auxiliary surface is also smooth and closed the currents on the auxiliary sources mas currents are the initial unknowns once they have been found one can easily determine the field due to them mas field at all points external to the auxiliary surface and in particular at all points external to the pec scatterer we show that in the limit n it is possible to have a convergent mas field together with divergent mas currents and that this phenomenon is accompanied by an abrupt behavior of the limiting value of the mas field we show this possibility through an analytical study of a two dimensional scattering problem involving a circular cylinder in which mas fields and currents can be determined explicitly the analytical study proceeds from first principles it involves fundamental electromagnetics and relatively simple mathematical manipulations numerical results supplement the analytical study and demonstrate the nature of the aforementioned divergence our study sheds light on other aspects of mas in particular it establishes interesting similarities and differences between mas and its continuous version and reveals many similarities between mas currents and numerical solutions of hallen s integral equation with the approximate kernel

on the computational model of a kind of deconvolution problem it is known that discretization of a continuous deconvolution problem can alleviate the ill posedness of the problem the currently used circulant matrix model however does not play such a role moreover the approximation of deconvolution problems by circulant matrix model is rational only if the size of the kernel function is very small we propose an aperiodic model of deconvolution for discrete and finite deconvolution problems the new model is an exact one in the general case the new model can lead to a nonsingular system of equations that has a lower condition number than the circulant one and the related computations in the deconvolution can be done efficiently by means of the dft technique as in the ease for circulant matrices the rationality of the new model holds without regard to the size of the kernel and the image the use of the aperiodic model is illustrated by gradient based algorithms

on the phenomenon of oscillations in the method of auxiliary sources when one applies the method of auxiliary sources to scattering problems involving perfect conductors one first seeks fictitious auxiliary currents located inside the conductor and then determines the field from these currents for a simple two dimensional problem involving an infinite circular cylinder illuminated by an electric current filament it has recently been shown analytically that it is possible to have divergent auxiliary currents to make this statement precise one must properly normalize the currents together with a convergent field it was also shown through numerical investigations that the aforementioned divergence appears as abnormal rapid oscillations in the present paper we investigate such phenomena in more detail with particular emphasis on oscillations for a perfectly conducting ground plane illuminated by an electric current filament we once again demonstrate the possibility of having divergent oscillating currents producing a convergent field we develop an asymptotic formula for the oscillating current values which sheds light on the nature of the oscillations we revisit the circular cylinder problem to develop a similar asymptotic formula we also discuss roundoff errors and possible generalizations to scatterers of other shapes the present study is to a great extent analytical with the analytical predictions confirmed and supplemented by numerical results

reply to comments on fundamentals of thin wire integral equations with the finite gap generator in papers 1 2 the authors extend the so called effective current method to the hallen s and pocklington s equations with the finite gap generator fgg the indicated method considered earlier in 3 with a reference to 4 is associated with application of the method of auxiliary sources to the analysis of cylindrical dipole antennas 5 7 the purpose of these comments is to draw the authors and readers attention to the existence ofpaper 8 where the pocklington s equation with the fgg is solved for the axial current considered there to be auxiliary the equation is solved by the galerkin method using the piecewise sinusoidal basis and testing functions the auxiliary axial current is used further for calculation of the surface current which is referred to as the effective current in 1 4 and the surface current itself is used for calculation of the input impedance so in some respects papers 1 7 just repeat the main idea and technique of paper 8 although of course papers 1 7 also contain a lot of their own new interesting and useful analytical and numerical results

multiattribute utility satisfying a preference for combining good with bad an important challenge in multiattribute decision analysis is the choice of an appropriate functional form for the utility function we show that if a decision maker prefers more of any attribute to less and prefers to combine good lotteries with bad as opposed to combining good with good and bad with bad her utility function should be a weighted average a mixture of multiattribute exponential utilities mixex utility in the single attribute case mixex utility satisfies properties typically thought to be desirable and encompasses most utility functions commonly used in decision analysis in the multiattribute case mixex utility implies aversion to any multivariate risk risk aversion with respect to any attribute decreases as that attribute increases under certain restrictions such risk aversion also decreases as any other attribute increases and a multivariate one switch property is satisfied one of the strengths of mixex utility is its ability to represent cases where utility independence does not hold but mixex utility can be consistent with mutual utility independence and take on a multilinear form an example illustrates the fitting of mixex utility to preference assessments

robust mean covariance solutions for stochastic optimization we provide a method for deriving robust solutions to certain stochastic optimization problems based on mean covariance information about the distributions underlying the uncertain vector of returns we prove that for a general class of objective functions the robust solutions amount to solving a certain deterministic parametric quadratic program we first prove a general projection property for multivariate distributions with given means and covariances which reduces our problem to optimizing a univariate mean variance robust objective this allows us to use known univariate results in the multidimensional setting and to add new results in this direction in particular we characterize a general class of objective functions the so called one or two point support functions for which the robust objective is reduced to a deterministic optimization problem in one variable finally we adapt a result from geoffrion 1967a to reduce the main problem to a parametric quadratic program in particular our results are true for increasing concave utilities with convex or concave convex derivatives closed form solutions are obtained for special discontinuous criteria motivated by bonus and commission based incentive schemes for portfolio management we also investigate a multiproduct pricing application which motivates extensions of our results for the case of nonnegative and decision dependent returns

intensity estimation from shot noise data the estimation of the intensity function of a poisson driven shot noise process is addressed using a regularization technique where the data is modeled as a signal term plus a signal dependent noise term a new data based method for selecting a pair of regularization parameters is presented and compared with the minimum unbiased risk method the detail in the intensity function can be recovered by both methods but the new method does a better job at suppressing spurious oscillations

stationary nonstationary and hybrid iterative method of moments solution schemes the purpose of this paper is to report on the convergence rates of two iterative matrix solution methods individually and then to combine the two methods into a hybrid scheme to achieve additional convergence rate benefits one iterative matrix solver investigated is the sparse iterative method sim which is a stationary jacobi like solver but uses a sparse and not a banded matrix with matrix elements corresponding to strong interactions rather than position in the matrix in this paper the sim is modified to include an adaptive relaxation scheme to improve its convergence speed and numerical stability another iterative scheme investigated is the nonstationary biconjugate gradient stabilized bicgstab method it is shown that the bicgstab is considerably improved when the method is preconditioned by the sparse matrix used in the sim method finally a hybrid scheme is proposed which combines both sim ar and bicgstab precon and it is shown that the hybrid gives best results on the problems considered examples giving convergence time versus accuracy are presented for two problems a wire grid plate and a wire grid partial helicopter

watson resummation of a class of hausdorff transformed power series in this paper we study a class of hausdorff transformed power series whose convergence is extremely slow for large values of the argument we perform a watson type resummation of these expansions and obtain by the use of the pollaczek polynomials a new representation whose convergence is much faster we can thus propose a new algorithm for the numerical evaluation of these expansions which include series playing a relevant role in the computation of the partition function in statistical mechanics by the same procedure we obtain also a solution of the classical hausdorff moment problem

fast numerical methods for bernoulli free boundary problems the numerical solution of the free boundary bernoulli problem is addressed an iterative method based on a level set formulation and boundary element method is proposed issues related to the implementation the accuracy and the generality of the method are discussed the efficiency of the approach is illustrated by numerical results