modelling weak disposability in data envelopment analysis under relaxed convexity assumptions the treatment of undesirable bad outputs in models of efficiency and productivity analysis often requires replacing the assumption of free disposability of outputs by their weak disposability in a recent publication the authors showed that the kuosmanen technology is the only correct representation of the fully convex technology exhibiting weak disposability of bad and good outputs in this paper we relax the assumption of full convexity and consider two further possibilities the case in which only the output sets are assumed convex and the case in which no convexity is assumed at all in the first case we show that although the traditional shephard technology of nonparametric production analysis satisfies the assumption of convex output sets it is larger than necessary based on the minimum extrapolation principle we develop a correct model that is based on the assumed axioms the second case leads to the development of a weakly disposable analogue of the free disposable hull to complete our study we give a full axiomatic definition of the shephard technology

separability of very noisy mixed states and implications for nmr quantum computing we give a constructive proof that all mixed states of n qubits in a sufficiently small neighborhood of the maximally mixed state are separable unentangled the construction provides an explicit representation of any such state as a mixture of product states we give upper and lower bounds on the size of the neighborhood which show that its extent decreases exponentially with the number of qubits the bounds show that no entanglement appears in the physical states at any stage of present nmr experiments though this result raises questions about nmr quantum computation further analysis would be necessary to assess the power of the general unitary transformations which are indeed implemented in these experiments in their action on separable states

unique decompositions faces and automorphisms of separable states let sk be the set of separable states on b cm cn admitting a representation as a convex combination of k pure product states or fewer if m 1 n 1 and k max m n we show that sk admits a subset vk such that vk is dense and open in sk and such that each state in vk has a unique decomposition as a convex combination of pure product states and we describe all possible convex decompositions for a set of separable states that properly contains vk in both cases we describe the associated faces of the space of separable states which in the first case are simplexes and in the second case are direct convex sums of faces that are isomorphic to state spaces of full matrix algebras as an application of these results we characterize all affine automorphisms of the convex set of separable states and all automorphisms of the state space of b cm cn that preserve entanglement and separability

convex input and output projections of nonconvex production possibility sets in this paper we characterize the smallest production possibility set that contains a specified set of input output combinations in accordance with neoclassical production economics this possibility set has convex projections into the input and output spaces convex isoquants and it satisfies the assumption of free disposability we obtain it by means of a possibly infinite recursion which builds the possibility set as an ever larger union of convex sets we remark on the nature of the approximations obtained by truncating the recursion and we obtain a necessary and sufficient condition checkable in one iteration for the recursion to stop in the next for the case in which the recursion stops we provide a succinct characterization of the dominance relations among the constituent sets produced by the procedure finally we present examples of both finite and infinite cases the example for the finite case illustrates the construction of the possibility set along with its associated production and consumption sets

estimating non convex production sets imposing convex input sets and output sets in data envelopment analysis abstract in this paper we present data envelopment analysis models for estimating non convex production sets in contrast to the banker et al banker r d charnes a and cooper w w 1984 management science 30 9 1078 1092 model these models give statistically consistent estimators for production sets that are non convex but do have convex input sets and or convex output sets as is typically assumed in micro economic theory in addition these models suffer less from a finite sample error than the free disposable hull deprins d simar l tulkens h 1984 in marchand m pestieu p tulkens h eds the performance of public enterprises north holland amsterdam pp 243 267 model

selective convexity in dea models in this paper we introduce a concept of selective convexity into the models of data envelopment analysis dea in this development each input and output can be judged individually with respect to its compliance with the convexity assumption the decision making units can be used to form convex combinations provided they are different only on the inputs and outputs for which the convexity assumption is accepted the free disposal hull standard variable returns to scale and quasi concave dea models are all special cases in the range of models obtained in this paper operationally the new models are solved as mixed integer linear programs both in the input and output oriented scenarios

on some semilattice structures for production technologies abstract tracing back from charnes et al 9 many approaches have been proposed to extend the dea production model to non convex technologies the fdh method were introduced by deprins et al 13 and it only assumes a free disposal assumption of the technology this paper continues further an earlier work by briec and horvath 7 among other things a new class of semilattice production technologies is introduced duality results as well as computational issues are proposed

subalgebras of the steenrod algebra and the action of matrices on truncated polynomial algebras let a t be the subalgebra of the steenrod algebra generated by sqi i 2t we determine which a module indecomposable summands of f2 x1 xn are free over a t by first showing this to be equivalent to the group theoretic question of determining which irreducible modular representations of mn f2 or gln f2 occur as composition factors in the truncated polynomial algebra f2 x1 xn x12 xn2 the second question is then answered

estimation of returns to scale using data envelopment analysis abstract generalization of the measure of returns to scale from a single number to an interval permits extension of the concept to dea data domains with multiple inputs and multiple outputs the key new approach is a partition of the optimal frontier into three parts corresponding respectively to increasing constant and decreasing returns to scale these parts are characterized in terms of optimal primal solutions and optimal dual solutions for both the original charnes cooper rhodes model 1978 and the later banker charnes cooper model 1984 and relying on concepts developed by r d banker 1984 and r m thrall 1988

the distillability of entanglement of bipartite reduced density matrices of a tripartite state the relation between the distillability of entanglement of three bipartite reduced density matrices from a tripartite pure state has been studied in phys rev a 84 012325 2011 we extend this result to the tripartite mixed state of rank at most three in particular we show that if the state has two bipartite reduced density operators with rank two then the third bipartite reduced density operator additionally having non positive partial transpose non ppt is distillable in contrast we show that the tripartite ppt state with two reduced density operators of rank two is a three qubit fully separable state we obtain these facts by proving a conjectured matrix inequality for the bipartite matrix m with schmidt rank at most three this is one of the main results of this paper we also prove it for some m with arbitrary schmidt rank

dea on relaxed convexity assumptions in a recent paper petersen petersen n c 1990 data envelopment analysis on a relaxed set of assumptions management sci 36 305 314 proposed to relax the convexity assumptions invoked in traditional data envelopment analysis dea unfortunately the new approach is not consistent with the relaxed assumptions also the efficiency evaluations in input and output spaces are based on different technologies assumptions the aim of this paper is to clarify which assumptions are actually involved and to develop modifications such that the input and output based measures are consistent in effect a family of dea methods based on relaxed convexity assumptions is identified

transconcave data envelopment analysis transconcave data envelopment analysis tdea extends standard data envelopment analysis dea in order to account for non convex production technologies such as those involving increasing returns to scale or diseconomies of scope tdea introduces non convexities by transforming the range and the domain of the production frontier thus replacing the standard assumption that the production frontier is concave with the more general assumption that the frontier is concave transformable tdea gives statistically consistent estimates for all monotonically increasing and concave transformable frontiers in addition monte carlo simulations suggest that tdea can substantially improve inefficiency estimation in small samples compared to the standard banker charnes and cooper model and the full disposable hull model fdh

obnoxious facility location and data envelopment analysis a combined distance based formulation abstract we have broadened the classic anti center models to include generalized distance measures it includes in the inherent proximity measures other cost benefit metrics unlike classic data envelopment analysis dea the combined location dea model proposed here assumes disposability of input output s only it represents a more flexible formulation the locations of multiple sites are analyzed using a binary integer program while evaluation is performed by the full strength of a dea model through a case study we show how location and dea models can be used together to more realistically characterize a siting decision

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

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

dea with efficiency classification preserving conditional convexity abstract we propose to relax the standard convexity property used in data envelopment analysis dea by imposing additional qualifications for feasibility of convex combinations we specifically focus on a condition that preserves the koopmans efficiency classification this yields an efficiency classification preserving conditional convexity property which is implied by both monotonicity and convexity but not conversely substituting convexity by conditional convexity we construct various empirical dea approximations as the minimal sets that contain all dmus and are consistent with the imposed production assumptions imposing an additional disjunctive constraint to standard convex dea formulations can enforce conditional convexity computation of efficiency measures relative to conditionally convex production set can be performed through disjunctive programming dp

optimal ensemble length of mixed separable states the optimal pure state ensemble length of a separable state a is the minimum number of pure states needed in convex combination to construct a we study the set of all separable states with optimal pure state ensemble length equal to k or fewer lower bounds on k are found below which these sets have measure 0 in the set of separable states in the bipartite case and the multiparticle case where one of the particles has significantly more quantum numbers than the rest the lower bounds are sharp a consequence of our results is that for all two particle systems except possibly those with one qubit or those with a nine dimensional hilbert space and for all systems with more than two particles the optimal pure state ensemble length for a randomly picked separable state is with probability 1 greater than the state s rank in bipartite systems with probabilty 1 it is greater than 1 4 the rank raised to the 3 2 power and in a system of p qubits with probability 1 it is greater than 22p 1 2p i e alm

generalizations of quantum discord the original definition of quantum discord of bipartite states was defined over projective measurements in this paper we discuss some generalizations of it these generalizations are defined over general measurements rank 1 general measurements or neumark extension measurements we investigate the non negativity zero discord sets of all these quantum discords and some properties of them

on the p adic completions of nonnilpotent spaces this paper deals with the p adic completion f p x developed by bousfield kan for a space x and prime p a space x is called f p good when the map x f p x is a mod p homology equivalence and called f p bad otherwise general examples of f p good spaces are established beyond the usual nilpotent or virtually nilpotent ones these include the polycyclic by finite spaces however the wedge of a circle with a sphere of positive dimension is shown to be f p bad this provides the first example of an f p bad space of finite type and implies that the p profinite completion of a free group on two generators must have nontrivial higher mod p homology as a discrete group