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

continuous time random walks and the fractional diffusion equation the average probability density p r t of random walks on fractals is revisited within the continuous time random walks formalism corrections to the accepted asymptotic stretched gaussian decay of p r t of the form ralpha are discussed it is shown that p r t obeys a diffusion equation with a fractional time derivative asymptotically and predictions about the value of alpha are presented

initial value boundary value problems for fractional diffusion wave equations and applications to some inverse problems abstract we consider initial value boundary value problems for fractional diffusion wave equation t u x t l u x t where 0 2 where l is a symmetric uniformly elliptic operator with t independent smooth coefficients first we establish the unique existence of the weak solution and the asymptotic behavior as the time t goes to and the proofs are based on the eigenfunction expansions second for 0 1 we apply the eigenfunction expansions and prove i stability in the backward problem in time ii the uniqueness in determining an initial value and iii the uniqueness of solution by the decay rate as t iv stability in an inverse source problem of determining t dependent factor in the source by observation at one point over 0 t

on maximal regularity for the cauchy dirichlet parabolic problem with fractional time derivative abstract we prove two maximal regularity results in spaces of continuous and holder continuous functions for a linear cauchy dirichlet problem with a fractional time derivative d t this derivative is intended in the sense of caputo and is taken in 0 2 in case 1 we obtain maximal regularity results for parabolic problems already known in mathematical literature

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

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 note on dea vs principal component analysis an improvement to joe zhu s approach abstract this paper considers a previous article published by zhu in the european journal of operational research which describes a joint use of data envelopment analysis dea and principal component analysis pca in ranking of decision making units dmus in zhu s empirical study dea and pca yield a consistent ranking however this paper finds that in certain instances dea and pca may yield inconsistent rankings the pca procedure adopted by zhu is slightly modified in this article by incorporating other important features of ranking that zhu has not considered numerical results reveal that both approaches show a consistency in ranking with dea when the data set has a small number of efficient units but when a majority of the dmus in the sample are efficient only the modified approach produces consistent ranking with dea

cauchy problem for fractional diffusion equations abstract we consider an evolution equation with the regularized fractional derivative of an order 0 1 with respect to the time variable and a uniformly elliptic operator with variable coefficients acting in the spatial variables such equations describe diffusion on inhomogeneous fractals a fundamental solution of the cauchy problem is constructed and investigated

some uniqueness and existence results for the initial boundary value problems for the generalized time fractional diffusion equation in this paper some uniqueness and existence results for the solutions of the initial boundary value problems for the generalized time fractional diffusion equation over an open bounded domain gx 0 t email protected r n are given to establish the uniqueness of the solution a maximum principle for the generalized time fractional diffusion equation is used in turn the maximum principle is based on an extremum principle for the caputo dzherbashyan fractional derivative that is considered in the paper too another important consequence of the maximum principle is the continuous dependence of the solution on the problem data to show the existence of the solution the fourier method of the variable separation is used to construct a formal solution under certain conditions the formal solution is shown to be a generalized solution of the initial boundary value problem for the generalized time fractional diffusion equation that turns out to be a classical solution under some additional conditions

a multiple criteria decision model with ordinal preference data abstract this paper develops a model for aggregating ordinal preference ranking across multiple criteria criteria weights are developed as part of the optimization process the model utilizes three levels of ordinal priorities 1 preferences among alternatives on the basis of each criterion 2 preferences among the criteria to reflect the importance of those criteria and 3 preferences among the criteria which express the degree to which the respondent can clearly distinguish among the alternatives the model is based upon a data envelopment analysis structure which permits a flexible weighting mechanism for each alternative being ranked

using rank statistics for determining programmatic efficiency differences in data envelopment analysis this paper presents an analytical approach based on rank statistics to the issue of comparing programs within data envelopment analysis dea efficiency evaluation framework the program evaluation procedure distinguishes between managerial and programmatic inefficiency and uses the mann whitney rank statistic to evaluate the statistical significance of the differences observed between a treatment program and its control group program after adjusting for differences in managerial efficiency between the programs a numerical example based on the data used to evaluate the educational enhancement of the program follow through is used to illustrate the proposed statistical procedures

the fiber of the secondary suspension map there are several different choices for the indexing this one works nicely for both odd primes and the prime 2 in this paper we will only consider the prime 2 the groups ek are an associated graded group to lrk qs0 filtered by the sphere of origin the ehp sequence from a quite general point of view is discussed in 13 the chain complex to calculate the e2 term is given by dl elknkn ek 1 n 1 if we invert the prime 2 then d1 is an isomorphism if k n 1 and n is odd the spectral sequence collapses at e2 this gives serre s theorem that rationally s2nis just k q 2n1

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

v1 and v2 periodicity in stable homotopy theory this paper we construct some self maps related to the elements v1 e 7r2 bp and v2 e 76 bp and use them to obtain families in the 2 primary stable homotopy of spheres in particular we obtain nonzero elements in the 48k 10 stem for all k 0 here bp denotes the brown peterson spectrum associated to p 2 although our results have convenient interpretations in the bp adamsnovikov spectral sequence 251 we make hardly any use of this spectral sequence except in the final step of one argument the only knowledge of bp required here is its homotopy ring our methods are those of the classical k z2 adams spectral sequence ass as we shall be working entirely in the stable category we will denote by x y the abelian group of stable homotopy classes of maps x to y when x is a finite cw complex and y a spectrum we will identify x y with eix y for any integer i and we will not distinguish between a map and its stable homotopy class if v e e x x vk denotes

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

a nonmetric approach to linear discriminant analysis abstract a new nonmetric linear discriminant analysis approach is proposed that is based on the maximization of an index of separation differing from that used by the classical method the possibility of choosing between fisher s classical discriminant function and the one proposed here enables us to reduce the number of misclassifications for given data the method is exemplified on empirical data and various simulations and is compared with the classical linear discriminant analysis

the image of j in the ehp sequence the ehp sequence is based on a result of james j who showed that there is h a map h such that s q sn s2n 1 is a fibration when localized at 2 the map sn sn is usually labeled e the boundary homomorphism in the homotopy sequence is usually labeled p for our purposes it will be most convenient to combine all the ehp sequences into one system this gives the following filtration of o201 s q s

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

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

a complete ranking of dmus using restrictions in dea models abstract data envelopment analyses dea is a linear programming based method which evaluates relative efficiency of decision making units dmus it can include multiple outputs and inputs without a priori weights and without requiring explicit specification of functional forms between inputs and outputs it computes a scalar measure of efficiency and determines efficient levels of inputs and outputs for each dmu under evaluation which has a range of zero to 1 hence it has the ability to rank dmus unless when some dmus are the same in efficiency score such as efficient dmus or inefficient dmus with the same efficiency score in many cases it is necessary to give a full ranking of the dmus hence this paper introduces a new method for complete ranking of decision making units which it does not need any changes in the models also for presentation of the ability of this method it is employed to rank the bank branch of a commercial bank branches in an empirical example

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

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

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

maximum principle for the generalized time fractional diffusion equation abstract in the paper a maximum principle for the generalized time fractional diffusion equation over an open bounded domain g 0 t g r n is formulated and proved the proof of the maximum principle is based on an extremum principle for the caputo dzherbashyan fractional derivative that is given in the paper too the maximum principle is then applied to show that the initial boundary value problem for the generalized time fractional diffusion equation possesses at most one classical solution and this solution continuously depends on the initial and boundary conditions

weak solutions to non homogeneous boundary value problems for time fractional diffusion equations abstract we discuss an initial boundary problem for a time fractional diffusion equation with non zero dirichlet boundary values which belong to l 2 in time t and to a sobolev space of negative order in space and prove the unique existence of weak solutions and a priori estimates the proof is based on the caputo fractional derivative in sobolev spaces and the transposition method we show one application to the existence of solution to an optimal control problem