stochastic data envelopment analysis in measuring the efficiency of taiwan commercial banks conventional data envelopment analysis dea for measuring the efficiency of a set of decision making units dmus requires the input output data to be constant in reality however many observations are stochastic in nature consequently the resulting efficiencies are stochastic as well this paper discusses how to obtain the efficiency distribution of each dmu via a simulation technique the case of taiwan commercial banks shows that firstly the number of replications in simulation analysis has little effect on the estimation of efficiency means yet 1000 replications are recommended to produce reliable efficiency means and 2000 replications for a good estimation of the efficiency distributions secondly the conventional way of using average data to represent stochastic variables results in efficiency scores which are different from the mean efficiencies of the presumably true efficiency distributions estimated from simulation thirdly the interval data approach produces true efficiency intervals yet the intervals are too wide to provide valuable information in conclusion when multiple observations are available for each dmu the stochastic data approach produces more reliable and informative results than the average data and interval data approaches do

inequalities for holomorphic functions of several complex variables sharp norm inequalities valid for functional hilbert spaces of holomorphic functions on the polydisk unit ball and c are established by using the notion of reproducing kernels these inequalities extend earlier results of saitoh and ours

the weighted russell measure of technical efficiency theoretical consideration of technical efficiency has existed since koopmans 10 defined it for production possibilities for which it is not possible to increase any output without simultaneously increasing any input ceteris paribus the nonparametric approach to efficiency measurement known as data envelopment analysis is based on the index of farrell 9 which measures radial reduction in all inputs consistent with observed output even after farrell efficiency is achieved however there may exist additional slack in individual inputs suggesting that the farrell index does not necessarily measure koopmans inefficiency to solve this problem the non radial russell measure was introduced this paper shows that problems may arise with the russell measure due to restrictive assumptions on the implicit weighting of inputs and outputs this paper develops a new measure the weighted russell measure that relaxes this assumption using simulated data the new measure is shown to be preferred to existing methods in addition the new method is applied to analyze the performance of new york state school districts

some properties of invariant measures of non symmetric dissipative stochastic systems we consider transition semigroups generated by stochastic partial differential equations with dissipative nonlinear terms we prove an integration by part formula and a logarithmic sobolev inequality for the invariant measure no symmetry or reversibility assumptions are made furthemore we prove some compactness results on the transition semigroup and on the embedding of the sobolev spaces based on the invariant measure we use these results to derive asymptotic properties for a stochastic reaction diffusion equation

a rigorous path integral for quantum spin using flat space wiener regularization adapting ideas of daubechies and klauder j math phys 26 2239 1985 we derive a rigorous continuum path integral formula for the semigroup generated by a spin hamiltonian more precisely we use spin coherent vectors parametrized by complex numbers to relate the coherent representation of this semigroup to a suitable schrodinger semigroup on the hilbert space l2 r2 of lebesgue square integrable functions on the euclidean plane r2 the path integral formula emerges from the standard feynman kac ito formula for the schrodinger semigroup in the ultradiffusive limit of the underlying brownian bridge on r2 in a similar vein a path integral formula can be constructed for the coherent representation of the unitary time evolution generated by the spin hamiltonian

a simple proof of wehrl s conjecture on entropy based on the hypercontractivity of the free harmonic oscillator hamiltonian and the canonical commutation relation we present a simple proof of wehrl s conjecture on the shannon entropy of phase space probability densities in the fock bargmann representation

technical efficiency estimation with multiple inputs and multiple outputs using regression analysis regression and linear programming provide the basis for popular techniques for estimating technical efficiency regression based approaches are typically parametric and can be both deterministic or stochastic where the later allows for measurement error in contrast linear programming models are nonparametric and allow multiple inputs and outputs the purported disadvantage of the regression based models is the inability to allow multiple outputs without additional data on input prices in this paper deterministic cross sectional and stochastic panel data regression models that allow multiple inputs and outputs are developed notably technical efficiency can be estimated using regression models characterized by multiple input multiple output environments without input price data we provide multiple examples including a monte carlo analysis

proof of an entropy conjecture for bloch coherent spin states and its generalizations wehrl used glauber coherent states to define a map from quantum density matrices to classical phase space densities and conjectured that for glauber coherent states the mininimum classical entropy would occur for density matrices equal to projectors onto coherent states this was proved by lieb in 1978 who also extended the conjecture to bloch su 2 spin coherent states for every angular momentum j this conjecture is proved here we also recall our 1991 extension of the wehrl map to a quantum channel from j to k j frac 1 2 j 1 with k infty corresponding to the wehrl map to classical densities these channels were later recognized as the optimal quantum cloning channels for each j and j k leqslant infty we show that the minimal output entropy for the channels occurs for a j coherent state we also show that coherent states both glauber and bloch minimize any concave functional not just entropy

integration of navier stokes equations using dual time stepping and a multigrid method efficient acceleration techniques typical of explicit steady state solvers are extended to tune accurate calcu lations stability restrictions are greatly reduced by means of a fully implicit time discretization a four stage runge kutta scheme with local tune stepping residual smoothing and multigridding is used instead of traditional computationally expensive factorizations two applications to natural unsteady viscous flows are presented to check for the capability of the procedure ecent progress in computational fluid dynamics along with the evolution of computer performance encourages scientists to look in to details of flow physics there are practical applications where the unsteadiness of the problem can not be neglected i e vortex shedding natural unsteadiness forced unsteadiness aeroe lasticity turbomachinery rotor stator interaction up to now most of the analysis and designing tools are based on a steady or quasi steady assumption even if the flow is known to be unsteady today due to the improvement in computer resources there is a strong interest in developing methodologies for efficient and reliable sim ulation of unsteady flow features it is a common experience while using time accurate explicit schemes to be forced to choose the time step on the basis of stability restrictions as a consequence unless the problem is a very high frequency one the number of time steps to be performed is much higher than the one required for time accuracy by means of some implicit factorization stability restrictions can be relaxed but the work required at each time step grows rapidly with grid dimension and complexity of the flow equations in addition application of boundary conditions in a fully implicit manner is difficult in viscous flow calculations the grid is clustered close to the shear layer and the characteristic time step varies several orders of mag nitude inside the computational domain even if in several practical applications the characteristic time step of the core flow region is comparable with the one required by time accuracy close to the walls the time step restrictions become extremely severe there fore highly vectorizable schemes with less stability restrictions on the allowable time step would be an interesting combination explicit schemes combined with acceleration techniques have proven to be very effective for solving steady problems 1 3 unfortu nately the computational efficiency of those time marching solvers is achieved by sacrificing the accuracy in time in this paper it is shown that the conventional steady state acceleration techniques specifically the multigrid techniques can still be applied to unsteady viscous problems the basic idea is to introduce a dual time stepping and to reformulate the governing equations so that they can be han dled by an explicit accelerated scheme 4 if the time discretization is made implicit stability restrictions are removed and accelera tion techniques can be used instead of traditional time consuming factorizations i e alternate directional implicit and lower upper

evaluating contextual variables affecting productivity using data envelopment analysis a dea based stochastic frontier estimation framework is presented to evaluate contextual variables affecting productivity that allows for both one sided inefficiency deviations as well as two sided random noise conditions are identified under which a two stage procedure consisting of dea followed by ordinary least squares ols regression analysis yields consistent estimators of the impact of contextual variables conditions are also identified under which dea in the first stage followed by maximum likelihood estimation mle in the second stage yields consistent estimators of the impact of contextual variables this requires the contextual variables to be independent of the input variables but the contextual variables may be correlated with each other monte carlo simulations are carried out to compare the performance of our two stage approach with one stage and two stage parametric approaches simulation results indicate that dea based procedures with ols maximum likelihood or even tobit estimation in the second stage perform as well as the best of the parametric methods in the estimation of the impact of contextual variables on productivity simulation results also indicate that dea based procedures perform better than parametric methods in the estimation of individual decision making unit dmu productivity overall the results establish dea as a nonparametric stochastic frontier estimation sfe methodology

sharp sobolev inequalities on the sphere and the moser trudinger inequality where de denotes normalized surface measure v is the conformal gradient and q 2n n 2 a modern folklore theorem is that by taking the infinitedimensional limit of this inequality one obtains the gross logarithmic sobolev inequality for gaussian measure which determines nelson s hypercontractive estimates for the hermite semigroup see 8 one observes using conformal invariance that the above inequality is equivalent to the sharp sobolev inequality on rn for which boundedness and extremal functions can be easily calculated using dilation invariance and geometric symmetrization the roots here go back to hardy and littlewood the advantage of casting the problem on the sphere is that the role of the constants is evident and one is led immediately to the conjecture that this inequality should hold whenever possible for example 2 q 0o if n 2 this is in fact true and will be demonstrated in section 2 a clear question at this point is what is the situation in dimension 2 two important arguments 25 26 27 dealt with this issue both motivated by geometric variational problems because q goes to infinity for dimension 2 the appropriate function space is the exponential class responding in part

wehrl s entropy of spin states and lieb s conjecture wehrl s entropy is the entropy of the probability distribution in the phase space corresponding to the q representation antinormal ordering of operators of a quantum state in terms of coherent states the hilbert space of a system of n spins or n two level atoms is of 2n dimensions the subspace with maximum total spin n 2 is of n 1 dimensions all discussions are restricted within this subspace the probability amplitude for an arbitrary pure state in this subspace is a polynomial of degree n which can be factorised into the product of n linear factors and each root can be identified with one point on the unit sphere hence an arbitrary state in the subspace can be represented geometrically by n unit vectors the general expression for the wehrl entropy is obtained as a finite series expansion in terms of some symmetric functions of sin2 omega ij 2 where omega ij is the angle between a pair of unit vectors the special cases of coherent and almost coherent spin states are then considered

on shannon entropies in μ deformed segal bargmann analysis we consider a deformation of the segal bargmann transform which is a unitary map from a deformed quantum configuration space onto a deformed quantum phase space the deformed segal bargmann space both of these hilbert spaces have canonical orthonormal bases we obtain explicit formulas for the shannon entropy of some of the elements of these bases we also consider two reverse log sobolev inequalities in the deformed segal bargmann space which have been proved in a previous work and show that a certain known coefficient in them is the best possible

renyi wehrl entropies as measures of localization in phase space we generalize the concept of the wehrl entropy of quantum states which gives a basis independent measure of their localization in phase space we discuss the minimal values and the typical values of these r enyi wehrl entropies for pure states for spin systems according to lieb s conjecture the minimal values are provided by the spin coherent states though lieb s conjecture remains unproven we give new proofs of partial results that may be generalized for other systems we also investigate random pure states and calculate the mean r enyi wehrl entropies averaged over the natural measure in the space of pure quantum states

small sample properties of ml cols and dea estimators of frontier models in the presence of heteroscedasticity the purpose of this paper is to examine the small sample properties of maximum likelihood ml corrected ordinary least squares cols and data envelopment analysis dea estimators of the parameters in frontier models in the presence of heteroscedasticity in the two sided or measurement error term using monte carlo methods we find that heteroscedasticity in the two sided error term introduces substantial biases into ml cols and dea estimators although none of the estimators perform well both ml and cols are found to be superior to dea in the presence of heteroscedasticity in the two sided error

a simulation study of dea and parametric frontier models in the presence of heteroscedasticity abstract this paper studies the effects of heteroscedasticity on the following five types of estimators 1 data envelopment analysis dea per se as well as dea joined to regression forms 2 corrected ordinary least squares based on maximum residual cols r 3 corrected ordinary least squares based on moments of residuals cols m 4 maximum likelihood estimation mle and 5 goal programming with one sided deviations as in aigner and chu a c this is accomplished with simulated data in an experiment designed around a single output single input production function which is piecewise cobb douglas robustness of results is confirmed with another experiment employing a shifted smooth cobb douglas production function the model has a composed error term consisting of two components one for measurement error and the other for inefficiency the simulation results indicate that heteroscedasticity does not have an adverse impact on dea based estimators and that dea based estimators are the best estimators of efficient output even under heteroscedasticity

a new approach for technical efficiency estimation in multiple output production the nonparametric technique of data envelopment analysis dea has been used to measure technical efficiency this approach has proven useful because unlike regression analyses it allows multiple outputs and does not require a priori functional form specification dea does however require correct model specification inclusion of inappropriate variables or omission of relevant variables leads to distortions the purpose of this paper is to develop an alternative methodology based on canonical correlation to measure technical efficiency for multiple output production correspondences using simulated data the new methodology is compared with dea the results indicate that the canonical regression approach outperforms dea in most cases

a lower bound for the wehrl entropy of quantum spin with sharp high spin asymptotics a lower bound for the wehrl entropy of a single quantum spin is derived the high spin asymptotics of this bound coincides with lieb s conjecture up to but not including terms of first and higher order in the inverse spin quantum number the result presented here may be seen as complementary to the verification of the conjecture in cases of lowest spin by schupp commun math phys 207 481 1999 the present result for the wehrl entropy is obtained from interpolating a sharp norm bound that also implies a sharp lower bound for the so called renyi wehrl entropy with certain indices that are evenly spaced by half of the inverse spin quantum number

how to generate regularly behaved production data a monte carlo experimentation on dea scale efficiency measurement abstract monte carlo experimentation is a well known approach used to test the performance of alternative methodologies under different hypotheses in the frontier analysis framework whatever the parametric or non parametric methods tested experiments to date have been developed assuming single output multi input production functions the data generated have mostly assumed a cobb douglas technology among other drawbacks this simple framework does not allow the evaluation of dea performance on scale efficiency measurement the aim of this paper is twofold on the one hand we show how reliable two output two input production data can be generated using a parametric output distance function approach a variable returns to scale translog technology satisfying regularity conditions is used for this purpose on the other hand we evaluate the accuracy of dea technical and scale efficiency measurement when sample size and output ratios vary our monte carlo experiment shows that the correlation between true and estimated scale efficiency is dramatically low when dea analysis is performed with small samples and wide output ratio variations

contractive inequalities for bergman spaces and multiplicative hankel forms we consider sharp inequalities for bergman spaces of the unit disc establishing analogues of the inequality in carleman s proof of the isoperimetric inequality and of weissler s inequality for dilations by contractivity and a standard tensorization procedure the unit disc inequalities yield corresponding inequalities for the bergman spaces of dirichlet series we use these results to study weighted multiplicative hankel forms associated with the bergman spaces of dirichlet series reproducing most of the known results on multiplicative hankel forms associated with the hardy spaces of dirichlet series in addition we find a direct relationship between the two type of forms which does not exist in lower dimensions finally we produce some counter examples concerning carleson measures on the infinite polydisc

analytic inequalities isoperimetric inequalities and logarithmic sobolev inequalities abstract there is a simple equivalence between isoperimetric inequalities in riemannian manifolds and certain analytic inequalities on the same manifold more extensive than the familiar equivalence of the classical isoperimetric inequality in euclidean space and the associated sobolev inequality by an isoperimetric inequality in this connection we mean any inequality involving the riemannian volume and riemannian surface measure of a subset and its boundary respectively we exploit the equivalence to give log sobolev inequalities for riemannian manifolds some applications to schrodinger equations are also given

hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n sphere a logarithmic sobolev inequality with respect to the probability measure a 1 x2 12 dx on 1 1 is proved for all 12 from this inequality sharp hypercontractive estimates are derived for the heat semigroups for ultraspherical polynomials and on the n sphere

on an integral criterion for hypercontractivity of diffusion semigroups and extremal functions abstract in the line of investigation of the works by d bakry and m emery lecture notes in math vol 1123 pp 175 206 springer verlag new york berlin 1985 and o s rothaus j funct anal 42 1981 102 109 j funct anal 65 1986 358 367 we study an integral inequality behind the 2 criterion of d bakry and m emery see previous reference and its applications to hypercontractivity of diffusion semigroups with in particular a short proof of the hypercontractivity property of the ornstein uhlenbeck semigroup our exposition unifies in a simple way several previous results interpolating smoothly from the spectral gap inequalities to logarithmic sobolev inequalities and even true sobolev inequalities we examine simultaneously the extremal functions for hypercontractivity and logarithmic sobolev inequalities of the ornstein uhlenbeck semigroup and heat semigroup on spheres

hypercontractivity and the bakry emery criterion for compact lie groups on etudie l ingredient essentiel du critere de bakry emery on utilise ce critere pour obtenir des estimations ameliorees de la constante hypercontractive

some integral identities and inequalities for entire functions and their application to the coherent state transform let be an entire function on cn and for any h 0 and r 0 define fr z r e 2 z 2h let d h denote h n times lebesgue measure on cn frs2 2 d h n sh frsd h from this and a logarithmic sobolev inequality we easily deduce qnq fr q pnp fr p for all 0 p q t8 where the lp norms are taken with respect to the measure d h above we apply these results to the study of the spaces ap consisting of all entire functions satisfying z pe 2 z 2h d h obtaining sharp bounds for some associated operators and proving denseness of analytic polynomials in ap for 1 p we then apply our results to the coherent state transform extending and simplifying some previously known results

on lieb s conjecture for the wehrl entropy of bloch coherent states lieb s conjecture for the wehrl entropy of bloch coherent states is proved for spin 1 and spin 3 2 using a geometric representation we solve the entropy integrals for states of arbitrary spin and evaluate them explicitly in the cases of spin 1 3 2 and 2 we also give a group theoretic proof for all spin of a related inequality

on a constrained 2 d navier stokes equation the planar navier stokes equation exhibits in absence of external forces a trivial asymptotics in time nevertheless the appearence of coherent structures suggests non trivial intermediate asymptotics which should be explained in terms of the equation itself motivated by the separation of the different time scales observed in the dynamics of the navier stokes equation we study the well posedness and asymptotic behaviour of a constrained equation which neglects the variation of the energy and moment of inertia

on the estimation of technical inefficiency in the stochastic frontier production function model abstract the error term in the stochastic frontier model is of the form v u where v is a normal error term representing pure randomness and u is a non negative error term representing technical inefficiency the entire v u is easily estimated for each observation but a previously unsolved problem is how to separate it into its two components v and u this paper suggests a solution to this problem by considering the expected value of u conditional on v u an explicit formula is given for the half normal and exponential cases

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

poincare inequality for weighted first order sobolev spaces on loop spaces abstract let e be the loop space over a compact connected riemannian manifold with a torsion skew symmetric connection let l d be the ornstein uhlenbeck operator on a nonempty connected component d of the loop space e and let v d r be the restriction on d of the potential in the logarithmic sobolev inequality found by l gross on the loop group by s aida and by f z gong and z m ma on the loop space respectively we prove that the schrodinger operator l v l d v always has a spectral gap at the bottom 0 v of its spectrum and thus has its ground state transformed operator 1 l v 0 v where is the unique ground state of l v in particular our result proves l gross s conjecture about the existence of a spectral gap for the ground state transform of the schrodinger operator studied by him on the loop group in addition in all the above cases we identify the domain of the dirichlet forms associated with the ground state transforms as weighted first order sobolev spaces with weight given by 2 thus establishing a poincare inequality for them all these results are consequences from some new results in this paper on dirichlet forms characterizing certain classes with spectral gaps and from results by s aida and m hino

uniqueness of non negative solutions of semilinear equations in rn on etudie l unicite des solutions positives classiques u x du probleme u f u 0 dans r n u x 0 quand x avec n 1 et x x 1 x n

uniqueness of gibbs states for quantum lattice systems we prove uniqueness of euclidean gibbs states for certain quantum lattice systems with unbounded spins we use dobrushin s uniqueness criterion the necessary estimates for the vasershtein distance between the corresponding one point conditional distributions with boundary conditions differing only at one side are obtained by proving a log sobolev inequality on the infinite dimensional single spin loop spaces some important classes of concrete examples to which all this applies are discussed

dirichlet forms and dirichlet operators for gibbs measures of quantum unbounded spin systems essential self adjointness and log sobolev inequality for each 0 1 we consider the dirichlet form mu gamma and the associated dirichlet operator h mu gamma for the gibbs measure of quantum unbounded spin systems interacting via superstable and regular potential the gibbs measure is related to the gibbs state of the system via a functional euclidean integral procedure the configuration space for the spin systems is given by omega e mathbb z v e left omega in c left left 0 1 right mathbb r d right omega left 0 right omega left 1 right right we formulate dirichlet forms in the framework of rigged hilbert spaces which are related to the space under appropriate conditions on the potential we show that the dirichlet operator h mu left gamma right is essentially self adjoint on the domain of smooth cylinder functions we give sufficient conditions on the potential so that the corresponding gibbs measure is uniformly log concave ulc this property gives the spectral gap of the dirichlet operator h mu left gamma right at the lower end of the spectrum furthermore we prove that under the conditions of ulc the unique gibbs measure satisfies the log sobolev inequality ls we use an approximate argument used in the study of the same subjects for loop spaces which in turn is a modification of the method originally developed by s albeverio yu g kondratiev and m rockner

the effects of exogenous variables in efficiency measurement a monte carlo study abstract a monte carlo study is conducted to compare the stochastic frontier method and the data envelopment analysis dea method in measuring efficiency in situations where firms are subject to the effects of factors which are beyond managerial control in making efficiency measurements and comparisons one must separate the effects of the environment the exogenous factors and the effects of the productive efficiency there are two basic approaches to account for the effects of exogenous variables 1 an one step procedure which includes the exogenous variables directly in estimating the efficiency measures and 2 a two step procedure which first estimates the relative gross efficiencies using inputs and outputs then analyzes the effects of the exogenous variables on the gross efficiency the results show that the magnitude of exogenous variables does not appear to have any significant effect on the performance of the one step stochastic frontier method as long as the exogenous variables are correctly identified and accounted for however the effects of exogenous variables are significant for the two step approach especially for the dea methods

on the structure of almost einstein manifolds in this paper we study the structure of the limit space of a sequence of almost einstein manifolds which are generalizations of einstein manifolds roughly speaking such manifolds are the initial manifolds of some normalized ricci flows whose scalar curvatures are almost constants over space time in the l1 sense ricci curvatures are bounded from below at the initial time under the non collapsed condition we show that the limit space of a sequence of almost einstein manifolds has most properties which is known for the limit space of einstein manifolds as applications we can apply our structure results to study the properties of kahler manifolds

optimal concentration for su 1 1 coherent state transforms and an analogue of the lieb wehrl conjecture for su 1 1 we derive a lower bound for the wehrl entropy in the setting of su 1 1 for asymptotically high values of the quantum number k this bound coincides with the analogue of the lieb wehrl conjecture for su 1 1 coherent states the bound on the entropy is proved via a sharp norm bound the norm bound is deduced by using an interesting identity for fisher information of su 1 1 coherent state transforms on the hyperbolic plane mathbb h 2 and a new family of sharp sobolev inequalities on mathbb h 2 to prove the sharpness of our sobolev inequality we need to first prove a uniqueness theorem for solutions of a semi linear poisson equation which is actually the euler lagrange equation for the variational problem associated with our sharp sobolev inequality on mathbb h 2 uniqueness theorems proved for similar semi linear equations in the past do not apply here and the new features of our proof are of independent interest as are some of the consequences we derive from the new family of sobolev inequalities

proof of the generalized lieb wehrl conjecture for integer indices larger than one gnutzmann and yczkowski have proposed the renyi wehrl entropy as a generalization of the wehrl entropy and conjectured that its minimum is obtained for coherent states we prove this conjecture for the renyi index q 2 3 in the cases of compact semisimple lie groups a general formula for the minimum value is given

symmetric ornstein uhlenbeck semigroups and their generators we provide necessary and sufficient conditions for a hilbert space valued ornstein uhlenbeck process to be reversible with respect to its invariant measure for a reversible process the domain of its generator in l p is characterized in terms of appropriate sobolev spaces thus extending the meyer equivalence of norms to any symmetric ornstein uhlenbeck operator we provide also a formula for the size of the spectral gap of the generator those results are applied to study the ornstein uhlenbeck process in a chaotic environment necessary and sufficient conditions for a transition semigroup r t to be compact hilbert schmidt and strong feller are given in terms of the coefficients of the ornstein uhlenbeck operator we show also that the existence of spectral gap implies a smoothing property of r t and provide an estimate for the appropriately defined gradient of r t finally in the hilbert schmidt case we show tha t for any the function r t is an almost classical solution of a version of the kolmogorov equation

proof of the wehrl type entropy conjecture for symmmetric su n coherent states the wehrl entropy conjecture for coherent highest weight states in representations of the heisenberg group which was proved in 1978 and recently extended by us to the group su 2 is further extended here to symmetric representations of the groups su n for all n this result gives further evidence for our conjecture that highest weight states minimize group integrals of certain concave functions for a large class of lie groups and their representations

stability of the bakry emery theorem on rn abstract we establish quantitative stability estimates for the bakry emery bound on logarithmic sobolev and poincare constants of uniformly log concave measures more specifically we show that if a 1 uniformly log concave measure has almost the same logarithmic sobolev or poincare constant as the standard gaussian measure then it almost splits off a gaussian factor our results are dimension free leading to dimension free stability estimates for gaussian concentration of lipschitz functions the proofs are based on stein s method optimal transport and an approximate integration by parts identity relating measures and near extremals in the associated functional inequality

a monte carlo comparison of two production frontier estimation methods corrected ordinary least squares and data envelopment analysis abstract this paper reports the results of an experiment with simulated data that compares the estimation accuracy of two simple and very different production frontier methods corrected ordinary least squares and data envelopment analysis the experimental design extends a previously published paper by introducing measurement errors a factor we show to be critical for comparative analysis of the frontier methods both low and high measurement error distributions are used resulting in 95 error intervals of roughly 10 and 40 respectively of outputs other variations include four inefficiency distributions covering a wide range of behavior four sample sizes from 25 to 200 and two piecewise cobb douglas technologies with two inputs and one output each results include 1 selection of the proper estimation method for a case can result in substantial gains in estimation accuracy for technical efficiencies from 15 to 40 in mean absolute deviations 2 cols performs better for the classical distribution case with sample sizes of 50 or over 3 dea performs better for all nonclassical inefficiency distributions even with relatively high measurement errors 4 dea provides surprisingly accurate estimates for the small sample size of 25 for all cases in the experiment 5 cols fails to decompose deviations into efficiency and measurement error components it assumes that deviations from the frontier are either totally due to measurement errors or technical inefficiencies and 6 neither method performs satisfactorally for high measurement errors

development and validation of navier stokes procedure for turbomachinery unsteady flow an unsteady viscous flow solver based on the runge kutta scheme has been developed three low reynolds number e turbulence models have been assessed for their ability to predict unsteady transitional flow the e model has been modified to incorporate leading edge effects a pseudo time approach has been used to accelerate the numerical algorithm for unsteady flows a sensitivity study has been carried out including the effects of the artificial dissipation the grid density and the physical and pseudo time steps the numerical simulation of the unsteady transitional flow in a compressor cascade has been carried out successfully the numerical solver has been able to prediet major features associated with the wake induced transition on a compressor blade wake induced transitional strip wake induced turbulent strip etc an analysis and an interpretation of the results from the unsteady flow simulation have been carried out to understand additional flow physics associated with the transitional flow

preconditioning applied to variable and constant density flows a time derivative preconditioning of the navier stokes equations suitable for both variable and constant density fluids is developed the ideas of low mach number preconditioning and artificial compressibility are combined into a unified approach designed to enhance convergence rates of density based time marching schemes for solving flows of incompressible and variable density fluids at all speeds the preconditioning is coupled with a dual time stepping scheme implemented within an explicit multistage algorithm for solving time accurate flows the resultant time integration scheme is used in conjunction with a finite volume discretization designed for unstructured solution adaptive mesh topologies this method is shown to provide accurate steady state solutions for transonic and low speed flow of variable density fluids the time accurate solution of unsteady incompressible flow is also demonstrated