generalised weak disposability and efficiency measurement in environmental technologies abstract weak disposability based models of environmental technologies typically assume equiproportionate trade offs between desired and undesired outputs we postulate a generalised version of weak disposability allowing for different types of trade offs between good and bad outputs and derive a new technology called piecewise cobb douglas environmental technology whose envelopments capture all three types of production structures concavity linearity and convexity to measure environmental performance with reference to this technology we develop radial and non radial directional hyperbolic distance functions we demonstrate that the value of these functions can be simply computed via the directional distance function as linear programs we use data from 112 us power plants to illustrate our approach

a novel implementation of multilevel fast multipole algorithm for higher order galerkin s method a new approach is proposed to reduce the memory requirements of the multilevel fast multipole algorithm mlfma when applied to the higher order galerkin s method this approach represents higher order basis functions by a set of point sources such that a matrix vector multiply is equivalent to calculating the fields at a number of points from given current sources at these points the mlfma is then applied to calculate the point to point interactions this permits the use of more levels in mlfma than applying mlfma to basis to basis interactions directly and thus reduces the memory requirements significantly

separation of variables and exact solution to the dirac equation in curvilinear orthogonal coordinates with cylindrical symmetry in the present article a complete separation of variables in the dirac equation for a free particle is achieved in parabolic cylinder and elliptical coordinates the resulting system of ordinary differential equations is solved and the asymptotic behavior of the spinor solution is discussed

exponential distance function and duality theory abstract charnes cooper seiford and stutz 1982 1983 and banker and maindiratta 1986 suggested multiplicative radial measures for efficiency gauging more recently peyrache and coelli 2009 presented a multiplicative directional distance function that was elaborated by mehdiloozad sahoo and roshdi 2014 in this paper we extend these studies and propose an exponential approach based upon a new exponential distance function endowed with a multiplicative production structure the main purposes of this paper are twofold one is to provide a general production theoretic basis for the approach and the other is to extend it to a nonparametric framework the first purpose is accomplished as follows 1 the exponential distance function is formally defined and its properties are established 2 it is shown how the exponential distance function is characterized under a napierian technology 3 a duality relationship between napierian profit and the exponential distance functions is established 4 shadow prices of inputs and outputs are derived based on the napierian technology the second purpose is accomplished by providing nonparametric programming extensions which include data envelopment analysis dea models productivity indexes and returns to scale models here the efficacy of our nonparametric theoretical results is demonstrated by applying dea to the data on accommodation establishments in oecd

a higher order parallelized multilevel fast multipole algorithm for 3 d scattering a higher order multilevel fast multipole algorithm mlfma is presented for solving integral equations of electromagnetic wave scattering by three dimensional 3 d conducting objects this method employs higher order parametric elements to provide accurate modeling of the scatterer s geometry and higher order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer s surface this higher order scheme leads to a significant reduction in the mesh density thus the number of unknowns without compromising the accuracy of geometry modeling it is applied to the electric field integral equation efie the magnetic field integral equation mfie and the combined field integral equation cfie using galerkin s testing approach the resultant numerical system of equations is then solved using the mlfma appropriate preconditioning techniques are employed to speedup the mlfma solution the proposed method is further implemented on distributed memory parallel computers to harness the maximum power from presently available machines numerical examples are given to demonstrate the accuracy and efficiency of the method as well as the convergence of the higher order scheme

accelerated cartesian expansions a fast method for computing of potentials of the form r ν for all real ν abstract the need to compute potentials of the form r for 1 occur in a variety of areas ranging from electromagnetics to biophysics to molecular dynamics to astrophysics etc for instance coulomb london lennard jones h bonds are of the form 1 5 6 and 12 10 respectively for a systems with n source observation points the cost of computing these potentials scales proportional to o n 2 methods to overcome this computational bottleneck have been a popular research topic for quite some time for instance the fast multipole method fmm and their cousins tree codes have revolutionized the computation of electrostatic potentials 1 these methods rely on a hierarchical decomposition of the computational domain i e construction of a regular oct tree decomposition and exploits the principle of divide and conquer to compute potentials at each observation point this paper presents two methods in the vein of fmm albeit based on cartesian tensors the salient features of the first are as follows i it relies on totally symmetric tensors and ii the errors are independent of the height of the tree the second method is presented specifically for 1 and relies on traceless totally symmetric cartesian tensors using the relationship between traceless cartesian tensors and spherical harmonics it will be shown that this technique has the same computational cost as the classical fmm generalization of the second method for 1 is trivial however one needs to use totally symmetric tensors instead finally in the whole computation scheme only the translation operator that used to traverse across the tree depends on convergence of the proposed method is proven for all r numerical results that validate the cost and accuracy are presented for several potential functions these include those typically encountered in the analysis of physical systems coulombic lennard jones lattice gas

on the identification of the global reference set in data envelopment analysis abstract it is well established that multiple reference sets may occur for a decision making unit dmu in the non radial dea data envelopment analysis setting as our first contribution we differentiate between three types of reference set first we introduce the notion of unary reference set urs corresponding to a given projection of an evaluated dmu the urs includes efficient dmus that are active in a specific convex combination producing the projection because of the occurrence of multiple urss we introduce the notion of maximal reference set mrs and define it as the union of all the urss associated with the given projection since multiple projections may occur in non radial dea models we further define the union of the mrss associated with all the projections as unique global reference set grs of the evaluated dmu as the second contribution we propose and substantiate a general linear programming lp based approach to identify the grs since our approach makes the identification through the execution of a single primal based lp model it is computationally more efficient than the existing methods for its easy implementation in practical applications our last contribution is to measure returns to scale using a non radial dea model this method effectively deals with the occurrence of multiple supporting hyperplanes arising either from multiplicity of projections or from non full dimensionality of minimum face finally an empirical analysis is conducted based on a real life data set to demonstrate the ready applicability of our approach

the generalized method of moments for electromagnetic boundary integral equations the generalized method of moments gmm is a partition of unity based technique for solving electromagnetic and acoustic boundary integral equations past work on gmm for electromagnetics was confined to geometries modeled by piecewise flat tessellations and suffered from spurious internal line charges in the present article we redesign the gmm scheme and demonstrate its ability to model scattering from pec scatterers composed of mixtures of smooth and non smooth geometrical features furthermore we demonstrate that because the partition of unity provides both functional and effective geometrical continuity between patches gmm permits mixtures of local geometry descriptions and approximation function spaces with significantly more freedom than traditional moment methods

measurement of returns to scale using a non radial dea model a range adjusted measure approach abstract this research theoretically explores the measurement of returns to scale rts using a non radial dea data envelopment analysis model a range adjusted measure ram is used as a representative of such non radial models historically a type of rts has been discussed within an analytical framework of radial models the radial based rts measurement is replaced by the non radial ram rts measurement in this study when discussing the non radial ram rts measurement this study finds a problem of multiple projections that cannot be found in the radial measurement in this research a new linear programming approach is proposed to identify all efficient dmus decision making units on a reference set the important feature of the proposed approach is that it can deal with a simultaneous occurrence of a multiple reference sets b multiple supporting hyperplanes and c multiple projections all of the three difficulties are handled by the proposed ram rts measurement in particular we discuss both when the three different types of multiple solutions occur on the ram rts measurement and how to deal with such difficulties our research results make it possible to measure not only the type of rts but also the magnitude of rts in the ram measurement

fast integral equation solution by multilevel green s function interpolation combined with multilevel fast multipole method a fast wideband integral equation ie solver combining the multilevel interpolatory fast fourier transform accelerated approach mlipfft with the multilevel fast multipole method mlfmm is discussed on electrically fine levels within an oct tree multilevel structure coupling computations are performed by mlipfft this method is based on a 3d lagrange factorization of the pertinent green s functions with a smooth approximation error in space and it does not suffer a low frequency breakdown as known from mlfmm for high frequency integral equation problems mlipfft has decreased computational efficiency as the nyquist theorem requires increasing numbers of samples in 3 dimensions due to a transition from the interpolation point based mlipfft source receive formulation towards an appropriate k space representation at a certain level within the oct tree the high frequency efficient mlfmm can be employed for coarse levels the hybrid algorithm is hence well suited for fast wideband integral equation solutions both mixed potential and direct field formulations are considered furthermore a method for mlipfft extrapolation error reduction based on fine level interpolation domain spreading is introduced in several numerical examples the performance of the proposed algorithm is demonstrated

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

identification of congestion in data envelopment analysis under the occurrence of multiple projections a reliable method capable of dealing with negative data abstract to detect the weak and strong congestion statuses of decision making units dmus via data envelopment analysis dea first a technology is constructed under the assumptions of convexity and strong output disposability then the congestion of any inefficient dmu is defined at its projection on the efficient frontier of this technology it has however been argued that this definition is not precise under the occurrence of multiple projections in this paper therefore we propose a single stage linear programming lp model to recognize the evidence of congestion our model precisely distinguishes between the dmus exhibiting weak but not strong congestion and those suffering from strong congestion and identifies the full efficient dmus as well to cope effectively with the occurrence of multiple projections we first prove that all relative interior points of a face exhibit the same type of congestion based on this finding we define the congestion of an inefficient dmu at its max projection a projection that lies in the relative interior of the corresponding minimum face then by showing that the global reference set spans the minimum face we propose an lp model for identifying the max projection we highlight a theoretically interesting and practically useful consequence of our results that the congestion status of an inefficient dmu can be determined based on those of its reference dmus furthermore our proposed method can deal with negative data and is also computationally more efficient than the existing approaches finally three numerical examples are presented to illustrate the use of our proposed method

a bi extremal principle for frontier estimation and efficiency evaluations a new approach is supplied for locating efficiency frontiers and evaluating the efficiency of decision making units dmu s this is accomplished from observational data by means of an envelopment procedure called dea data envelopment analysis originally developed by charnes cooper and rhodes charnes a w w cooper e rhodes 1978 measuring the efficiency of decision making units eur j oper res 2 6 see also short communication eur j oper res 3 1979 339 in connection with their ratio formulation for relative efficiency measurement the current variant employs a bi extremal principle which though nonlinear is subsequently shown to be reducible to a finite sequence of linear programming problems the development is illustrated by means of multiple output functions which are piecewise of cobb douglas or general log linear type and which also allow for increasing decreasing and constant returns to scale more than one production function for the dmu s is also allowed the reduction of the bi extremal principle to linear programming equivalence is also accomplished for much more general classes of functions a numerical example illustrates some of these ideas and also provides a springboard for a new theorem which relates these efficiency measures to ones which were supplied earlier in the charnes cooper and rhodes s work charnes a w w cooper e rhodes 1978 measuring the efficiency of decision making units eur j oper res 2 6 see also short communication eur j oper res 3 1979 339

sensitivity analysis of the additive model in data envelopment analysis abstract sensitivity analysis of the additive model in data envelopment analysis is studied in this paper sufficient conditions for simultaneous change of all outputs and all inputs of an efficient decision making unit which preserves efficiency are established a numerical illustration is provided

mixed integer programming approach of extended dea discriminant analysis abstract several unique features of data envelopment analysis dea are incorporated into discriminant analysis da such a combined use of the two approaches is referred to as dea da eur j operat res 1999 115 564 sueyoshi eur j operat res 2001 131 324 has recently extended dea da in a manner that it can deal with a negative value in data the new version is referred to as extended dea da an important feature of extended dea da is that it can estimate weights of a linear discriminant function by minimizing the total deviation of misclassified observations as an extension of his research this research proposes a new type of mixed integer programming formulations that provide these weight estimates by minimizing the total number of misclassified observations

solving dea models in a single optimization stage can the non archimedean infinitesimal be replaced by a small finite epsilon abstract single stage dea models aim to assess the input or output radial efficiency of a decision making unit and potential mix inefficiency in a single optimization stage this is achieved by incorporating the sum of input and output slacks multiplied by a small theoretically non archimedean infinitesimal value epsilon in the envelopment model or equivalently by using this value as the lower bound on the input and output weights in the dual multiplier model when this approach is used it is common practice to select a very small value for epsilon this is based on the expectation that for a sufficiently small epsilon the radial efficiency and optimal slacks obtained by solving the single stage model should be approximately equal to their true values obtained by the two separate optimization stages however as well known selecting a small epsilon may lead to significant computational inaccuracies in this paper we prove that there exists a threshold value referred to as the effective bound such that if epsilon is smaller than this bound the solution to the single stage program is not approximate but precise exactly the same as in the two stage approach provided there are no computational errors

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

returns to scale in dynamic dea two different types of inputs variable inputs and quasi fixed inputs are incorporated into an analytical framework of dynamic data envelopment analysis dea a unique feature of the quasi inputs is that those are considered as outputs at the current period while being treated as inputs at the next period the dynamic dea can measure interdependency among consecutive periods this study incorporates the concept of returns to scale into the dynamic dea

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

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

choosing weights from alternative optimal solutions of dual multiplier models in dea in this paper we propose a two step procedure to be used for the selection of the weights that we obtain from the multiplier model in a dea efficiency analysis it is well known that optimal solutions of the envelopment formulation for extreme efficient units are often highly degenerate and consequently have alternate optima for the weights different optimal weights may then be obtained depending for instance on the software used the idea behind the procedure we present is to explore the set of alternate optima in order to help make a choice of optimal weights the selection of weights for a given extreme efficient point is connected with the dimension of the efficient facets of the frontier our approach makes it possible to select the weights associated with the facets of higher dimension that this unit generates and in particular it selects those weights associated with a full dimensional efficient facet fdef if any in this sense the weights provided by our procedure will have the maximum support from the production possibility set we also look for weights that maximize the relative value of the inputs and outputs included in the efficiency analysis in a sense to be described in this article

separation of variables and exact solution of the dirac equation in nonstatic minkowski spacetimes using a second order formalism a complete separation of variables in the dirac equation for a free particle in nonstatic orthogonal curvilinear coordinates of the form t f u v x g u v y z is presented it is shown that the dirac equation is separable in eight nonequivalent coordinate systems where the klein gordon equation separates exact solutions of the dirac equation in the systems of coordinates obtained are presented

variations on the theme of slacks based measure of efficiency in dea in dea there are typically two schemes for measuring efficiency of dmus radial and non radial radial models assume proportional change of inputs outputs and usually remaining slacks are not directly accounted for inefficiency on the other hand non radial models deal with slacks of each input output individually and independently and integrate them into an efficiency measure called slacks based measure sbm in this paper we point out shortcomings of the sbm and propose four variants of the sbm model the original sbm model evaluates efficiency of dmus referring to the furthest frontier point within a range this results in the hardest score for the objective dmu and the projection may go to a remote point on the efficient frontier which may be inappropriate as the reference in an effort to overcome this shortcoming we first investigate frontier facet structure of the production possibility set then we propose variation i that evaluates each dmu by the nearest point on the same frontier as the sbm found however there exist other potential facets for evaluating dmus therefore we propose variation ii that evaluates each dmu from all facets we then employ clustering methods to classify dmus into several groups and apply variation ii within each cluster this variation iii gives more reasonable efficiency scores with less effort lastly we propose a random search method variation iv for reducing the burden of enumeration of facets the results are approximate but practical in usage

a higher order multilevel fast multipole algorithm for scattering from mixed conducting dielectric bodies a higher order multilevel fast multipole algorithm mlfma is presented for computing electromagnetic scattering from three dimensional bodies comprising both conducting and dielectric objects the problem is formulated using the poggio miller chang harrington wu tsai 1973 1977 approach for multiple homogeneous dielectric objects and the combined field approach for conducting objects the resultant integral equations are discretized by the method of moments mom in which the conducting and dielectric surfaces interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using higher order vector basis functions such a discretization yields a highly accurate representation of the unknown currents without compromising the accuracy of geometrical modeling an implicit matrix filling scheme is employed to facilitate the treatment of complex scatterers having multiple junctions the resultant numerical system is then solved by mlfma which is tailored to accommodate the material properties of dielectric scatterers and the solution is accelerated using an incomplete lu decomposition preconditioner numerical examples are presented to demonstrate the accuracy and versatility of this approach in dealing with a wide array of scattering problems

linear production functions and the data envelopment analysis abstract this paper shows that the data envelopment analysis or farrell method is not nonparametric in the sense that the method implicitly employs linear production functions frontiers to measure efficiency deriving positive multiplier linear production frontiers and grouping the dmus by their corresponding frontiers can simplify the estimation procedures when there are new dmus included and can easily determine how many inputs should be reduced or and how many outputs should be increased to make an inefficient dmu efficiently this procedure can also circumvent the problems of the non archimedean infinitesmal in the ccr literature it is also shown that because of the linear production functions both banker s and the banker charnes cooper methods fail in testing for returns to scale

a point adaptive grouping scheme of mlfma for electrically large scattering simulation a gaussian point adaptive grouping scheme for the multilevel fast multipole algorithm mlfma has been proposed in this communication to significantly reduce the heavy memory cost resulted from using the basis functions defined on large patches without sacrificing the accuracy of the numerical solutions the grouping process in the mlfma has been considered as a single objective optimization problem and is solved by using the clustering algorithm for gaussian quadrature points on each patch meanwhile the constraint of the addition theorem for mlfma is still satisfied as a result the presented scheme is able to acquire an optimal number of multipoles for each basis function compared to the conventional octree grouping scheme or other grouping schemes used in the past the method in this communication is advantageous in terms of the memory efficiency and the solution accuracy numerical examples have been given to demonstrate the validity and effectiveness of the proposed scheme

indicators of ill conditioned data sets and model misspecification in data envelopment analysis an extended facet approach date envelopment analysis dea employs mathematical programming to measure the relative efficiency of decision making units dmus this paper is concerned with development of indicators to determine whether or not the specification of the input and output space is supported by data in the sense that the variation in data is sufficient for estimation of a frontier of the same dimension as the input output space insufficient variation in data implies that some inputs outputs can be substituted along the efficient frontier but only in fixed proportions data thus locally supports variation in a subspace of a lower dimension rather than in the input output space of full dimension each segment of the efficient frontier is in this sense subject to local collinearity insufficient variation in data provides a bound on admissible disaggregations in cases where substitution in fixed proportions is incompatible with a priori information concerning the production process a data set incapable of estimating a fro

a mixed potential mlfma for higher order moment methods with application to the generalized method of moments the application of the multilevel fast multipole algorithm mlfma to higher order moment method discretizations is a continuing open problem herein we present a point based mixed potential variant of the mlfma algorithm that exhibits an mlfma tree of arbitrary height with no restriction related to basis function support size efficient nearfield precomputation and that maintains favorable scaling for any mixture of low and high order bases the flexibility of the algorithm is also leveraged to accelerate the precomputation of algebraic preconditioners we demonstrate the method through application to the generalized method of moments gmm a recently introduced moment method discretization capable of combining both low and high order bases and geometries in the same simulation however the method may be used to accelerate other higher order moment methods as well

higher order frequency domain computational electromagnetics a review of the higher order computational electromagnetics cem for antenna wireless and microwave engineering applications is presented higher order cem techniques use current field basis functions of higher orders defined on large e g on the order of a wavelength in each dimension curvilinear geometrical elements which greatly reduces the number of unknowns for a given problem the paper reviews all major surface volume integral and differential equation electromagnetic formulations within a higher order computational framework focusing on frequency domain solutions with a systematic and unified review of generalized curved parametric quadrilateral triangular hexahedral and tetrahedral elements and various types of higher order hierarchical and interpolatory vector basis functions in both divergence and curl conforming arrangements a large number of actual higher order techniques representing various combinations of formulations elements bases and solution procedures are identified and discussed the examples demonstrate the accuracy efficiency and versatility of higher order techniques and their advantages over low order discretizations the most important one being a much faster higher order convergence of the solution it is demonstrated that both components of the higher order modeling namely higher order geometrical modeling and higher order current field modeling are essential for accurate and efficient cem analysis of general antenna scattering and microwave structures

the measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyperplane this research theoretically explores the measurement of rts returns to scale under a possible occurrence of multiple solutions in dea data envelopment analysis in this study the occurrence of multiple solutions is classified into type i and type ii type i is an occurrence of multiple solutions in a reference set type ii is an occurrence of multiple solutions on a supporting hyperplane passing on the reference set both types i and ii are very well known among dea researchers but previous research has not sufficiently explored a simultaneous occurrence of type i and type ii in the rts measurement the two types of multiple solutions influence a degree of rts in the dea measurement such a quantitative issue on rts is examined from the perspective of the type i and type ii problems to deal with such difficulties a new linear programming approach is proposed to identify all efficient dmus decision making units that consist of a reference set even if multiple solutions occur on the reference set based upon the research result we can identify when multiple solutions of type i and or type ii occur on the rts measurement and how to deal with such difficulties our research result makes it possible to measure a degree of scale economies rts under the simultaneous occurrence of type i and type ii

a novel hierarchical two level spectral preconditioning technique for electromagnetic wave scattering a new set of higher order hierarchical basis functions based on curvilinear triangular patch is proposed for expansion of the current in electrical field integral equations solved by method of moments the hierarchical two level spectral preconditioning technique is developed for the generalized minimal residual iterative method in which the multilevel fast multipole method is used to accelerate matrix vector product the sparse approximate inverse sai preconditioner based on the higher order hierarchical basis functions is used to damp the high frequencies of the error and the low frequencies is eliminated by a spectral preconditioner in a two level manner defined on the lower order basis functions the spectral preconditioner is combined with sai preconditioner to obtain a hierarchical two level spectral preconditioner numerical experiments indicate that the new preconditioner can significantly reduce both the iteration number and computational time

dea discriminant analysis methodological comparison among eight discriminant analysis approaches abstract discriminant analysis da is a classification method that can predict the group membership of a newly sampled observation recently a new type of non parametric da approach is proposed to provide a set of weights of a discriminant function consequently yielding an evaluation score for the determination of group membership the non parametric da is referred to as data envelopment analysis discriminant analysis dea da because it maintains its discriminant capabilities by incorporating the non parametric feature of dea into da in this study a use of the mixed integer approach of dea da is compared with other da methods it is confirmed that it performs at least as well as the other well known da methods the proposed approach is further reformulated in a manner that it can deal with classification of more than two groups

multilevel fast multipole method for higher order discretizations the multi level fast multipole method mlfmm for a higher order ho discretization is demonstrate do n high frequency hf problems illustrating for the first time how an efficient mlfmm for ho can be achieved even for very large groups applying several novel ideas beneficial to both lower order and higher order discretizations results from a low memory high speed mlfmm implementation of a ho hierarchical discretization are shown these results challenge the general view that the benefits of ho and hf mlfmm cannot be combined

sensitivity analysis of network dea nsbm versus nram abstract users of data envelopment analysis dea often presume efficiency estimates to be robust while traditional dea has been exposed to various sensitivity studies network dea has so far escaped similar scrutiny thus there is a need to investigate the sensitivity of efficiency estimates further compounded by the recent attention network dea has been receiving in literature we compare network slacks based measure nsbm with network range adjusted measure nram where the latter is developed for the first time following various data perturbations overall findings indicate positive and significant rank correlations when new results are compared against baseline results suggesting resilience key findings show that a as in traditional dea greater sample size brings greater discrimination b removing a relevant input improves discrimination c introducing an extraneous input leads to a moderate loss of discrimination d simultaneously adjusting data in opposite directions for inefficient versus efficient branches shows a mostly stable estimates e swapping divisional weights produces a substantial drop in discrimination f stacking perturbations has the greatest impact on efficiency estimates with substantial loss of discrimination and g layering suggests that the core inefficient cohort is resilient against omission of benchmark branches further insight gained by comparing nsbm with nram includes h identical benchmark groups across both formulations i a narrower range of efficiency estimates and a more stable mean across different sample sizes under nram j distribution of nram efficiency estimates is negatively skewed whereas nsbm estimates are mostly positively skewed and k there is no evidence of inefficient unit size bias among nram estimates whereas larger inefficient units appear more inefficient under nsbm

an occurrence of multiple projections in dea based measurement of technical efficiency theoretical comparison among dea models from desirable properties this study discusses nine desirable properties that a measure of technical efficiency te needs to satisfy from the perspective of production economics and optimization seven data envelopment analysis dea models are theoretically compared from a viewpoint of nine te criteria all the seven dea models suffer from a problem of multiple projections even though a unique projection for efficiency comparison is one of the nine desirable properties furthermore all the dea models violate the property on aggregation of inputs and outputs thus the seven dea models do not satisfy all desirable te properties in addition the comparison provides us with the following guidelines a the additive model violates all desirable te properties b russell measure and sbm ergm perform as well as ram as a non radial measure if we are interested in strict monotonicity the two models outperform the other dea models including ram in contrast if we are interested in translation invariance ram is better than russell measure and sbm ergm c the radial measures ccr and bcc have the property of linear homogeneity d the ccr model is useful for measuring a frontier shift among different periods e if a data set contains a negative value ram becomes a dea model to handle the negative value because it has the property of translation invariance after examining the desirable te properties this study proposes a new approach to deal with an occurrence of multiple projections the proposed approach includes a test to examine an occurrence of multiple projections a mathematical expression of a projection set and a selection process of a unique reference set as the largest one covering all the possible reference sets

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

on separable solutions of dirac s equation for the electron the properties of coordinate systems that admit separation of the laplacian and hamilton jacobi operators have been thoroughly explored so that the nature of solutions in separable form of laplace s equation the wave equation schrodinger s equation and the hamilton jacobi equation are well understood the corresponding problems for the dirac operator in flat space time have been less completely examined and this paper contains studies intended to produce a more systematic account of possible solutions of dirac s equation because the dirac operator differs from the laplacian in being a first degree differential operator and in having matrix coefficients it is not possible to discuss possible solutions in as general a way and the separable solutions are far less rich than for equations with the laplacian in particular the forms of the potentials for which separable solutions are possible are not for the most part of physical interest although the discussion is confined to coordinates in flat space time some of the procedures are derived from those developed to solve dirac s equation in coordinates with a kerr metric

computational strategy for russell measure in dea second order cone programming abstract in aggregation for data envelopment analysis dea a jointly measured efficiency score among inputs and outputs is desirable in performance analysis a separate treatment between output oriented efficiency and input oriented efficiency is often needed in the conventional radial dea models such radial measures usually need to measure both that a current performance attains an efficiency frontier and that all the slacks are zero on optimality in the analytical framework of the radial measure russell measure is proposed to deal with such a difficulty a major difficulty associated with the russell measure is that it is modeled by a nonlinear programming formulation hence a conventional linear programming algorithm usually applied for dea cannot solve the russell measure this study newly proposes a reformulation of the russell measure by a second order cone programming socp model and applies the primal dual interior point algorithm to solve the russell measure

probabilistic characterization of directional distances and their robust versions in productivity analysis the performance of production units is measured through the distance of the individual decision making units dmu to the technology which is defined as the frontier of the production set most of the existing methods farrell debreu and shephard radial measures input or output oriented and hyperbolic distance functions rely on multiplicative measures of the distance and so require to deal with strictly positive inputs and outputs this can be critical when the data contain zero or negative values as in financial data bases for the measure of funds performances directional distance function is an alternative that can be viewed as an additive measure of e ciency we show in this paper that using a probabilistic formulation of the production process the directional distance can be expressed as simple radial or hyperbolic distance up to a simple transformation of the inputs outputs space this allows to propose simple methods of estimation but also to transfer easily most of the known properties of the estimators shared by the radial and hyperbolic distances in addition the formulation allows to define robust directional distances in the lines of quantileor order m partial frontiers finally we can also define conditional directional distance functions conditional to environmental factors to illustrate the methodology we show how it can be implemented using a mutual funds database

analyzing properties of k cones in the generalized data envelopment analysis model abstract we study the properties of the k cone in a generalized data envelopment analysis dea model this model includes the following four important classes of models charnes et al 1978 model banker et al 1984 and charnes et al 1985 model fare and grosskopf 1985 model and seiford and thrall 1990 model as its special cases the main contribution of this paper is to introduce to the above four models a the input output preference cone w to represent the relative importance of different input output categories viewed by the evaluator one who evaluates the decision making units dmus and b the so called predilection cone to describe preference of the evaluator to selected dmus we discuss the new characterizations of dea efficient dmus in the case of k cone we also describe the use of elementary predilection operators to achieve special preference for one or more dmus this method can be easily applied to find all the dea efficient dmus that are on a common efficient face as one or more prespecified dmus the method provided in this paper is complete in the sense that only those dmus that are on a common efficient face with the predileccted ones will be dea efficient after predilection we believe that the results of this paper will play in important role in determining the structure of efficient frontiers

a note on imposing strong complementary slackness conditions in dea abstract a new dea model has been introduced recently combining the primal and the dual models in order to impose strong complementary slackness conditions it was claimed that a reference set that contains the maximum number of efficient units can then be determined the model is very interesting as a theoretical idea however not only does the computational burden increase significantly but it seems also that the basic matrices may be inherently ill conditioned leading to erroneous results numerical experiments have been carried out on two real datasets of medium size with 163 and 920 units these experiments using well known reliable software show pervasive existence of ill conditioned matrices leading to obviously wrong estimates of efficiency scores and units declared as efficient reference units while actually being inefficient

direction selection in stochastic directional distance functions abstract researchers rely on the distance function to model multiple product production using multiple inputs a stochastic directional distance function sddf allows for noise in potentially all input and output variables yet when estimated the direction selected will affect the functional estimates because deviations from the estimated function are minimized in the specified direction specifically the parameters of the parametric sddf are point identified when the direction is specified we show that the parameters of the parametric sddf are set identified when multiple directions are considered further the set of identified parameters can be narrowed via data driven approaches to restrict the directions considered we demonstrate a similar narrowing of the identified parameter set for a shape constrained nonparametric method where the shape constraints impose standard features of a cost function such as monotonicity and convexity our monte carlo simulation studies reveal significant improvements as measured by out of sample radial mean squared error in functional estimates when we use a directional distance function with an appropriately selected direction and the errors are uncorrelated across variables we show that these benefits increase as the correlation in error terms across variables increase this correlation is a type of endogeneity that is common in production settings from our monte carlo simulations we conclude that selecting a direction that is approximately orthogonal to the estimated function in the central region of the data gives significantly better estimates relative to the directions commonly used in the literature for practitioners our results imply that selecting a direction vector that has non zero components for all variables that may have measurement error provides a significant improvement in the estimator s performance we illustrate these results using cost and production data from samples of approximately 500 us hospitals per year operating in 2007 2008 and 2009 respectively and find that the shape constrained nonparametric methods provide a significant increase in flexibility over second order local approximation parametric methods

a generalized multiplicative directional distance function for efficiency measurement in dea abstract for measuring technical efficiency relative to a log linear technology a generalized multiplicative directional distance function gmddf is developed using the framework of multiplicative directional distance function mddf furthermore a computational procedure is suggested for its estimation the gmddf serves as a comprehensive measure of efficiency in revealing pareto efficient targets as it accounts for all possible input and output slacks this measure satisfies several desirable properties of an ideal efficiency measure such as strong monotonicity unit invariance translation invariance and positive affine transformation invariance this measure can be easily implemented in any standard dea software and provides the decision makers with the option of specifying preferable direction vectors for incorporating their decision making preferences finally to demonstrate the ready applicability of our proposed measure an illustrative empirical analysis is conducted based on real life data set of 20 hardware computer companies in india

higher order hierarchical legendre basis functions for electromagnetic modeling this paper presents a new hierarchical basis of arbitrary order for integral equations solved with the method of moments mom the basis is derived from orthogonal legendre polynomials which are modified to impose continuity of vector quantities between neighboring elements while maintaining most of their desirable features expressions are presented for wire surface and volume elements but emphasis is given to the surface elements in this case the new hierarchical basis leads to a near orthogonal expansion of the unknown surface current and implicitly an orthogonal expansion of the surface charge in addition all higher order terms in the expansion have two vanishing moments in contrast to existing formulations these properties allow the use of very high order basis functions without introducing ill conditioning of the resulting mom matrix numerical results confirm that the condition number of the mom matrix obtained with this new basis is much lower than existing higher order interpolatory and hierarchical basis functions as a consequence of the excellent condition numbers we demonstrate that even very high order mom systems e g tenth order can be solved efficiently with an iterative solver in relatively few iterations

nonconformal discretization of electric current volume integral equation with higher order hierarchical vector basis functions a nonconformal discretization of the electric current volume integral equation jvie is presented for the electromagnetic scattering analysis of inhomogeneous dielectric objects this jvie is based on higher order geometrical and current modeling where curved tetrahedral elements and higher order hierarchical vector hohv basis functions are adopted in order to implement the nonconformal discretization the half face based hohv basis function is introduced to address the nonconformal volumetric elements compared to the conventional low order conformal nonconformal vie our nonconformal hohv based jvie has the advantage of improving the computational efficiency and accuracy compared to the previous vie discretized by other higher order functions our nonconformal jvie is based on the higher order geometric modeling and the hohv bases in order to improve the efficiency the basis expansion and recombination technique is introduced to significantly accelerate the matrix filling moreover the flexibility of basis order selection is further enhanced by the mixed order schemes numerical results are given to demonstrate its accuracy efficiency and flexibility

a diagonalized multilevel fast multipole method with spherical harmonics expansion of the k space integrals diagonalization of the fast multipole method fmm for the helmholtz equation is usually achieved by expanding the multipole representation in propagating plane waves the resulting k space integral over the ewald sphere is numerically evaluated storing the k space quadrature samples of the method of moments mom basis functions constitutes a large portion of the overall memory requirements of the resulting algorithm for solving the integral equations of scattering and radiation problems in this paper it is proposed to expand the k space representation of the basis functions by spherical harmonics in order to reduce the sampling redundancy introduced by numerical quadrature rules aggregations plane wave translations and disaggregations in the realized multilevel fast multipole method mlfmm are carried out using the k space samples of a numerical quadrature rule however the incoming plane waves on the finest mlfmm level are expanded in spherical harmonics again thus due to the orthonormality of spherical harmonics the testing integrals for the individual testing functions are simplified into series over products of spherical harmonics expansion coefficients overall the resulting mlfmm can save a considerable amount of memory without compromising accuracy and numerical speed

double higher order method of moments for surface integral equation modeling of metallic and dielectric antennas and scatterers a novel double higher order galerkin type method of moments based on higher order geometrical modeling and higher order current modeling is proposed for surface integral equation analysis of combined metallic and dielectric antennas and scatterers of arbitrary shapes the technique employs generalized curvilinear quadrilaterals of arbitrary geometrical orders for the approximation of geometry metallic and dielectric surfaces and hierarchical divergence conforming polynomial vector basis functions of arbitrary orders for the approximation of electric and magnetic surface currents within the elements the geometrical orders and current approximation orders of the elements are entirely independent from each other and can be combined independently for the best overall performance of the method in different applications the results obtained by the higher order technique are validated against the analytical solutions and the numerical results obtained by low order moment method techniques from literature the examples show excellent accuracy flexibility and efficiency of the new technique at modeling of both current variation and curvature and demonstrate advantages of large domain models using curved quadrilaterals of high geometrical orders with basis functions of high current approximation orders over commonly used small domain models and low order techniques the reduction in the number of unknowns is by an order of magnitude when compared to low order solutions