coherent anomaly method in self avoiding walk problems abstract self avoiding walk saw being a nonequilibrium cooperative phenomenon is investigated with a finite order restricted walk finite orw or forw coherent anomaly method cam the coefficient 1 r in the asymptotic form c nr 1 r n 1 r for the total number c nr of r orw s with respect to the step number n is investigated for the first time an asymptotic form for saw s is thus obtained form the series of forw approximants c nr br g n 1 a r n as the envelope curve c n b ae g g n n g numerical results are given by c n 1 424 n 0 2788 4 1507 n and c n 1 179 n 0 1587 10 005 n for the plane triangular lattice and f c c lattice respectively a good coincidence of the total numbers estimated from the above simple formulae with exact enumerations for finite step saw s implies that the essential nature of saw non markov process can be understood from forw markov process in the cam framework

examination of the 1 d expansion method from exact enumeration for a self interacting self avoiding walk the 1 d expansion method for polymer chains is examined by comparing these expansions for several thermodynamic and structural quantities with the results of standard series analysis of exact enumeration data the comparisons cover a wide range of spatial dimensions d including non integer ones and are performed for particular values of interaction energy good agreement is generally found for d 4 whereas discrepancies become conspicuous as d decreases to d 2 reasonable values are obtained for the exponents v and gamma in d 2 4 by applying the coherent anomaly method of suzuki 1986 to our 1 d expansions through fifth order in d 1

renormalisation group recursions by mean field approximations within a renormalisation group strategy different rescaled mean field approximations for the magnetisation are combined good qualitative estimates are obtained for the critical properties of classical and quantum spin systems a particularly simple realisation of the method yields recursions for arbitrary dimensionality d the critical couplings are accurate for all d and have the correct asymptotic behaviour for d approaching infinity

utilizing prior information in the estimation of volume fraction distribution for many industrial processes the bulk volume fraction of one phase such as gas or solid can be of considerable importance for this reason it is often controlled within certain limits and therefore is known at least vaguely tomographic imaging of volume fraction can provide very valuable information not only on the bulk volume fraction but also on the spatial distribution of the phase of interest prior information on the bulk volume fraction can assist in tomographic inversion even if this information is not precise in this paper we propose an electrical impedance tomography approach for imaging volume fraction distribution a vague bulk volume fraction prior is utilized in the estimation two dimensional numerical examples are used to demonstrate the proposed method copyright 2005 john wiley sons ltd

tame linear extension operators for smooth whitney functions abstract for a compact set k r d we present a rather easy construction of a linear extension operator e e k c r d for the space of whitney jets e k which satisfies linear tame continuity estimates sup e f x m x r d c m e f r e m where s denotes the s th whitney norm the construction turns out to be possible if and only if the local markov inequality lmi s introduced by bos and milman holds for every s r on k in particular e k admits a tame linear extension operator if and only if the local markov inequality lmi s holds on k for some s 1

a linearized inverse boundary value problem for maxwell s equations abstract in this paper we consider the problem of determining the electromagnetic state of a body from measurements made on the surface of the body we study the full set of maxwell s equations that govern time harmonic electric and magnetic fields we seek to reconstruct the magnetic permeability the electric permitivity and the electric conductivity in the interior of the body from measurements made on the surface we exhibit appropriate boundary measurements in the form of a boundary mapping specifically the mapping from the tangential components of the electric field to the tangential components of the magnetic field this data can be used to reconstruct and approximately provided they deviate only slightly from known constants we also estimate the reconstruction errors

finite element implementation of maxwell s equations for image reconstruction in electrical impedance tomography traditionally image reconstruction in electrical impedance tomography eit has been based on laplace s equation however at high frequencies the coupling between electric and magnetic fields requires solution of the full maxwell equations in this paper a formulation is presented in terms of the maxwell equations expressed in scalar and vector potentials the approach leads to boundary conditions that naturally align with the quantities measured by eit instrumentation a two dimensional implementation for image reconstruction from eit data is realized the effect of frequency on the field distribution is illustrated using the high frequency model and is compared with laplace solutions numerical simulations and experimental results are also presented to illustrate image reconstruction over a range of frequencies using the new implementation the results show that scalar vector potential reconstruction produces images which are essentially indistinguishable from a laplace algorithm for frequencies below 1 mhz but superior at frequencies reaching 10 mhz

1 d expansions for critical amplitudes the author shows how to expand critical amplitudes in inverse powers of the dimensionality d the technique which is rather general is applied to the classical n vector model with particular emphasis on the self avoiding walk n 0 and ising n 1 cases the existence of these expansions and of similar ones for critical points and critical constants suggests that 1 d expansions for non universal quantities are analogous to the epsilon expansions for universal quantities

discontinuity of the magnetization in one dimensional 1 x y 2 ising and potts models results from percolation theory are used to study phase transitions in one dimensional ising and q state potts models with couplings of the asymptotic form j sub x y approx const absolute value x y sup 2 for translation invariant systems with well defined lim sub x infinity x sup 2 j sub x j sup possibly o or infinity we establish 1 there is no long range order at inverse temperatures beta with beta j sup less than or equal to1 2 if beta j sup q then by sufficiently increasing j sub 1 the spontaneous magnetization m is made positive 3 in models with 0 j sup infinity the magnetization is discontinuous at the transition point as originally predicted by thouless and obeys m beta sub c less than or equal to 1 beta sub c j sup sup 1 2 4 for ising q 2 models with j sup infinity it is noted that the correlation function decays as beta approx c beta absolute value x y sup 2 whenever beta beta sub c points 1 3 are deduced from previous percolation results by utilizing the fortuin kasteleyn representation which also yields other results of independent interest relating potts models with different values of q

1 d expansions for the free energy of weakly embedded site animal models of branched polymers we give the 1 d expansion to order 1 d5 for the limiting reduced free energy of a weakly embedded two variable site animal model of branched polymers hence we are able to derive expansions for the free energy of related one variable models and the growth constant of weakly and strongly embedded trees again to order 1 d5 we argue that the free energy expansions are asymptotically correct for a small range of fugacities only exact results show that animals with a compact hypercubic structure make the overwhelming contribution to the total number of weakly embedded site animals especially for large d this result is not reflected in the free energy 1 d expansions where trees make the dominant contribution we also derive new exact enumeration data for lattice animals using intermediate calculations in the derivation of the 1 d expansions thus we give partition functions for the general d dimensional hypercubic lattice for one to 13 sites

application of stochastic galerkin fem to the complete electrode model of electrical impedance tomography abstract the aim of electrical impedance tomography is to determine the internal conductivity distribution of some physical body from boundary measurements of current and voltage the most accurate forward model for impedance tomography is the complete electrode model which consists of the conductivity equation coupled with boundary conditions that take into account the electrode shapes and the contact resistances at the corresponding interfaces if the reconstruction task of impedance tomography is recast as a bayesian inference problem it is essential to be able to solve the complete electrode model forward problem with the conductivity and the contact resistances treated as a random field and random variables respectively in this work we apply a stochastic galerkin finite element method to the ensuing elliptic stochastic boundary value problem and compare the results with monte carlo simulations

an approach to critical phenomena from one subsystem based on the cam analysis two systematic series of multi body effective field approximations are constructed and the cam analyses are performed for the ising mode on the two dimensional square lattice in the first series a two body effective field is introduced in addition to the usual one body one and a set of strips are used the critical temperature and the critical index of the susceptibility are estimated as t c approximately 2 2697 j kb and gamma approximately 1 749 in the second series only a three line strip is used and applied with increasing numbers of multi body effective fields the expected cam scaling behaviour has also been observed

series of effective field approximations and coherent anomaly in kosterlitz thouless transitions a series of effective field approximations are formulated for the kosterlitz thouless transition in the sine gordon model by means of the cumulant expansion and the variational method effective field essential singularities xi approximately exp xi n kc n k 1 are obtained for the correlation length as first derived by saito in a single approximation however a systematic variance of the effective field critical coefficient xi n approximately 2ln j 2y0 n 1 pi is found when the order of approximation n increases the true critical exponent nu of the kosterlitz thouless transition is thus revealed to be less than the effective field exponent nu 0 nu nu 0 1 from suzuki s coherent anomaly method the phase transition in the two dimensional xy model is studied from its relation to the sine gordon model the critical exponent eta c of the spin spin correlation function at the critical point is found to be eta c 1 4 1 pi 2

one dimensional ising models with long range interactions we consider ising models with long range ferromagnetic pair interactions decaying as for we first find approximate values for the critical temperature we use a cluster mean field approach combined with finite size scaling and vanden broeck and schwartz transformations for we find which can be compared with recent results of luijten and blote who found and which is two orders of magnitude more accurate than any previous results since we use a mean field cluster approximation as part of our approach the accuracy for larger values of decreases significantly in addition to we obtain approximate values for the critical exponents and using the coherent anomaly method for we obtain and all extremely close to the predictions of renormalization group calculations which say that these exponents should take on their classical values for this value of

the critical behaviour of the long range potts chain from the largest cluster probability distribution abstract we present the numerical study of the one dimensional potts model with power law decaying ferromagnetic interactions the largest cluster probability distribution is obtained by monte carlo simulations using the swendsen wang cluster algorithm with cumulative probabilities the finite size scaling analysis of the largest cluster is used to derive the critical behaviour in the non classical regime of this model for various values of q

shrinking and boundedly complete schauder frames in frechet spaces abstract we study schauder frames in frechet spaces and their duals as well as perturbation results we define shrinking and boundedly complete schauder frames on a locally convex space study the duality of these two concepts and their relation with the reflexivity of the space we characterize when an unconditional schauder frame is shrinking or boundedly complete in terms of properties of the space several examples of concrete schauder frames in function spaces are also presented

tsallis scaling and the long range ising chain a transfer matrix approach a numerically efficient transfer matrix tm approach is introduced to investigate the long range ising spin chain results obtained within this procedure are primarily used to verify the tsallis scaling hypothesis for long range systems with an ensuremath alpha power law decay of the interaction constants both in the extensive ensuremath alpha g1 and nonextensive ensuremath alpha l1 regimes results for finite size systems taking into account all interactions between spins up to 24 sites apart show that the conjecture is satisfied with a very good precision less than 0 004 for all temperature intervals this tm procedure is further used to investigate several other thermodynamic and critical properties of this system and it may also be extended to similar one dimensional long range systems

from dilute to dense self avoiding walks on hypercubic lattices a field theoretic representation is presented to count the number of configurations of a single self avoiding walk on a hypercubic lattice ind dimensions with periodic boundary conditions we evaluate the connectivity constant as a function of the fractionf of sites occupied by the polymer chain the meanfield approximation is exact in the limit of infinite dimensions and corrections to it in powers ofd 1 can be systematically evaluated the connectivity constant and the site entropy calculated throughout second order compare well with known results in two and three dimensions we also find that the entropy per site develops a maximum atf 1 2d 1 ford 2 d 3 this maximum occurs atf 0 80 f 0 86 and its value is about 50 30 higher than the entropy per site of a hamiltonian walk f 1

accurate solutions of maxwell s equations around pec corners and highly curved surfaces using nodal finite elements a method is presented for computing accurate solutions of maxwell s equations in the presence of perfect electrical conductors pecs with sharp corners and highly curved surfaces using conventional nodal finite elements and a scalar vector s v potential formulation this technique approximates the pec with an impedance boundary condition ibc where the impedance is small critically it couples both potentials through this boundary condition rather than setting the scalar potential to zero this permits cancellation of the tangential components of the vector potential resulting in an accurate normal electric field the cause for the inaccuracies that nodal methods experience in the presence of sharp pec corners or highly curved pec surfaces is elucidated it is then shown how the inclusion of the scalar potential cures these deficiencies permitting accurate solutions spectral analysis of the resulting finite element matrices are shown validating the boundary conditions used examples are presented comparing a benchmark solution conventional pec and ibc boundary conditions and the new s v potential ibc on a pec wedge and pec ellipse in both cases the new s v ibc produces superior results

whitney extension operators with arbitrary loss of differentiability abstract for a compact set k r d we characterize the existence of a linear extension operator e e k c r d for the space of whitney jets e k with a certain loss of derivatives that is the operator satisfies the following continuity estimates for all n n 0 and all f e k sup e f x n x r d c n f n where n denotes the whitney norm and the map n 0 n 0 is monotonically increasing with n n and 0 0 from our main result it follows directly that if a compact set k admits an extension operator then it is always possible to construct a second extension operator resembling the original whitney operators e n e n k c n r d where the evaluations of the jet occurring in the taylor polynomials are approximated by measures

the efficient determination of the percolation threshold by a frontier generating walk in a gradient the frontier in gradient percolation is generated directly by a type of self avoiding random walk the existence of the gradient permits one to generate an infinite walk on a computer of finite memory from this walk the percolation threshold pc for a two dimensional lattice can be determined with apparently maximum efficiency for a naive monte carlo calculation or n 12 for a square lattice the value pc 0 592745 or 0 000002 is found for a simulation of n 2 6 1011 total steps occupied and blocked perimeter sites the power of the method is verified on the kagome site percolation case

the one dimensional potts model with long range interactions a renormalization group approach the one dimensional q state potts model with ferromagnetic pair interactions which decay with the distance r as is considered we calculate through a real space renormalization group technique using kadanoff blocks of length b the critical temperature and the correlation length critical exponent as a function of for different values of q some of the very few known rigorous results for general q are reproduced by our approach several asymptotic behaviours are derived analytically for q 2 3 in the limit we also obtain extrapolated critical temperatures for arbitrary values of and for q 2 3 4 which we believe approximate the exact ones well except in the region near furthermore the use of another extrapolation procedure suitable only in the vicinity of led us to conjecture that the exact critical temperature is the same for any value of q we also verify that which is consistent with a recent conjecture of tsallis

equivalence of the global and local markov inequalities in the complex plane abstract we prove that a compact subset of the complex plane satisfies the global markov inequality if and only if it admits an extension property and a kolmogorov type inequality in jackson norms generalizing a result established by bos and milman in the real case we also show that the global markov inequality is equivalent to the local markov property for all compact subsets of the complex plane admitting the jackson property the latter is a generalization of jackson s approximation inequality closely connected with the boundary behavior of the green s function finally we construct an example showing that there is no equivalence in general

markov s inequality and polynomial mappings markov s inequality is a certain estimate for the norm of the derivative of a polynomial in terms of the degree and the norm of this polynomial it has many interesting applications in approximation theory constructive function theory and in analysis for instance to sobolev inequalities or whitney type extension problems one of the purposes of this paper is to give a solution to an old problem studied among others by baran and ple niak and concerning the invariance of markov s inequality under polynomial mappings polynomial images we also address the issue of preserving markov s inequality when taking polynomial preimages lastly we give a sufficient condition for a subset of a markov set to be a markov set

universality in branched polymers on d dimensional hypercubic lattices the authors have derived series for weakly and strongly embeddable trees in d dimensional simple hypercubic lattices for arbitrary integral d for d 2 3 9 they present series evidence that such trees are in the same universality class as lattice animals in addition they have derived expansions in inverse powers of sigma 2d 1 for the growth parameters for bond and site trees and compare these with the corresponding results for animals

topological properties of convolutor spaces via the short time fourier transform we discuss the structural and topological properties of a general class of weighted l 1 convolutor spaces our theory simultaneously applies to weighted d l1 spaces as well as to convolutor spaces of the gelfand shilov spaces k m p in particular we characterize the sequences of weight functions m p p is an element of n for which the space of convolutors of k m p is ultrabornological thereby generalizing grothendieck s classical result for the space o c of rapidly decreasing distributions our methods lead to the first direct proof of the completeness of the space o c of very slowly increasing smooth functions

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

scaling of self avoiding walks in high dimensions we examine self avoiding walks in dimensions 4 to 8 using high precision monte carlo simulations up to length n 16 384 providing the first such results in dimensions d 4 on which we concentrate our analysis we analyse the scaling behaviour of the partition function and the statistics of nearest neighbour contacts as well as the average geometric size of the walks and compare our results to 1 d expansions and to excellent rigorous bounds that exist in particular we obtain precise values for the connective constants 5 8 838 544 3 6 10 878 094 4 7 12 902 817 3 8 14 919 257 2 and give a revised estimate of 4 6 774 043 5 all of these are by at least one order of magnitude more accurate than those previously given from other approaches in d 4 and all approaches in d 4 our results are consistent with most theoretical predictions though in d 5 we find clear evidence of anomalous n 1 2 corrections for the scaling of the geometric size of the walks which we understand as a non analytic correction to scaling of the general form n 4 d 2 not present in pure gaussian random walks

critical indices for the two dimensional ising model with nearest neighbor and next nearest neighbor interactions ii strip cluster approximation the spin pair correlation functions are calculated for the ising model with nearest neighbor interaction j 0 and next nearest neighbor interaction j on the square lattice in terms of three approximations of the simplified cluster variation method with strip clusters as the basic clusters the critical indices and are estimated from the obtained spin pair correlation functions with the aid of the coherent anomaly method for j j 0 5 we confirm that the system belongs to the onsager universality class in the sense of the weak universality hypothesis

reconstruction of permittivity profile from boundary capacitance data we present numerical methods of reconstructing permittivity profile of material flow from data collected in electrical capacitance tomography ect based on a formula for the sensitivity maps from a partial differential equation model we propose a unified framework of iterative algorithms using updated sensitivity maps to properly incorporate the non linear nature of the problem and a regularization mechanism to address the ill posedness for two and three phase flows the total variation tv regularization method is shown to be effective in reconstructing the permittivity profiles accurately in a few iterations without any a priori knowledge of the unknown permittivity values

nodal based finite element modeling of maxwell s equations weak forms are derived for maxwell s equations which are suitable for implementation on conventional c sup 0 elements with scalar bases the governing equations are expressed in terms of general vector and scalar potentials for the electric field intensity vector gauge theory is invoked to close the system and dictates the continuity requirements for the potentials at material interfaces as well as the blend of boundary conditions at exterior boundaries two specific gauges are presented both of which lead to helmholtz weak forms which are parasite free and enjoy simple physically meaningful boundary conditions a general and numerically efficient procedure for enforcing the jump discontinuities on the normal components of vector fields at dielectric interfaces and boundary conditions on curved surfaces is also given

multi effective field theory applications to the cam analysis of the two dimensional ising model abstract a multi effective field theory is formulated and applied to the two dimensional ising model from the viewpoint of the coherent anomaly method cam two necessary conditions to construct the cam canonical series are shown two series of approximations are derived on 3 3 and 4 4 clusters and with the use of the cam we estimate the critical exponent of the susceptibility within an error of 0 37 and 0 45 percent respectively for the exact value 1 75 where the exact t c is assumed this accuracy of the estimation shows the effectiveness of this theory it is generally proved that certain kinds of approximations with different combinations of effective fields yield exactly the same approximate critical temperature and mean field coefficient

continuous potential maxwell solutions on nodal based finite elements a nodal based finite element approach for computing electric fields in heterogeneous media is presented the primary calculation is formulated in terms of continuous potentials so that no special care is required on element assembly at dielectric interfaces the resulting galerkin weak form matrices exhibit the special helmholtz structure which guarantees the absence of parasitic solutions in driven problems with physically well posed boundary conditions the enhanced sparsity of the helmholtz form mitigates the extra coupling effort associated with introduction of a fourth degree of freedom relative to direct e solution e can be extracted from the computed potentials as a postprocessing step either at nodal positions or element centroids solutions obtained with this approach for several benchmark and practical problems are shown to be parasite free and essentially indistinguishable from previously reported direct e computations

a weighted minimum gradient problem with complete electrode model boundary conditions for conductivity imaging we consider the inverse problem of recovering an isotropic electrical conductivity from interior knowledge of the magnitude of one current density field generated by applying current on a set of electrodes the required interior data can be obtained by means of mri measurements on the boundary we only require knowledge of the electrodes their impedances and the corresponding average input currents from the mathematical point of view this practical question leads us to consider a new weighted minimum gradient problem for functions satisfying the boundary conditions coming from the complete electrode model cem of somersalo cheney and isaacson siam j appl math 52 1992 pp 1023 1040 we show that this variational problem has nonunique solutions the surprising discovery is that the physical data is still sufficient to determine the geometry of the connected components of the level sets of the minimizers we thus obtain an interesting phase retrieval result knowledge of the input current at the boundary allows determination of the full current vector field from its magnitude we characterize locally the nonuniqueness in the variational problem in two and three dimensions we also show that additional measurements of the voltage potential along a curve joining the electrodes yield unique determination of the conductivity the proofs involve a maximum principle and a new regularity up to the boundary result for the cem boundary conditions a nonlinear algorithm is proposed and implemented to illustrate the theoretical results

new method of analysing self avoiding walks in four dimensions a new method based on the concept of fractal dimensionality is used to study the problem of self avoiding walks in a four dimensional lattice the authors find from monte carlo simulations that the confluent logarithmic exponent related to the end to end distance is 1 8 or 0 01 in excellent agreement with the prediction derived from the n to 0 vector model

geometry of holomorphic mappings and holder continuity of the pluricomplex green function we provide a solution to a long standing open problem that lives in the interface of pluripotential theory and multivariate approximation theory the problem is to characterize the holomorphic maps which preserve holder continuity of the pluricomplex green function associated with a compact subset of mathbb c n we also prove under mild restrictions that nondegenerate holomorphic maps preserve markov s inequality for polynomials

new lattice model for interacting avoiding polymers with controlled length distribution a new lattice spin model for many self avoiding polymers is introduced in which the chain length distribution is fully controllable with a single generating magnetic field the model utilises spins with additional internal symmetry degrees of freedom to impose a causal connectivity of the polymer bonds on the lattice use of the method of random fields then produces an equivalent n to 0 limit field theory the flory huggins theory for a polymer solution emerges simply from this field theory in the mean field approximation polymer polymer interactions between polymer segments on nearest neighbour lattice are introduced into the field theory and the low polymer volume fraction limit of the theory reduces to the edwards type field theory for dilute through semidilute polymer solutions a sketch is provided towards the treatment of branched polymers with fully controllable chain and branch length distributions and branching probabilities as well as a kinetic polymerisation system governed by specified propagation and termination probabilities

coherent anomaly method applied to the eight vertex model abstract the coherent anomaly method cam in terms of the multi effective field theory is applied to the eight vertex model in which critical exponents depend on interaction energies of the hamiltonian and vary continuously with them series of approximations are constructed by the rule which we have already proposed and the critical exponent is estimated using the exact critical temperature t c the results that are obtained lie within an error of 1 2 percent for the exact value in a region of interaction energies and this shows that the cam is applicable to a model which does not satisfy the ordinary universality hypothesis

atomic decomposition for the harmonic fock spaces in the plane abstract the main purpose of this paper is to extend the certain functional analytic properties from the analytic fock spaces to the harmonic fock spaces in the plane firstly we found the pointwise estimate for the arbitrary function in the harmonic fock space h p where 1 p then we describe the atomic decomposition for h p

a two dimensional ising model with non universal critical behaviour it is shown that the two dimensional square lattice ising model with the nearest neighbour ferromagnetic interaction j the next nearest neighbour antiferromagnetic interaction j 0 and the four body interaction jint shows non universal critical behaviour when j is small the estimations of critical temperature tc and the critical exponent of susceptibility are performed within errors of 0 003 and 1 2 respectively

extension operators for smooth functions on compact subsets of the reals we introduce sufficient as well as necessary conditions for a compact set k such that there is a continuous linear extension operator from the space of restrictions c infty k f k f in c infty mathbb r to c infty mathbb r this allows us to deal with examples of the form k a n n in mathbb n cup 0 for a n rightarrow 0 previously considered by fefferman and ricci as well as vogt

the coherent anomaly method and long range one dimensional ising models the authors present the results of the coherent anomaly method when applied to ising models in one dimension with long range interactions this class of systems acts as an interesting and challenging test for the method because the critical exponents as well as the critical temperature values of which are given by the method depend on the rate of fall off of the interactions thus one can see how accurately the method gives results which correctly reflect this dependency the results obtained from this method are compared with results obtained by a variety of other methods

mityagin s extension problem progress report abstract given a compact set k r d let e k denote the space of whitney jets on k the compact set k is said to have the extension property if there exists a continuous linear extension operator w e k c r d in 1961 b s mityagin posed a problem to give a characterization of the extension property in geometric terms we show that there is no such complete description in terms of densities of hausdorff contents or related characteristics also the extension property cannot be characterized in terms of growth of markov s factors for the set

cam approach to the ground state phase transition in the two dimensional transverse ising model the double cluster approximation dca and the multi effective field approximation mefa are formulated for the two dimensional s 1 2 transverse ising model on a square lattice in the ground state these two cluster effective field approximations expand the sizes of clusters effectively combining some suitable series of these approximations with the coherent anomaly method cam the authors have analysed the critical phenomenon of this model they have obtained g c 1 528 or 0 016 and gamma 1 25 or 0 08 using the dca and gamma 1 26 or 0 10 using the mefa these estimates are consistent with the other results g c approximately 1 52 and gamma approximately 1 24 their scheme is expected to be useful in the study of frustrated systems because various shapes of clusters can be used in their calculations

multifrequency trans admittance scanner mathematical framework and feasibility a trans admittance scanner tas is a device for breast cancer diagnosis based on numerous experimental findings that complex conductivities of breast tumors significantly differ from those of surrounding normal tissues in tas we apply a sinusoidal voltage between a hand held electrode and a scanning probe placed on the breast skin to make current travel through the breast the scanning probe has an array of electrodes at zero voltage we measure exit currents neumann data through the electrodes that provide a map of trans admittance data over the breast surface the inverse problem of tas is to detect a suspicious abnormality underneath the breast skin from the measured neumann data previous anomaly detection methods used the difference between the measured neumann data and a reference neumann data obtained beforehand in the absence of anomaly however in practice the reference data is not available and its computation is not possible since the inhomogeneous complex conductivity of the normal breast is unknown to deal with this problem we propose a frequency difference tas fdtas in which a weighted frequency difference of the trans admittance data measured at a certain moment is used for anomaly detection this paper provides a mathematical framework and the feasibility of fdtas by showing the relationship between the anomaly information and the weighted frequency difference of the neumann data

tikhonov regularization and prior information in electrical impedance tomography the solution of impedance distribution in electrical impedance tomography is a nonlinear inverse problem that requires the use of a regularization method the generalized tikhonov regularization methods have been popular in the solution of many inverse problems the regularization matrices that are usually used with the tikhonov method are more or less ad hoc and the implicit prior assumptions are thus in many cases inappropriate in this paper the authors propose an approach to the construction of the regularization matrix that conforms to the prior assumptions on the impedance distribution the approach is based on the construction of an approximating subspace for the expected impedance distributions it is shown by simulations that the reconstructions obtained with the proposed method are better than with two other schemes of the same type when the prior is compatible with the true object on the other hand when the prior is incompatible with the true object the method will still give reasonable estimates

critical behaviour of a long range non equilibrium system the critical behaviour of a long range one dimensional non equilibrium system where the desorption rate decreases with distance as some power approximately r alpha d is studied by means of the coherent anomaly method the alpha dependence of the critical parameter lambda c and the critical exponent beta is determined

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

lattice trees with specified topologies the authors study the total numbers of lattice trees with specified topologies for strongly embeddable or site clusters with ni branching points of degree i they show how to prove rigorously that the growth constants exist and are all equal to the neighbour avoiding walk limit nu they derive some exact upper bounds for the critical exponents associated with the star comb and brush topologies exact enumeration data are derived and analysed for both weak and strong embeddings of some stars combs and brushes on the square triangular simple cubic and d 4 simple hypercubic lattices using the exact enumeration data for the general d dimensional simple hypercubic lattice and the exact results for the interior of a bethe lattice they derive expansions for the growth constants in inverse powers of the dimensionality these results are consistent with the growth constants being equal to the appropriate walk limits mu or nu

projective electrical impedance reconstruction with two measurements this paper presents a projective reconstruction method of electrical impedance distribution using two boundary measurements of current voltage data the proposed method has a major advantage over existing electrical impedance tomography systems relatively high resolution impedance image in a near surface region underneath the voltage sensing probe that is placed on a skin surface we attach two pairs of electrodes on the border of the probe in such a way that each pair of electrodes generates electrical current flowing underneath the voltage sensing probe and two currents flow across each other a careful analysis of the measured data with respect to local perturbation of admittivity leads to the projective reconstruction method and its rationale numerical simulations show that the proposed method successfully reconstructs high resolution image of local perturbation of admittivity due to object position changes or admittivity value changes or the both in a near surface region underneath the probe

self avoiding walk contacts and random walk self intersections in variable dimensionality the average number of nearest neighbor nn contacts m of self avoiding walks saw s on a hypercubic lattice is calculated using direct enumeration and 1 d expansion methods where d is the spatial dimension these calculations are compared with exact analytic determinations for the asymptotic number of random walk rw self intersections in the limit of long chains n ensuremath rightarrow ensuremath infty the number of rw binary ternary etc self intersections is a function of the probability mathit c mathit d mathrm that a rw escapes from the origin to infinity and an accurate tabulation of mathit c mathit d mathrm is given in the dimension range 2d10 we find that the number of saw nn contacts m mathrm mathrm saw has an asymptotic behavior m mathrm mathrm saw ensuremath sim mathit a mathrm ensuremath infty n similar to that for the number of rw self intersections m mathrm mathrm rw ensuremath sim mathit a mathrm rw n as first suggested by domb but the corrections to this leading scaling differ for the rw and saw problems the contact amplitude mathit a mathrm ensuremath infty determined from direct enumeration data and ratio extrapolation exhibits a maximum near d 3 dimensions as does mathit a mathrm rw comparison of the numerical estimates for mathit a mathrm ensuremath infty to the 1 d expansion calculation of mathit a mathrm ensuremath infty shows significant deviation for d5 reflecting the strong fluctuations in contacts that arise in lower dimensions the correction to the scaling exponent mathrm ensuremath delta mathit m for saw nn contacts exhibits a maximum near d 2 dimensions a behavior similar to previous observations for the saw exponent ensuremath gamma estimates of the ensuremath theta point for interacting saw s the critical temperature of the o m model and other lattice constants e g bond and site percolation thresholds are obtained in terms of saw and rw lattice parameters

marriage of exact enumeration and 1 d expansion methods lattice model of dilute polymers we consider the properties of a self avoiding polymer chain with nearestneighbor contact energy on ad dimensional hypercubic lattice general theoretical arguments enable us to prescribe the exact analytic form of then segment chain partition functionc n and unknown coefficients for chains of up to 11 segments are determined using exact enumeration data ind 2 6 this exact form provides the main ingredient to produce a large n expansion ind 1of the chain free energy through fifth order with the full dependence on the contact energy retained the dependent chain connectivity constant and free energy amplitude are evaluated within thed 1expansion too d 5 our general formulation includes for the first time self avoiding walks neighboravoiding walks theta and collapsed chains as particular limiting cases

non universal critical behaviour of the two dimensional ising model with crossing bonds abstract the two dimensional square lattice ising model with the nearest neighbour ferromagnetic interaction j and the next nearest neighbour antiferromagnetic interaction j is investigated in the interaction range j j 0 8 this model is shown to violate the ordinary universality hypothesis estimations of critical temperature as a function of j j by means of an extrapolation method results in the exact critical temperature t c when j j 0 and in an approximate t c accurate up to the fourth digit when j j is small the critical exponent is estimated as a function of j j with the use of the multi effective field theory and the coherent anomaly method it is shown consequently that varies continuously as j j increases

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

hypercubic lattice saw exponents nu and gamma 3 99 dimensions revisited the self avoiding walk saw exponents nu and gamma are computed over a range of dimensions 1 or d infinity from exact expressions for the mean square end to end distance rn2 and the partition function qn of saws having a limited number of steps n or 11 saw exponents nu gamma for arbitrary dimension d are estimated by applying standard extrapolation techniques to the direct enumeration data which has been analytically continued to variable dimension exponent estimates obtained from continuum theories of self avoiding paths are compared with the saw calculations