compensation of modelling errors due to unknown domain boundary in electrical impedance tomography electrical impedance tomography is a highly unstable problem with respect to measurement and modeling errors this instability is especially severe when absolute imaging is considered with clinical measurements accurate knowledge about the body shape is usually not available and therefore an approximate model domain has to be used in the computational model it has earlier been shown that large reconstruction artefacts result if the geometry of the model domain is incorrect in this paper we adapt the so called approximation error approach to compensate for the modeling errors caused by inaccurately known body shape this approach has previously been shown to be applicable to a variety of modeling errors such as coarse discretization in the numerical approximation of the forward model and domain truncation we evaluate the approach with a simulated example of thorax imaging and also with experimental data from a laboratory setting with absolute imaging considered in both cases we show that the related modeling errors can be efficiently compensated for by the approximation error approach we also show that recovery from simultaneous discretization related errors is feasible allowing the use of computationally efficient reduced order models

three periodic solutions for perturbed second order hamiltonian systems in this paper we study the existence of three distinct solutions for the following problem u a t u f t u g t u a e in 0 t u t u 0 u t u 0 0 where r t is a real positive number a 0 t rn n is a continuous map from the interval 0 t to the set of n order symmetric matrices we propose sufficient conditions only on the potential f more precisely we assume that g satisfies only a usual growth condition which allows us to use a variational approach

chaos control in multistable delay differential equations and their singular limit maps the multistability exhibited by first order delay differential equations dde s at large delay to response ratios r is useful for the design of dynamical memory devices this paper first characterizes multistability in the mackey glass dde at large r the extended control of its unstable periodic orbits upo s based on additional feedback terms evaluated at many times in the past is then presented the method enhances the control of upo s and of their harmonics further the discrete time map obtained in the singular perturbation limit of the controlled dde is useful to characterize the range of parameters where this extended control occurs our paper then shows how this singular limit map leads to an improved method of controlling upo s in continuous time difference equations and in discrete time maps the performance of the method in the general contexts of extended additive and parametric control is evaluated using the logistic map and the mackey glass map the applicability of the method is finally illustrated on the nagumo sato discrete time neural network model

different regimes of synchronization in nonidentical time delayed maps abstract we study the synchronization of time delayed nonidentical maps subject to unidirectional master slave coupling the individual dynamics of the maps have a delay n 1 and the coupling acts with a delay n 2 we show analytically that suitably tuning the slave map parameters two distinct synchronization regimes can occur in one regime the lag time between the slave and the master maps is given by the delay of the coupling n 2 while in the other regime is given by the difference between the delays n 1 n 2 we analyze the effect of the coupling strength on the different synchronization regimes in logistic and henon maps

infinitely many nontrivial periodic solutions for damped vibration problems with asymptotically linear terms in this paper we study a class of damped vibration problem with asymptotically quadratic terms at infinity we obtain infinitely many nontrivial periodic solutions by variational method to the best of our knowledge there is no published result focusing on this class of damped vibration problem with asymptotically quadratic terms at infinity

periodic solutions of classical hamiltonian systems without palais smale condition abstract in this paper we study the existence of periodic solutions for classical hamiltonian systems without the palais smale condition we prove that the information of the potential function contained in a finite domain is sufficient for the existence of periodic solutions moreover we establish the existence of infinitely many periodic solutions without any symmetric condition on the potential function v

anticipated synchronization in coupled chaotic maps with delays abstract we study the synchronization of two chaotic maps with unidirectional master slave coupling both maps have an intrinsic delay n1 and coupling acts with a delay n2 depending on the sign of the difference n1 n2 the slave map can synchronize to a future or a past state of the master system the stability properties of the synchronized state are studied analytically and we find that they are independent of the coupling delay n2 these results are compared with numerical simulations of a delayed map that arises from discretization of the ikeda delay differential equation we show that the critical value of the coupling strength above which synchronization is stable becomes independent of the delay n1 for large delays

the inverse conductivity problem with an imperfectly known boundary in three dimensions we consider the inverse conductivity problem in a strictly convex domain whose boundary is not known usually the numerical reconstruction from the measured current and voltage data is done assuming that the domain has a known fixed geometry however in practical applications the geometry of the domain is usually not known this introduces an error and effectively changes the problem into an anisotropic one the main result of this paper is a uniqueness result characterizing the isotropic conductivities on convex domains in terms of measurements done on a different domain which we call the model domain up to an affine isometry as data for the inverse problem we assume the robin to neumann map and the contact impedance function on the boundary of the model domain to be given also we present a minimization algorithm based on the use of cotton york tensor which finds the push forward of the isotropic conductivity to our model domain and also finds the boundary of the original domain up to an affine

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

determining anisotropic real analytic conductivities by boundary measurements if an electrical potential is applied to the surface of a solid body the current flux across the surface depends on the conductivity in the interior of the body we want to consider the inverse problem of determining the conductivity by these boundary measurements

eigenvalues and the one dimensional p laplacian we consider the boundary value problem p u f t u 0 with p 1 t 0 1 u 0 u 1 0 and with 0 the value of is chosen so that the boundary value problem has a positive solution in addition we derive an explicit interval for such that for any in this interval the existence of a positive solution to the boundary value problem is guaranteed in addition the existence of two positive solutions for in an appropriate interval is also discussed

periodic solutions of non autonomous second order systems with a p laplacian abstract in this paper we investigate non autonomous second order systems with a p laplacian and obtain existence results for periodic solutions with the dual least action principle

periodic solutions for second order systems with not uniformly coercive potential abstract the existence and multiplicity of periodic solutions are obtained for the nonautonomous second order systems with locally coercive potential that is f t x as x for a e t in some positive measure subset of 0 t by using an analogy of egorov s theorem the properties of subadditive functions the least action principle and a three critical point theorem proposed by brezis and nirenberg

high dimensional chaotic behavior in systems with time delayed feedback abstract the nature of high dimensional chaos exhibited by a class of delay differential equation is investigated by various methods this delay differential equation models systems with time delayed feedback such as nonlinear optical resonators we first describe briefly the bifurcation phenomena exhibited by the system with an increase in a control parameter representing the energy flow rate periodic states bi multi furcate themselves successively forming a hierarchy of multistable periodic states with increasing complexities finally each branch of multistable periodic states makes transition to chaos the possibility of applying such a multistability as a memory device for complicated information is discussed in the chaotic regime each of the bifurcated states in turn merge successively into fewer sets of states with larger attractor dimensions and finally a single developed chaos with a very large attractor dimension is formed lyapunov analysis is introduced to study the high dimensional chaotic states the lyapunov vectors as well as lyapunov spectrum are shown to be very useful to understand the underlying mechanism of the successive merging process mentioned above characteristics of developed chaos are investigated by high pass filtered time series hfts the intermittency characteristics of the hfts changes markedly at a certain frequency the lyapunov analysis reveals that this frequency corresponds to a characteristic lyapunov mode number this characteristic number can be looked upon as the dimension of subspace in which active chaotic information is generated and is different from the attractor dimension in the customary sense

electrical impedance tomography problem with inaccurately known boundary and contact impedances in electrical impedance tomography eit electric currents are injected into a body with unknown electromagnetic properties through a set of contact electrodes at the boundary of the body the resulting voltages are measured on the same electrodes and the objective is to reconstruct the unknown conductivity function inside the body based on these data all the traditional approaches to the reconstruction problem assume that the boundary of the body and the electrode skin contact impedances are known a priori however in clinical experiments one usually lacks the exact knowledge of the boundary and contact impedances and therefore approximate model domain and contact impedances have to be used in the image reconstruction however it has been noticed that even small errors in the shape of the computation domain or contact impedances can cause large systematic artefacts in the reconstructed images leading to loss of diagnostically relevant information in a recent paper kolehmainen 2006 we showed how in the 2 d case the errors induced by the inaccurately known boundary can be eliminated as part of the image reconstruction and introduced a novel method for finding a deformed image of the original isotropic conductivity using the theory of teichmuller mappings in this paper the theory and reconstruction method are extended to include the estimation of unknown contact impedances the method is implemented numerically and tested with experimental eit data the results show that the systematic errors caused by inaccurately known boundary and contact impedances can efficiently be eliminated by the reconstruction method

the inverse conductivity problem with an imperfectly known boundary we show how to eliminate the error caused by an incorrectly modeled boundary in electrical impedance tomography eit in practical measurements one usually lacks exact knowledge of the boundary because of this the numerical reconstruction from the measured eit data is done using a model domain that represents the best guess for the true domain however it has been noticed that an inaccurate model of the boundary causes severe errors for the reconstructions we introduce a new algorithm to find a deformed image of the original isotropic conductivity based on the theory of teichmuller spaces and we implement it numerically

periodic solutions of non autonomous second order systems we obtain an existence theorem of periodic solutions of non autonomous second order systems with classical theorems of variational calculus

existence and multiplicity results for nonlinear nonautonomous second order systems in this paper we consider nonlinear periodic systems driven by the ordinary p laplacian and having a nonsmooth potential function under minimal and natural hypotheses on the nonsmooth potential and using variational methods based on the nonsmooth critical point theory we prove four existence theorems and a multiplicity theorem we conclude the paper with an existence theorem for the scalar problem in which the energy functional is indefinite i e it is unbounded both above and below

notes on periodic solutions of subquadratic second order systems some existence theorems are obtained for periodic solutions of the subquadratic second order systems by the minimax methods in critical point theory

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

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

some critical point theorems and their applications to periodic solution for second order hamiltonian systems abstract some critical point theorems without the compactness assumptions are obtained by the reduction method the perturbation argument and the least action principle as applications some existence results of periodic solutions are obtained for nonautonomous second order hamiltonian systems which unify and generalize some recent corresponding results

periodic problems for strongly nonlinear second order differential inclusions in this paper we study periodic problems for second order differential inclusions in rn with a maximal monotone term the nonlinear differential operator is not necessarily homogeneous does not obey any growth condition and incorporates as a special case the one dimensional p laplacian using techniques from multivalued analysis and the theory of operators of monotone type we prove the existence of solutions for both the convex and nonconvex problems when the maximal monotone term a is defined everywhere and when it is not defined everywhere case of variational inequalities

existence and uniqueness for electrode models for electric current computed tomography the following experiment is considered to a body of given conductivity a number of electrodes are attached through which current is sent on the same electrodes the resulting voltages are measured this experiment can be described by a number of mathematical models k s cheng et al ieee transactions on biomedical engineering 36 1989 pp 918 924 these models are discussed and their predictions compared with experiment in particular a model is exhibited that is capable of predicting the experimentally measured voltages to within 0 1 percent for this model existence and uniqueness of the associated electrical potential is proved

periodic solutions of non autonomous second order systems with γ quasisubadditive potential abstract the existence of periodic solutions to non autonomous second order systems with quasisubadditive potential is proved with classical theorems of variational calculus