seminonparametric bayesian estimation of the asymptotically ideal production model abstract recently it has been shown that seminonparametric methods can be used to produced high quality approximations to a firm s technology unlike the local approximations provided by the conventional class of flexible functional forms seminonparametric methods generate global spans within large classes of functions however that approach usually spans a much larger space than the neoclassical function space relevant to most production modeling an exception is the asymptotically ideal model aim generated from the muntz szatz series expansion since every basis function in that expansion is within the neoclassical function space a straightforward method exists for imposing neoclassical regularity when all factors are substitutes since the relevant constraints are inequality restrictions we implement the approach using bayesian methods to avoid the problems of sampling distribution truncation that would occur from sampling theoretic methods we further discuss the relevant extensions that would permit complementary factors nonconstant returns to scale and technological change

integrability of derivatives of inverses of maps of exponentially integrable distortion in the plane abstract the k quasiconformal maps form a category which is invariant under inversion i e f and f 1 are simultaneously k quasiconformal maps of exponentially integrable distortion are a useful class for extending the beltrami equation to a degenerate setting this class is not invariant under inversion in this note we show that the inverses of homeomorphisms of exponentially p integrable distortion have integrable distortion for all p but not necessarily for p

regularity of inverses of sobolev deformations with finite surface energy abstract let u be a sobolev w 1 p map from a bounded open set r n to r n we assume u to satisfy some invertibility properties that are natural in the context of nonlinear elasticity namely the topological condition inv and the orientation preserving constraint det d u 0 these deformations may present cavitation which is the phenomenon of void formation we also assume that the surface created by the cavitation process has finite area if p n 1 we show that a suitable defined inverse of u is a sobolev map a partial result is also given for the critical case p n 1 the proof relies on the techniques used in the study of cavitation

mappings of finite distortion discreteness and openness we establish a sharp integrability condition on the partial derivatives of a mapping with l p integrable distortion for some p n 1 to guarantee discreteness and openness we also show that a mapping with exponentially integrable distortion and integrable jacobian determinant is either constant or both discrete and open we give an example demonstrating the preciseness of our criterion

superselection in the presence of constraints superselection and constraints occur together in many gauge theories and here we begin a study of such systems our main focus will be to analyze compatibility questions between constraining and superselection and we will develop an example modelled on qed in which our framework is realized we proceed from a generalization of doplicher roberts superselection theory to the case of the nontrivial center and a set of dirac quantum constraints and find conditions under which the superselection structures will survive constraining in some form this involves an analysis of the restriction and factorization of superselection structures

on global implicit function theorem abstract we study some certain maximal implicit functions and we apply our results to prove the local and global existence and local unicity of the solutions of the corresponding differential equation

bi sobolev mappings and elliptic equations in the plane abstract suppose that f u v is a homeomorphism in the plane of the sobolev class w loc 1 1 such that its inverse is of the same sobolev class we prove that u and v have the same set of critical points as an application we show that u and v are distributional solutions to the same non trivial degenerate elliptic equation in divergence form we study similar properties also in higher dimensions

estimating substitution elasticities with the fourier cost function some monte carlo results abstract the fourier flexible form possesses desirable asymptotic properties that are not shared by other flexible forms such as the translog generalized leontief and generalized box cox one of them is that an elasticity of substitution can be estimated with negligible bias in sufficiently large samples regardless of what the true form actually is save that it be smooth enough this article reports the results of an experiment designed to determine whether or not this property obtains in samples of the sizes customarily encountered in practice a three input homothetic version of the generalized box cox cost function was used to generate technologies that were oriented in a two dimensional design space according to a central composite rotatable design the two factors of the design were the box cox parameter and a measure of the dispersion of the substitution matrix the fourier cost function was used to estimate the substitution elasticities at each design point and the bias at each point was estimated using the monte carlo method a response surface over the entire design space was fitted to these estimates an examination of the surface reveals that the bias is small over the entire design space roughly speaking the estimates of elasticities of substitution are unbiased to three significant digits using the fourier flexible form no matter what the true technology our conclusion is that the small bias property of the fourier form does obtain in samples of reasonable size this claim must be tampered by the usual caveats associated with inductive inference

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

weak regularity of the inverse under minimal assumptions let omega subset mathbb r 3 be a domain and let f in bv text loc omega mathbb r 3 be a homeomorphism such that its distributional adjugate is a finite radon measure we show that its inverse has bounded variation f 1 in bv text loc the condition that the distributional adjugate is finite measure is not only sufficient but also necessary for the weak regularity of the inverse

nonparametric efficiency analysis a multivariate conditional quantile approach this paper focuses on nonparametric efficiency analysis based on robust estimation of partial frontiers in a complete multivariate setup multiple inputs and multiple outputs it introduces quantile efficiency scores a nonparametric estimator is proposed achieving strong consistency and asymptotic normality then if increases to one as a function of the sample size we recover the properties of the fdh estimator but our estimator is more robust to the perturbations in data since it attains a finite gross error sensitivity environmental variables can be introduced to evaluate efficiencies and a consistent estimator is proposed numerical examples illustrate the usefulness of the approach

endomorphisms of c algebras cross products and duality for compact groups on definit une nouvelle sorte de produit croise d une c algebre par des semigroupes d endomorphismes avec des proprietes reliees a la symetrie de permutation et a l existence de conjugues un groupe compact est alors defini intrinsequement par son action duale sur le produit croise cette construction donne une caracterisation des duaux de groupes compacts abstraits qui est hors d atteinte de la theorie de dualite de taunaka kein et est independante de cette theorie ceci resout le probleme de demontrer l existence d un groupe de jauge global compact en physique des particules etant seulement donnees les observables locales

the co area formula for sobolev mappings we extend federer s co area formula to mappings f belonging to the sobolev class w 1 p r n r m 1 m m and more generally to mappings with gradient in the lorentz space l m 1 r n this is accomplished by showing that the graph of f in r n m is a hausdorff n rectifiable set

radial symmetry of p harmonic minimizers it is still not known if the radial cavitating minimizers obtained by ball philos trans r soc lond a 306 557 611 1982 and subsequently by many others are global minimizers of any physically reasonable nonlinearly elastic energy this quotation is from sivaloganathan and spector ann inst henri poincare anal non lineaire 25 1 201 213 2008 and seems to be still accurate the model case of the p harmonic energy is considered here we prove that the planar radial minimizers are indeed the global minimizers provided we prescribe the admissible deformations on the boundary in the traction free setting however even the identity map need not be a global minimizer

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

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

systems with outer constraints gupta bleuler electromagnetism as an algebraic field theory since there are some important systems which have constraints not contained in their field algebras we develop here in ac context the algebraic structures of these the constraints are defined as a groupg acting as outer automorphisms on the field algebra g aut g inn and we find that the selection ofg invariant states on is the same as the selection of states onm g m g mathop times limits alpha f by ug 1 g g whereug m g m g mathop times limits alpha f are the canonical elements implementing g these states are taken as the physical states and this specifies the resulting algebraic structure of the physics inm g m g mathop times limits alpha f and in particular the maximal constraint free physical algebra a nontriviality condition is given for to exist and we extend the notion of a crossed product to deal with a situation whereg is not locally compact this is necessary to deal with the field theoretical aspect of the constraints next thec algebra of the ccr is employed to define the abstract algebraic structure of gupta bleuler electromagnetism in the present framework the indefinite inner product representation structure is obtained and this puts gupta bleuler electromagnetism on a rigorous footing finally as a bonus we find that the algebraic structures just set up provide a blueprint for constructive quadratic algebraic field theory

statistical inference for dea estimators of directional distances in productivity and efficiency analysis the technical efficiency of a production unit is measured through its distance to the efficient frontier of the production set the most familiar non parametric methods use farrell debreu shephard or hyperbolic radial measures these approaches require that inputs and outputs be non negative which can be problematic when using financial data recently chambers et al 1998 have introduced directional distance functions which can be viewed as additive rather than multiplicative measures efficiency directional distance functions are not restricted to non negative input and output quantities in addition the traditional input and output oriented measures are nested as special cases of directional distance functions consequently directional distances provide greater flexibility however until now only free disposal hull fdh estimators of directional distances and their conditional and robust extensions have known statistical properties simar and vanhems 2012 this paper develops the statistical properties of directional d estimators which are especially useful when the production set is assumed convex we first establish that the directional data envelopment analysis dea estimators share the known properties of the traditional radial dea estimators we then use these properties to develop consistent bootstrap procedures for statistical inference about directional distance estimation of confidence intervals and bias correction the methods are illustrated in some empirical examples

on the bias in flexible functional forms and an essentially unbiased form the fourier flexible form abstract the fourier flexible form and its derived expenditure system are introduced subject to smoothness conditions on the consumer s true indirect utility function the consumer s true expenditure system must be of the fourier form over the region of interest in an empirical investigation arbitrarily accurate finite parameter approximations of the consumer s true expenditure system are obtained by dropping all high order terms of the fourier expenditure system past an appropriate truncation point the resulting finite parametersystem is tractable in empirical studies the reader who is primarily interested in applications need only read the second and fifth sections the remainder of the article is concerned with the verification of these claims and an investigation of some aspects of the bias in translog specifications

unbiased determination of production technologies abstract to determine whether an industry exhibits constant returns to scale whether the production function is homothetic or whether inputs are separable a common approach is to specify a cost function estimate its parameters using data such as prices and quantities of inputs and then test the parametric restrictions corresponding to constant returns a homothetic technology or separability statistically such inferences are valid if the true cost function is a member of the parametric class considered otherwise the inference is biased that is the true rejection probability is not necessarily adequately approximated by the nominal size of the statistical test the use of fixed parameter flexible functional forms such as the translog the generalized leontief or the box cox will not alleviate this problem the fourier flexible form differs fundamentally from other flexible forms in that it has a variable number of parameters and a known bound depending on the number of parameters on the error as measured by the sobolev norm of approximation to an arbitrary cost function thus it is possible to construct statistical tests for constant returns a homothetic technology or separability which are asymptotically size by letting the number of parameters of the fourier flexible form depend on sample size that is the true rejection probability converges to the nominal size of the test as sample size tends to infinity the rate of convergence depends on the smoothness of the true cost function the more times is differentiable the true cost function the faster the convergence the method is illustrated using the data on aggregate u s manufacturing of berndt and wood 1975 1979 and berndt and khaled 1979

efficient estimation of monotone boundaries let g 0 1 0 1 be a monotone nondecreasing function and let g be the closure of the set x y is an element of 0 1 x 0 1 0 less than or equal to y less than or equal to g x we consider the problem of estimating the set g from a sample of i i d observations uniformly distributed in g the estimation error is measured in the hausdorff metric we propose the estimator which is asymptotically efficient in the minimax sense

on the bi sobolev planar homeomorphisms and their approximation abstract the first goal of this paper is to give a short description of the planar bi sobolev homeomorphisms providing simple and self contained proofs for some already known properties in particular for any such homeomorphism u one has d u x 0 for almost every point x for which j u x 0 as a consequence one can prove that 8 d u d u 1 notice that this estimate holds trivially if one is allowed to use the change of variables formula but this is not always the case for a bi sobolev homeomorphism as a corollary of our construction we will show that any w 1 1 homeomorphism u with w 1 1 inverse can be approximated with smooth diffeomorphisms or piecewise affine homeomorphisms u n in such a way that u n converges to u in w 1 1 and at the same time u n 1 converges to u 1 in w 1 1 this positively answers an open conjecture see for instance iwaniec et al 2011 question 4 for the case p 1

homeomorphisms of bounded variation we show that the inverse of a planar homeomorphism of bounded variation is also of bounded variation in higher dimensions we show that f 1 is of bounded variation provided that f w1 1 rn is a homeomorphism with df in the lorentz space ln 1 1

fracture surfaces and the regularity of inverses for bv deformations motivated by nonlinear elasticity theory we study deformations that are approximately differentiable orientation preserving and one to one almost everywhere and in addition have finite surface energy this surface energy mathcal e was used by the authors in a previous paper and has connections with the theory of currents in the present paper we prove that mathcal e measures exactly the area of the surface created by the deformation this is done through a proper definition of created surface which is related to the set of discontinuity points of the inverse of the deformation in doing so we also obtain an sbv regularity result for the inverse

bi sobolev mappings with differential matrices in orlicz zygmund classes abstract bi sobolev mappings f r 2 onto r 2 have been defined as those homeomorphisms such that f and f 1 belong to w loc 1 1 we deduce regularity properties of the distortion of f from the regularity of the differential matrix d f 1 and conversely

extremal mappings of finite distortion the theory of mappings of finite distortion has arisen out of a need to extend the ideas and applications of the classical theory of quasiconformal mappings to the degenerate elliptic setting where one finds concrete applications in non linear elasticity and the calculus of variations in this paper we initiate the study of extremal problems for mappings with finite distortion and extend the theory of extremal quasiconformal mappings by considering integral averages of the distortion function instead of its supremum norm for instance we show the following suppose that f o is a homeomorphism of the circle with f o 1 in cal w 1 2 2 then there is a unique extremal extension to the disk which is a real analytic diffeomorphism with non vanishing jacobian determinant the condition on f o is sharp classically the mapping f o is assumed to be quasisymmetric then there is an extremal quasiconformal mapping with boundary values f o but it is not always unique and it is seldom smooth indeed even when f o is quasisymmetric the cal l 1 minimiser for the distortion function will almost never be quasiconformal we further find that there are many new and unexpected phenomena concerning existence uniqueness and regularity for these extremal problems where the functionals are polyconvex but typically not convex these seem to differ markedly from phenomena observed when studying multi well type functionals

mappings of finite distortion the degree of regularity this paper investigates the self improving integrability properties of the so called mappings of finite distortion let k x 1 be a measurable function defined on a domain rn n 2 and such that exp k x lloc1 0 we show that there exist two universal constants c1 n c2 n with the following property let f be a mapping in wloc1 1 rn with df x n k x j x f for a e x and such that the jacobian determinant j x f is locally in l1log c1 n l then automatically j x f is locally in l1logc2 n l this result constitutes the appropriate analog for the self improving regularity of quasiregular mappings and clarifies many other interesting properties of mappings of finite distortion namely we obtain novel results on the size of removable singularities for bounded mappings of finite distortion and on the area distortion under this class of mappings

nonparametric frontier estimation a robust approach most nonparametric methods for estimating production frontiers data envelopment analysis and free disposal hall fdh are based on envelopment techniques statistical inference based on these estimators is available but by construction they are very sensitive to extreme values or outliers we propose a nonparametric estimator which is more robust to these extreme values it is based on a concept of expected minimum input function or expected maximal output function we show how this function is related to the efficient frontier itself the resulting estimator is related to the fdh estimator but it will not envelop all the data the asymptotic theory is provided our approach includes the multiple input and multiple output cases c 2002 elsevier science s a all rights reserved

on the degenerate beltrami equation we study the well known beltrami equation under the assumption that its measurable complex valued coefficient z has the norm 1 sufficient conditions for the existence of a homeomorphic solution to the beltrami equation on the riemann sphere are given in terms of the directional dilatation coefficients of a uniqueness theorem is also proved when the singular set sing of is contained in a totally disconnected compact set with an additional thinness condition on sing

deformations of annuli with smallest mean distortion we determine the extremal mappings with smallest mean distortion for mappings of annuli as a corollary we find that the nitsche harmonic maps are dirichlet energy minimizers among all homeomorphisms h mathbb a r r to mathbb a r r however outside the nitsche range of the modulus of the annuli within the class of homeomorphisms no such energy minimizers exist in this case we identify the bv limits of minimizers

hyperelastic deformations and total combined energy of mappings between annuli abstract we consider the so called combined energy of a deformation between two concentric annuli and minimize it provided that it keep order of the boundaries it is an extension of the corresponding result of euclidean energy it is interesting that the minimizers are certain radial mappings and they exist if and only if the annulus on the image domain is not too thin provided that the original annulus is fixed this in turn implies a nitsche type phenomenon next we consider the combined distortion and obtain certain related results which are dual to the results for combined energy which also involve some nitsche type phenomenon the main part of the paper is concerned with the total combined energy a certain integral operator defined as a convex linear combination of the combined energy and combined distortion of diffeomorphisms between two concentric annuli a 1 r and b 1 r first we construct radial minimizers of total combined energy then we prove that those radial minimizers are absolute minimizers on the class of all mappings between the annuli under certain constraint this extends the main result obtained by iwaniec and onninen in 9

bi sobolev mappings and kp distortions in the plane abstract in this paper we introduce the class of the inner p quasiconformal mappings that are homeomorphisms f d o n t o d f w loc 1 1 d d where d r 2 is the unit disk such that there exists a constant k p 0 for which the following distortion inequality d f x p k p j f x p 1 a e x d is satisfied the study of such mappings is motivated by the fact that their inverses satisfy the distortion inequality introduced in 11 here we give a characterization of them so that their components solve a suitable uniformly elliptic p harmonic system moreover for mappings satisfying the previous distortion inequality with k p k p f x not necessarily constant we identify the homeomorphism f whose p distortion function k p f x is minimal in l 1 norm

measuring the robustness of empirical efficiency valuations we study the robustness of empirical efficiency valuations of production processes in an extended farrell model based on input and output data an empirical efficiency status efficient or inefficient is assigned to each of the processes this status may change if the data of the observed processes change as illustrated by a capacity planning problem for hospitals in germany the need arises to gauge the robustness of empirical efficiency valuations the example suggests to gauge the robustness of the efficiency valuation for a process with respect to perturbations of prespecified elements of the data a natural measure of robustness is the minimal perturbation in terms of a suitable distance function of the chosen data elements that is necessary to change the efficiency status of the process under investigation farrell s 1957 efficiency score is an example of such a robustness measure we give further examples of relevant data perturbations for which the robustness measure can be computed efficiently we then focus on weighted maximum norm distance functions such as the maximal absolute or percentage deviation but allow for independent perturbations of the elements of an arbitrary a priori fixed subset of the data in this setting the robustness measure is naturally related to a certain threshold value for a linear monotone one parameter family of perturbations and can be calculated by means of a linear programming based bisection method closed form solutions in terms of farrell s efficiency score are obtained for specific perturbations following the theoretical developments we revisit the hospital capacity planning problem to illustrate the managerial relevance of our techniques

asymptotic rigidity of layered structures and its application in homogenization theory in the context of elasticity theory rigidity theorems allow one to derive global properties of a deformation from local ones this paper presents a new asymptotic version of rigidity applicable to elastic bodies with sufficiently stiff components arranged into fine parallel layers we show that strict global constraints of anisotropic nature occur in the limit of vanishing layer thickness and give a characterization of the class of effective deformations the optimality of the scaling relation between layer thickness and stiffness is confirmed by suitable bending constructions beyond its theoretical interest this result constitutes a key ingredient for the homogenization of variational problems modeling high contrast bilayered composite materials where the common assumption of strict inclusion of one phase in the other is clearly not satisfied we study a model inspired by hyperelasticity via gamma convergence for which we are able to give an explicit representation of the homogenized limit problem it turns out to be of integral form with its density corresponding to a cell formula

injectivity and self contact in nonlinear elasticity let be a bounded open connected subset of 3 with a sufficiently smooth boundary the additional condition det dx vol is imposed on the admissible deformations of a hyperelastic body whose reference configuration is we show that the associated minimization problem provides a mathematical model for matter to come into frictionless contact with itself but not interpenetrate we also extend j ball s theorems on existence to this case by establishing the existence of a minimizer of the energy in the space w1 p 3 p 3 that is injective almost everywhere

neohookean deformations of annuli existence uniqueness and radial symmetry let mathbb x x in mathbb r 2 r x r and mathbb y y in mathbb r 2 r ast y r ast be annuli in the plane we consider the class fancyscript f mathbb x mathbb y of all orientation preserving homeomorphisms h mathbb x overset textnormal tiny onto longrightarrow mathbb y in the sobolev space fancyscript w 1 2 mathbb x mathbb y which keep the boundary circles in the same order this means that lim x searrow r h x r ast and lim x nearrow r h x r ast we study the neohookean energy integral mathcal e h int limits mathbb x dh 2 phi rm det dh quad rm for h in fancyscript f mathbb x mathbb y quad quad quad 1 where phi in fancyscript c infty 0 infty is positive and strictly convex we assume in addition that the function psi z 1 ddot phi z and its derivative extend continuously to 0 with 0 0 then we prove

theory and statistical properties of quantile data envelopment analysis abstract this research proposes quantile data envelopment analysis qdea as a procedure that accounts for the sensitivity of data envelopment analysis dea to data or firm outliers when using dea to estimate comparative efficiency or benchmarking performance metrics the qdea methodology endogenously identifies the distance to a qdea hyperplane while allowing up to proportion q 1 of the data observations to lie external to the qdea hyperplane the ability of qdea to provide more conventional quantile based benchmarking information is discussed the statistical properties of the qdea estimator are examined utilizing ncm subsampling and monte carlo procedures monte carlo simulations indicate that qdea distance estimates share the desirable root n convergence and large sample normality properties of the robust free disposal hull fdh based order m and order estimators

regularity of the inverse of a planar sobolev homeomorphism let be a domain suppose that f w1 1loc r2 is a homeomorphism such that df x vanishes almost everywhere in the zero set of j f we show that f 1 w1 1loc f r2 and that df 1 y vanishes almost everywhere in the zero set of sharp conditions to quarantee that f 1 w1 q f r2 for some 1 q 2 are also given

approximation of planar bv homeomorphisms by diffeomorphisms abstract we show that a planar bv homeomorphism can be approximated in the area strict sense together with its inverse with smooth or piecewise affine homeomorphisms

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

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

existence of energy minimal diffeomorphisms between doubly connected domains the paper establishes the existence of homeomorphisms between two planar domains that minimize the dirichlet energy

hyperelastic deformations of smallest total energy throughout this article mathbb x and mathbb y will be nonempty bounded domains in mathbb r n n geqq 2 the term deformation of mathbb x subset mathbb r n onto mathbb y subset mathbb r n refers to an orientation preserving homeomorphism h mathbb x overset textnormal tiny onto longrightarrow mathbb y in the sobolev class fancyscript w 1 1 mathbb x mathbb y whose inverse f mathbb y overset textnormal tiny onto longrightarrow mathbb x lies in fancyscript w 1 1 mathbb y mathbb x the general law of hyperelasticity asserts that there exists an energy integral mathcal e mathbb x h int mathbb x e x h dh rm dx such that the elastic deformations have the smallest energy we assume here that e is conformally coerced and polyconvex some additional regularity conditions are also imposed under those conditions we establish the existence and global invertibility of the minimizers the key tools in obtaining an extremal deformation h mathbb x overset textnormal tiny onto longrightarrow mathbb y regardless of its boundary values are the free lagrangians finding suitable free lagrangians and using them for a specific stored energy function e is truly a work of art we have done it here for the so called total harmonic energy and a pair of annuli in the plane in fact this challenging problem illustrates rather clearly the strength of the concept of free lagrangians

a new duality theory for compact groups the tannaka krein duality theory characterizes the category g of finite dimensional continuous unitary representations of a compact group as a subcategory of the category of hilbert spaces we prove a more powerful result characterizing g as an abstract category every strict symmetric monoidalc category with conjugates which has subobjects and direct sums and for which thec algebra of endomorphisms of the monoidal unit reduces to the complex numbers is isomorphic to a category g for a compact groupg unique up to isomorphism

quasiconformal mappings and sharp estimates for the distance to l in some function spaces abstract we provide several estimates which involve the distance to l in some function spaces the composition operator induced by a quasiconformal mapping and the logarithm of the jacobian of a quasiconformal mapping our results are sharp in the two dimensional case

algebraic quantization of systems with a gauge degeneracy systems with a gauge degeneracy are characterized either by supplementary conditions or by a set of generators of gauge transformations or by a set of constraints deriving from dirac s canonical constraint method these constraints can be expressed either as conditions on the field algebra or on the states on in ac algebra framework we show that the state conditions give rise to a factor algebra of a subalgebra of the field algebra this factor algebra is free of state conditions in this formulation we show also that the algebraic conditions can be treated in the same way as the state conditions the connection between states on and states on is investigated further within this framework as is also the set of transformations which are compatible with the set of constraints it is also shown that not every set of constraints can give rise to a nontrivial system finally as an example the abstract theory is applied to the electromagnetic field and this treatment can be generalized to all systems of bosons with linear constraints the question of dynamics is not discussed

recent studies on sobolev mappings abstract a homeomorphism u of the unit disk d r 2 u u 1 u 2 d onto d is a quasiharmonic map if u i w l o c 1 1 i 1 2 are solutions to the system 0 1 div b y u 1 0 a e in d div b y u 2 0 a e in d for a symmetric degenerate elliptic conductivity b b y i e 0 2 2 h y b y h y 2 a e in y d r 2 where h d onto 1 is measurable a sufficient condition that the sobolev homeomorphism u w l o c 1 1 is a quasiharmonic map is that u 1 w loc 1 1 this condition is not necessary because we construct a quasiharmonic map u such that u 1 bv w loc 1 1 see theorem 1 1