conformal invariance and finite one dimensional quantum chains based on previous work of cardy 1984 the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions the method is illustrated in the case of the three and four state potts models where the anomalous dimensions of the para fermionic operators are found

hamiltonian studies of the two dimensional n component cubic model ii the cubic transition for part i see ibid vol 19 p 563 74 1986 the phase transition behaviour of the hamiltonian version of the two dimensional n component cubic model is studied along the cubic transition line 1 n expansion and anisotropy expansion around the 2n state potts point are used to determine the phase transition line and the latent heat the latent heat depends on the value of the coupling whereas the crossover value of n where the transition changes from second to first order does not it is nc 2 the latent heat has an essential singularity at n 2 along the cubic transition line

stochastic data envelopment analysis in measuring the efficiency of taiwan commercial banks conventional data envelopment analysis dea for measuring the efficiency of a set of decision making units dmus requires the input output data to be constant in reality however many observations are stochastic in nature consequently the resulting efficiencies are stochastic as well this paper discusses how to obtain the efficiency distribution of each dmu via a simulation technique the case of taiwan commercial banks shows that firstly the number of replications in simulation analysis has little effect on the estimation of efficiency means yet 1000 replications are recommended to produce reliable efficiency means and 2000 replications for a good estimation of the efficiency distributions secondly the conventional way of using average data to represent stochastic variables results in efficiency scores which are different from the mean efficiencies of the presumably true efficiency distributions estimated from simulation thirdly the interval data approach produces true efficiency intervals yet the intervals are too wide to provide valuable information in conclusion when multiple observations are available for each dmu the stochastic data approach produces more reliable and informative results than the average data and interval data approaches do

the relation between amplitudes and critical exponents in finite size scaling the relation between critical exponents and the amplitude of the correlation length divergence at the critical point of two dimensional systems as a function of finite size is investigated and generalised in two ways correlations more general than those of order order type are included a form appropriate for anisotropic systems is proposed the authors present a exact results for the ising and gaussian models and b numerical results for the symmetric eight vertex baxter continuous q state potts and continuous n component cubic models

on the phase diagram of the discrete z6 spin models we point out some problems with the previously proposed phase diagram of the z6 spin models consideration of the diagram near to the decoupling surface using both exact and approximate arguments suggests a modification which remedies these deficiencies with the aid of a new parametrization of the phase space we study the models numerically with results which support our conjectures

polyhedral cone ratio dea models with an illustrative application to large commercial banks abstract polyhedral cone ratio data envelopment analysis models generalizing the ccr ratio model are developed for situations with a finite number of dmus and employing polyhedral cones of virtual multipliers they provide improved definitions of efficiency over ccr models whose input output data and or numbers of dmus are inadequate to capture aspects or restrictions which should be involved the focus here is on the sum form for cones which easily provides for capturing exogenous expert opinion as well as mathematical reduction to the old form with its very powerful software transformation from the usual intersection form to it and vice versa is explicitly given thereby the advantages of either or both are available the theory is illustrated with two dimensional examples and by real banking examples for motivation

fuzzy scores of technical efficiency abstract this paper suggests to extend scores of technical efficiency as used in for example data envelopment analysis dea to efficiency scores defined as so called fuzzy intervals fuzzy scores allow the decision maker to use scores of technical efficiency in combination with other sources of available performance information e g expert opinions key figures etc in this sense fuzzy scores become formal images of the evaluation otherwise done implicitly by the decision maker and may therefore enhance a more consistent evaluation it is shown how to rank a set of fuzzy scores

fuzzy dea a perceptual evalution method abstract dea data envelopment analysis is a non parametric technique for measuring and evaluating the relative efficiencies of a set of entities with common crisp inputs and outputs in fact in a real evaluation problem input and output data of entities evaluated often fluctuate these fluctuating data can be represented as linguistic variables characterized by fuzzy numbers for reflecting a kind of general feeling or experience of experts based on the fundamental ccr model a fuzzy dea model is proposed to deal with the efficiency evaluation problem with the given fuzzy input and output data furthermore an extension of the fuzzy dea model to a more general form is also proposed with considering the relationship between dea and ra regression analysis using the proposed fuzzy dea models the crisp efficiency in ccr model is extended to be a fuzzy number to reflect the inherent uncertainty in real evaluation problems

imprecise data envelopment analysis idea a review and improvement with an application abstract the standard data envelopment analysis dea method requires that the values for all inputs and outputs be known exactly when some outputs and inputs are unknown decision variables such as bounded data ordinal data and ratio bounded data the dea model becomes a non linear programming problem and is called imprecise dea idea there are two different approaches in dealing with imprecise outputs and inputs one uses scale transformations and variable alternations to convert the non linear idea model into a linear program the other converts imprecise data into exact data and then uses the standard linear dea model the current paper reviews and compares the two approaches through an efficiency analysis of a set of telephone offices a simplified approach is developed to reduce the computational burden if one uses the first approach the treatment of weight restrictions in idea is discussed it is shown that weight restrictions on imprecise data are redundant new developments and improvements to both approaches are provided

finite size scaling in strips antiperiodic boundary conditions the exact values of the universal amplitude a relating the correlation length xi approximately l a to the strip width l at the critical point of ising and 3 state potts models are obtained for the case of antiperiodic or twisted boundary conditions predictions are also made for the finite size scaling behaviour of the interfacial tension

the atiyah jones conjecture for rational surfaces we show that if the atiyah jones conjecture holds for a surface x then it also holds for the blow up of x at a point since the conjecture is known to hold for and for ruled surfaces it follows that the conjecture is true for all rational surfaces

the topology of instanton moduli spaces i the atiyah jones conjecture in this paper we study the global geometry and topology of the moduli spaces of based su 2 instantons over the 4 sphere s4 these instanton moduli spaces have a rich history and have been analyzed from many points of view originally these spaces which we denote by mk were defined as solution spaces modulo gauge equivalence to certain partial differential equations namely the self duality equations associated to the yang mills functional in su 2 gauge theory they have been successfully studied from this point of view by taubes t1 t2 uhlenbeck u and others an important alternative approach was initiated by ward w who related instantons to certain holomorphic bundles on cp3 and was continued by atiyah and ward in aw this allowed the classification of instantons on 4 in terms of quaternionic linear algebra by atiyah drinfeld hitchin and manin adhm this holomorphic approach was further extended by donaldson d who showed that these bundles were determined by their restriction to a cp2 and that the restricted bundles only had to satisfy the constraint of being trivial on a fixed line in c2r2 hurtubise hul then exploited this fact to study the moduli spaces mk as did atiyah a to show that mk arise naturally in the theory of holomorphic maps into loop groups this latter approach was continued by gravesen g atiyah and jones aj obtained the first results and formulated the foundational questions on the global topology of these moduli spaces recall that an element of mk is a based gauge equivalence class of a connection on the principal su 2 bundle over 4 denoted by pk with second chern class k satisfying the self duality equations there is a natural forgetful map to the based equivalence classes of all connections in pk atiyah and jones aj showed that this target space which we denote by bk is homotopy equivalent

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

on estimation of monotone and concave frontier functions abstract when analyzing the productivity of firms one may want to compare how the firms transform a set of inputs x typically labor energy or capital into an output y typically a quantity of goods produced the economic efficiency of a firm is then defined in terms of its ability to operate close to or on the production frontier the boundary of the production set the frontier function gives the maximal level of output attainable by a firm for a given combination of its inputs the efficiency of a firm may then be estimated via the distance between the attained production level and the optimal level given by the frontier function from a statistical viewpoint the frontier function may be viewed as the upper boundary of the support of the population of firms density in the input and output space it is often reasonable to assume that the production frontier is a concave monotone function then a famous estimator in the univariate input and output case is the data envelopment analysis dea estimato

stochastic efficiency measures for production units with correlated data abstract while the real world is stochastic in nature in many cases deterministic data envelopment analysis dea models are used to measure the relative efficiency of a set of production units for simplicity however deterministic dea models are not able to differentiate efficient units more seriously the decision maker will be over confident with the presumably uncertain and probably misleading results by applying a standard normal transformation this paper develops a stochastic dea model which is able to take the correlation between the input output factors of each production unit to be evaluated into account to obtain the distribution of the stochastic efficiency the efficiency distribution is more discriminative and informative than the single valued efficiency in that the probability that the stochastic efficiency of a unit is greater than that of another unit can be calculated the case of twenty five taiwanese commercial banks discussed in a previous study that assumed the input output factors to be independent is used to illustrate the characteristics of different models the data is shown to be correlated and the results confirm that ignoring the correlations between the input output factors in measuring efficiency obtains misleading rankings

sensitivity analysis of efficiency scores how to bootstrap in nonparametric frontier models efficiency scores of production units are generally measured relative to an estimated pro duction frontier nonparametric estimators dea fdh are based on a finite sample of observed production units the bootstrap is one easy way to analyze the sensitivity of efficiency scores relative to the sampling variations of the estimated frontier the main point in order to validate the bootstrap is to define a reasonable data generating process in this complex framework and to propose a reasonable estimator of it this paper provides a general methodology of bootstrapping in nonparametric frontier models some adapted methods are illustrated in analyzing the bootstrap sampling variations of input efficiency measures of electricity plants

operator content of n state quantum chains in the c 1 region the authors conjecture the operator content for n state quantum chains n or 5 in the domains of the coupling constants where the central charge of the virasoro algebra is equal to one free boundary conditions as well as boundary conditions compatible with the torus are considered the conjectured operator content is compared with finite size scaling estimates

chance constrained efficiency evaluation a model for efficiency evaluation based upon the theory of chance constrained programming is developed the model uses a piecewise linear envelopment of confidence regions for observed stochastic multiple input multiple output combinations in the data envelopment analysis dea tradition the model allows for an exogenous decomposition of the total variation in data for each decision making unit dmu by varying certain probability levels the model can provide estimates of the sensitivity of efficiency scores regarding an unknown amount of noise in date an application of the method in an evaluation of the research activities in economic departments at danish universities is presented

finite size scaling and the two dimensional xy model shows that the finite size scaling assumption and particularly a conjectured relation involving the exponent eta are valid in the low temperature phase of the 2d xy model order by order in a perturbative expansion of the two point correlation function

criticality of the discrete n vector ferromagnet in planar self dual lattices the authors study an extended version of the discrete n vector or cubic ferromagnetic model within a real space renormalisation group approach which preserves the two spin correlation function the n evolution for real values of n of the wheatstone bridge hierarchical lattice phase diagram which presents paramagnetic intermediate nematic like and ferromagnetic phases as well as of the thermal nu and crossover phi critical exponents is presented the self avoiding walk problem is recovered in the n to o limit and the so called corner rule is re obtained in a larger context the ising n and 2n state potts ferromagnets are recovered as particular cases an interchange of stability occurs at n n approximately 6 9 in such a way that the 2n state potts special point where all three existing phases join is multicritical if n n but only critical if n n consistently phi n o for the cubic model nu n presents a maximum at n nmax approximately 1 5 the results are exact for all n for the wheatstone bridge hierarchical lattice and approximate for n or 2 for the square lattice last but not least they discuss the connection between the present approach and the phenomenological renormalisation group

on the diffeomorphism types of certain algebraic surfaces i l invariant de donaldson la geometrie de certaines surfaces rationnelles surfaces dolgachev generalites sur des formes de type 1 n la classe canonique d une chambre et un coin le cone de kahler d une bonne surface generique une etude de p cellules les super p cellules

the nekrasov conjecture for toric surfaces the nekrasov conjecture predicts a relation between the partition function for n 2 supersymmetric yang mills theory and the seiberg witten prepotential for instantons on mathbb r 4 the conjecture was proved independently and using different methods by nekrasov okounkov and nakajima yoshioka we prove a generalized version of the conjecture for instantons on noncompact toric surfaces

rank two bundles on the blow up ofc2 in this paper we study holomorphic rank two vector bundles on the blow up ofc2with vanishing chern class the restriction of such a bundle over the exceptional divisor splits as o j o j for some integerj we denote by mjthe moduli space of holomorphic bundles on the blow up ofc2whose restriction to the exceptional divisor is o j o j we prove that mjis generically a complex projective space of dimension 2j 3

a fuzzy systems approach in data envelopment analysis abstract the use of fuzzy set theoretic measures is explored here in the context of data envelopment analysis which utilizes a nonparametric approach to measure efficiency three types of fuzzy statics are employed here e g fuzzy mathematical programme fuzzy regression and fuzzy entropy to illustrate the types of decisions and solutions that are achievable when the data are vague and prior information is inexact and imprecise

path connected yang mills moduli spaces on utilise des techniques de min max dans le calcul des variations pour demontrer que les espaces modules des connexions auto duales sur des fibres principaux su 2 ou su 3 sur s 4 sont chemin connexe

a monte carlo renormalisation group study of the two dimensional discrete cubic model a hint for superconformal invariance the discrete cubic model for six states of the lattice variables is investigated at one special point of the phase diagram where a number of contradicting results are known concerning the order of the phase transition and the critical exponents a new implementation of the mcrg method is used for determining the critical point with great accuracy and for calculating the critical exponents a continuous phase transition is found following the recent results for six state self dual quantum chains with cubic symmetry where for a special point superconformal invariance is discovered the critical exponents obtained are explained in the framework of this theory indicating a superconformal point with a conformal anomaly of c 1 25

a new approach to the calculation of the central charge the author shows that the central charge c of the virasoro algebra is determined by the spectrum of the hamiltonian l0 nl0 corresponding to a partition function which is invariant under the subgroup of modular transformations generated by s using this result he discusses in detail a new possibility of determining c for a given system at criticality which turns out to give excellent estimates even if the lattices accessible to numerical calculation are very small this enables him to predict the central charge of some spin systems furthermore his approach to the determination of c leads to new universal functions interpolating between criticality and off criticality

data envelopment analysis with imprecise data abstract in original data envelopment analysis dea models inputs and outputs are measured by exact values on a ratio scale cooper et al management science 45 1999 597 607 recently addressed the problem of imprecise data in dea in its general form we develop in this paper an alternative approach for dealing with imprecise data in dea our approach is to transform a non linear dea model to a linear programming equivalent on the basis of the original data set by applying transformations only on the variables upper and lower bounds for the efficiency scores of the units are then defined as natural outcomes of our formulations it is our specific formulation that enables us to proceed further in discriminating among the efficient units by means of a post dea model and the endurance indices we then proceed still further in formulating another post dea model for determining input thresholds that turn an inefficient unit to an efficient one

interval efficiency measures in data envelopment analysis with imprecise data the conventional data envelopment analysis dea measures the relative efficiencies of a set of decision making units dmus with exact values of inputs and outputs for imprecise data i e mixtures of interval data and ordinal data some methods have been developed to calculate the upper bound of the efficiency scores this paper constructs a pair of two level mathematical programming models whose objective values represent the lower bound and upper bound of the efficiency scores respectively based on the concept of productive efficiency and the application of a variable substitution technique the pair of two level nonlinear programs is transformed to a pair of ordinary one level linear programs solving the associated pairs of linear programs produces the efficiency intervals of all dmus an illustrative example verifies the idea of this paper a real case is also provided to give some interpretation of the interval efficiency interval efficiency not only describes the real situation in better detail psychologically it also eases the tension of the dmus being evaluated as well as the persons conducting the evaluation

a fuzzy mathematical programming approach to the assessment of efficiency with dea models in many real applications the data of production processes cannot be precisely measured this is particularly worrying when assessing efficiency with frontier type models such as data envelopment analysis dea models since they are very sensitive to possible data errors for this reason the possibility of having available a methodology that allows the analyst to deal with imprecise data becomes an issue of great interest in these contexts to that end we develop some fuzzy versions of the classical dea models in particular the bcc model by using some ranking methods based on the comparison of cuts the resulting auxiliary crisp problems can be solved by the usual dea software we show in a numerical example how our models become specially useful for detecting sensitive decision making units our approaches can be seen as an extension of the dea methodology that provides users and practitioners with models which represent some real life processes more appropriately

critical behaviour of the discrete n vector model in a planar self dual lattice a renormalization group approach within a real space renormalization group which preserves two site correlation functions the authors study for all values and signs of the coupling constants the criticality of an extended version of the cubic model c n all results are exact for the associated planar self dual hierarchical lattice the phase diagram typically exhibits five different phases the n evolution for n real of the thermal and crossover critical exponents is determined as well in addition they present an operational procedure the break collapse method which considerably simplifies the exact calculation of the correlation function associated with two terminal c n graphs

three applications of instanton numbers we use instanton numbers to i stratify moduli of vector bundles ii calculate relative homology of moduli spaces and iii distinguish curve singularities

maximum likelihood consistency and data envelopment analysis a statistical foundation this paper provides a formal statistical basis for the efficiency evaluation techniques of data envelopment analysis dea dea estimators of the best practice monotone increasing and concave production function are shown to be also maximum likelihood estimators if the deviation of actual output from the efficient output is regarded as a stochastic variable with a monotone decreasing probability density function while the best practice frontier estimator is biased below the theoretical frontier for a finite sample size the bias approaches zero for large samples the dea estimators exhibit the desirable asymptotic property of consistency and the asymptotic distribution of the dea estimators of inefficiency deviations is identical to the true distribution of these deviations this result is then employed to suggest possible statistical tests of hypotheses based on asymptotic distributions

criticality of the discrete n vector ferromagnet in a cubic lattice with a free surface we study a discrete n component spin ferromagnet with hamiltonian h nk i j si sj n2l i j si sj 2 in a semi infinite cubic lattice the coupling constants at the surface ks and ls are allowed to be different from the bulk ones kb and lb using a simple real space renormalization group procedure we obtain the n evolution n real of the phase diagram including the n 0 and n limits the thermal v and crossover critical exponents at various critical and multicritical points are calculated

instantons and jumping lines we study the behaviour under deformation of holomorphic bundles of rank 2 over 1 this is then applied to the description of the moduli space tilde m n of framed su 2 instantons of chargen tilde m n is shown to map to n with equidimensional fibers we use this to provide a stratification of tilde m n and compute the strata explicitly to codimension 4 this then yields 1 tilde m n 2 and for the standard moduli spacem n 1 m n 0 forn odd 2 forn even

toroidal boundary conditions in n state quantum chains the author considers one dimensional n state quantum chains having as symmetry an abelian group a of order n generalised ising chain these hamiltonians depend on 2 n 1 coupling constants for special values of the coupling constants the symmetry of the quantum chains is larger than a corresponding to a in general non abelian group g with m elements m n for each element of g he finds explicitly a boundary condition which leaves the hamiltonian translationally invariant this problem is relevant in finite size scaling studies at the critical point of a second order phase transition

phase diagram and critical properties of the 1 1 dimensional ashkin teller model the 1 1 dimensional ashkin teller model is studied by the renormalisation group method and by the finite lattice extrapolation technique the possible phases and their boundaries in an extended space of couplings are determined from the degeneracy structure of the low lying levels in the thermodynamic limit the critical behaviour is investigated for ferromagnetic couplings using increasing block sizes in the renormalisation transformation the line of fixed points and its bifurcation at the potts fixed point is studied

a parametric approach to fuzzy linear programming in this paper we discuss how to deal with decision problems that are described with lp models and formulated with elements of imprecision and uncertainty more precisely we will study lp models in which the parameters are not fully known but only with some degree of precision even with incomplete information the model builder or model user is normally able to give a realistic interval for the parameters of an lp model for the constraint vector this is combined with some wishes or some leeway on the constraints even with ambiquity in the objective function there is normally some preference ordering to be found among alternative ways of action we will demonstrate that these modelling complications can be handled with the help of some results developed in the theory of fuzzy sets after an overview of some central contributions to fuzzy linear programming we will develop an lp model in which the parameters are not fully known only with some degree of precision and show that the model can be parametrised in such a way that the optimal solution becomes a function of the degree of precision the fuzzy lp model derived in this way appears to be fairly easy to handle computationally which is demonstrated with a numerical example

dual models of interval dea and its extension to interval data abstract the purpose of this paper is to develop a new dea with an interval efficiency an original dea model is to evaluate each dmu optimistically there is another model called inverted dea to evaluate each dmu pessimistically but there are no relations essentially between dea and inverted dea thus we formulate a dea model with an interval efficiency which consists of efficiencies obtained from the optimistic and pessimistic viewpoints thus two end points can construct an interval efficiency with the same idea we deal with the interval inefficiency model which is inverse to interval efficiency finally we extend the proposed dea model to interval data and fuzzy data

hunting for the central charge of the virasoro algebra six and eight state spin models in two dimensions conformal invariance has important implications for the finite size scaling properties of the spectra of transfer matrices and quantum chains at the critical point some relations between the finite size scaling amplitudes are obtained which can be used as a test of conformal invariance and implicitly to distinguished between second order and first order phase transitions the numerical values of the scaling amplitudes give the scale dimensions of various operators six and eight state self dual quantum chains with cubic symmetries are considered at the critical point for three values of the coupling constant the systems are found to be conformal invariant and estimates for several critical exponents are obtained based on the approximate values of the critical exponent one tries to find the values of the corresponding central charges of the virasoro algebras

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

hamiltonian studies of the two dimensional n component cubic model i the phase diagram and the critical properties of the hamiltonian version of the two dimensional n component cubic model are investigated judging from the results of simple limits mean field calculation and rg transformations the phase diagram of the one dimensional quantum system is similar to that of the two dimensional classical model several rg transformations were used to investigate the critical properties using different cell sizes in the transformation the coincidence of critical and tricritical fixed points and the presence of a marginal operation showed the formation of the ashkin teller fixed line and the breaking of the universality the cubic transition is found to be first order for n 2

fuzzy efficiency measures in data envelopment analysis abstract the existing data envelopment analysis dea models for measuring the relative efficiencies of a set of decision making units dmus using various inputs to produce various outputs are limited to crisp data to deal with imprecise data the notion of fuzziness has been introduced this paper develops a procedure to measure the efficiencies of dmus with fuzzy observations the basic idea is to transform a fuzzy dea model to a family of conventional crisp dea models by applying the cut approach a pair of parametric programs is formulated to describe that family of crisp dea models via which the membership functions of the efficiency measures are derived since the efficiency measures are expressed by membership functions rather than by crisp values more information is provided for management by extending to fuzzy environment the dea approach is made more powerful for applications

a monte carlo comparison of two production frontier estimation methods corrected ordinary least squares and data envelopment analysis abstract this paper reports the results of an experiment with simulated data that compares the estimation accuracy of two simple and very different production frontier methods corrected ordinary least squares and data envelopment analysis the experimental design extends a previously published paper by introducing measurement errors a factor we show to be critical for comparative analysis of the frontier methods both low and high measurement error distributions are used resulting in 95 error intervals of roughly 10 and 40 respectively of outputs other variations include four inefficiency distributions covering a wide range of behavior four sample sizes from 25 to 200 and two piecewise cobb douglas technologies with two inputs and one output each results include 1 selection of the proper estimation method for a case can result in substantial gains in estimation accuracy for technical efficiencies from 15 to 40 in mean absolute deviations 2 cols performs better for the classical distribution case with sample sizes of 50 or over 3 dea performs better for all nonclassical inefficiency distributions even with relatively high measurement errors 4 dea provides surprisingly accurate estimates for the small sample size of 25 for all cases in the experiment 5 cols fails to decompose deviations into efficiency and measurement error components it assumes that deviations from the frontier are either totally due to measurement errors or technical inefficiencies and 6 neither method performs satisfactorally for high measurement errors

finite size scaling of the quantum ising chain with periodic free and antiperiodic boundary conditions the authors give exact results for the energy spectrum of a chain of n ising spins in a transverse field with periodic free and antiperiodic boundary conditions the dependence of the energy gaps on boundary conditions is compatible with predictions of conformal invariance for correlation lengths in two dimensional strips the feasibility of calculating surface critical indices using phenomenological renormalisation with free boundary conditions and the convergence for large n are discussed