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

b spline level set method for shape reconstruction in electrical impedance tomography a b spline level set bls based method is proposed for shape reconstruction in electrical impedance tomography eit we assume that the conductivity distribution to be reconstructed is piecewise constant transforming the image reconstruction problem into a shape reconstruction problem the shape interface of inclusions is implicitly represented by a level set function lsf which is modeled as a continuous parametric function expressed using b spline functions starting from modeling the conductivity distribution with the b spline based lsf we show that the shape modeling allows us to compute the solution by restricting the minimization problem to the space spanned by the b splines as a consequence the solution to the minimization problem is obtained in terms of the b spline coefficients we illustrate the behavior of this method using simulated as well as water tank data in addition robustness studies considering varying initial guesses differing numbers of control points and modeling errors caused by inhomogeneity are performed both simulation and experimental results show that the bls based approach offers clear improvements in preserving the sharp features of the inclusions in comparison to the recently published parametric level set method

pointwise inner automorphisms of injective factors abstract it is shown that for the injective factor of type iii 1 with separable predual an automorphism is pointwise inner if and only if it is the composition of an inner and a modular automorphism

coefficient ideals in and blowups of a commutative noetherian domain abstract the ratliff rush ideal associated to a nonzero ideal i in a commutative noetherian domain r with unity is n 1 in 1 rin is r s b i where b i r i a p a i 0 p spec r i a is the blowup of i we observe that certain ideals are minimal or even unique in the class of ideals having the same associated ratliff rush ideal if r m is local quasi unmixed and analytically unramified and if i is m primary then we show that the coefficient ideal i k of i i e the largest ideal containing i whose hilbert polynomial agrees with that of i in the highest k terms is also contracted from a blowup b i k which is obtained from b i by a process similar to s2 ification this allows us to generalise the notion of coefficient ideas we investigate these ideas in the specific context of a two dimentional regular local ring observing the interaction of these notions with the zariski theory of complete ideals

the characteristic square of a factor and the cocycle conjugacy of discrete group actions on factors this paper has three main purposes rst to associate to any separable factor m a canonical commuting exact square of groups called the characteristic square ofm secondly to formulate at least in a preliminary way a methodology for approaching non smooth classi cation problems in analysis and thirdly to use this approach in conjunction with the characteristic square to complete the cocycle conjugacy classi cation of actions of discrete amenable groups on injective factors of type iii1 this result and previous works on the cocyle conjugacy classi cation problem combine to produce a cocycle conjugacy classi cation theorem which applies simultaneously to all countable amenable groups and all injective separable factors and in which the characteristic square and our new methodology play a crucial role the cocycle conjugacy classi cation problem has by now a long and distinguished history beginning with connes ground breaking outer conjugacy classi cation of single automorphisms of the approximately nite dimensional or afd factor r0 of type ii1 c3 in the intervening 20 years enormous progress has been made the rst step was taken by v jones j who identi ed the true nature of the cocycle conjugacy invariants and completed the classi cation of actions of nite groups on r0 ocneanu o re ned this work and introduced new analytic techniques enabling him to extend the classi cation to countable amenable groups acting on the semi nite afd factor r0 1 and to some actions on afd factors of type iii also sutherland and takesaki using groupoid and duality techniques originating in jt extended the classi cation results to invent math 132 331 380 1998

noetherian intersections of regular local rings of dimension two abstract let d be a 2 dimensional regular local ring and let q d denote the quadratic tree of 2 dimensional regular local overrings of d we describe the desingularization of projective models over d both algebraically in terms of the saturation of complete ideals and order theoretically in terms of the quadratic tree q d we prove that this describes all the noetherian rings that are intersections of rings in q d

numerical solution method for the dbar equation in the plane a fast method for solving equations of the form v tv is presented where v and t are complex valued functions of two real variables the multigrid method of vainikko int soc anal appl comput 5 2000 is adapted to the problem with a fft implementation convergence with rate o h is proved for the method applied to equations of the form above one grid and two grid versions of the method are implemented and their effectiveness is demonstrated on an application arising in electrical impedance tomography eit

blowing up finitely supported complete ideals in a regular local ring let i be a finitely supported complete m primary ideal of a regular local ring r m we consider singularities of the projective models projr it and projr it over spec r where r it denotes the integral closure of the rees algebra r it a theorem of lipman implies that the ideal i has a unique factorization as a product of special simple complete ideals with possibly negative exponents for some of the factors if projr it is regular we prove that projr it is the regular model obtained by blowing up the finite set of base points of i extending work of lipman and huneke sally in dimension 2 we prove that every local ring s on projr it that is a unique factorization domain is regular moreover if dim s 2 and s dominates r then s is an infinitely near point to r that is s is obtained from r by a finite sequence of local quadratic transforms

compact abelian group actions on injective factors we classify compact abelian group actions on injective type iii factors up to conjugacy which completes the final step of classification of compact abelian group actions on injective factors

castelnuovo mumford regularity and ratliff rush closure abstract we establish strong relationships between the castelnuovo mumford regularity and the ratliff rush closure of an ideal our results have several interesting consequences on the computation of the ratliff rush closure the stability of the ratliff rush filtration the invariance of the reduction number and the computation of the castelnuovo mumford regularity of the rees algebra and the fiber ring in particular we prove that the castelnuovo mumford regularity of the rees algebra and of the fiber ring are equal for large classes of monomial ideals in two variables thereby verifying a conjecture of eisenbud and ulrich for these cases

asymptotic properties of infinite directed unions of local quadratic transforms abstract let r m be a regular local ring of dimension at least 2 for each valuation domain birationally dominating r there is an associated sequence r n of local quadratic transforms of r we consider the case where this sequence r n n 0 is infinite and examine properties of the integrally closed local domain s n 0 r n in the case where s is not a valuation domain for this sequence there is an associated boundary valuation ring v n 0 i n v i where v i is the order valuation ring of r i there exists a unique minimal proper noetherian overring t of s t is the regular noetherian ufd obtained by localizing outside the maximal ideal of s and s v t in the present paper we define functions w and e where w is the asymptotic limit of the order valuations and e is the limit of the orders of transforms of principal ideals we describe v explicitly in terms of w and e and prove that v is either rank 1 or rank 2 we define an invariant associated to s that is either a positive real number or if is finite then s is archimedean and t is not local in this case the function w defines the rank 1 valuation overring w of v and w dominates s the rational dependence of over w t determines whether s is completely integrally closed and whether v has rank 1 we give examples where s is completely integrally closed if is infinite then s is non archimedean and t is local in this case the function e defines the rank 1 valuation overring e of v the valuation ring e is a dvr and e dominates t and in certain cases we prove that e is the order valuation ring of t

d bar method for electrical impedance tomography with discontinuous conductivities the effects of truncating the approximate scattering transform in the d bar reconstruction method for two dimensional electrical impedance tomography are studied the method is based on the uniqueness proof of nachman ann of math 2 143 1996 pp 71 96 that applies to twice differentiable conductivities however the reconstruction algorithm has been successfully applied to experimental data which can be characterized as piecewise smooth conductivities the truncation is shown to stabilize the method against measurement noise and to have a smoothing effect on the reconstructed conductivity thus the truncation can be interpreted as regularization of the d bar method numerical reconstructions are presented demonstrating that features of discontinuous high contrast conductivities can be recovered using the d bar method further a new connection between calderon s linearization method and the d bar method is established and the two methods are compared numerically and analytically

equivariant kirchberg phillips type absorption for amenable group actions we show an equivariant kirchberg phillips type absorption theorem for pointwise outer actions of discrete amenable groups on kirchberg algebras with respect to natural model actions on the cuntz algebras mathcal o infty and mathcal o 2 this generalizes results known for finite groups and poly mathbb z groups the model actions are shown to be determined up to strong cocycle conjugacy by natural abstract properties which are verified for some examples of actions arising from tensorial shifts we also show the following homotopy rigidity result which may be understood as a precursor to a general kirchberg phillips type classification theory if two outer actions of an amenable group on a unital kirchberg algebra are equivariantly homotopy equivalent then they are conjugate this marks the first c dynamical classification result up to cocycle conjugacy that is applicable to actions of all amenable groups

equivalence of normal states on von neumann algebras and the flow of weights abstract let m be a von neumann algebra two positive normal functionals on m are called equivalent if is in the norm closure of the orbit of under the action of inner automorphisms our main result is an isometric characterization of the quotient space m we construct a natural isometry a g4 of m into the set of positive normal functionals on the smooth flow of weights of m where the smooth flow of weights is realized as the center z n of the crossed product n m r for some faithful normal semifinite weight on m as an application we obtain that an automorphism on a factor m with separable predual acts trivially on m if and only if acts trivially on the smooth flow of weights i e the connes takesaki modulus mod of vanishes we also obtain a new proof of the diameter formula diam s n m 2 1 1 for the quotient of the state space of a factor of type iii 0 1

the tree of quadratic transforms of a regular local ring of dimension two abstract let d be a 2 dimensional regular local ring and let q d denote the quadratic tree of 2 dimensional regular local overrings of d we explore the topology of the tree q d and the family r d of rings obtained as intersections of rings in q d if a is a finite intersection of rings in q d then a is noetherian and the structure of a is well understood however other rings in r d need not be noetherian the two main goals of this paper are to examine topological properties of the quadratic tree q d and to examine the structure of rings in the set r d

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

quasi one fibered ideals in two dimensional muhly local domains abstract in this paper a two dimensional integrally closed noetherian local domain r m with algebraically closed residue field is said to be a muhly local domain if the associated graded ring is an integrally closed domain using the theory of degree functions developed by rees and sharp and the zariski lipman theory of complete ideals in two dimensional regular local rings we study m primary ideals of r having among their rees valuations exactly one valuation ord r we therefore call these ideals quasi one fibered some consequences are deduced

the non commutative flow of weights on a von neumann algebra abstract the flow of weights of connes and takesaki is a canonical functor from the category of separable factors to the category of ergodic flows the non commutative flow of weights is another canonical functor from the category of separable factors to the category of covariant systems of semi finite von neumann algebras equipped with trace scaling one parameter automorphism groups with conjugations as morphisms the constructions of these two functors are very similar the flow of weights functor is obtained by looking at all semi finite normal weights on a factor with the murray von neumann equivalence relation the non commutative flow of weights functor is obtained by relating an arbitrary pair of faithful semi finite normal weights by the connes cocycle not only does this construction put a period to the search for a canonical construction of the core of a factor of type iii but it also allows us to put the characteristic square of a factor obtained by katayama sutherland and takesaki in a new perspective the power of this new approach is seen in an ultimate solution to a long standing question of extending the extended modular automorphism of a dominant weight to an arbitrary weight which has been left open ever since the introduction of extended modular automorphisms by connes and takesaki over 20 years ago the construction of the functor ties together the theory of l p spaces of haagerup kosaki hilsum terp and izumi to the structure theory of a factor of type iii in fact the non commutative flow of weights is obtained by the analytic continuation of l p spaces to a pure imaginary value of p

a class of projectively full ideals in two dimensional muhly local domains abstract let r m be a regular local domain of dimension d 2 and let x 1 x d be a regular system of parameters then ciuperca heinzer ratliff jr and rush have proved that every ideal of the form i x 1 n x 2 x d r with n n is projectively full if r m is a two dimensional muhly local domain i e an integrally closed noetherian local domain with algebraically closed residue field and the associated graded ring an integrally closed domain then we are able to prove a similar result for every minimal ideal basis x 1 x d of m such that x 1 rad x 2 x d

the structure of the automorphism group of an injective factor and the cocycle conjugacy of discrete abelian group actions we complete classification of discrete abelian or finite group actions on injective type iii1 factors up to cocycle conjugacy we also give a proof for connes characterization of the ker mod and cnt m for an injective factor m of type iii 0 introduction the purpose of this paper is to give a proof of connes announcement on approximately inner automorphisms and centrally trivial automorphisms of an injective 1980 mathematics subject classification 1985 revision 46l40

ratliff rush closures and coefficient modules let r m be ad dimensional noetherian local domain supposemis a finitely generated torsion freer module and supposefis a freer module containingm in analogy with a result of ratliff and rush indiana univ math j 27 1978 929 934 concerning ideals we define and prove existence and uniqueness of theratliff rushclosureofminf we also discuss properties of ratliff rush closure in addition to the preceding assumptions supposef mhas finite length as anr module then we define thebuchsbaum rimpolynomialofminf in analogy with the work of k shah trans amer math soc 327 1991 373 384 we definecoefficientmodulesofminf under the assumption thatris quasi unmixed we prove existence and uniqueness of coefficient modules ofminf

liftable derivations for generically separably algebraic morphisms of schemes we consider dominant generically algebraic e g generically fi nite and tamely ramified if the characteristic is positive morphisms n x s y s of s schemes where y 5 are ncetherian and integral and x is a krull scheme e g normal ncetherian and study the sheaf of tangent vector fields on y that lift to tangent vector fields on x we give an easily com putable description of these vector fields using valuations along the critical locus we apply this to answer the question when the liftable derivations can be defined by a tangency condition along the discriminant in particular if it is a blow up of a coherent ideal we show that tangent vector fields that preserve the ratliff rush ideal equals in 1 n for high n associated to are liftable and that all liftable tangent vector fields preserve the integral closure of we also generalise in positive characteristic seidenberg s theorem that all tangent vector fields can be lifted to the normalisation assuming tame ramification

bounds on the a invariant and reduction numbers of ideals abstract let r be a d dimensional standard graded ring over an artinian local ring let m be the unique maximal homogeneous ideal of r let hi r n denote the length of the nth graded component of the local cohomology module h i m r define the eisenbud goto invariant eg r of r to be the number q 0 d 1 d 1 q h q m r 1 q we prove that the a invariant a r of the top local cohomology module h m d r satisfies the inequality a r e r l r1 d 1 l r0 1 eg r this bound is used to get upper bounds for the reduction number of an m primary ideal i of a cohen macaulay local ring r m when the associated graded ring of i has depth at least d 1

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

finitely supported simple complete ideals in a regular local ring abstract let i be a finitely supported complete m primary ideal of a regular local ring r m a theorem of lipman implies that i has a unique factorization as a product of special simple complete ideals with possibly negative exponents for some of the factors the existence of negative exponents occurs if dim r 3 because of the existence of finitely supported simple ideals that are not special we consider properties of special simple complete ideals such as their rees valuations and point basis let r m be a d dimensional equicharacteristic regular local ring with m x 1 x d r we define monomial quadratic transforms of r and consider transforms and inverse transforms of monomial ideals for a large class of monomial ideals i that includes complete inverse transforms we prove that the minimal number of generators of i is completely determined by the order of i we give necessary and sufficient conditions for the complete inverse transform of a product of monomial ideals to be the product of the complete inverse transforms of the factors this yields examples of finitely supported simple monomial ideals that are not special we prove that a finitely supported simple monomial ideal with linearly ordered base points is special simple

a simple mesh generator in matlab creating a mesh is the first step in a wide range of applications including scientific computing and computer graphics an unstructured simplex mesh requires a choice of meshpoints vertex nodes

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

effect of domain shape modeling and measurement errors on the 2 d d bar method for eit the d bar algorithm based on nachman s 2 d global uniqueness proof for the inverse conductivity problem nachman 1996 is implemented on a chest shaped domain the scattering transform is computed on this chest shaped domain using trigonometric and adjacent current patterns and the complete electrode model for the forward problem is computed with the finite element method in order to obtain simulated voltage measurements the robustness and effectiveness of the method is demonstrated on a simulated chest with errors in input currents output voltages electrode placement and domain modeling

hilbert coefficients of hilbert filtrations adic filtrations see 7 11 18 21 wx in the first section of this paper we extend most of the techniques of 4 w5 to the case of hilbert filtrations and by doing so we are also able toxoffer alternative simple proofs of some results of 7 wxin the second section thanks to the setting just described if

strongly self absorbing c dynamical systems iii abstract in this paper we accomplish two objectives firstly we extend and improve some results in the theory of semi strongly self absorbing c dynamical systems which was introduced and studied in previous work in particular this concerns the theory when restricted to the case where all the semi strongly self absorbing actions are assumed to be unitarily regular which is a mild technical condition the central result in the first part is a strengthened version of the equivariant mcduff type theorem where equivariant tensorial absorption can be achieved with respect to so called very strong cocycle conjugacy secondly we establish completely new results within the theory this mainly concerns how equivariantly z stable absorption can be reduced to equivariantly uhf stable absorption with respect to a given semi strongly self absorbing action combining these abstract results with known uniqueness theorems due to matui and izumi matui we obtain the following main result if g is a torsion free abelian group and d is one of the known strongly self absorbing c algebras then strongly outer g actions on d are unique up to very strong cocycle conjugacy this is new even for z 3 actions on the jiang su algebra

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

first coefficient ideals and the s2 ification of a rees algebra let a m k be a d dimensional d 1 quasi unmixed analytically unramified local domain with infinite residue field if i is an m primary ideal shah defined the first coefficient ideal of i to be the largest ideal i 1 containing i such that ei i ei i 1 for i 0 1 assume that a is s2 and let s n zintn be the s2 ification of the extended rees algebra s a it t 1 we prove that in in 1 for every n 1 one of the consequences is a procedure of computing first coefficient ideals