determining conductivity by boundary measurements ii interior results abstract in a recent paper the authors showed that an unknown real analytic conductivity gamma may be determined from static boundary measurements in this document they extend this analysis by demonstrating that a similar result holds for piecewise real analytic conductivities in addition for the special case of a layered structure it is shown that a three times continuously differentiable conductivity is identifiable by boundary measurements originator supplied keywords include inversion convergence algorithms estimates coefficients

an inverse boundary value problem for schrodinger operators with vector potentials we consider the schrodinger operator for a magnetic potential a and an electric potential q which are supported in a bounded domain in r n with n 3 we prove that knowledge of the dirichlet to neumann map associated to the schrodinger operator determines the magnetic field rot a and the electric potential 4 simultaneously provided rot a is small in the l topology

algorithm and mechanization to cauchy problem of parabolic equation the present paper discusses the algorithm and mechanization to the cauchy problem of parabolic equation the author uses the initial data to construct the solutions that satisfy the initial condition and obtain a brief algorithm to this problem thereafter the algorithm is used in maple to solve this cauchy problem automatically

comment on a p calderon s paper on an inverse boundary value problem in seminar on numerical analysis and its applications to continuum physics rio de janeiro 1980 65 73 soc brasil mat rio de janeiro 1980 mr0590275 81k 35160

effects of measurement precision and finite numbers of electrodes on linear impedance imaging algorithms impedance imaging systems reconstruct approximations to the conductivity inside a body from electrical measurements made on the boundary the linearized problem was studied by calderon who showed that if the conductivity differs little from a constant then it can be reconstructed approximately in his work calderon assumed that arbitrary current densities can be applied anywhere on the body s surface and the resulting voltages perfectly measured in practice however imaging systems apply currents through a finite number of electrodes on the surface and measure the resulting voltages with a limited precision in this paper linear algorithms are described for approximating the electrical conductivity in a disk from finitely many limited precision measurements the effects of finite precision and electrode number on a two dimensional version of calderon s method are studied it is shown that as the measurement errors go to zero and the electrodes proliferate in a space filling manner the finite electro

the inverse scattering problem on a fixed energy level for the two dimensional schrodinger operator this paper contains a solution with complete proofs of the main problems of the inverse scattering at fixed energy e for the schrodinger two dimensional operator with decreasing coefficients uniqueness of the reconstruction a reconstruction procedure characterization of the scattering data most completed results are obtained under the condition of smallness of coefficients in comparison with the number e this paper develops and generalizes several preceded papers

a mechanical algorithm for solving ordinary differential equation in this paper by using the theories and methods of mathematics analysis ordinary differential equation and computer algebra a reliable algorithm for solving ordinary differential equation ode was established and a new maple procedure mechodeproc was established too the results of the examples indicated that the procedure mechodeproc based on taylor polynomial method was simple and effective and could provide an accuracy approximate solution or exact solution of the ordinary differential equation this would be useful for solving differential equation

nonholonomic systems controllability and complexity abstract this paper presents a survey of recent combinatorial results arising in the study of nonholonomic control systems it addresses the question of deciding whether a system is controllable or not basic concepts in differential geometric control theory are first introduced and illustrated through the classical example of a multibody mobile robot we then summarize recent results obtained on polynomial systems

uniqueness for the inverse boundary value problem with singular potentials in 2d in this paper we consider the inverse boundary value problem for the schrodinger equation with potential in l p class p 4 3 we show that the potential is uniquely determined by the boundary measurements

a new algorithm for symbolic integral with application in this paper by using the theories and methods of mathematical analysis and computer algebra a new algorithm of symbolic integral was established a new maple procedure myint for it was established too and it was applied to the automatic proving the mean value theorems for derivatives the results indicated that the algorithm of symbolic integral had been established in this paper had advantage of simple idea excellent property for operation and powerful competence this would be useful for the problem of solving differential equations automatic proving some mathematical theorems and so on

an anisotropic inverse boundary value problem we consider the impedance tomography problem for anisotropic conductivities given a bounded region in space a diffeomorphism from to itself which restricts to the identity on and a conductivity on it is easy to construct a new conductivity which will produce the same voltage and current measurements on we prove the converse in two dimensions i e if 1 and 2 produce the same boundary measurements then 1 2 for an appropriate for conductivities which are near a constant

inverse scattering for singular potentials in two dimensions we consider the schrodinger equation for a compactly supported potential having jump type singularities at a subdomain of r2 we prove that knowledge of the scattering amplitude at a fixed energy determines the location of the singularity as well as the jump across the curve of discontinuity this result follows from a similar result for the dirichlet to neumann map associated to the schrodinger equation for a compactly supported potential with the same type of singularities 1 introduction and statement of the results in this paper we consider the schrodinger equation for a compactly supported potential q having jump type singularities at a subdomain of k2 we prove that knowledge of the scattering amplitude at a fixed energy ao determines the location of the singularity as well as the jump across the curve of discontinuity this problem is reduced to the study of the dirichlet to neumann map for the schrodinger operator a q x in a bounded domain of r2 for the application considered here it is enough to consider the domain to be a ball containing the support of q we prove that in dimension two the dirichlet to neumann map for the schrodinger operator a q x determines uniquely the location of the singularity of q as well as its jump across the curve of discontinuity the scattering amplitude of a potential q l rn with compact support is defined via the outgoing eigenfunctions namely mx r 0 co s x there exists i x x co solution of

algorithm and mechanization to cauchy problem of wave equation with linear damping and source terms this paper discusses the cauchy problem of wave equation with linear damping and source terms the author reduces the problem to a parabolic one and uses the corresponding initial value to construct the solutions of the resulting parabolic problem thereafter he obtains a brief algorithmization formula to this problem with mechanization in maple

a uniqueness theorem for an inverse boundary value problem in electrical prospection we show that a near constant conductivity of a two dimensional body can be uniquely determined by steady state direct current measurements at the boundary mathematically we show that the coefficient in the operator is uniquely determined by its dirichlet integrals

on the uniqueness of inverse problems from incomplete boundary data we present a generalization of our previous results on the uniqueness of inverse coefficient problems for elliptic equations the theorem proved here is formulated for piecewise constant coefficients with piecewise smooth interfaces of discontinuities which require local boundary data we consider problems with coefficients unknown at one side as well as at both sides of the boundary the uniqueness of the former is proven the latter can yield up to two solutions the proofs are based on a simple analysis of singularities of the green functions the presented approach exactly conforms to some important inverse problems arising in applications of electromagnetic geophysics

recovery of singularities for formally determined inverse problems in this paper we considered several formally determined problems in two dimensions there are no global identifiability results for these problems however we can recover an important feature of these functions namely their singularities more precisely we prove that one can determine the location and strength of singularities of anl compactly supported potential by knowing the associated scattering amplitude at a fixed energy also we prove that one can determine the location and strength of the singularities of the sound speed of a medium by making measurements just on the boundary of the medium

an algorithm for solving the high order nonlinear volterra fredholm integro differential equation with mechanization abstract in this paper by using the theories and methods of mathematics analysis and computer algebra a reliable algorithm for solving high order nonlinear volterra fredholm integro differential equations was established and a new maple procedure voltfredproc was established too the results of the examples indicated that the procedure voltfredproc of taylor polynomial method is simple and effective and could provide an accuracy approximate solution or exact solution of the high order nonlinear volterra fredholm integro differential equation this would be useful for solving integro differential equation integral equations and ordinary differential equation

a real time algorithm for the location search of discontinuous conductivities with one measurement we consider an inverse problem for finding the anomaly of discontinuous electrical conductivity by one current voltage observation we develop a real time algorithm for determining the location of the anomaly this new idea is based on the observation of the pattern of a simple weighted combination of the input current and the output voltage combined with the size estimation result this algorithm gives a good initial guess for newton type schemes we give the rigorous proof for the location search algorithm both the mathematical analysis and its numerical implementation indicate our location search algorithm is very fast stable and efficient 2001 john wiley sons inc

a bound for the degree of nonholonomy in the plane let v1 vs be a system made with vector fields v1 vs in rn whose coordinates are polynomials of degree d to such a system is associated the control system x u1v1 it is proven that in the case n 2 the degree of nonholonomy of such a system is bounded by a function 2 d 6d2 2d 2

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

a method for solving an inverse biharmonic problem this paper deals with the problem of determining of an unknown coefficient in an inverse boundary value problem using a nonconstant overspecified data it has been shown that the solution to this inverse problem exists and is unique

inverse problems in quasilinear anisotropic media we consider the question of whether one can determine the anisotropic quasilinear conductivity of a medium by making voltage and current measurements at the boundary we prove that all the known results for the linear case also hold in the quasilinear case

uniqueness for formally determined inverse boundary value problems abstract in this paper we study the inverse conductivity problem in two dimensions this problem is reduced to a formally determined inverse boundary value problem for the schrodinger equation some recent generic uniqueness results for the inverse problems will be discussed and a new continuous dependence result presented

on the construction of a potential from cauchy data abstract we investigate the problem of recovering a potential q y in the differential equation u q y u 0 x y 0 1 0 1 u 0 y u 1 y u x 0 0 u x 1 f x u y x 1 g x the method of separation of variables reduces the recovery of q y to a nonstandard inverse sturm liouville problem an asymptotic formula is developed that suggests that under appropriate conditions on the cauchy pair f g q y is uniquely determined up to the mean moreover the recovery of q y is comparable to finding a function from its polynomial moments a reconstruction scheme is suggested and numerical examples are considered

an implementation for the algorithm of hirota bilinear form of pde in the maple system abstract in this paper based on the hirota bilinear method a reliable algorithm for generating bilinear form of a class of nonlinear partial differential equations npde is described and a maple package bilinearization is established the package will be helpful for looking for the bilinear form of npde by logarithm transformation

an algorithm for solving daes with mechanization in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of pade approximation method for solving differential algebraic equation systems was established and a new maple procedures mainproc was established too ten examples are presented to illustrate the implementation of the program

an algorithm for solving nonlinear singular perturbation problems with mechanization in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of pade approximation method for solving nonlinear singular perturbation problems was established a new maple procedure spp was established too the procedure spp give not only the approximate analytic solutions but also the numerical solutions of spp six examples are presented to illustrate the implementation of the program the method is very simple and effective for most of singular perturbation problems this would be useful for solving differential equations

finite determination of accessibility and singular points of nonlinear systems an algebraic approach abstract exploiting tools from algebraic geometry the problem of determination of accessibility strong accessibility is investigated for polynomial systems and also for analytic systems that are immersible into polynomial systems the results are constructive and algorithms are given to find the maximum depth of lie brackets necessary for deciding accessibility strong accessibility of the system at any point called here accessibility strong accessibility index of the system and known as the degree of non holonomy in the literature alternatively upper bounds on the accessibility strong accessibility index are obtained which can be computed easier in each approach the entire set of accessibility strong accessibility singular points are obtained as a limiting algebraic set of a strictly increasing chain of ideals that stabilizes in finite time several examples demonstrate the applicability of the results using computer algebra tools

transparent potentials at fixed energy in dimension two fixed energy dispersion relations for the fast decaying potentials for the two dimensional schrodinger equation delta v x psi e psi x in mathbb r 2 e e fixed 0 at a fixed positive energy with a fast decaying at infinity potentialv x dispersion relations on the scattering data are given under small norm assumption using these dispersion relations we give without a complete proof of sufficiency a characterization of scattering data for the potentials from the schwartz classs c 2 for the potentials with zero scattering amplitude at a fixed energyefixed transparent potentials we give a complete proof of this characterization as a consequence we construct a family parametrized by a function of one variable of two dimensional spherically symmetric real potentials from the schwartz classs transparent at a given energy for the two dimensional case without assumption that the potential is small we show that there are no nonzero real exponentially decreasing at infinity potentials transparent at a fixed energy for any dimension greater or equal to 1 we prove that there are no nonzero real potentials with zero forward scattering amplitude at an energy interval we show that kdv type equations in dimension 2 1 related with the scattering problem the novikov veselov equations do not preserve in general these dispersion relations starting from the second one as a corollary these equations do not preserve in general the decay rate faster than x 3 for initial data from the schwartz class

identification of small inhomogeneities of extreme conductivity by boundary measurements a theorem on continuous dependence we consider an electrostatic problem for a conductor consisting of finitely many small inhomogeneities of extreme conductivity embedded in a spatially varying reference medium firstly we establish an asymptotic formula for the voltage potential in terms of the reference voltage potential the location of the inhomogeneities and their geometry secondly we use this representation formula to prove a lipschitz continuous dependence estimate for the corresponding inverse problem this estimate bounds the difference in the location and in certain geometric properties of two sets of inhomogeneities by the difference in the boundary voltage potentials corresponding to a fixed current distribution

a new mechanical algorithm for solving the second kind of fredholm integral equation integral equation has been one of principal tool of various areas of applied mathematics physics and engineering in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm for solving the second kind of fredholm integral equation is established and a mechanical maple algorithm fredholmproc is established too the algorithm can provide the continuous solution of the second kind of fredholm integral equation ten examples are presented to illustrate the efficiency and accuracy of the algorithm this will be useful for solving the integral equation

inverse spectral problems on hyperbolic manifolds and their applications to inverse boundary value problems in euclidean space we propose a new approach to solve the inverse boundary value problems in the euclidean space the idea consists of embedding the problem into hyperbolic manifolds and using their spectral properties as a by product one can discuss the reconstruction of local conformal deformation of the metric of hyperbolic manifolds from the spectral data at infinity we also propose a new spectral data observed from the cusp neighborhood at infinity

on excursions of reflecting brownian motion on etudie les proprietes des excursions d un mouvement brownien reflechissant sur un domaine lisse borne dans r d et on donne une procedure de construction du processus

direct reconstructions of conductivities from boundary measurements the problem of reconstructing an unknown electric conductivity from boundary measurements has applications in medical imaging geophysics and nondestructive testing a nachman ann of math 2 143 1996 pp 71 96 proved global uniqueness for the two dimensional inverse conductivity problem using a constructive method of proof based on this proof siltanen mueller and isaacson inverse problems 16 2000 pp 681 699 presented a new numerical reconstruction method that solves the nonlinear problem directly without iteration the method was verified with nonnoisy rotationally symmetric examples in this paper the method is extended by introducing a new regularization scheme which is analyzed theoretically and tested on symmetric and nonsymmetric numerical examples containing computer simulated noise

a mechanical algorithm for solving the volterra integral equation in this paper by using the theories and methods of integral equation and computer algebra a reliable algorithm for solving the volterra integral equation is established and a new maple algorithm mainproc is established too some examples are presented to illustrate the implementations of the algorithm the results of the examples indicate that the algorithm of taylor polynomial method is simple and effective and can provide an accuracy approximate solution or exact solution of the volterra integral equation and integro differential equation this will be useful for solving a system of integral equation or integro differential equation

mechanization for solving spp by reducing order method in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of reduction of order approximation method for solving singular perturbation problems was established a new maple procedure redordproc was established too the procedure redordproc give not only the approximate analytic solutions but also the numerical solutions of the kinetics problems some examples are presented to illustrate the implementation of the program

global uniqueness for a two dimensional inverse boundary value problem we show that the coefficient y x of the elliptic equation vie qyvu 0 in a two dimensional domain is uniquely determined by the corresponding dirichlet to neumann map on the boundary and give a reconstruction pro

comment on calderon s paper on an inverse boundary value problem calder6n determined a method to approximate the conductivity a of a con ducting body in rn for n 2 based on measurements of boundary data the approximation is good in the l norm provided that the conductivity is a small perturbation from a constant we calculate the approximation exactly for the case of homogeneous concentric conducting disks in r2 with different conductivities here the difference in the conductivities is the perturbation we show that the approximation yields precise information about the spatial variation of a even when the perturbation is large this ability to distinguish spatial regions with different conductivities is important for clinical monitoring applications

maple packages for computing hirota s bilinear equation and multisoliton solutions of nonlinear evolution equations abstract the hirota method for generating hirota s bilinear equation and constructing soliton solutions of nonlinear evolution equations is discussed and illustrated two maple programs bilinearization and multisoliton are presented to automatically calculate hirota s bilinear equations for nonlinear evolution equations and to compute their n soliton solutions for n 1 2 or 3 respectively different kinds of examples are used to demonstrate the effectiveness of the packages

mechanical algorithm for solving the second kind of volterra integral equation in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm for solving the second kind of volterra integral equation is established and a new maple procedure voltproc is established too in particular the algorithm can provide the exact solution of the second kind of volterra integral equation by the methods of neumann series and mathematical induction i e the algorithm also can computing the nth term by finite terms of the iterative kernel some examples are presented to illustrate the efficiency and accuracy of the algorithm this will be useful for the integral equation solving and mathematical theorems automatic proving

computations of multi resultant with mechanization abstract resultant is a classical algebraic tool for determining whether or not a polynomial systems have a common root without explicitly solving for the roots but the complexity of resultants can be very high in practice in this paper by using the theories and methods of computer algebra two reliable algorithms for computing multi resultant problems dixon resultant and macaulay resultant were established two new maple procedures dixonres and macaulayres were established too some examples are presented to illustrate the implementations of the programs this would be useful for solving a system of polynomial equations

perturbation method for abstract second order inverse problems abstract we are concerned with an abstract second order inverse problem we restrict ourselves here to abstract inverse problems in which in order to solve the differential equation for u t it is necessary to know the value of some operator or functional u t g t as a function of the argument t a new approach based on the perturbation theory of linear operators is introduced among the results obtained we point out sufficient conditions of existence and uniqueness of a solution as a possible application of the abstract theorems some applications from elasticity theory are given

a uniqueness theorem for an inverse boundary value problem in two dimensions abstract we consider the inverse problem to determine the potential q entering the schrodinger equation u qu 0 in a bounded smooth domain in r 2 in terms of the boundary measurements dirichlet to neumann map when n 3 the uniqueness for the inverse problem was well established in this paper we prove the uniqueness in two dimensions under the assumption that the lp p 2 norm of q is small this result improves a uniqueness result of sylvester uhlmann under the assumption that the w1 norm of q is small

global uniqueness for a two dimensional semilinear elliptic inverse problem for a general class of nonlinear schrodinger equations au a x u 0 in a bounded planar domain 2 we show that the function a x u can be recovered from knowledge of the corresponding dirichlet to neumann map on the boundary dq

computer aided solving the high order transition probability matrix of the finite markov chain in this paper by using theories of stochastic process and computer algebra a reliable algorithm for computing the high order transition probability matrix of finite markov chain is established a new mechanical procedure markovproc is established too the procedure markovproc give not only the exact expression of the markov chains but also the limiting probability some examples are presented to illustrate the implementation of the algorithm

variations on a theme of jost and pais abstract we explore the extent to which a variant of a celebrated formula due to jost and pais which reduces the fredholm perturbation determinant associated with the schrodinger operator on a half line to a simple wronski determinant of appropriate distributional solutions of the underlying schrodinger equation generalizes to higher dimensions in this multi dimensional extension the half line is replaced by an open set r n n n n 2 where has a compact nonempty boundary satisfying certain regularity conditions our variant involves ratios of perturbation determinants corresponding to dirichlet and neumann boundary conditions on and invokes the corresponding dirichlet to neumann map as a result we succeed in reducing a certain ratio of modified fredholm perturbation determinants associated with operators in l 2 d n x n n to modified fredholm determinants associated with operators in l 2 d n 1 n 2 applications involving the birman schwinger principle and eigenvalue counting functions are discussed