overview and comparison of localic and fixed basis topological products this paper studies localic products traditional topological products and l topological products and gives a complete outline of the localic product comparisons of localic and l topological products are generally absent in the literature and this paper answers longstanding open questions in that area as well as provides a complete proof of the classical comparison theorem for localic and traditional topological products this paper contributes several l valued comparison theorems one of which states the localic and l topological products of l topologies are order isomorphic if and only if the localic product is l spatial providing l is itself spatial and the family of l topological spaces is prime separated these last two conditions always hold in the traditional setting capturing the traditional comparison theorem as a special case and the prime separation condition is satisfied by important lattice valued examples that include the fuzzy real line and the fuzzy unit interval for l any complete boolean algebra and the alternative fuzzy real line and fuzzy unit interval for l any semi frame separation conditions help control the sloppy behavior of the l topological product when l 2 and several separation conditions are studied in this context and it should be noted that localic products have a point free version of the product separation condition considered in this paper the traditional comparison theorem is carefully proved both to fill gaps in the extant literature and to motivate the l valued comparison theorem quoted above and reveal the special role played by cross sums of prime l open subsets en route characterizations are given of prime l open subsets of certain l products which in turn yield characterizations of prime open and irreducible closed subsets of traditional product spaces

on greedy randomized kaczmarz method for solving large sparse linear systems for solving large scale systems of linear equations by iteration methods we introduce an effective probability criterion for selecting the working rows from the coefficient matrix and construct a

a generalization of handscomb s quantum monte carlo scheme application to the 1d hubbard model a recently introduced generalization of handscomb s quantum monte carlo scheme 1962 is further developed expressions for expectation values of various observables are studied in detail a more efficient algorithm for importance sampling in a space of state vectors and operator strings is constructed using the 1d hubbard model as an illustrative example as a test of the method 32 site rings at band fillings 1 4 3 8 and 1 2 are studied at a low temperature results for spin and charge density structure factors and static susceptibilities are presented

perturbation series for the mass gap of the 1 1 dimensional o 2 model the strong coupling mass gap series to 10th order in the dimensionless coupling is presented for the 1 1 dimensional o 2 model the second logarithmic derivative of the euler transformed series is examined using pade techniques to yield the critical parameter estimates lambda c approximately 0 89 0 02 and sigma approximately 0 50 or 0 08 these results are consistent with the model exhibiting a kosterlitz thouless transition

point set lattice theoretic topology this essay attempts to survey in a coherent way certain aspects of point set lattice theoretic or poslat topology by which we mean fuzzy topology grounded in notions of sets functions powersets and powerset operators the latter two being lattice theoretic in nature and examined from a lattice theoretic point of view using methods of category theory connections with other related issues and developments are frequently given

critical behaviour of the two dimensional potts model with a continuous number of states a finite size scaling analysis we investigate the critical behaviour of the two dimensional q state potts model using finite size scaling and transfer matrix methods for the continuous transition range 0 these results for continuous q were obtained from a transfer matrix constructed for a generalized whitney polynomial representing the potts models an effective algorithm to compute the dominant eigenvalues of this essentially nonsymmetric transfer matrix is developed

the 2 1 d ising model on a triangular lattice the 2 1 d ising model on a triangular lattice is explored for lattices of up to 5 5 sites finite size scaling techniques are used to estimate the critical parameters xc 0 2096 2 nu 0 627 4 beta 0 322 6 gamma 1 236 8 these agree with previous estimates within errors and with the hypotheses of universality and hyperscaling the behaviour at low temperatures is also studied and theoretical predictions of finite size scaling at a first order transition are confirmed

accurate estimates of 3d ising critical exponents using the coherent anomaly method abstract an analysis of the critical behavior of the three dimensional ising model using the coherent anomaly method cam is presented various sources of errors in cam estimates of critical exponents are discussed and an improved scheme for the cam data analysis is tested using a set of mean field type approximations based on the variational series expansion approach accuracy comparable to the most precise conventional methods has been achieved our results for the critical exponents are given by 0 108 5 0 327 4 1 237 4 and 4 77 5

finite lattice extrapolations for z3 and zs models a method is presented to accelerate the convergence of finite lattice sequences to their bulk limit the calculation of highly accurate estimates of the critical parameters of the bulk system is then possible applied to the hamiltonian version of the z3 model three state potts model in 1 1 dimensions these techniques yield estimates for the exponents gamma 1 444 or 0 0001 nu 0 8333 or 0 0003 and alpha 0 33 or 0 01 for the z5 model the presence of a kosterlitz thouless transition is confirmed

density matrix formulation for quantum renormalization groups a generalization of the numerical renormalization group procedure used first by wilson for the kondo problem is presented it is shown that this formulation is optimal in a certain sense as a demonstration of the effectiveness of this approach results from numerical real space renormalization group calculations for heisenberg chains are presented

sobriety and spatiality in varieties of algebras the paper considers a generalization of the classical papert papert isbell adjunction between the categories of topological spaces and locales to an arbitrary variety of algebras and illustrates the obtained results by the category of algebras over a given unital commutative quantale

convergence speeding convergence and summability abstract four general principles are proposed for use in constructing convergence speeding methods five old methods and about 15 more recent non linear methods are discussed with reference to their range of applicability and rate of convergence speeding when applied to alternating monotonic slightly erratic fourier and alternating divergent series several of these methods are proved to give analytic continuations while even asymptotic series with zero radius of convergence can be summed accurately divergent series of positive terms may also in some cases be interpreted with moderate accuracy using four different methods convergence tests are reviewed in the light of these convergence speeding methods and analytic continuation

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 studies of the potts model i the simple cubic ising model the finite lattice method of series expansion is generalized to the q state potts model on the simple cubic lattice it is found that the computational effort grows exponentially with the square of the number of series terms obtained unlike two dimensional lattices where the computational requirements grow exponentially with the number of terms for the ising q 2 case the authors have extended the low temperature series for the partition functions magnetization and zero field susceptibility to u26 from u20 the high temperature series for the zero field partition function is extended from nu 18 to nu 22 subsequent analysis gives critical exponents in agreement with those from field theory

the high temperature susceptibility and spin spin correlation function of the three dimensional ising model the series analysis protocol developed in a preceding paper ibid vol 20 p 1839 1987 is applied to the susceptibility and correlation function of the three dimensional ising model for the spin 1 2 ising data the author argues that the protocol needs modification to take account of trends in the data which trends arise from the nature of the series in this way the author obtains gamma 1 239 or 0 003 for all cubic lattices and for a variety of spin values the diamond lattice data lies outside this range and it is argued that this series is effectively far shorter than the others the author also estimates nu 0 632 0 002 0 003 for the bcc lattice and obtains critical point estimates for all lattice and spin models studied

finite size scaling and universality in the 2 1 d ising model the energy and magnetisation density of the 2 1 d ising model are investigated for the thermal exponent the author finds xepsilon 1 42 or 0 02 in agreement with hyperscaling the privman fisher universality hypothesis is confirmed by two methods first the author presents at the critical point numerical data for the finite size scaling amplitudes of the singular free energy magnetisation susceptibility and surface tension and checks them for universality second using the explicitly computed eigenvectors of the hamiltonian it is shown that the ratios of matrix elements of the energy and magnetisation density are universal

amplitude exponent relation for the correlation length in the 2 1 dimensional ising model for the critical 2 1 d ising model defined on a square lattice with antiperiodic boundary conditions numerical studies suggest relations among the critical exponents and the finite size scaling amplitudes of correlation lengths similar to those obtained in 1 1 dimensions from conformal invariance

a monte carlo study of leading order scaling corrections of phi 4 theory on a three dimensional lattice we present a monte carlo study of the one component 4 model on a cubic lattice in three dimensions leading order scaling corrections are studied using the finite size scaling method we compute the corrections to scaling exponent with high precision we determine the value of the coupling at which leading order corrections to scaling vanish using this result we obtain estimates for critical exponents that are more precise than those obtained with field theoretic methods

critical properties of an s 1 multispin coupling ising model strong and weak coupling series expansions are used to investigate the critical properties of the s 1 multispin coupling ising chain in the presence of a transverse field the order of the transition goes from second order to first order when more than three spins are coupled according to the numerical results the two spin and three spin coupling models belong to the ising and the four state potts universality classes respectively thus the critical properties of the model do not depend on the value of the spin even when three spins are coupled

the critical behaviour of a quantum spin problem with thee spin coupling the critical behaviour of an ising like model with three spin coupling is studied in a transverse field a self dual renormalisation group transformation can be applied which gives well converging results for the critical exponents when large enough cells are taken finite size scaling on the same model give comparable results

composite variety based topological theories motivated by the recent result of rodabaugh on categorical redundancy of lattice valued bitopology the paper considers another viewpoint on the topic based on the notion of composite variety based topological theory the new concept apart from providing a variable basis generalization of bitopology incorporates the most important approaches to topology currently developed in the fuzzy community bringing forward their categorically algebraic properties which are cleared from point set lattice theoretic dependencies dwelling on different ways of interaction between composite topology and topology e g embedding the former into the latter as a full bicoreflective subcategory we finally arrive at the conclusion that variable basis bitopological theories still deserve to be studied on their own

stochastic truncation for the 2 1 d ising model the method of symmetrized stochastic truncation is applied to the 2 1 dimensional ising model to calculate the ground state energy mass gap magnetization and susceptibility on lattices of sizes up to 6 6 sites the method is shown to be a powerful and accurate monte carlo technique provided the lattice size is not too large and the model is suitably convergent finite size scaling estimates of the critical indices are nu 0 627 2 alpha 0 12 2 beta 0 324 3 and delta 1 23 1 an estimate of the combination gamma nu 2 beta nu 3 000 1 is obtained in outstanding agreement with the expected hyperscaling relation

parallel application of block iterative methods in medical imaging and radiation therapy some row action algorithms which exploit special objective function and constraints structure have proven advantageous for solving huge and sparse feasibility or optimization problems recently developed block iterative versions of such special purpose methods enable parallel computation when the underlying problem is appropriately decomposed this opens the door for parallel computation in image reconstruction problems of computerized tomography and in the inverse problem of radiation therapy treatment planning all in their fully discretized modelling approach since there is more than one way of deriving block iterative versions of any row action method the choice has to be made with reference to the underlying real world problem

randomized block kaczmarz method with projection for solving least squares abstract the kaczmarz method is an iterative method for solving overcomplete linear systems of equations a x b the randomized version of the kaczmarz method put forth by strohmer and vershynin iteratively projects onto a randomly chosen solution space given by a single row of the matrix a and converges linearly 1 in expectation to the solution of a consistent system in this paper we analyze two block versions of the method each with a randomized projection designed to converge in expectation to the least squares solution often faster than the standard variants our approach utilizes both a row and column paving of the matrix a to guarantee linear convergence when the matrix has consistent row norms called nearly standardized and a single column paving when the row norms are unbounded the proposed methods are an extension of the block kaczmarz method analyzed by needell and tropp and the randomized extended kaczmarz method of zouzias and freris the contribution is thus two fold unlike the standard kaczmarz method our results demonstrate convergence to the least squares solution of inconsistent systems both methods in the nearly standardized case and the second method in other cases by using appropriate blocks of the matrix this convergence can be significantly accelerated as is demonstrated by numerical experiments

magnetisations from finite size scaling a method of obtaining the spontaneous magnetisation from finite lattice matrix elements of the magnetic field operator due to yang 1952 and uzelac 1980 is discussed the method is demonstrated for the case of the ising model in 1 1 dimensions and is shown to provide smooth and rapidly convergent finite lattice sequences applied to the case of the three state potts z3 model in 1 1 dimensions the method yields an estimate beta 0 111 09 or 0 000 05 for the critical exponent this confirms alexander s conjecture of universality with the hard hexagonal model

category theoretic properties of fuzzy topological spaces abstract in this paper we establish some important category theoretic properties in particular smallness conditions for categories of fuzzy topological spaces we also obtain a non existence of compactifications

critical exponents of two dimensional potts and bond percolation models critical exponents of the two dimensional q state potts model are calculated by means of finite size scaling and transfer matrix techniques for continuous q results for the temperature exponent agree accurately with the conjecture of den nijs 1979 the magnetic exponent is found to behave in accordance with the conjecture of nienhuis et al 1980

quantales finite observations and strong bisimulation abstract it has often been claimed that bisimulation makes distinctions that cannot be observed in practice abramsky and vickers proposed an algebraic framework based on quantales for describing observations on concurrent processes without hidden transitions and used it in order to provide an observational explanation of several process equivalences ranging from hoare trace equivalence to ready simulation we follow their approach and argue that strong bisimulation can be explained in the same way at least in the case of image computable labelled transition systems

critical exponents of the n vector model recently the series for two renormalization group functions corresponding to the anomalous dimensions of the fields and of the three dimensional field theory have been extended to next order seven loops by murray and nickel we examine the influence of these additional terms on the estimates of critical exponents of the n vector model using some new ideas in the context of the borel summation techniques the estimates have slightly changed but remain within the errors of the previous evaluation exponents such as related to the field anomalous dimension which were poorly determined in the previous evaluation of le guillou zinn justin have seen their apparent errors significantly decrease more importantly perhaps summation errors are better determined the change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values finally because an error has been discovered in the last order of the published expansions order we have also re analysed the determination of exponents from the expansion the conclusion is that the general agreement between expansion and three dimensional series has improved with respect to le guillou zinn justin

finite lattice methods in quantum hamiltonian field theory i o 2 and o 3 heisenberg models for pt i see ibid vol 14 p 241 57 1981 two efficient methods for finding the low lying states of hamiltonians on finite lattices are described the first involves constructing a finite representation of the hamiltonian using strong coupling eigenstates while the second is based on the lanczos recursion method the methods are used to determine the mass gap of the o 2 and o 3 heisenberg hamiltonians in 1 1 dimensions for a sequence of finite chains the critical behaviour of the infinite chain is then analysed by extrapolating the finite lattice estimates using finite size scaling a remarkably sensitive test is developed for the presence of a phase transition for the o 2 model data this test yields strong evidence for a phase transition with the weak coupling phase massless while in the o 3 case the test supports although more weakly the absence of any transition

finite lattice extrapolation algorithms two algorithms for sequence extrapolation due to van den broeck and schwartz 1979 and bulirsch and stoer 1964 are reviewed and critically compared applications to three state and six state quantum chains and to the 2 1 d ising model show that the algorithm of bulirsch and stoer is superior in particular if only very few finite lattice data are available

universal amplitudes in finite size scaling generalisation to arbitrary dimensionality the relationship between the correlation length and critical exponents in finite width strips in two dimensions is generalised to cylindrical geometries of arbitrary dimensionality d for d not 2 these correspond however to curved spaces the result is verified for the spherical model

quantum phase transitions in the j j heisenberg and xy spin antiferromagnets on a square lattice finite size scaling analysis we investigate the critical parameters of an order disorder quantum phase transition in the spin j j heisenberg and xy antiferromagnets on a square lattice based on the excitation gaps calculated by the exact diagonalization technique for systems up to 32 spins and finite size scaling analysis we estimate the critical couplings and exponents of the correlation length for both models our analysis confirms the universal critical behaviour of these quantum phase transitions they belong to 3d o 3 and 3d o 2 universality classes respectively

cluster expansions for the ising and heisenberg spin models in hamiltonian lattice field theory cluster expansion methods are applied to calculate high temperature series for the vacuum energy the susceptibility and the mass gap for the ising model and the o 2 and o 3 heisenberg models in 1 1 dimensions and 2 1 dimensions critical points and critical indices are estimated for the line the square and the triangular lattices the results demonstrate universality with the normal euclidean versions of these models within errors

conformal structure in the spectrum of an altered quantum ising chain the ising model with an infinite line of defects is mapped onto a strip with two defect lines the hamiltonian spectrum is studied at the bulk critical point its exact diagonal form is found for an infinite number of sites the spectrum of physical excitations contains an infinite number of primary fields while the leading ground state energy correction is independent of the defect strength a novel algebraic structure interpolating between those belonging to periodic and free boundary conditions is signalled

series expansions for the zero temperature transverse ising model series expansions are presented for the magnetisation susceptibility magnetic field derivatives of the susceptibility and specific heat of the zero temperature transverse ising model coefficients in these series have been calculated to tenth order in lambda 2 where lambda is the transverse field for the linear chain to eighth order for the square lattice and to seventh order for the triangular lattice these series yield estimates of the low temperature critical exponents alpha beta gamma and delta of the two and three dimensional ising models they provide good evidence for the symmetry of exponents above and below the critical point e g gamma gamma

asymptotic degeneracy of the transfer matrix spectrum for systems with interfaces relation to surface stiffness and step free energy two and three dimensional ising type systems are considered in the finite cross section cylindrical geometry an interface is forced along the cylinder strip in 2d by the antiperiodic or boundary conditions detailed predictions are presented for the largest asymptotically degenerate set of the transfer matrix eigenvalues for rough interfaces i e for 0 t tc in 2d tr t tc in 3d the eigenvalues are split algebraically and the spectral gaps are governed by thesurface stiffness coefficient for rigid interfaces i e 0 t tr in 3d the eigenvalues are split exponentially with the gaps determined by thestep free energy

stiffening of fluid membranes due to thermal undulations density matrix renormalization group study it has been considered that the effective bending rigidity of fluid membranes should be reduced by thermal undulations however recent thorough investigation by pinnow and helfrich revealed the significance of measure factors for the partition sum accepting the local curvature as a statistical measure they found that fluid membranes are stiffened macroscopically in order to examine this remarkable idea we performed extensive ab initio simulations for a fluid membrane we set up a transfer matrix that is diagonalized by means of the density matrix renormalization group our method has an advantage in that it allows us to survey various statistical measures as a consequence we found that the effective bending rigidity flows toward strong coupling under the choice of local curvature as a statistical measure on the contrary for other measures such as normal displacement and tilt angle we found a clear tendency toward softening

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

conformal invariance and correction to finite size scaling applications to the three state potts model corrections to finite size scaling are determined numerically for several levels of the three state potts quantum chain with various boundary conditions it is found that the leading correction term behaves like wo in the case of periodic and twisted boundary conditions the coefficients of the n o term are determined by the three point correlation functions of the conformal theory

numerical comparisons of nonlinear convergence accelerators as part of a continuing program of numerical tests of convergence accelerators we have compared the iterated aitken s a2 method wynn s algorithm brezinski s 0 algorithm and levin s u transform on a broad range of test problems linearly convergence alternating monotone and irregular sign series logarithmically convergent series power method and bernoulli method sequences alternating and monotone asymptotic series and some perturba tion series arising in applications in each category either the algorithm or the u transform gives the best results of the four methods tested in some cases differences among methods are slight and in others they are quite striking 1 introduction we reported in 19 on a numerical test program that compared eleven different scalar convergence accelerators on a broad range of infinite series problems in an attempt to find an across the board accelerator that would handle both linear and logarithmic convergence and both alternating and monotone series or sequences the best candidates to emerge from that study were levin s u transform 14 and brezinski s 0 algorithm 6 we also provided some theoretical support for that conclusion in terms of the wide range of series summed exactly by these methods and by proving that 02 and the levin transforms all accelerate linear convergence the other levin transforms t and v produced essentially equivalent numerical results to u except that t fails on logarithmic convergence we have continued the test program started with 19 to include monotone linearly convergent series series with irregular sign patterns specifically fourier series and sequences whose terms do not depend explicitly on the previous term and or the index e g bernoulli s method since convergence accelerators are often known to transform divergent series to convergent ones we have also included in our test program divergent power series asymptotic series and a few perturbation series the methods considered in this paper are the u and 0 algorithms noted above and

finite size scaling in the 2 1 d ising model hamiltonian eigenvalues are calculated for the 2 1 d ising model on lattices up to 5 5 sites finite size scaling techniques are used to estimate the critical coupling xc 0 329 or 0 001 and index v 0 635 or 0 005 the prospects are discussed for further applications of these methods in three and four dimensions

on the meany inequality with applications to convergence analysis of several row action iteration methods the meany inequality gives an upper bound in the euclidean norm for a product of rank one projection matrices in this paper we further derive a lower bound related to this inequality we discuss the internal relationship between the upper bounds given by the meany inequality and by the inequality in smith et al bull am math soc 83 1227 1270 1977 in the finite dimensional real linear space we also generalize the meany inequality to the block case in addition by making use of the block meany inequality we improve existing results and establish new convergence theorems for row action iteration schemes such as the block kaczmarz and the householder bauer methods used to solve large linear systems and least squares problems

cluster expansions in the 2 1 d ising model the cluster expansion methods of nickel are applied to calculate high temperature series for the vacuum energy and specific heat the susceptibility and the mass gap in the 2 1 d ising model critical points and critical exponents are estimated for the square and triangular lattices the results demonstrate universality with the 3d ising model within errors exact linked cluster expansions are formulated for the quantities above and their convergence and scaling properties are investigated

universal ratios of scaling amplitudes in the hamiltonian limit of the 3d ising model the scaling amplitudes of the spin spin and energy energy correlation lengths for the hamiltonian limit of the 3d ising model are computed on a square lattice both periodic and antiperiodic boundary conditions are considered the ratios of the scaling amplitudes are found to be universal

iterative algorithms for large partitioned linear systems with applications to image reconstruction abstract we present a unifying framework for a wide class of iterative methods in numerical linear algebra in particular the class of algorithms contains kaczmarz s and richardson s methods for the regularized weighted least squares problem with weighted norm the convergence theory for this class of algorithms yields as corollaries the usual convergence conditions for kaczmarz s and richardson s methods the algorithms in the class may be characterized as being group iterative and incorporate relaxation matrices as opposed to a single relaxation parameter we show that some well known iterative methods of image reconstruction fall into the class of algorithms under consideration and are thus covered by the convergence theory we also describe a novel application to truly three dimensional image reconstruction

accurate monte carlo critical exponents for ising lattices abstract a careful monte carlo investigation of the phase transition very close to the critical point t t c h 0 in relatively large d 3 s 1 2 ising lattices did produce critical exponents 3 d 0 3126 4 5 16 3 d 1 0 1997 4 1 5 and 3 d 1 253 4 5 4 our results indicate that within experimental error they are given by simple fractions corresponding to the linear interpolations between the respective two dimensional onsager and four dimensional mean field critical exponents an analysis of our inverse susceptibility data 1 t vs t t c shows that these data lead to a value of 3 d compatible with and t c 4 51152 12 while values obtained recently by high and low temperature series expansions and renormalization group methods are not

finite size scaling studies of the o 2 heisenberg spin model in d 1 dimensions the finite size scaling behaviour of the o 2 heisenberg spin model in d 1 dimensions d 1 and 2 is computed in the low temperature region using the stochastic truncation monte carlo method the numerical results so obtained agree very well with effective lagrangian theory and with spin wave perturbation theory

phenomenological renormalisation of monte carlo data for percolation the accuracy of a phenomenological renormalisation which is based on monte carlo data is tested by investigating site percolation in a simple cubic lattice the method appears to be very accurate and can yield precise estimates of the quantities of interest with small to moderate lattice sizes the site percolation threshold of the lattice is predicted to be 0 3115 or 0 0005 if nu is the exponent of correlation length the author finds beta nu approximately 0 48 or 0 01 for the exponent of percolation probability and beta b nu approximately 1 1 or 0 03 for the backbone exponent in agreement with most accurate data currently available an analysis of the data at the percolation threshold based on the standard finite size scaling method also supports the results

the anharmonic oscillator complex eigenvalues for the ground state with negative quartic or cubic energy distortion the perturbed ground state eigenvalues for the harmonic oscillator with negative quartic and with cubic energy distortion are calculated by numerical integration these agree with the author s results using an asymptotic series

series expansions for the 3d transverse ising model at t 0 both weak coupling and strong coupling series expansions are calculated for the ising model in a transverse field at zero temperature in three dimensions series are obtained for the ground state energy the magnetization the susceptibility and the energy gaps on the simple cubic the body centred cubic and the face centred cubic lattices the analysis of the critical behaviour is consistent with the behaviour predicted by renormalization group theory for the four dimensional simple ising model there is a remarkable degree of universality between all three lattices

finite size effects in fluid interfaces abstract finite size effects in interfacial tensions of fluid interfaces are studied at the level of the gaussian model of capillary waves it had been suggested that such effects might play a significant role in surface tension measurements based on capillary rise between plates spaced a small distance d apart the finite size correction varying as 1 d a reconsideration of the thermodynamics of finite size effects followed by careful calculations for the gaussian model leads to a finite size correction varying as 1 d 2 with a universal coefficient the effect is too small to be noticeable in current experiments the calculations have been carried out for rectangular interfaces of arbitrary dimensionality and general shapes subject to many types of boundary conditions they also have implications for finite size effects in interfacial free energies in two and three dimensional ising models which are discussed in connection with recent exact and monte carlo calculations

on partially randomized extended kaczmarz method for solving large sparse overdetermined inconsistent linear systems abstract for solving large sparse overdetermined and inconsistent system of linear equations by iteration methods by further reconstructing the randomized extended kaczmarz method proposed by zouzias and freris in 2013 siam j matrix anal appl 34 2013 773 793 we propose a partially randomized extended kaczmarz method when the coefficient matrix is assumed to be of full column rank we prove the convergence and derive an upper bound for the expected convergence rate of the partially randomized extended kaczmarz method this bound could be smaller than that of the randomized extended kaczmarz method under certain conditions moreover with numerical results we show that the partially randomized extended kaczmarz method can be much more effective than the randomized extended kaczmarz method

coherent anomaly method with a new mean field type approximation abstract in the present paper we propose a new mean field type approximation based on multispin effective fields determined from self consistency conditions for some correlation functions of a cluster using the transfer matrix method we investigate finite width strips of spins for square honeycomb and triangle lattices the results obtained exhibit good scaling properties and can be analyzed with suzuki s coherent anomaly method yielding a very accurate estimation of the critical temperature and the critical exponent

row action methods for huge and sparse systems and their applications this paper brings together and discusses theory and applications of methods identified and labelled as row action methods for linear feasibility problems find x in bf r n such that ax leqq b linearly constrained optimization problems minimize f x subject to ax leqq b and some interval convex programming problems minimize f x subject to c leqq ax leqq b the main feature of row action methods is that they are iterative procedures which without making any changes to the original matrix a use the rows of a one row at a time such methods are important and have demonstrated effectiveness for problems with large or huge matrices which do not enjoy any detectable or usable structural pattern apart from a high degree of sparaseness fields of application where row action methods are used in various ways include image reconstruction from projection operations research and game theory learning theory pattern recognition and transportation theory a row action method for the

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

fuzzy points and attachment in this paper a binary relation between l sets called attachment is defined by means of a suitable family of completely coprime filters in l examples are given using several kinds of lattice ordered algebras and a class of attachments is determined whose elements generalize pu liu s quasi coincidence relation mapping any l set on x to the set of the attached l points one gets a frame map from the l powerset l x to the powerset p s x of the set s x of l points on x this allows one to define functors from the category l top of l topological spaces either to the category top of topological spaces or to the category topsys of topological systems a comparison with the hypergraph functor is also included

critical temperatures of the d 3 s 1 2 ising model the effect of confluent corrections to scaling much attention has been paid to the d 3 s 1 2 ising model on the bcc lattice in recent years because the best high temperature series expansions were available for this lattice however in order to compare series estimates of critical exponents and temperatures with independent evaluations via the monte carlo method lattices of lower coordination number must be considered since monte carlo studies are usually made on these a study of extant susceptibility series on the fcc sc diamond and tetrahedron lattices is reported on and some comments are made on aspects of recent monte carlo analyses of the d 3 s 1 2 ising model on the sc and diamond lattices

strong coupling expansion analysis of the false vacuum decay rate of the lattice phi4 model in 1 1 dimensions strong coupling expansion is performed for the lattice 4 model in 1 1 dimensions because the strong coupling limit itself is not solvable we employed numerical calculations so as to set up unperturbed eigensystems restricting the number of hilbert space bases we performed linked cluster expansion up to 11th order we carried out an alternative simulation by means of the density matrix renormalization group thereby we confirmed that our series expansion data with a convergence acceleration trick are in good agreement with the simulation result through the analytic continuation to the domain of negative biquadratic interaction we obtain the false vacuum decay rate contrary to common belief that the tunnelling phenomenon lies out of perturbative treatments our series expansion reproduces the instanton theory behaviour for a high potential barrier for a shallow barrier in contrast our result tells us that the relaxation is no longer described by an instanton but the decay rate acquires notable enhancement

on convergence rate of the randomized kaczmarz method abstract for consistent system of linear equations with the coefficient matrix being flat we conduct an exact closed form formula for the mean squared error of the iterate generated by the randomized kaczmarz method which completes the existing closed form formula derived only for the tall coefficient matrix based upon these formulas we further estimate an upper bound for the convergence rate of the randomized kaczmarz method both theoretical analysis and numerical experiments demonstrate that this bound can significantly improve the existing ones

a variational sinc collocation method for strong coupling problems we have devised a variational sinc collocation method vscm which can be used to obtain accurate numerical solutions to many strong coupling problems sinc functions with an optimal grid spacing are used to solve the linear and nonlinear schrodinger equations and a lattice 4 model in 1 1 our results indicate that errors decrease exponentially with the number of grid points and that a limited numerical effort is needed to reach high precision

interweaving algebra and topology lattice valued topological systems this paper is primarily dedicated to understanding the natural role that topological systems and lattice valued topological systems play in understanding the relationship between algebra and topology a relationship expressed by an interweaving of embeddings of essentially algebraic and topological categories this natural role is revealed by how various categories for systems relate to locales topological spaces and various categories for lattice valued topology

latent heats from finite size scaling a method of obtaining the latent heat at a first order transition from finite lattice matrix elements is discussed and demonstrated for the case of the 1 1 d potts model the method is shown to provide smoothly convergent finite lattice sequences the structure of the finite lattice hamiltonian eigenvalues is exhibited and a characteristic signal of the first order transition is proposed the finite size scaling behaviour at the transition is also discussed

on the error estimate of the randomized double block kaczmarz method abstract in this paper we consider the convergence analysis of the randomized double block kaczmarz method and improve the upper bound of the error estimate in expectation of the randomized double block kaczmarz method numerical experiments are given to demonstrate the theoretical results and to show a large gap between the new and the old bound

critical behavior of the fidelity susceptibility for the d 2 transverse field ising model abstract the overlap inner product between the ground state eigenvectors with proximate interaction parameters the so called fidelity plays a significant role in the quantum information theory in this paper the critical behavior of the fidelity susceptibility is investigated for a two dimensional transverse field quantum ising model by means of the numerical diagonalization method in order to treat a variety of system sizes n 12 14 32 we adopt the screw boundary condition finite size artifacts scaling corrections of the fidelity susceptibility appear to be suppressed as compared to those of the binder parameter as a result we estimate the fidelity susceptibility critical exponent as f 0 715 20

finite size scaling in the transverse ising model on a square lattice energy eigenvalues and order parameters are calculated by exact diagonalization for the transverse ising model on square lattices of up to 6 6 sites finite size scaling is used to estimate the critical parameters of the model confirming universality with the three dimensional classical ising model critical amplitudes are also estimated for both the energy gap and the ground state energy

high temperature series expansions for the 2 1 dimensional ising model using efficient cluster expansion methods the known high temperature series for the vacuum energy specific heat susceptibility and mass gap of the 2 1 dimensional ising model on the square and triangular lattices have been extended by several terms estimates of the critical indices demonstrate very convincing universality with the euclidean version of the model

on limits and colimits of variety based topological systems the paper provides variety based extensions of the concepts of lattice valued interchange system and space introduced by denniston melton and rodabaugh and shows that variety based interchange systems incorporate topological systems of vickers state property systems of aerts chu spaces over the category of sets in the sense of pratt of p h chu and contexts of formal concept analysis of wille the paper also provides an explicit description of co limits in the category of variety based topological systems and applies the obtained results to extend the claim of denniston et al that the category of topological systems of vickers is small initially topological over the category of sets

l topological spaces as spaces of points the main background of this paper is a functor from the category of l topological spaces to the category of topological spaces which is defined by means of an attachment a notion recently introduced in the lattice l and has very nice properties under the assumption of spatiality the pu liu s quasi coincidence relation largely used to study 0 1 topological spaces is determined by a suitable attachment in 0 1 so the results described here apply to that situation this functor allows to import topological concepts into the fuzzy setting directly from the classical context meanwhile this provides an evaluation of the relevance and of the consistency of basic notions in fuzzy topology as well as a critical view on how these have been introduced and treated up to now an overview of the relationship between spatial attachments and textures is outlined in the last part of the paper

the 1 1 do 2 model a finite lattice analysis finite size methods and the theory of conformal invariance are applied to the 1 1 do 2 or x y planar model the critical point is found to be xc approximately 2 0 the value sigma 0 501 or 0 005 is obtained for the index governing the critical divergence of the correlation length and the conformal anomaly is confirmed to be c 1 the kosterlitz thouless features of a low temperature phase with zero spontaneous magnetisation but algebraic decay of correlations together with a standard high temperature phase are observed the critical exponent eta is determined as a function of coupling constant and compared with theoretical expectations