fully discrete entropy conservative schemes of arbitrary order we consider weak solutions of hyperbolic or hyperbolic elliptic systems of conservation laws in one space dimension and their approximation by finite difference schemes in conservative form the systems under consideration are endowed with an entropy entropy flux pair we introduce a general approach to construct second and third order accurate fully discrete in both space and time entropy conservative schemes in general these schemes are fully nonlinear implicit but in some important cases can be explicit or linear implicit furthermore semidiscrete entropy conservative schemes of arbitrary order are presented the entropy conservative schemes are used to construct a numerical method for the computation of weak solutions containing nonclassical regularization sensitive shock waves finally specific examples are investigated and tested numerically our approach extends the results and techniques by tadmor in numerical methods for compressible flows finite difference element and volume techniques asme new york 1986 pp 149 158 lefloch and rohde siam j numer anal 37 2000 pp 2023 2060

on the convergence of a finite element method for a nonlinear hyperbolic conservation law we consider a space time finite element discretization of a time dependent nonlinear hyperbolic conservation law in one space dimension burgers equation the finite element method is higher order accurate and is a petrov galerkin method based on the so called streamline diffusion modification of the test functions giving added stability we first prove that if a sequence of finite element solutions converges boundedly almost everywhere as the mesh size tends to zero to a function u then u is an entropy solution of the conservation law this result may be extended to systems of conservation laws with convex entropy in several dimensions we then prove using a compensated compactness result of murat tartar that if the finite element solutions are uniformly bounded then a subsequence will converge to an entropy solution of burgers equation we also consider a further modification of the test functions giving a method with improved shock capturing finally we present the results of some numerical experiments

local entropy averages and projections of fractal measures we show that for families of measures on euclidean space which satisfy an ergodic theoretic form of self similarity under the operation of re scaling the dimension of linear images of the measure behaves in a semi continuous way we apply this to prove the following conjecture of furstenberg let m n be integers which are not powers of the same integer and let x y be closed subsets of the unit interval which are invariant respectively under times m mod 1 and times n mod 1 then for any non zero t dim x ty min 1 dim x dim y a similar result holds for invariant measures and gives a simple proof of the rudolph johnson theorem our methods also apply to many other classes of conformal fractals and measures as another application we extend and unify results of peres shmerkin and nazarov and of moreira concerning projections of products self similar measures and gibbs measures on regular cantor sets we show that under natural irreducibility assumptions on the maps in the ifs the image measure has the maximal possible dimension under any linear projection other than the coordinate projections we also present applications to bernoulli convolutions and to the images of fractal measures under differentiable maps

preference voting and project ranking using dea and cross evaluation cook and kress 1990 using data envelopment analysis dea as their starting point proposed a procedure to rank order the candidates in a preferential election notionally each candidate is permitted to choose the most favourable weights to be applied to his her standings first place second place etc votes in the usual dea manner with the additional assurance region restriction that the weight for a j place vote should be more than that for a j 1 amount we consider that this freedom to choose weights is essentially illusory when maximum discrimination between the candidates is sought in which case the weights used to evaluate and rank the candidates are as if imposed externally at the outset to avoid this we present an alternative procedure which retains cook and kress central idea but where as well as using each candidate s rating of him herself we now make use of each candidate s ratings of all the candidates we regard the so called cross evaluation matrix as the summary of a self and peer rating process in which the candidates seek to interpret the voters preferences as favourably for themselves relative to the other candidates as possible the problem then becomes one of establishing an overall rating for each candidate from these individual ratings for this for each candidate we use a weighted average of all the candidates ratings of that candidate where the weights themselves are in proportion to each candidate s overall rating the overall ratings are therefore proportional to the components of the principal left hand eigenvector of the cross evaluation matrix these ideas are then applied to the selection of r d projects to comprise an r d program thus indicating thier wider applicability

arbitrarily high order accurate entropy stable essentially nonoscillatory schemes for systems of conservation laws we design arbitrarily high order accurate entropy stable schemes for systems of conservation laws the schemes termed tecno schemes are based on two main ingredients i high order accurate entropy conservative fluxes and ii suitable numerical diffusion operators involving eno reconstructed cell interface values of scaled entropy variables numerical experiments in one and two space dimensions are presented to illustrate the robust numerical performance of the tecno schemes

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

increasing the efficiency in integer simulation optimization reducing the search space through data envelopment analysis and orthogonal arrays abstract the development of various heuristics has enabled optimization in simulation environments nevertheless this research area remains underexplored primarily with respect to the time required for convergence of these heuristics in this sense simulation optimization is influenced by the complexity of the simulation model the number of variables and by their ranges of variation within this context this paper proposes a method capable of identifying the best ranges for each integer decision variable within the simulation optimization problem thereby providing a reduction in computational cost without loss of the quality in the response the proposed method combines experimental design techniques discrete event simulation and data envelopment analysis the experimental designs called orthogonal arrays are used to generate the input scenarios to be simulated and super efficiency analysis is applied in a data envelopment analysis model with variable returns to scale to rank the input scenarios the use of the super efficiency concept enables to distinguish the most efficient input scenarios which allows for the ranking of all the orthogonal array scenarios used the values of the variables of the two input scenarios that present the highest values of super efficiency are adopted as the new range of the optimization problem to illustrate this method s use and advantages it was applied to real cases associated with integer simulation optimization problems based on the results the effectiveness of this approach is verified because it delivered considerable reductions in the search space and in the computational time required to obtain a solution without affecting the quality

a new dea ranking system based on changing the reference set this research proposes a new ranking system for extreme efficient dmus decision making units based upon the omission of these efficient dmus from reference set of the inefficient dmus we state and prove some facts related to our model a numerical example where the proposed method is compared with traditional ranking approaches is shown

using monte carlo method for ranking efficient dmus for ranking efficient dmus some methods have been developed these methods are not able to rank non extreme efficient dmus in this paper using monte carlo method a method has been developed which is able to rank all extreme and non extreme efficient dmus

entropy stable shock capturing space time discontinuous galerkin schemes for systems of conservation laws we present a streamline diffusion shock capturing spacetime discontinuous galerkin dg method to approximate nonlinear systems of conservation laws in several space dimensions the degrees of freedom are in terms of the entropy variables and the numerical flux functions are the entropy stable finite volume fluxes we show entropy stability of the formally arbitrarily high order accurate method for a general system of conservation laws furthermore we prove that the approximate solutions converge to the entropy measure valued solutions for nonlinear systems of conservation laws convergence to entropy solutions for scalar conservation laws and for linear symmetrizable systems is also shown numerical experiments are presented to illustrate the robustness of the proposed schemes

a new ranking method to fuzzy data envelopment analysis due to its wide practical use data envelopment analysis dea has been adapted to many fields to deal with problems that have occurred in practice one adaptation has been in the field of ranking decision making units dmus most methods of ranking dmus assume that all input and output data are exactly known but in real life the data cannot be precisely measured thus this paper will carry out some researches to dea under fuzzy environment a fuzzy comparison of fuzzy variables is defined and the ccr model is extended to be a fuzzy dea model based on credibility measure in order to rank all the dmus a full ranking method will be given since the ranking method involves a fuzzy function a fuzzy simulation is designed and embedded into the genetic algorithm to establish a hybrid intelligent algorithm however it is shown to be possible to avoid some of the need for dealing with these nonlinear problems by identifying conditions under which they can be replaced by linear problems finally we will provide a numerical example to illustrate the fuzzy dea model and the ranking method

preference aggregation and dea an analysis of the methods proposed to discriminate efficient candidates abstract there are different ways to allow the voters to express their preferences on a set of candidates in ranked voting systems each voter selects a subset of the candidates and ranks them in order of preference a well known class of these voting systems are scoring rules where fixed scores are assigned to the different ranks and the candidates with the highest score are the winners one of the most important issues in this context is the choice of the scoring vector since the winning candidate can vary according to the scores used to avoid this problem cook and kress w d cook m kress a data envelopment model for aggregating preference rankings management science 36 11 1990 1302 1310 using a dea ar model proposed to assess each candidate with the most favorable scoring vector for him her however the use of this procedure often causes several candidates to be efficient i e they achieve the maximum score for this reason several methods to discriminate among efficient candidates have been proposed the aim of this paper is to analyze and show some drawbacks of these methods

ranking of decision making units in data envelopment analysis a distance based approach in non parametric methods many units are evaluated as efficient several methods for prioritizing efficient units are reported in the literature andersen et al and thereafter mehrabian et al proposed two methods for ranking efficient units but both methods break down in some cases this paper describes a new dea ranking approach that uses l 2 norm in proposed dea ranking approach the difficulties of the existing methods have been removed

dea efficiency assessment using ideal and anti ideal decision making units this paper introduces two virtual decision making units dmus called ideal dmu idmu and anti ideal dmu admu into the data envelopment analysis dea the resultant dea models are respectively referred to as the data envelopment analysis with ideal and anti ideal decision making units one evaluates dmus from the viewpoint of the best possible relative efficiency while the other evaluates them from the perspective of the worst possible relative efficiency the two distinctive efficiencies are combined to form a comprehensive index called the relative closeness rc to the idmu just like the well known topsis approach in multiple attribute decision making madm the rc index is then used as the evidence of overall assessment of each dmu based on which an overall ranking for all the dmus can be obtained two numerical examples are provided to illustrate the applications of the proposed dea models and the rc index

maximally productive input output units abstract technical or pareto koopmans efficiency models can be based on ratios of weighted sums of outputs to weighted sums of inputs differing meanings have been considered for such factor weights in this paper we use value or cost rate meanings depending on model orientation these meanings permit considering the simultaneous assignment of input and output factor weights along with optimal intensity values for a virtual composite unit constructed from the observed units an optimization principle we call the winners take all criterion is proposed for determining the maximally productive unit s no assumptions are required on the internal transformation processes of the units the model simultaneously determines the intensities and factor weights and results in indefinite quadratic programming problems that simplify to linear programming in certain cases for the general case genetic search is applied numerical illustrations are provided for faculty merit scoring and for the 15 hospital dataset of sherman

strict vs weak ordinal relations for multipliers in data envelopment analysis in a recent paper golany 1988 proposes an interesting extension of data envelopment analysis to the situation where ordinal relations among weights corresponding to certain dimensions exist however the development of the extended model contains mathematical errors and the proposed equivalence is incorrect we establish the correct model equivalence and prove that weak ordinal relations require a nonstandard dea model we also show that the case of strict ordinal relations can be handled with the standard dea model these results hold for the ccr bcc additive and multiplicative models and for relations involving both input and output multipliers

the numerical viscosity of entropy stable schemes for systems of conservation laws i discrete approximations to hyperbolic systems of conservation laws are studied the amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison to this end conservative schemes which are also entropy conservative are constructed these entropy conservative schemes enjoy second order accuracy moreover they can be interpreted as piecewise linear finite element methods and hence can be formulated on various mesh configurations it is then shown that conservative schemes are entropy stable if and for three point schemes only they contain more viscosity than that present in the above mentioned entropy conservative ones

entropy stable high order discontinuous galerkin methods with suitable quadrature rules for hyperbolic conservation laws abstract it is well known that semi discrete high order discontinuous galerkin dg methods satisfy cell entropy inequalities for the square entropy for both scalar conservation laws jiang and shu 1994 39 and symmetric hyperbolic systems hou and liu 2007 36 in any space dimension and for any triangulations however this property holds only for the square entropy and the integrations in the dg methods must be exact it is significantly more difficult to design dg methods to satisfy entropy inequalities for a non square convex entropy and or when the integration is approximated by a numerical quadrature in this paper we develop a unified framework for designing high order dg methods which will satisfy entropy inequalities for any given single convex entropy through suitable numerical quadrature which is specific to this given entropy our framework applies from one dimensional scalar cases all the way to multi dimensional systems of conservation laws for the one dimensional case our numerical quadrature is based on the methodology established in carpenter et al 2014 5 and gassner 2013 19 the main ingredients are summation by parts sbp operators derived from legendre gauss lobatto quadrature the entropy conservative flux within elements and the entropy stable flux at element interfaces we then generalize the scheme to two dimensional triangular meshes by constructing sbp operators on triangles based on a special quadrature rule a local discontinuous galerkin ldg type treatment is also incorporated to achieve the generalization to convection diffusion equations extensive numerical experiments are performed to validate the accuracy and shock capturing efficacy of these entropy stable dg methods

estimation and inference in two stage semi parametric models of production processes many papers have regressed non parametric estimates of productive efficiency on environmental variables in two stage procedures to account for exogenous factors that might affect firms performance none of these have described a coherent data generating process dgp moreover conventional approaches to inference employed in these papers are invalid due to complicated unknown serial correlation among the estimated efficiencies we first describe a sensible dgp for such models we propose single and double bootstrap procedures both permit valid inference and the double bootstrap procedure improves statistical efficiency in the second stage regression we examine the statistical performance of our estimators using monte carlo experiments

a procedure for ranking efficient units in data envelopment analysis data envelopment analysis dea evaluates the relative efficiency of decision making units dmus but does not allow for a ranking of the efficient units themselves a modified version of dea based upon comparison of efficient dmus relative to a reference technology spanned by all other units is developed the procedure provides a framework for ranking efficient units and facilitates comparison with rankings based on parametric methods

stochastic multicriteria acceptability analysis using the data envelopment model abstract data envelopment analysis dea and stochastic multicriteria acceptability analysis smaa 2 are methods for evaluating alternatives based on multiple criteria while dea is mainly an ex post tool used for classifying alternatives into efficient and inefficient ones smaa 2 is an ex ante tool for supporting multiple criteria decision making both methods use a kind of value function where the importance of criteria is modeled using weights unlike many other methods neither dea nor smaa 2 requires decision makers weights as input instead these so called non parametric methods explore the weight space in order to identify weights favorable for each alternative this paper introduces the smaa d method which is a combination of dea and smaa 2 smaa d can be characterized as an extension of dea to handle uncertain or imprecise data to provide stochastic efficiency measures alternatively the combined method can be seen as a variant of smaa 2 with a dea type value function

non parametric unconditional quantile estimation for efficiency analysis with an application to federal reserve check processing operations abstract this paper examines the technical efficiency of us federal reserve check processing offices over 1980 2003 we extend results from park et al park b simar l weiner c 2000 fdh efficiency scores from a stochastic point of view econometric theory 16 855 877 and daouia and simar daouia a simar l 2007 nonparametric efficiency analysis a multivariate conditional quantile approach journal of econometrics 140 375 400 to develop an unconditional hyperbolic quantile estimator of efficiency our new estimator is fully non parametric and robust with respect to outliers when used to estimate distance to quantiles lying close to the full frontier it is strongly consistent and converges at rate root n thus avoiding the curse of dimensionality that plagues data envelopment analysis dea estimators our methods could be used by policymakers to compare inefficiency levels across offices or by managers of individual offices to identify peer offices

using the gradient line for ranking dmus in dea in this paper a method based on using gradient line for ranking dmus is proposed the advantage of this method is its stability and robustness where data have special structure some numerical examples are presented to show the results

convergence of the finite volume method for multidimensional conservation laws we establish the convergence of the finite volume method applied to multidimensional hyperbolic conservation laws and based on monotone numerical flux functions our technique applies with a fairly unrestrictive assumption on the triangulations flat elements are allowed and to lipschitz continuous flux functions we treat the initial and boundary value problem and obtain the strong convergence of the scheme to the unique entropy discontinuous solution in the sense of kruzkov the proof of convergence is based on a convergence framework coquel and lefloch math comp 57 1991 pp 169 210 and j numer anal 30 1993 pp 675 700 from a convex decomposition of the scheme we derive a new estimate for the rate of entropy dissipation and a new formulation of the discrete entropy inequalities these estimates are shown to be sufficient for the passage to the limit in the discrete equation convergence follows from diperna s uniqueness result in the class of entropy measure valued solutions

a statistical test for detecting influential observations in dea this paper deals with the problem of detecting influential observations in deterministic nonparametric dea models the technique we present is intended to classify for a further analysis those sample observations considerably affecting the measured efficiency for the remaining units then the analyst will have to check whether these observations are contaminated by data errors or not this approach also allows to determine when efficiency changes due to the presence of a given unit in the sample are statistically significant thus ours is a statistical alternative to approach the problem of detecting influential observations in deterministic nonparametric dea models

sigma mu efficiency analysis a methodology for evaluating units through composite indicators abstract we propose a methodology to employ composite indicators for performance analysis of units of interest using and extending the family of stochastic multiattribute acceptability analysis we start evaluating each unit by means of weighted sums of their elementary indicators in the whole set of admissible weights for each unit we compute the mean and the standard deviation of its evaluations clearly the former has to be maximized while the latter has to be minimized as it denotes instability in the evaluations with respect to the variability of weights we consider a unit to be pareto koopmans efficient with respect to and if there is no convex combination of and of the rest of the units with a value of that is not smaller and a value of that is not greater with at least one strict inequality the set of all pareto koopmans efficient units constitutes the first pareto koopmans frontier in the spirit of context dependent data envelopment analysis we assign each unit to one of the sequence of pareto koopmans frontiers we measure the local efficiency of each unit with respect to each frontier but also its global efficiency taking into account all frontiers in the plane thus enhancing the explicative power of the proposed approach to illustrate its potential we present a case study of world happiness based on the data of the homonymous report that is annually produced by the united nations sustainable development solutions network

modified maj model for ranking decision making units in data envelopment analysis abstract efficiency data envelopment analysis dea models assessing decision making units dmus are unable to discriminate between efficient dmus from experience we know that usually plural dmus are efficient to discriminate between these efficient dmus is an interesting subject to this aim super efficiency models are proposed in this paper we study a super efficiency model namely maj each time an efficient dmu is excluded from the set of the observed dmus a new production possibility set pps is obtained in this model ranking is done based on the position of each excluded efficient dmu in relation to its corresponding new pps if the efficient dmus and the new ppss remain unchanged it is expected that the ranking also remain unchanged but in this paper we show that the technique used for rendering this model unit invariant causes the ranking to change when some inputs of some inefficient dmus change without causing any change in the new pps in this paper we modify this model so that this problem will not occur

a selection method for a preferential election this paper deals with a recently proposed method for a ranked voting system it is based on a data envelopment analysis model it is shown that the number of problems to be solved and the number of constraints in the model can be decreased in addition the winner can be selected with a fewer efforts and in some cases without solving any problems the obtained results also illustrate the importance of selecting a proper norm in the model

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

split form nodal discontinuous galerkin schemes with summation by parts property for the compressible euler equations fisher and carpenter 2013 12 found a remarkable equivalence of general diagonal norm high order summation by parts operators to a subcell based high order finite volume formulation this equivalence enables the construction of provably entropy stable schemes by a specific choice of the subcell finite volume flux we show that besides the construction of entropy stable high order schemes a careful choice of subcell finite volume fluxes generates split formulations of quadratic or cubic terms thus by changing the subcell finite volume flux to a specific choice we are able to generate in a systematic way all common split forms of the compressible euler advection terms such as the ducros splitting and the kennedy and gruber splitting although these split forms are not entropy stable we present a systematic way to prove which of those split forms are at least kinetic energy preserving with this we construct a unified high order split form dg framework we investigate with three dimensional numerical simulations of the inviscid taylorgreen vortex and show that the new split forms enhance the robustness of high order simulations in comparison to the standard scheme when solving turbulent vortex dominated flows in fact we show that for certain test cases the novel split form discontinuous galerkin schemes are more robust than the discontinuous galerkin scheme with over integration

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

a method for discriminating efficient candidates with ranked voting data abstract ranked voting data arise when voters select and rank more than one candidate with order of preference cook and kress management science 36 11 1990 1302 introduced data envelopment analysis dea to analyze ranked voting data by using dea each candidate may use the most favorable weights for him her to estimate his her own preference score however dea often suggests that more than one unit are equally efficient so a method to discriminate these efficient candidates is needed some methods of such purpose are proposed however these methods have a weak point that the order of efficient candidates may be changed by existence of an inefficient candidate in this paper we propose a new method our method does not use information about inefficient candidates to discriminate efficient candidates it is based on a very simple idea and is realizable visually so we hope that it is acceptable to election officials

scaling scenery of m n invariant measures abstract we study the scaling scenery and limit geometry of invariant measures for the non conformal toral endomorphism x y m x mod 1 n y mod 1 that are bernoulli measures for the natural markov partition we show that the statistics of the scaling can be described by an ergodic cp chain in the sense of furstenberg invoking the machinery of cp chains yields a projection theorem for bernoulli measures which generalises in part earlier results by hochman shmerkin and ferguson jordan shmerkin we also give an ergodic theoretic criterion for the dimension part of falconer s distance set conjecture for general sets with positive length using cp chains and hence verify it for various classes of fractals such as self affine carpets of bedford mcmullen lalley gatzouras and baranski class and all planar self similar sets

when does data envelopment analysis outperform a naive efficiency measurement model abstract this paper compares the results from data envelopment analysis dea to a naive efficiency measurement model which generates a scalar efficiency score by averaging all output input ratios random data and real life data are used to test the relative performance of the naive model against various dea models the results suggest that the proposed the naive model replicates dea efficiency scores almost perfectly for constant return to scales and low heterogeneity in output input data it is therefore concluded that heterogeneity in output input data is important to take advantage of the capability of dea it is also shown that heterogeneity is more relevant to efficiency measurement than the number of dimensions

the weighted additive distance function abstract distance functions in production theory are mathematical structures that characterize the belonging to the reference technology through a numerical value behave as technical efficiency measures when the focus is analyzing an observed input output vector within its production possibility set and present a dual relationship with some support function profit revenue cost function in this paper we endow the well known weighted additive models in data envelopment analysis with a distance function structure introducing the weighted additive distance function and showing its main properties

dea and the discriminant analysis of ratios for ranking units the purpose of this study is to develop a new method which provides for given inputs and outputs the best common weights for all the units that discriminate optimally between the efficient and inefficient units as pregiven by the data envelopment analysis dea in order to rank all the units on the same scale this new method discriminant data envelopment analysis of ratios dr dea presents a further post optimality analysis of dea for organizational units when their multiple inputs and outputs are given we construct the ratio between the composite output and the composite input where their common weights are computed by a new non linear optimization of goodness of separation between the two pregiven groups a practical use of dr dea is that the common weights may be utilized for ranking the units on a unified scale dr dea is a new use of a two group discriminant criterion that has been presented here for ratios rather than the traditional discriminant analysis which applies to a linear function moreover non parametric statistical tests are employed to verify the consistency between the classification from dea efficient and inefficient units and the post classification as generated by dr dea

identifying the anchor points in dea using sensitivity analysis in linear programming abstract in this paper the anchor points in dea as an important subset of the set of extreme efficient points of the production possibility set pps are studied a basic definition utilizing the multiplier dea models is given then two theorems are proved which provide necessary and sufficient conditions for characterization of these points the main results of the paper lead to a new interesting connection between dea and sensitivity analysis in linear programming theory by utilizing the established theoretical results a successful procedure for identification of the anchor points is presented

a general framework to construct schemes satisfying additional conservation relations application to entropy conservative and entropy dissipative schemes abstract we are interested in the approximation of a steady hyperbolic problem in some cases the solution can satisfy an additional conservation relation at least when it is smooth this is the case of an entropy in this paper we show starting from the discretization of the original pde how to construct a scheme that is consistent with the original pde and the additional conservation relation since one interesting example is given by the systems endowed by an entropy we provide one explicit solution and show that the accuracy of the new scheme is at most degraded by one order in the case of a discontinuous galerkin scheme and a residual distribution scheme we show how not to degrade the accuracy this improves the recent results obtained in 1 2 3 4 in the sense that no particular constraints are set on quadrature formula and that a priori maximum accuracy can still be achieved we study the behavior of the method on a non linear scalar problem however the method is not restricted to scalar problems

a multivariate statistical approach to reducing the number of variables in data envelopment analysis abstract the usefulness of data envelopment analysis dea depends on its ability to calculate the relative efficiency of decision making units dmus using multiple inputs and outputs unfortunately the greater the number of input and output variables the less discerning the analysis in practice the input and output variables are usually highly correlated with one another often reflecting no more than the relative size of each dmu to counteract the limited distinction provided by a dea with many variables analysts for many years have taken the approach of retaining only some of the variables originally planned for the analysis omitting on an ad hoc basis variables that are highly correlated with those retained in this paper we describe a systematic statistical method for deciding which of the original correlated variables can be omitted with least loss of information and which should be retained results on a number of published datasets reveal that even omitting variables that are highly correlated and thereby contain little additional information on performance can have a major influence on the computed efficiency measures

a note on dea efficiency assessment using ideal point an improvement of wang and luo s model abstract evaluating the efficiency of organizational units continues to be a difficult problem to solve especially when the multiplicity of inputs resources costs and outputs services products associated with these units is considered this paper considers a previous article published by wang and luo y wang y luo dea efficiency assessment using ideal and anti ideal decision making units applied mathematics and computation 173 2 2006 902 915 in the journal of applied mathematics and computation where data envelopment analysis dea and the technique for order preference by similarity to ideal solution topsis are integrated in ranking of decision making units dmus wang and luo 2006 contribute to a very interesting topic by showing that the topsis idea can be combined to dea for a comprehensive ranking of dmus however this paper finds that their approach is problematic in employing the negative ideal point nip for dea computation their ideal point based models rely on using conflicting efficiency concepts we slightly revised the models so that a dea analysis using topsis idea can be performed numerical demonstration reveals that our approach produces a ranking result that is consistent with that in previous studies

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

technologies ranking in the presence of both cardinal and ordinal data ranking of technologies is an important phase for technology transfer to rank the best technologies in the presence of both cardinal and ordinal data this paper proposes an innovative approach which is based on imprecise data envelopment analysis idea the objective of this paper is to propose a comprehensive reference that discusses the use of idea in technology ranking a numerical example demonstrates the application of the proposed method

estimating the hyperbolic distance function a directional distance function approach abstract fare grosskopf and lovell 1985 merged farrell s input and output oriented technical efficiency measures into a new graph type approach known as hyperbolic distance function hdf in spite of its appealing special structure in allowing for the simultaneous and equiproportionate reduction in inputs and increase in outputs hdf is a non linear optimization and it is hard to solve particularly when dealing with technologies operating under variable returns to scale by connecting hdf to the directional distance function we propose a linear programming based procedure for estimating the exact value of hdf within the non parametric framework of data envelopment analysis we illustrate the computational effectiveness of the algorithm on several real world and simulated data sets generating the optimal value of hdf through generally solving at most two linear programs moreover our approach has several desirable properties such as 1 introducing a computational dual formulation for the hdf and providing an economic interpretation in terms of shadow prices 2 being readily adaptable to measure hyperbolic oriented super efficiency and 3 being flexible to deal with hdf based efficiency measures on environmental technologies

a note on including ordinal relations among multipliers in data envelopment analysis data envelopment analysis dea evaluates the efficiency of decision making units without imposing a priori weights on the input and output dimensions involved this note extends dea to situations where ordinal relations among weights corresponding to certain dimensions exist the extended model is reduced to the original dea formulation where some of the input and output factors are accumulated an illustrative example is provided and potential areas of applications are pointed out

ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis it has been widely recognized that data envelopment analysis dea lacks discrimination power to distinguish between dea efficient units this paper proposes a new methodology for ranking decision making units dmus the new methodology ranks dmus by imposing an appropriate minimum weight restriction on all inputs and outputs which is decided by a decision maker dm or an assessor in terms of the solutions to a series of linear programming lp models that are specially constructed to determine a maximin weight for each dea efficient unit the dm can decide how many dmus to be retained as dea efficient in final efficiency ranking according to the requirement of real applications which provides flexibility for dea ranking three numerical examples are investigated using the proposed ranking methodology to illustrate its power in discriminating between dmus particularly dea efficient units

scaling units via the canonical correlation analysis in the dea context abstract this paper deals with the evaluation of decision making units which have multiple inputs and outputs a new method cca dea is developed where the canonical correlation analysis cca is utilized to provide a full rank scaling for all the units rather than a categorical classification for efficient and inefficient units as done by the data envelopment analysis dea the cca dea approach is an attempt to bridge the gap between the frontier approach of dea and the average tendencies of statistics econometrics nonparametric statistical tests are employed to validate the consistency between the classification from the dea and the postclassification that was generated by the cca dea

on some methods for performance ranking and correspondence analysis in the dea context two novel methods named performance baseline and performance correspondence matrices are proposed to evaluate the performance of decision making units dmus based on the techniques of singular value decomposition svd the performance baseline matrix can be used to rank all the dmus because it provides a common basis for performance comparison the performance correspondence matrix can be used to conduct performance cluster analysis with which to explore the structure of input output variables that are associated with dmus the analysis can reveal the performance difference of the dmus and the key input output variables determining the efficiency of a certain dmu and provides valuable quantitative information for adjusting variables to improve efficiency of the dmu three case studies are presented to demonstrate that the proposed methods in this work are effective and easy to use and can provide insights into proper selection of input output variables for performance comparison to avoid over manipulating dea models in practice

dimension theory of iterated function systems let si l i 1 be an iterated function system ifs on d with attractor k let denote the one sided full shift over the alphabet 1 l we define the projection entropy function h on the space of invariant measures on e associated with the coding map k and develop some basic ergodic properties about it this concept turns out to be crucial in the study of dimensional properties of invariant measures on k we show that for any conformal ifs respectively the direct product of finitely many conformal ifss without any separation condition the projection of an ergodic measure under is always exactly dimensional and its hausdorff dimension can be represented as the ratio of its projection entropy to its lyapunov exponent respectively the linear combination of projection entropies associated with several coding maps furthermore for any conformal ifs and certain affine ifss we prove a variational principle between the hausdorff dimension of the attractors and that of projections of ergodic measures 2008 wiley periodicals inc

on the convergence of shock capturing streamline diffusion finite element methods for hyperbolic conservation laws we extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shock capturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the meh size with this term present we prove a maximum norm bound for finite element solutionsof burgers equation an thus complete an earlier convergence proof for this equation we further prove using entropy variables that a strong limit of finite element solutions is a weak solution of the system of conservation laws and satisfies the entropy inequality asociated with the entropy variables results of some numerical experiments for the time dependent compressible euler equations in two dimensions are also reported

super efficiencies or super inefficiencies insights from a joint computation model for slacks based measures in dea abstract the slacks based measure sbm can incorporate input and output slacks that would otherwise be neglected in the classical dea model in parallel the super efficiency model for sbm s sbm has been developed for the purpose of ranking sbm efficient decision making units dmus when implementing sbm in conjunction with s sbm however several issues can arise first unlike the standard super efficiency model s sbm can only solve for super efficiency scores but not sbm scores second the s sbm model may result in weakly efficient reference points third the s sbm and sbm scores for certain dmus may be discontinuous with a perturbation to their inputs and outputs making it hard to interpret and justify the scores in applications and the efficiency scores may be sensitive to small changes errors in data due to this discontinuity the s sbm model may overestimate the super efficiency score this paper extends the existing sbm approaches and develops a joint model j sbm that addresses the above issues namely the j sbm model can 1 simultaneously compute sbm scores for inefficient dmus and super efficiency for efficient dmus 2 guarantee the reference points generated by the joint model are pareto efficient and 3 the j sbm scores of a firm are continuous in the input and output space interestingly the radial dea efficiency and super efficiency scores for a dmu are continuous in the input output space the j sbm model combines the merits of the radial and sbm models i e continuity and pareto efficiency

integrating dea oriented performance assessment and target setting using interactive molp methods data envelopment analysis dea and multiple objective linear programming molp are tools that can be used in management control and planning whilst these two types of model are similar in structure dea is directed to assessing past performances as part of management control function and molp to planning future performance targets this paper is devoted to investigating equivalence models and interactive tradeoff analysis procedures in molp such that dea oriented performance assessment and target setting can be integrated in a way that the decision makers preferences can be taken into account in an interactive fashion three equivalence models are investigated between the output oriented dual dea model and the minimax reference point formulations namely the super ideal point model the ideal point model and the shortest distance model these models can be used to support efficiency analysis in the same way as the conventional dea model does and also support tradeoff analysis for setting target values by individuals or groups a case study is conducted to illustrate how dea oriented efficiency analysis can be conducted using the molp methods and how such performance assessment can be integrated into an interactive procedure for setting realistic target values

using monte carlo method for ranking interval data abstract some methods have been presented for ranking efficient decision making units dmus in data envelopment analysis dea this paper addresses the ranking of interval data by using monte carlo method this method is based on a paper g r jahanshahloo f hosseinzadeh lotfi h zhiani rezai f rezai balf using monte carlo method for ranking efficient dmus applied mathematics and computation 162 2005 371 379 the worthwhile this method is its ability in ranking of extreme and non extreme efficient dmus